Diamond magneto-optical trap and gravimeter

Abstract

The present disclosure provides a system including a three-dimensional diamond magneto-optical trap (3D DMOT). The 3D DMOT includes a cold-atom-trapping mirror assembly having a first set of reflection surfaces oriented towards an input light beam and a second set of reflection surfaces oriented opposite to the input light beam. The first and second sets of reflection surfaces are arranged parallel to each other, define a central through hole, and have inclined angles between 45° and 90° relative to a plane perpendicular to a first axis. The cold-atom-trapping mirror assembly may include planar or conical reflective surfaces and may include a central gap for optical access. Multiple 3D DMOTs may be aligned to share a single input light beam for gravimetry applications

Description

DIAMOND MAGNETO-OPTICAL TRAP AND GRAVIMETERSTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with government support under grant number 2328663 awarded by the National Science Foundation. The government has certain rights in the invention.BACKGROUND

[0002] Magneto-optical traps (MOTs) serve as the primary workhorse for creating cold samples of neutral atoms and have been demonstrated in configurations ranging from traditional setups requiring three orthogonal pairs of laser beams to compact configurations using only a single laser beam. These cold-atom systems have facilitated the development of a broad range of quantum sensors, including atomic clocks for timekeeping and atom interferometers for inertial sensing. Single-beam MOTs, which rely on laser beam reflections from pyramidal, conical, or tetrahedral mirrors, as well as diffractive optics such as gratings, Fresnel reflectors, and metasurface optical chips, simplify the complexity of preparing cold atoms and have given rise to transportable atomic gravimeters and gradiometers, compact atomic inertial sensors, and miniaturized atomic clocks. Despite these advances, existing single-beam MOT designs present limitations in terms of scalability, access to the cold atomic cloud for probing or interaction, and the ability to simultaneously generate multiple cold atomic clouds, all of which are increasingly important for next-generation quantum sensing applications.

[0003] Existing pyramidal MOT geometries have been modified by prior work (such as placing two pyramidal mirrors back-to-back and opening a central through-hole), but a general and flexible design framework for back-to-back mirror configurations, along with a systematic exploration of the resulting single-beam MOT configurations and their experimental demonstration, has yet to be achieved. There exists, therefore, a need in the art for improved single-beam MOT configurations based on back-to-back mirror geometries that offer increased access to the atomic cloud, the ability to create multiple simultaneous MOTs using a single laser beam, and a compact, scalable form factor suitable for deployment in portable and miniaturized quantum sensing devices.1HB: 4931-4976-1177.3SUMMARY

[0004] This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.

[0005] The present disclosure provides a system for trapping and manipulating cold atoms using a three-dimensional diamond magneto-optical trap (3D DMOT). The system includes a cold-atom-trapping mirror assembly including two parallel sets of reflection surfaces with inclined angles between 45° and 90° relative to an input light beam axis, defining a central through hole. A laser source generates a circularly polarized, collimated input beam, while a retroreflector assembly reflects the beam. The system may utilize planar or conical mirror configurations and may incorporate multiple aligned 3D DMOTs sharing a single input beam. When configured as a gravimeter, the system may measure absolute gravity, gravity gradient, and gravity curvature using vertically separated DMOTs and atom interferometry techniques.

[0006] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive.BRIEF DESCRIPTION OF FIGURES

[0007] Non-limiting and non-exhaustive examples are described with reference to the following figures.

[0008] FIG. 1A illustrates a side-view schematic of a magneto-optical trap configuration, according to aspects of the present disclosure.

[0009] FIG. IB illustrates another side-view schematic of a magneto-optical trap configuration, according to aspects of the present disclosure.

[0010] FIG. 2 illustrates a side-view schematic of a magneto-optical trap with a central gap, according to aspects of the present disclosure.

[0011] FIG. 3 illustrates a side-view schematic of a dual magneto-optical trap configuration, according to aspects of the present disclosure.

[0012] FIG. 4 illustrates an isometric view of a planar mirror assembly for a magneto-optical trap, according to aspects of the present disclosure.2HB: 4931-4976-1177.3

[0013] FIG. 5 illustrates an isometric view of a conical mirror assembly for a magneto-optical trap, according to aspects of the present disclosure.

[0014] FIG. 6A illustrates a side-view schematic of a gravimeter according to aspects of the present disclosure.

[0015] FIG. 6B illustrates another side-view schematic of a gravimeter according to aspects of the present disclosure.

[0016] FIG. 6C illustrates yet another side-view schematic of a gravimeter according to aspects of the present disclosure.

[0017] FIG. 7 illustrates a side-view schematic of a gravimeter with multiple magneto-optical traps in a vacuum tube, according to aspects of the present disclosure.

[0018] FIG. 8 illustrates a block diagram of a magneto-optical trap system, according to aspects of the present disclosure.

[0019] FIG. 9A illustrates an orthogonal view of a magneto-optical trap configuration in a first state, according to aspects of the present disclosure.

[0020] FIG. 9B illustrates an orthogonal view of a magneto-optical trap configuration in a second state, according to aspects of the present disclosure.

[0021] FIG. 10 depicts a matrix of magneto-optical trap fluorescence images under varying conditions, according to aspects of the present disclosure.

[0022] FIG. HA depicts experimental measurement data of atomic cloud width with respect to free-fall time from a diamond magneto-optical trap, according to aspects of the present disclosure.

[0023] FIG. 1 IB depicts a second set of experimental measurement data of atom number with respect to MOT loading time from a diamond magneto-optical trap, according to aspects of the present disclosure.

[0024] FIG. 12 depicts experimental measurement data of atom number with respect to average intensity of a single-incident cooling laser beam, according to aspects of the present disclosure.

[0025] FIG. 13A illustrates long-term stability measurements of atom number with respect to time in a diamond magneto-optical trap, according to aspects of the present disclosure.

[0026] FIG. 13B illustrates long-term stability measurements of atom number with respect to temperature in a diamond magneto-optical trap, according to aspects of the present disclosure.3HB: 4931-4976-1177.3

[0027] FIG. 14 depicts an example fringe of atom interferometry with a pulse separation time of 1 ms, according to aspects of the present disclosure.

[0028] FIG. 15 depicts an example fringe of atom interferometry with a series of pulse separation times, according to aspects of the present disclosure.

[0029] FIG. 16A depicts simulated gravity measurements with respect to different positions relative to a sensor, according to aspects of the present disclosure.

[0030] FIG. 16B depicts simulated gradients at different positions relative to a test mass, according to aspects of the present disclosure.DETAILED DESCRIPTION

[0031] The following description sets forth example aspects of the present disclosure relating to magneto-optical trap systems that use a back-to-back mirror assembly to trap and cool atoms using a single input laser beam. The technology addresses the challenge of creating compact, scalable cold-atom sources for quantum sensing applications, including gravimetry, by employing a cold-atom-trapping mirror assembly comprising two sets of inclined reflection surfaces that define a central through hole and a diamond-shaped trapping volume. Features described in connection with one example can be combined with features described in connection with other examples, and no feature is limited to the particular example in which it is described.

[0032] FIG. 1A illustrates a side-view schematic of a magneto-optical trap system 100. The magneto-optical trap system 100 may include an upper mirror 101 and a lower mirror 102 arranged in a back-to-back configuration. A retroreflector assembly 103 may be positioned below the mirrors 101, 102.

[0033] Without being bound by a particular theory, a magneto-optical trap utilizes a combination of laser cooling and magnetic fields to confine and cool atoms to extremely low temperatures. Laser light interacts with the atoms through the Doppler effect, slowing them down by absorbing and re-emitting photons. This process reduces the kinetic energy of the atoms, effectively cooling them. The laser frequency may be tuned slightly below the resonant frequency of the atoms, ensuring that atoms moving towards the laser beam are more likely to absorb photons, thus experiencing a net force opposite to their motion.

[0034] In conjunction with the laser cooling, a magnetic field gradient may be applied to create a position-dependent force on the atoms. For example, this magnetic field may be generated by a 4HB: 4931-4976-1177.3pair of anti -Helmholtz coils, producing a quadrupole magnetic field with a magnitude of zero at a center point of the trap. The combination of the laser light and magnetic field creates a restoring force that pushes atoms towards the center of the trap when the atoms move away from it. As atoms approach the center of the trap, they may experience less force, allowing them to accumulate in a small volume. The interplay between the laser cooling and magnetic confinement may result in a dense cloud of cold atoms, typically reaching temperatures in the microkelvin range or lower. This trapped atomic cloud may serve as a starting point for various experiments in atomic physics, quantum optics, and precision measurements.

[0035] In the instance depicted in FIG. 1 A, a first length LI represents a horizontal extent of each reflection surface, while a second length L2 represents a total horizontal span including the separation between the mirrors.

[0036] The upper mirror 101 and the lower mirror 102 may each have reflection surfaces positioned at a mirror angle 0 relative to a horizontal axis, with a mirror height d defining their vertical extent. For ease of explanation, the angles of the upper mirror 101 are described herein as positive, and the angles of the lower mirror 102 are described as negative (e.g., an upper mirror surface 112 is described as angled by a positive angle 0 and a lower mirror surface 114 is described as angled by a negative angle -0). The first length LI may thus be represented by LI = d / tan(0). The second length L2 may thus be represented by L2 = -d tan(20). To make a reflection from the upper mirror 101 propagate toward the lower mirror 102, 0 may be any angle between 45° to 90°, corresponding to a pyramidal top angle of 180° - 20. It has been observed that a smaller 0 may lead to a mirror assembly with a longer length in the x-axis and thus a larger trapping volume. Practically, a value of 0 between 50° and 70° may provide a reasonable size of the mirror assembly and trapping volume.

[0037] A retroreflector 103 may reflect light in the opposite direction (e.g., from positive z-oriented to negative z-oriented) after rotating a polarity of the light, which may avoid interference with oncoming light. The upper mirror 101 and the lower mirror 102 together may form a cold-atom-trapping mirror assembly with a first set of reflection surfaces oriented towards the input light beam and a second set of reflection surfaces oriented opposite to the input light beam. The first and second sets of reflection surfaces may be arranged parallel to each other and define a central through hole. The mirror angle 0 may be between 45° and 90° relative to a plane perpendicular to the first axis. As shown in later figures, the reflection surfaces may be flat or 5HB: 4931-4976-1177.3conical, creating even or gradient laser intensity distributions in the diamond-shaped trapping volume. Additionally, the diamond-shaped trapping volume may still be formed when the upper and lower mirrors are separated with a gap shorter than d, though the trapping volume may be reduced. Such a gap may provide additional optical access to the magneto-optical trap.

[0038] The geometry of the reflectors may create a diamond-shaped trapping volume 113 in a region of the intersection of transmitted and reflected laser beams. For example, the volume 113 may have a shape defined by the intersection of reflected and transmitted laser beam paths within the cold-atom-trapping mirror assembly, which may vary in aspect ratio depending on mirror angle and geometry. As illustrated, the trapping volume 113 may correspond to the intersection of laser light traveling in three directions (where reflected portions traveling in the y-direction are present but unillustrated). When a laser beam 107 enters the system (e.g., traveling in the z-direction), an outer portion (defined by LI) of the beam 107 may first strike the upper mirror surface 112 at an angle determined by mirror angle 0. The beam may reflect off the surface 112 at a complementary angle towards the lower reflective surface 114, causing the beam to be redirected downward and inward across the center of the system. The beam may then be reflected by the lower mirror surface 112 in the opposite direction, re-orienting the beam to the z-direction. The beam may then be reversed by the retroreflector assembly 103 and follow the same path in the reverse direction. The laser beam 107 may be a circularly polarized and substantially collimated single input light beam propagating along a first axis.

[0039] For example, paths of two rays 116, 117 are shown in FIG. 1 A to illustrate the path of a reflected beam and the extent of the reflected beam trapping volume 113. In practice, each upper mirror surface 112 and lower mirror surface 114 may have a corresponding reflected beam in a symmetrical geometry. As shown, the rays 116, 117 begin in the z-direction. Ray 116 begins at an outer edge of the left upper mirror 101 (e.g., x=0), while ray 117 begins at an inner edge of the upper mirror 101 (e.g., x=Ll). Rays 116, 117 reflect off of upper mirror surface 112 at the complementary angle to 0 and travel to an opposite edge of the right lower mirror surface 114 (e.g., ray 116 travels from x=0 to x=L2 and ray 117 travels from x=Ll to x=Ll+L2). Rays 116, 117 then reflect from lower mirror surface 114 in the opposite manner and are reoriented in the z-direction. The rays 116, 117 then reflect off of a flat mirror 109 and follow their same path in reverse. In the instance, shown, the central region where the reflected beams intersect (with each other and the central portion of laser beam 107) forms a diamond-shaped trapping volume 113 to 6HB: 4931-4976-1177.3trap cold atoms 115. The agneto-optical trap may be configured to trap a cold-atom sample at the center point of the cold-atom-trapping mirror assembly.

[0040] The size and shape of this trapping volume 113 may be directly influenced by the mirror angle 0, with larger angles creating a more elongated diamond shape and smaller angles producing a wider, more compact diamond. The horizontal position of the trapping volume 113 may be determined by the separation between the upper mirror 101 and the lower mirror 102, while the vertical extent may be influenced by the mirror height d. By the way of some nonlimiting examples, the mirror angle 0 may be between approximately 50° and 70° (e.g., approximately 55°) and the mirror height d may be between approximately 5 mm and 30 mm (e.g., approximately 12 mm). Corresponding horizontal extents LI and L2 may scale with d and 0 according to the geometric relations described above, yielding input laser beam diameters in a range of approximately 20 mm to 60 mm (e.g., approximately 26 mm). The intensity of laser radiation within the trapping volume 113 may be maximized at the center of the diamond shape, creating a region for atom trapping where cooling forces are balanced from multiple directions.

[0041] In magneto-optical trapping, a magnetic field gradient may be employed to create a position-dependent force on the atoms, complementing the laser cooling effect. Magnetic coils 104 positioned above and below the mirror assembly may generate magnetic fields for magnetooptical trap operation. In some cases, the magnetic coils 104 may be arranged in an antiHelmholtz configuration, producing a quadrupole field with a zero point at the center of the trap. In some cases, the magnetic field gradient may increase with distance from the trap center, providing a restoring force that pushes atoms towards the center when the atoms move away from it. In some implementations, permanent magnets may be used instead of or in combination with electromagnetic coils to generate the magnetic field gradient. The strength and shape of the magnetic field gradient may be tailored to optimize the trapping efficiency and the characteristics of the trapped atomic cloud. The magnetic coils 104 may form a magnetic field generator configured to create a quadrupole magnetic field having a magnitude of zero at a center point of the cold-atom -trapping mirror assembly.

[0042] The retroreflector assembly 103 may further enhance the trapping efficiency by reflecting the laser beam back through the system 100, effectively doubling the number of beam intersections and creating a more uniform trapping force throughout the diamond-shaped volume. The retroreflector assembly 103 may include a quarter waveplate 108 and a flat mirror 7HB: 4931-4976-1177.3109 that reflect the laser beam 107 back through the system. The retroreflector assembly 103 may be positioned below the cold-atom-trapping mirror assembly and be oriented perpendicular to the first axis. When the circularly polarized laser beam 107 passes through the quarter waveplate 108 twice (once before and once after reflection from the flat mirror 109), the circular polarization direction may be reversed from right-handed to left-handed or vice versa, which may prevent interference with the incoming beam while maintaining the polarization characteristics for atom trapping.

[0043] The magneto-optical trap system 100 may be used with different atoms, each having a corresponding laser wavelength. Advantageously, flexibility in atom selection may allow for adaptation of the trap to various experimental or application contexts. The laser beam 107 may be adjusted to match the specific wavelength needed for the chosen atom species, enabling efficient cooling and trapping across a range of atomic elements. For example, when trapping rubidium (Rb) atoms, the laser beam 107 may be tuned to approximately 780 nm in wavelength to address the D2 transition line of 87Rb. As another example, when trapping cesium (Cs) atoms, the laser beam 107 may be adjusted to approximately 852 nm in wavelength to address the D2 transition line of 133Cs. The magneto-optical trap system may form a three-dimensional diamond magneto-optical trap (3D DMOT) with a laser source configured to generate the circularly polarized and substantially collimated single input light beam.

[0044] The laser light reflected from the angled reflective surfaces 112, 114 may have components in the x- and y- axes as well as the z-axis, providing three dimensions of confinement without laser light in the central region of the chamber between the mirrors.Accordingly, the system 100 may also be suitable for use with various different laser beam intensity profiles. For example, the beam 107 may span a width L1+L2 and may have continuous intensity profiles, such as a Gaussian intensity profile, a flat-top profile, a super-Gaussian profile, or other suitable intensity profiles.

[0045] FIG. IB illustrates an example implementation of the system 100 of FIG. 1. with an annular laser beam 121. In this example, the laser beam 121 is imparted with a hollow-core intensity profile, and the central region 122 between the mirrors has low or no beam intensity, while leaving the central core free of laser light outside the trapping volume 113. In further examples, the annular beam 121 may extend into the central region by some amount, which may support tuning and configuration of the laser power within the trapping region 113. Hence, while 8HB: 4931-4976-1177.3the following examples are generally illustrated with a beam that spans the width of the vacuum chamber, they may be implemented with annular beams as well.

[0046] FIG. 2 illustrates a side-view schematic of a magneto-optical trap 200. The magnetooptical trap 200 may include an upper mirror 201 and a lower mirror 202 arranged in a back-to-back configuration. The upper mirror 201 and the lower mirror 202 may each include mirror surfaces 212, 214 respectively, arranged at an inclined angle 9 relative to the horizontal axis.

[0047] A laser beam 207 may enter from above and interact with mirror surfaces 212, 214 to create a trapping volume 213 between the upper mirror 201 and the lower mirror 202. The trapping volume 213 may have a diamond-shaped configuration where trapped atoms 215 may be contained. A central gap 218 may change the height of trapping volume 213 compared to trapping volume 113 in FIG. 1A and may provide access to the trapping volume 213 for imaging, atom injection, additional experimental lasers, or other suitable purposes.

[0048] Dimensions of the upper mirror 201 and the lower mirror 202 may be defined by several parameters. In the instance shown in FIG. 2, a first length LI may represent a horizontal extent of each mirror surface, while a second length L2 may represent a total horizontal span including the separation between mirror surfaces. A mirror height d may indicate a vertical height of each mirror section. A central gap 218 may be added to the mirror height d to increase the total height compared to the example of FIG. 1A. In some cases, the central gap 218 may be as large as the mirror height d, and a size of the trapping volume 213 may decrease as the central gap 218 increases. In some implementations, the central gap 218 may be adjustable, which may be used to tune the size and shape of trapping volume 213.

[0049] Two example laser beam paths are shown by rays 216 and 217. Ray 216 originates at the laser beam periphery, and ray 217 originates at LI, illustrating the bounds of trapping volume 213. Ray 216 propagates down to the left upper mirror 201 and is reflected at an outer edge of upper mirror surface 212, directing ray 216 to the right lower mirror 202 where ray 216 is reflected by an inner edge of lower mirror surface 214. Ray 217 follows a similar path but with reversed inner and outer edge reflections. Compared to the paths of rays 116 and 117 in FIG. 1 A, ray 216 is reflected lower on the upper mirror surface 212, resulting in less total reflective surface used. This difference in beam paths may result in a modified trapping volume 213 compared to trapping volume 113 in FIG. 1A.9HB: 4931-4976-1177.3

[0050] The central gap 218 between the upper mirror 201 and the lower mirror 202 may provide additional functionality to the magneto-optical trap 200. For example, the central gap 218 may be used as an access port for sensors, atom supply, or other suitable experimental equipment. This access may allow for enhanced monitoring or manipulation of trapped atoms 21 within the trapping volume 213 without significantly disrupting the trapping process. The configuration of the magneto-optical trap 200 with the central gap 218 may also provide flexibility in experimental setups while maintaining the ability to trap and cool atoms using a single input laser beam. The adjustable nature of the central gap 218 may further allow for fine-tuning of the trapping volume 213 to optimize atom trapping for specific experimental or application contexts.

[0051] FIG. 3 illustrates a side-view schematic of a dual magneto-optical trap configuration comprising two vertically aligned magneto-optical traps 300a, 300b. The configuration includes a first magneto-optical trap 300a and a second magneto-optical trap 300b, each having an upper mirror 301a, 301b and a lower mirror 302a, 302b, respectively. A retroreflector assembly 303 may be positioned below the second magneto-optical trap 300b. Magnetic coils 304a may be positioned above and below the first magneto-optical trap 300a, while magnetic coils 304b may be positioned above and below the second magneto-optical trap 300b. A single laser beam 307 may enter from above and pass through both magneto-optical traps 300a, 300b.

[0052] The laser beam 307 may interact with the mirror surfaces to create trapping volumes 313a, 313b in each magneto-optical trap. Trapping volumes 313a, 313b may have diamondshaped configurations where trapped atoms 315a, 315b may be contained. The laser beam paths may be shown by rays 316a in the first magneto-optical trap 300a and rays 316b in the second magneto-optical trap 300b. The configuration may allow a single laser beam 307 to create two separate trapping regions, with the laser beam 307 maintaining collimation as the laser beam 307 passes through the first magneto-optical trap 300a to the second magneto-optical trap 300b. This collimation preservation may be achieved through the specific geometry of the upper mirrors 301a, 301b and the lower mirrors 302a, 302b. The angles and dimensions of these mirrors may be designed to ensure that the laser beam 307 exits each trap as a collimated beam, maintaining beam quality and intensity for subsequent traps.

[0053] In some cases, two or more magneto-optical traps may be placed in a row and illuminated by one input laser beam to create multiple cold-atom samples. This arrangement may allow for efficient use of a single laser source to generate multiple trapping regions, potentially increasing 10HB: 4931-4976-1177.3experimental throughput or enabling comparative studies between trapped atom populations. Different magneto-optical traps in the configuration may have different parameters. For example, the first magneto-optical trap 300a and the second magneto-optical trap 300b may have different mirror angles 0, different ratios of a first length LI to a second length L2, or varying presence and height of central gaps. Additionally, magnetic field gradient configurations generated by the magnetic coils 304a and 304b may differ between traps, allowing for customization of trapping conditions in each magneto-optical trap. In further implementations, any or all of these parameters may be tunable during operation. For instance, a tunable gap between mirrors may be used to configure trapping volume size. As another example, the distance between the traps may be configurable.

[0054] The retroreflector assembly 303 may reflect the laser beam 307 back through both trapping regions along the laser beam 307's original path. This reflection may enhance trapping efficiency by creating counter-propagating beam paths, which may increase the cooling and trapping forces acting on trapped atoms 315a, 315b. In some implementations, additional optical elements may be introduced between the first magneto-optical trap 300a and the second magneto-optical trap 300b to further control or manipulate the laser beam 307. These elements may include, for example, additional waveplates or beam-shaping optics to fine-tune the properties of the laser beam 307 for each trapping region.

[0055] FIG. 4 illustrates an isometric view of a planar mirror assembly 400 comprising four reflector bodies 401, 402, 403, 404 arranged to form a square configuration with a central opening. The planar mirror assembly 400 may be an example implementation of the upper mirror 101 and the lower mirror 102 described in FIG. 1 A. Each reflector body 401, 402, 403, 404 may include a planar reflective surface 405 oriented at an angle relative to the central axis of planar mirror assembly 400. The angle of planar reflective surface 405 may correspond to the mirror angle 0 described in FIG. 1A and FIG. 2, which may be between 45° and 90° relative to a plane perpendicular to the central axis. Reflector bodies 401, 402, 403, 404 may be positioned such that planar reflective surfaces 405 face inward toward the central opening. The planar mirror assembly 400 may incorporate a first set of reflection surfaces oriented towards the input light beam and a second set of reflection surfaces oriented opposite to the input light beam. Both sets of reflection surfaces may be inclined at an angle between 45° and 90° relative to a plane11HB: 4931-4976-1177.3perpendicular to the first axis. The first and second sets of reflection surfaces may be arranged parallel to each other and define a central through hole.

[0056] The square configuration of the planar mirror assembly 400 may provide reflection surfaces spanning two dimensions for a trapping volume. A first pair of reflector bodies (e.g., reflector bodies 401 and 403) may provide reflections along the x-axis, while a second pair of reflector bodies (e.g., reflector bodies 402 and 404) may provide reflections along the y-axis.

[0057] FIG. 5 illustrates an isometric view of a conical mirror assembly 500 comprising four reflector bodies 501, 502, 503, 504 arranged in a cylindrical configuration. The conical mirror assembly 500 may be an alternative implementation of the upper mirror 101 and the lower mirror 102 described in FIG. 1A. Each reflector body 501, 502, 503, 504 may include a conical reflective surface 505 oriented at an angle relative to the central axis of conical mirror assembly 500. The angle of the conical reflective surface 505 may correspond to the mirror angle 0 described in FIG. 1 A and FIG. 2, which may be between 45° and 90° relative to a plane perpendicular to the central axis. Similar to the planar mirror assembly, the conical mirror assembly 500 may feature a first set of reflection surfaces oriented towards the input light beam and a second set oriented opposite to the input beam, with both sets inclined at angles between 45° and 90° relative to a plane perpendicular to the first axis. Reflector bodies 501, 502, 503, 504 may be positioned such that conical reflective surfaces 505 face inward toward the central opening. In some implementations, the conical mirror assembly 500 may be machined from a cylinder 506.

[0058] The conical configuration of the conical mirror assembly 500 may have different characteristics compared to the planar mirror assembly 400. The conical reflective surfaces 505 may focus the laser beam 107 to a line on the z-axis in the center of the trapping volume (e.g. the trapping volume 113 of FIG. 1A). Both the planar mirror assembly 400 and the conical mirror assembly 500 may provide the geometry to create a diamond-shaped trapping volume. In some cases, mirror assemblies with different numbers of reflector bodies may be used. For example, hexagonal or octagonal configurations may be implemented to provide additional reflection surfaces. As another example, a circular profile may be used to create a continuous reflective surface around the central opening. The central through hole defined by the parallel arrangement of the first and second sets of reflection surfaces in both the planar mirror assembly 400 and the12HB: 4931-4976-1177.3conical mirror assembly 500 may allow the laser beam 107 to pass through. The size of this central opening may be adjusted.

[0059] In some implementations, the reflective surfaces of the planar mirror assembly 400 or the conical mirror assembly 500 may be coated with highly reflective materials. These coatings may be optimized for the specific wavelength of laser beam 107 used in the magneto-optical trap system 100. The dimensions of reflector bodies 401, 402, 403, 404 in the planar mirror assembly 400 and the reflector bodies 501, 502, 503, 504 in the conical mirror assembly 500 may be designed to achieve specific trapping volume characteristics. For example, the vertical extent of the reflective surfaces may correspond to the mirror height d described in FIG. 1 A, while the horizontal dimensions may be related to the first length LI and the second length L2.

[0060] In some examples, the trapping volume of the cold-atom -trapping mirror assembly may be characterized as a function of inclination angle 0. As 0 decreases from 90 degrees toward 45 degrees, the mirror assembly may become wider along the x-axis, and the trapping volume may increase. In examples where the reflective surfaces are planar (pyramidal configuration), the trapping volume may be approximated as a double pyramid. In examples where the reflective surfaces are conical, the trapping volume may be approximated as a double cone. In one nonlimiting example, a back-to-back conical mirror with a half-height in a range of approximately 10 mm to 15 mm (e.g., approximately 12 mm) and an inclination angle in a range of approximately 50° to 60° (e.g., approximately 55°) may provide a trapping volume of approximately 1 cm3to 2 cm3(e.g., approximately 1.7 cm3), an outer diameter in a range of approximately 35 mm to 55 mm (e.g., approximately 44 mm), and a central hole diameter in a range of approximately 20 mm to 35 mm (e.g., approximately 26 mm). Other inclination angles and mirror dimensions may be selected depending on the application, and other trapping volume values will be apparent to those of ordinary skill in the art.

[0061] In some examples, the reflective surfaces of the cold-atom-trapping mirror assembly may be fabricated from a metallic substrate, such as aluminum or other suitable metallic material, using a CNC machining process or other suitable manufacturing method. The reflective surfaces may be polished to an RMS surface deviation of approximately 120 nm or other suitable surface quality and may be coated with a highly reflective metallic coating, such as protected silver or other suitable reflective materials, to achieve a reflectivity of approximately 95% or greater at the laser wavelength of interest. In various examples, a metallic coating may be selected to 13HB: 4931-4976-1177.3preserve the circular polarization of the laser beam upon reflection. In other examples, a dielectric coating may be used, where the coating provides a substantially equal phase shift between the two orthogonal polarizations of the laser beam. Other coating materials and processes may be used depending on the laser wavelength, polarization specifications, and surface quality specifications.

[0062] In some examples, the hollow-core incident laser beam configuration described with respect to FIG. IB and the central gap configuration described with respect to FIG. 2 may be combined in a single magneto-optical trap system. In such combined examples, the cold-atomtrapping mirror assembly may include a central gap between the upper and lower sets of reflection surfaces, and the laser source may be configured to generate a laser beam having a hollow central core aligned with the central through hole. This combined configuration may allow laser beams and particle beams to reach the magneto-optical trap along all axes, including the first axis via the central through hole and hollow core, and the radial direction via the central gap. In various implementations, the combination of both access modalities may provide flexibility for interacting with the cold atomic cloud for purposes including fluorescence detection, probing, atom injection, or other suitable interactions. Other combinations of access configurations will be apparent from the description herein.

[0063] In some examples, the shape of the trapped atomic cloud may vary depending on the alignment between the input laser beam and the cold-atom-trapping mirror assembly, as well as the magnetic field configuration. In examples where the cold-atom-trapping mirror assembly comprises conical reflective surfaces, the ring-shaped cloud morphology may be attributed to two cooperating effects: wave vectors of the laser beams reflected from the conical surfaces may not be parallel to the lines of the quadrupole magnetic field, introducing polarization components that are not optimally oriented for atom trapping at all positions within the trapping volume; and the conical reflection surfaces may focus the laser beams to a line along the first axis at the center of the trapping volume, causing the laser intensity distribution to vary with the alignment between the counterpropagating laser beams and the mirror axis. In various examples, when the zero-magnitude position of the quadrupole magnetic field moves toward the center of the trapping volume and the counterpropagating laser beams are perpendicularly aligned with the conical mirror, the trapped atomic cloud may approach a ring shape. In other examples,14HB: 4931-4976-1177.3adjustment of the laser alignment or the magnetic field gradient may restore a substantially ballshaped cloud.

[0064] In some examples, the atom number of the magneto-optical trap may vary as a function of the incident cooling laser intensity. In examples where the cold-atom-trapping mirror assembly comprises conical reflective surfaces, the atom number may saturate at lower cooling laser intensities compared with a planar-mirror assembly having a similar trapping volume, because the conical surfaces may focus the cooling laser beam toward the center of the trapping volume, increasing the local laser intensity in the trapping region. For reference, the saturation intensity Is of the 87Rb F=2 to F'=3 transition with sigma-plus-polarized light is approximately 1.67 mW / cm squared. Other reflective surface geometries may exhibit intermediate behavior.

[0065] In some examples implementing the scalable multi-trap configuration of FIG. 3, a plurality of cold-atom-trapping mirror assemblies may be mounted on a shared support structure, such as a 3D-printed or machined spacer or other suitable support. The incident laser beam, after passing through a first cold-atom-trapping mirror assembly, may exhibit an inner circle corresponding to the portion of the beam that passes through the central through hole and an outer ring corresponding to the portion reflected by the conical or planar surfaces. A small gap may appear between the inner circle and the outer ring due to imperfect reflections at the edge of the surface; such edge effects may have a minimal effect on trap performance because the edge rays contribute to the outermost layer of the trapping volume. In various examples, the laser beam may remain substantially collimated after passing through each cold-atom-trapping mirror assembly, and diffraction effects may be negligible at distances of approximately 0.3 m or greater from each assembly. In some examples, tilt between stacked cold-atom-trapping mirror assemblies may affect the shape and position of the trapped atomic cloud, and laser power losses through successive mirror assemblies may reduce the atom number in traps farther from the laser source. These factors may be mitigated by careful alignment of the mirror assemblies and selection of mirror coatings with high reflectivity.

[0066] In some examples, the shape of the trapped atomic cloud may be varied by adjusting the alignment of the retroreflector assembly. When the retroreflected laser beam is misaligned relative to the incident beam axis by an angle in a range of approximately 2 degrees to 3 degrees, the laser intensity distribution within the cold-atom trapping volume may be modified, and the trapped atomic cloud may form a ring-shaped configuration, a dual-cloud configuration, or a tri- 15HB: 4931-4976-1177.3cloud configuration within the trapping volume. Other misalignment angles may produce intermediate morphologies or a substantially ball-shaped cloud. The specific angular range that produces each cloud configuration may vary depending on the mirror geometry, magnetic field gradient, laser power, or other suitable parameters.

[0067] In some examples, the laser system may be based on modulating a distributed Bragg reflector (DBR) laser with a wavelength of approximately 780 nm and an output power of approximately 180 mW, or other suitable wavelength and power. The main laser output may serve as the cooling beam, with frequency detuning adjusted by a fiber-based electro-optical modulator (EOM). The first-order sideband may be locked to the 85Rb F=3 to F-4 transition via modulation transfer spectroscopy. A diffracted port of the laser output modulated by another fiber-based EOM may serve as the repumping beam, resonating at the 87Rb F=1 to F'=2 transition. The cooling and repumping beams may be combined at a polarizing beam splitter and then collimated to a diameter of approximately 45 mm to 60 mm (1 / e2) (e.g., approximately 54 mm) or other suitable diameter. In some implementations, the cooling beam may have a laser power of approximately 25 mW to 30 mW (e.g., approximately 27 mW), and the repumping beam may have a power of approximately 1 mW. The averaged cooling beam intensity may be approximately 1.53 mW / cm squared, which may be approximately 43% of the saturation intensity of the 87Rb F=2 to F'=3 transition. When loading atoms from the background vapor to the magneto-optical trap, the cooling beam may be detuned approximately 5 to 7 MHz below the 87Rb F=2 to F'=3 transition. The laser frequency may be stabilized using a combination of modulation transfer spectroscopy and frequency modulation spectroscopy techniques, providing robust frequency locking for the laser system. Other laser types, wavelengths, and stabilization techniques may be used depending on the atom species and application.

[0068] After initial loading, polarization gradient cooling may be used to further cool the atoms by gradually increasing the detuning and reducing the power of the cooling beam. This process may allow for achieving lower temperatures in the atomic sample, potentially reaching temperatures as low as approximately 5 pK for 87Rb atomic clouds. The repumping beam, which may have a power of approximately 1 mW, functions in the cooling process by preventing atoms from accumulating in states that do not interact with the cooling light. The repumping beam may resonate at the 87Rb F=1 to F'=2 transition, ensuring that atoms remain in the cooling cycle.16HB: 4931-4976-1177.3

[0069] To image free-fall atomic clouds, a detection beam may be produced comprising the cooling beam resonating at the 87Rb F=2 to F-3 transition and the repumping beam resonating at the 87Rb F=1 to F'=2 transition. A photodetector with an imaging lens may detect the atoms' fluorescence. By switching the repumping frequency, atoms in F=1 and F=2 states may be detected separately, enabling normalized detection and providing robustness to atom number fluctuations in the magneto-optical traps.

[0070] In some examples, the magnetic field configuration may include an anti-Helmholtz coil pair positioned above and below the cold-atom-trapping mirror assembly and three Helmholtz coil pairs arranged around the vacuum chamber for bias field compensation. The magnetic gradient in the cold-atom trapping volume may be approximately 12 G / cm or another suitable gradient. In some implementations, each coil may have a diameter of approximately 10 cm and may contain approximately 120 turns of copper wire or other suitable geometry. Other coil configurations and materials may be used.

[0071] Without being bound by a particular theory, the magneto-optical trap (MOT) operates on the principle of combining laser cooling with a spatially varying magnetic field. A single laser beam, consisting of a cooling beam and a repumping beam, interacts with the atoms in the trapping region. The laser beam may be circularly polarized and substantially collimated, propagating along a first axis. Simultaneously, a magnetic field generator may create a quadrupole magnetic field with a magnitude of zero at the center point of the cold-atom-trapping mirror assembly. As atoms enter the trap, they experience a position-dependent Zeeman shift due to the magnetic field. This shift, combined with the laser detuning, creates a situation where atoms preferentially absorb photons when moving towards a laser beam, resulting in a velocitydependent force that slows the atoms. This process, known as Doppler cooling, forms the basis of the initial cooling stage in the MOT.

[0072] The laser cooling in the MOT may be achieved through the interaction of atoms with the laser beam. The laser frequency may be tuned slightly below the resonant frequency of the atoms, ensuring that atoms moving towards the laser beam are more likely to absorb photons, thus experiencing a net force opposite to their motion. This process reduces the kinetic energy of the atoms, effectively cooling them. In some cases, the cooling beam may be detuned approximately 5 to 7 MHz below the 87Rb F=2 to F'=3 transition when loading atoms from the background vapor to the magneto-optical trap. The averaged cooling beam intensity may be 17HB: 4931-4976-1177.3approximately 1.53 mW / cm squared, which may be approximately 43% of the saturation intensity of the 87Rb F=2 to F -3 transition.

[0073] Once the atoms are sufficiently slowed by Doppler cooling, polarization gradient cooling may be employed to further reduce their temperature. This process involves the creation of a polarization gradient in the standing waves formed by the counter-propagating laser beams, leading to additional cooling through optical pumping and light shifts. To implement polarization gradient cooling, the cooling beam intensity may be decreased and the detuning increased. This adjustment in laser parameters creates conditions where atoms experience a spatially varying light shift, resulting in a more efficient cooling mechanism. The polarization gradient cooling may allow for achieving lower temperatures in the atomic sample, potentially reaching temperatures as low as approximately 5 pK for 87Rb atomic clouds.

[0074] The magnetic field generator, which may include magnetic coils arranged in an antiHelmholtz configuration, produces a quadrupole field with a zero point at the center of the trap. The strength and shape of the magnetic field gradient may be tailored to optimize the trapping efficiency and the characteristics of the trapped atomic cloud.

[0075] The retroreflector assembly, consisting of a quarter waveplate and a flat mirror, may enhance the trapping efficiency by reflecting the laser beam back through the system.Advantageously, this reflection effectively doubles the number of beam intersections and creates a more uniform trapping force throughout the diamond-shaped trapping volume. The trapped atomic cloud formed through this process of laser cooling and magnetic confinement may serve as a starting point for various experiments in atomic physics, quantum optics, and precision measurements. The ability to cool atoms to such low temperatures may open up possibilities for studying quantum phenomena and developing highly sensitive measurement devices.

[0076] FIG. 6A illustrates a side-view schematic of a gravimeter 600 comprising three vertically aligned magneto-optical traps: an upper trap 601, a middle trap 602, and a lower trap 603. The gravimeter 600 may be arranged in a vertical configuration to enable gravity measurements at different heights. A laser beam 612 may enter from above and interact sequentially with the upper trap 601, middle trap 602, and lower trap 603. A laser beam 612 may create three distinct trapping regions: an upper trapping volume 605, a middle trapping volume 606, and a lower trapping volume 607. Within these trapping volumes, atoms may be confined, represented by upper trapped atoms 608, middle trapped atoms 609, and lower trapped atoms 610.18HB: 4931-4976-1177.3

[0077] The laser beam 612 may maintain collimation as the laser beam 612 passes through each trap, enabling efficient interaction with all three trapping regions. At the bottom of the gravimeter 600, a retroreflector 613 may reflect the laser beam 612 back through the system along the laser beam 612's original path. Each trap may consist of a 3D DMOT configuration that reflects the laser beam 612 to create the respective trapping volumes. The vertical spacing between the traps may allow for sequential measurements of atomic samples at different heights, enabling gravity measurements at multiple positions using a single laser beam path.

[0078] In some cases, the upper trap 601, middle trap 602, and lower trap 603 may be separated by various distances. For example, the three diamond-shaped mirrors may be separated by approximately 0.26 meters. This separation may correspond to a free-fall time of approximately 230 ms between adjacent traps, allowing for distinct measurements at each height. The middle trap 602 may be positioned at various locations within the gravimeter 600. The placement of the middle trap 602 may not be restricted to the center of the gravimeter 600, allowing for flexibility in experimental design and measurement configurations.

[0079] The dimensions of each trap may be optimized based on their position within the gravimeter 600. These dimensions may be adjusted to optimize the trapping volume and laser interaction for each individual trap. In some implementations, the upper trap 601, middle trap 602, and lower trap 603 may have different configurations to account for various experimental factors. For example, the configuration may be adjusted to compensate for optical losses as the laser beam 612 propagates through the gravimeter 600. To increase the trapping volume farther from the laser source, the geometry of each trap may be modified. In some cases, the upper trap 601 may include a central gap with a height g, the middle trap 602 may include a central gap with a height g1, and the lower trap 603 may be gapless. This arrangement may allow for optimization of trapping efficiency at each level of the gravimeter 600.

[0080] The use of different configurations for each trap may provide several advantages. For instance, the varying gap sizes may allow for customization of the trapping volumes to compensate for changes in laser intensity as the laser beam 612 propagates through the gravimeter 600. Additionally, the different configurations may enable optimization of the trapping parameters for each specific height. The gravimeter 600 may utilize magnetic coils (not shown) positioned around each trap to generate the magnetic field gradients for magneto-optical19HB: 4931-4976-1177.3trapping. These magnetic fields, in conjunction with the laser beam 612, may create the conditions for cooling and trapping atoms at each level of the gravimeter 600.

[0081] The multi-level configuration of the gravimeter 600 may allow for simultaneous measurements of gravity at different heights. By comparing the behavior of trapped atoms at each level, the gravimeter 600 may provide information about the vertical gravity gradient and potentially higher-order derivatives of the gravitational field.

[0082] Gravimeters may include various numbers of DMOTs. For example, FIG. 6B illustrates a side-view schematic of a gravimeter 620 comprising a single DMOT 621. For instance, using one 3D DMOT in a gravimeter may support measuring the vertical absolute gravity value by implementing cold-atom interferometry while dropping cold atoms. As another example, FIG.6C illustrates a gravimeter 630 comprising two DMOTs 631. For instance, the gravimeter 630 may be used as a gradiometer for measuring the vertical absolute gravity values and gravity gradient by implementing cold-atom interferometry while dropping cold atoms. These capabilities may be particularly useful for applications in geophysics, geodesy, and fundamental physics research. In further implementations, the number of DMOTs may be reconfigurable (e.g., may be added or removed by users).

[0083] FIG. 7 illustrates a side-view schematic of a gravimeter 700, which may be an example implementation of the gravimeter 400 shown in FIG. 6A. The gravimeter 700 comprises a vacuum tube 708 with bias coils and magnetic shielding, which houses multiple magneto-optical traps arranged in a vertical configuration. At the upper portion of the vacuum tube 708, a rubidium dispenser 702 may be positioned. The rubidium dispenser 702 may allow for injecting rubidium atoms to be trapped into the vacuum tube 708.

[0084] Below the rubidium dispenser 702, three magneto-optical traps are vertically arranged: a first magneto-optical trap 703, a second magneto-optical trap 704, and a third magneto-optical trap 705. These magneto-optical traps may be spaced apart within the vacuum tube 708 to allow for sequential atomic measurements at different heights. For example, the magneto-optical traps may be separated by approximately 0.2 to 0.3 meters, corresponding to a free-fall time of approximately 200 to 250 ms between adjacent traps. The arrangement of the first magnetooptical trap 703, second magneto-optical trap 704, and third magneto-optical trap 705 may correspond to the upper trap 601, middle trap 602, and lower trap 603 described in FIG. 6A. In20HB: 4931-4976-1177.3some implementations, the vacuum tube 708 may have a total length of approximately 0.8 to 1.2 meters and an inner diameter of approximately 4 to 6 centimeters.

[0085] An imaging viewport 706 may be located near the bottom of vacuum tube 708, providing optical access for detecting and measuring the atomic samples. Adjacent to imaging viewport 706, an ion pump 707 may be connected to remove untrapped rubidium atoms and maintain the vacuum conditions within the vacuum tube 708. The positioning of the rubidium dispenser 702 above the magneto-optical traps and ion pump 707 next to the imaging viewport 706 may achieve a differential pumping rate. This configuration may result in a higher rubidium vapor pressure in the magneto-optical trap area, potentially accelerating an atom loading speed and increasing atom numbers in the traps. Conversely, the lower rubidium vapor pressure in the imaging area may decrease background imaging noise and improve the signal-to-noise ratio.

[0086] The arrangement of gravimeter 700 may allow a single laser beam to interact with all three magneto-optical traps sequentially, creating three separate regions for trapping and cooling atoms. The vertical spacing between the first magneto-optical trap 703, second magneto-optical trap 504, and third magneto-optical trap 705 may enable gravity measurements at different heights using the same laser beam path through the vacuum tube 708. In some cases, cold-atom interferometry may be used to measure the absolute gravity value at three heights corresponding to the positions of the first magneto-optical trap 703, second magneto-optical trap 704, and third magneto-optical trap 705. This configuration may allow for simultaneous measurements of vertical gravity, gravity gradient, and gravity curvature.

[0087] The implementation of the gravimeter 700 may involve several stages of operation. Initially, a laser beam consisting of a cooling beam and a repumping beam may be illuminated from the top viewport. A retroreflector at the bottom may reflect these laser beams. To obtain atomic clouds at approximately 5 pK, the cooling beam intensity may be decreased and the detuning increased to conduct polarization gradient cooling. As the atomic clouds start freely falling, a Doppler-insensitive Raman pulse may select atoms in specific states with a narrow velocity bandwidth. A pushing pulse may remove atoms in other states. During the atom interferometry stage, matter wave splitters based on Doppler-sensitive two-photon Raman transitions may drive the atoms between different hyperfine ground states.

[0088] For detecting the outputs of atom interferometers, a standing laser beam may be illuminated horizontally through the imaging viewport 706. This beam may consist of a resonant 21HB: 4931-4976-1177.3frequency and a repumping frequency. A photodetector with an imaging lens may detect the atoms' fluorescence. By switching the repumping frequency, atoms in different states may be detected, enabling normalized detection and providing robustness to atom number fluctuations in the magneto-optical traps. The design of the gravimeter 700 may allow for the use of the same detection laser beam and photodetector to read the outputs of all three interferometers. This may be possible due to the sufficient separation in free-fall time between adjacent atom interferometers, which may be approximately 0.2 seconds. This approach may simplify the overall system design and operation.

[0089] In some cases, the multi-trap configuration may be used to measure gravity through atom interferometry techniques. The process may involve several stages, including state preparation, Raman transitions, and detection. In a multi-trap configuration (see, e.g., FIG. 6A, FIG. 7), as the atomic clouds start freely falling from the trapping volumes (e.g., trapping volumes 605, 606, 607), a Doppler-insensitive Raman pulse may select atoms in the F=2 and mF=0 states with a narrow velocity bandwidth. This selection process may help to reduce the initial momentum spread of the atomic ensemble, which may improve the coherence and sensitivity of the subsequent interferometry steps. Following the state selection, a pushing pulse may be applied to remove atoms in other mF states, ensuring that only atoms in the desired quantum state participate in the interferometry sequence, potentially reducing noise and improving the signal quality.

[0090] The atom interferometry stage may utilize matter wave splitters based on Doppler-sensitive two-photon Raman transitions. These transitions may drive the atoms between different hyperfine ground states, creating a superposition of momentum states. In some cases, a Mach-Zehnder geometry of 7t / 2-7t-7t / 2 pulses may be implemented for the atom interferometry sequence. The 7t / 2 pulse may place the atom in a superposition of two states, effectively creating a beam splitter for the matter waves. A mirror may be formed by a % pulse, which may have a 100% probability of changing the state. The final / 2 pulse may recombine the matter waves to obtain interference fringes. During the free-fall period, the atomic wave packets may accumulate a phase difference proportional to the local gravitational acceleration. By measuring this phase difference, the system may determine the absolute gravity value at each trap location.

[0091] For detecting the outputs of the atom interferometers (see, e.g., FIG. 7), a standing laser beam may be illuminated horizontally through imaging viewport 706 in the imaging area. This 22HB: 4931-4976-1177.3beam may consist of a resonant frequency and a repumping frequency. A photodetector with an imaging lens may detect the atoms' fluorescence. By switching the repumping frequency, atoms in F=1 and F=2 states may be detected separately, enabling normalized detection. This approach may provide robustness to atom number fluctuations in the magneto-optical traps. In some cases, the free-fall time between adjacent atom interferometers may be separated by approximately 0.2 seconds. This separation may allow for the use of the same detection laser beam and photodetector to read the outputs of all three interferometers, potentially simplifying the overall system design and operation.

[0092] The vertically separated configuration of the traps (see, e.g., FIG. 6A, upper trap 601, middle trap 602, lower trap 603; FIG. 7, first magneto-optical trap 703, second magneto-optical trap 704, third magneto-optical trap 705) may allow for simultaneous measurements of gravity at different heights. By comparing the gravity values obtained from each trap, the system may calculate the vertical gravity gradient. The gravity gradient may be determined by the difference in gravity measurements between adjacent traps divided by their vertical separation.Furthermore, the three-trap configuration may enable the measurement of the gravity curvature, for example, by comparing the gravity gradient between the upper and middle traps with the gradient between the middle and lower traps.

[0093] In some examples, gravity measurement may be performed by forming atom interferometry using a freely falling cold atomic cloud released from the cold-atom trapping volume. Atom interferometry may be performed as the cold atomic cloud freely falls underneath the cold-atom-trapping mirror assembly. Doppler-sensitive two-photon Raman transitions, driven by two laser beams with wave vectors kl and k2, may create atomic superpositions between the 87Rb F=1 and F=2 hyperfine ground states. In some examples, a Mach-Zehnder geometry may be implemented using a sequence of three pulses: a ni pulse that places the atoms into a superposition of two states; a 7t pulse that fully transfers atoms between states; and a final 7t / 2 pulse that combines the superposition states. The three pulses may be equally spaced by a pulse separation time T. The population fractions of the atoms in the two states may be used to measure the phase difference A(p between the two interferometer arms according to P = P0 + (C / 2) cos(Acp), where P0 is the normalized background population and C is the contrast. For gravity measurement applications, the phase difference may be given by A(p = (keffg - a) T2, where keff = kl - k2 is the effective wave vector of the interferometer beams, g is the23HB: 4931-4976-1177.3gravitational acceleration, T is the pulse separation time, and a is the laser frequency chirp rate. Because the atoms are in free fall, they experience a Doppler-shifted laser frequency; to compensate for this effect, the laser frequency difference between the two beams may be linearly ramped at the rate a. Interference fringes may be obtained by varying a. The cosine dependence of the fringes may introduce an ambiguity in the gravity measurement. In some examples, this ambiguity may be resolved by first performing a measurement with a short pulse separation time T of several milliseconds to obtain a unique but coarse measurement, and then performing finer measurements with progressively longer T values. For each T, the wave vectors may be reversed to reduce systematic effects from the magnetic field gradient and the first-order light shift. This procedure may be performed automatically at the start of each new measurement. Other measurement protocols may be used.

[0094] The multi-trap configuration may provide several advantages for gravity field measurements. By simultaneously measuring absolute gravity values at three different heights, the system may offer enhanced sensitivity to local mass density changes. This capability may be particularly useful for applications such as geophysical surveys, underground water level monitoring, or the detection of subsurface structures. The ability to measure gravity curvature may provide additional information about the gravitational field structure. In some cases, the gravity curvature may be more sensitive to horizontal resolutions in mining exploration or the detection of near subsurface or shallow density structures. This information may be valuable for modeling the Earth's gravitational field or investigating systematic effects in measurements of Newton's gravitational constant.

[0095] The atom interferometry technique employed in this system may offer high precision and accuracy in gravity measurements. The use of cold atoms and quantum superposition states may allow for measurements with sensitivities potentially surpassing those of classical gravimeters. In some implementations, the system may be designed to be portable, allowing for in-field gravity surveys. The use of a single laser beam for multiple traps (see, e.g., FIG. 3, laser beam 307; FIG.6A, laser beam 612; FIG. 7) may contribute to the compactness and simplicity of the apparatus, potentially making it suitable for mobile applications in geophysics, civil engineering, navigation, or other suitable fields.

[0096] The scalable atomic gravimeter may have various applications in fields involving precise gravity measurements. In geophysics surveys, the ability to simultaneously measure gravity at 24HB: 4931-4976-1177.3multiple heights may provide enhanced sensitivity to local mass density changes. This capability may be particularly useful for detecting subsurface structures, such as caves, caverns, salt domes, buried fault systems, or other suitable geological features. The system may enable more detailed mapping of underground features, potentially improving the efficiency and accuracy of geological surveys.

[0097] For monitoring underground water levels, the scalable atomic gravimeter may offer advantages over other methods. The ability to measure gravity gradients and curvature may provide more sensitive detection of changes in subsurface water distribution. This may be especially valuable in areas where direct access to groundwater is limited or challenging. In gravity field cartography, the system may contribute to creating more detailed and accurate maps of the Earth's gravitational field. The simultaneous measurement of gravity at three different heights may allow for the calculation of vertical gravity gradients and curvature with high precision. This information may be valuable for geophysicists studying the Earth's internal structure and composition.

[0098] The compact design of the scalable atomic gravimeter, as illustrated in FIG. 6A and FIG.6, may make it suitable for in-field gravity surveys. The use of a single laser beam to create multiple trapping regions may contribute to the system's portability, potentially allowing for measurements in remote or challenging environments. This compact configuration may also facilitate the integration of the gravimeter into mobile platforms for dynamic gravity mapping. The multi-level configuration of the gravimeter, as shown in FIG. 6A, may allow for simultaneous measurements of gravity at different heights. By comparing the behavior of trapped atoms at each level, the gravimeter may provide information about the vertical gravity gradient and potentially higher-order derivatives of the gravitational field. This capability may be particularly useful for applications in geophysics, geodesy, and fundamental physics research.

[0099] The third-order derivative of the gravitational potential (the so-called curvature) may be more sensitive to local mass density changes compared to absolute gravity or gravity gradient measurements. The ability to measure gravity curvature may enhance the system's capability to provide horizontal resolutions in mining exploration, detect near subsurface or shallow density structures, and model the Earth's gravitational field with greater detail. In some implementations, the scalable atomic gravimeter may be used to investigate systematic effects in measurements of25HB: 4931-4976-1177.3Newton's gravitational constant. The high precision and multi-height measurement capability may allow for more detailed studies of gravitational interactions at different scales.

[0100] The system's ability to measure higher-order vertical gravity derivatives may be particularly useful in surveying along geophysics boreholes for monitoring underground water leveling. The increased sensitivity to vertical changes in the gravitational field may provide more accurate data on subsurface fluid movements and distributions. As further described with respect to FIG. 8 below, the control system of the magneto-optical trap system may allow for precise management of the trapping and measurement processes. This level of control may enable the optimization of measurement parameters for specific applications, potentially improving the overall sensitivity and accuracy of gravity measurements in various field conditions.

[0101] The scalable atomic gravimeter may also find applications in long-baseline atom interferometers, where it may be used to correct for Newtonian noise. The ability to measure gravity gradients and curvature with high precision may allow for better characterization and mitigation of gravitational noise sources in sensitive experiments. The scalable atomic gravimeter may offer advantages in terms of measurement precision, spatial resolution, and portability compared to other gravimetry techniques. These features may make it a valuable tool for a wide range of applications in geophysics, hydrology, and fundamental physics research.

[0102] FIG. 8 illustrates a block diagram of a magneto-optical trap system 800. The magnetooptical trap system 800 may include a magneto-optical trap device 801 containing a laser 802 and a vacuum tube 803. Field gradient coils 804 may be arranged around the vacuum tube 803. Inside the vacuum tube 803, a trapping reflector 805 may be positioned relative to a retroreflector 806. A sensor 807 may be coupled to the system 800. The magneto-optical trap system 800 may include a control system 808 that manages the operation of various components. The control system 808 may comprise a laser controller 809 connected to the laser 802, a processor 810, and a magnet controller 811 connected to the magnetic field source 804. The control system 808 may also include a data input module 812 and a memory 813. In some implementations, the magneto-optical trap system 800 may be configured as a gravimeter, for example as described with respect to FIGS. 6A, 6B, 6C, and 7, in which the processor 810 receives signals from the sensor 807 corresponding to atoms released from one or more coldatom trapping volumes and generates gravitational measurements based on those signals.26HB: 4931-4976-1177.3

[0103] The laser controller 809 may regulate laser 802 output while the magnet controller 811 may control the magnetic fields generated by magnetic field source 804. The processor 810 may coordinate the operation of these controllers based on input from the data input module 812 and instructions stored in the memory 813. The sensor 807 may provide feedback to the control system 808 regarding the atomic samples within the vacuum tube 803. The trapping reflector 805 and the retroreflector 806 may work together to create the laser beam paths for atom trapping within the vacuum tube 803. The laser beam from the laser 802 may interact with these reflectors to form the trapping region where atoms may be confined and cooled.

[0104] While FIG. 8 illustrates a system with a single trapping reflector, the magneto-optical trap system 800 may include any number of trapping reflectors arranged within the vacuum tube 803. For example, the system 800 may incorporate multiple trapping reflectors as illustrated in the configurations of FIG. 3 with two vertically aligned magneto-optical traps 300a and 300b, FIG. 6A with three vertically aligned traps (upper trap 601, middle trap 602, and lower trap 603), or FIG. 7 with three magneto-optical traps (first magneto-optical trap 703, second magnetooptical trap 704, and third magneto-optical trap 705). These multiple-trap configurations may all be controlled by a single control system 808 using a single laser 802 to create multiple trapping regions within the same vacuum tube 803.

[0105] In some cases, the laser 802 may be any suitable laser device capable of producing the wavelength and power for atom trapping and cooling. For example, the laser 802 may be a diode laser, a fiber laser, a solid-state laser, or another suitable laser type, depending on the specific parameters of the magneto-optical trap system 800.

[0106] The sensor 807 may comprise various different types of sensors. For example, the sensor 807 may include photodetectors for measuring atomic fluorescence, charge-coupled devices (CCDs) or digital cameras for imaging atomic clouds, magnetic field sensors for monitoring the magnetic field gradient, imaging lenses coupled with photodetectors to detect atoms' fluorescence, or other suitable sensor types. For detecting the outputs of atom interferometers, the sensor 807 may include a standing laser beam illuminated horizontally through an imaging viewport with a photodetector and an imaging lens arrangement to detect atoms' fluorescence in different states. The specific type and configuration of the sensor 807 may depend on the particular measurements and data for the operation and analysis of the magneto-optical trap system 800.27HB: 4931-4976-1177.3

[0107] The processor 810 may be any type of computational device capable of executing instructions and processing data. In some cases, the processor 810 may be a microcontroller, a digital signal processor (DSP), a field-programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or other suitable processing device. The choice of the processor 810 may depend on factors such as processing speed, power consumption constraints, and the complexity of the control algorithms for the magneto-optical trap system 800.

[0108] The memory 813 may include any data storing medium capable of retaining information for use by the control system 808. In some cases, the memory 813 may comprise volatile memory such as random-access memory (RAM), non-volatile memory such as read-only memory (ROM), flash memory, or a combination of these. The memory 813 may also include removable storage media such as solid-state drives (SSDs), hard disk drives (HDDs), or other suitable storage media. The capacity and type of memory 813 may be selected based on the data storage needs of magneto-optical trap system 800.

[0109] The memory 813 may store instructions to operate the magneto-optical trap system 800, including procedures for tuning the laser 802 and controlling the magnetic field generated by the magnetic field source 804. These instructions may include algorithms for adjusting laser frequency and intensity, controlling magnetic field gradients, and processing data from the sensor 807. The memory 813 may also store calibration data, experimental parameters, and measurement results.

[0110] In some cases, the magneto-optical trap system 800 may include additional components that are not illustrated in FIG. 8 for ease of explanation. For example, an atom supply system for introducing atoms into the vacuum tube 803 may be present but not shown. Similarly, vacuum pumps for maintaining the vacuum level within the vacuum tube 803 may be included in the system but omitted from the diagram.

[0111] The data input module 812 may allow for the input of experimental parameters, control settings, and other relevant information into the control system 808. In some cases, the data input module 812 may include a user interface for manual input or a communication interface for receiving data from external devices or systems. The magnetic field source 804 may include coils, such as anti-Helmholtz coils, Helmholtz coils, or other suitable coil configurations designed to generate the specific magnetic field gradients for atom trapping and manipulation.28HB: 4931-4976-1177.3

[0112] The control system 808 may coordinate the operation of various components to achieve and maintain the desired conditions for atom trapping and cooling. For example, the control system 808 may adjust the output of the laser 802 via the laser controller 809 to maintain the appropriate laser frequency and intensity for atom cooling. Simultaneously, the control system 808 may regulate the magnetic field gradient through the magnet controller 811 to ensure proper atom confinement within the trapping region.

[0113] The feedback provided by the sensor 807 may allow the control system 808 to make realtime adjustments to the trapping and cooling parameters. For instance, if the sensor 807 detects a decrease in the number of trapped atoms, the control system 808 may adjust the laser intensity or magnetic field gradient to optimize the trapping conditions.

[0114] In some implementations, the control system 808 may also manage more complex operations, such as the sequential trapping and release of atoms in multiple trapping regions, as described in previous figures. This may involve coordinating the timing of laser pulses, magnetic field changes, and sensor measurements to perform precise atom interferometry experiments or gravity measurements.

[0115] The following describes working examples and experimental results of the magnetooptical trap configurations illustrated in FIGS. 1 A through 8. These working examples demonstrate practical realizations of the mirror configurations and trapping volumes described herein. Other examples within the scope of the claims will be apparent from the description herein.

[0116] The experimental setup used a 3.38-inch cubic vacuum chamber (CU6-0337, Kurt J. Lesker) with a 5 L / s ion pump (5S TiTan, Gamma) to maintain the background pressure at approximately 1.5 * 10”9Torr. A back-to-back conical mirror was held in the center of the vacuum chamber by four aluminum rods. A rubidium dispenser (RB / NF / 4.8 / 17 FT10+10, SAES) was mounted on an electrical feedthrough at one side of the vacuum chamber. The magnetic field was controlled by an anti -Helmholtz coil pair installed outside the top and bottom viewports and three Helmholtz coil pairs around the vacuum chamber. Each MOT coil had a diameter of approximately 10 cm and contained 120 turns of copper wire. The magnetic gradient around the MOT trapping volume was 12 G / cm. The incident laser beam illuminated the back-to-back conical mirror from the top viewport. A retroreflector consisting of a quarter-wave plate and a flat mirror under the bottom viewport reflected the laser beam back to its original path. The 29HB: 4931-4976-1177.3transmission loss through each viewport was approximately 5%. Two digital cameras were used for imaging: a CS165MU1 (Thorlabs) positioned toward the top viewport, and a Stingray F-125B (Allied Vision) positioned toward a side viewport.

[0117] The laser system was based on modulating a 780-nm, 180-mW distributed Bragg reflector laser (780.241DBRH-MHFL-TO8, Photodigm), with frequency detuning adjusted by fiber-based electro-optical modulators (EOMs). The main laser output served as the cooling beam. The first-order sideband was locked to the 85Rb F=3 to F -4 transition via modulation transfer spectroscopy. A diffracted part of the laser output modulated by another fiber-based EOM served as the repumping beam, resonating at the 87Rb F=1 to F-2 transition. The cooling beam with a laser power of approximately 27 mW and the repumping beam with approximately 1 mW were combined at a polarizing beam splitter and then collimated to a diameter of approximately 54 mm (1 / e2). When loading atoms from the background vapor to the MOT, the cooling beam was detuned approximately 7 MHz below the 87Rb F=2 to F -3 transition.

[0118] The back-to-back conical mirror was fabricated from aluminum using a CNC machine. The half-height of the mirror was 12.4 mm. The inclination angle of the reflection surface was 54.7 degrees. The outer diameter of the mirror was 44 mm and the diameter of the central hole was 26.4 mm. The MOT trapping volume was 1.7 cm3. The conical surfaces were polished to an RMS surface deviation of approximately 120 nm and coated with protected silver. The reflectivity of the conical surface was approximately 95% at 780 nm. Metallic coatings were selected to preserve circular polarization upon reflection. It is also contemplated that in other examples, dielectric coatings may be used if an equal phase shift between the two orthogonal polarizations may be achieved.

[0119] The magneto-optical trap configuration produced both ball-shaped and ring-shaped atomic clouds, as illustrated in FIG. 9 A and FIG. 9B. FIG. 9A shows a side view of the trapping region in a first state, where a circular trapping volume formed in the center of the diamondshaped region. The trapping volume appears as a circular area surrounded by a darker outer region. FIG. 9B shows a side view of the trapping region in a second state, where a ring-shaped trapping volume formed. The ring-shaped volume appeared as an annular region with a darker center area. The outer dimensions remained consistent between the two states, as indicated by the 1 cm scale bar provided in both images.30HB: 4931-4976-1177.3

[0120] The shape of the atomic cloud varied depending on the alignment between the input laser beam and the magneto-optical trap mirror, as well as the magnetic field configuration. FIG. 10 depicts a matrix of magneto-optical trap fluorescence images showing the effects of varying misalignment and coil current parameters. The vertical axis shows misalignment between the input laser beam and magneto-optical trap mirror at values of 0, 0.3, 0.5, and 0.7 degrees. The horizontal axis shows upper magneto-optical trap coil current values of 1.9, 2.1, 2.3, and 2.5 amperes. Each image in the matrix displays the fluorescence pattern of trapped atoms under these different operating conditions, with shading representing lower intensity and shading representing higher intensity fluorescence.

[0121] The fluorescence patterns in FIG. 10 evolved from small point-like distributions at lower currents to larger crescent shapes at higher currents, with the pattern shape and intensity also varying with the degree of misalignment. This behavior was attributed to the interplay between the laser beam alignment, magnetic field gradient, and the geometry of the trapping region. The ability to manipulate the shape and distribution of the atomic cloud through these parameters provided flexibility in optimizing the trap for specific experimental configurations.

[0122] A ring-shaped MOT, a dual-MOT, and a tri-MOT were also observed when the retroreflected laser beam was misaligned between approximately 2 degrees and 3 degrees relative to the incident beam axis. During these observations, the top and bottom MOT coils were each operated at 3 A. The incident laser beam was perpendicular to the back-to-back conical mirror. The misaligned reflected laser beam modified the laser intensity distribution within the MOT trapping volume, producing the observed changes in cloud morphology.

[0123] The hollow-core beam configuration was also demonstrated experimentally. A circular object with a diameter of 10 mm was inserted into the optical path to block a part of the laser beam passing through the central hole of the back-to-back conical mirror. As the object was moved around, the MOT was tolerant of the object's position. The number of atoms in the MOT and the shape of the MOT were similar to the original MOT without blocking the incident laser beam.

[0124] To verify the scalable MOT configuration, a second back-to-back conical mirror was placed above the vacuum chamber viewport. The distance between the two back-to-back conical mirrors was approximately 16 cm. The shape and position of the MOT changed due to tilt between the two back-to-back conical mirrors, and the atom number in the MOT decreased due 31HB: 4931-4976-1177.3to laser power loss through the upper back-to-back conical mirror. The laser beam after passing through each back-to-back conical mirror exhibited an inner circle corresponding to the portion of the beam passing through the central hole and an outer ring corresponding to the reflected beam. A small ring-shaped gap appeared between the inner circle and the outer ring due to imperfect reflection at the edge of the conical surface. The contributions of edge rays to the outermost layer of the trapping volume were minimal and the MOT performance was not materially affected by these edge imperfections.

[0125] The atom loading and cooling process involved illuminating a laser beam consisting of a cooling beam and a repumping beam from the top viewport, with a retroreflector at the bottom to reflect the laser beams. Polarization gradient cooling was implemented by decreasing the cooling beam intensity and increasing detuning to obtain approximately 5 pK 87Rb atomic clouds. As the atomic clouds began freely falling, a Doppler-insensitive Raman pulse selected atoms in the F=2 and mF=0 states with a narrow velocity bandwidth, followed by a pushing pulse to remove atoms in other mF states. During the atom interferometry stage, matter wave splitters based on Doppler-sensitive two-photon Raman transitions drove the atoms between the F=1 and F=2 hyperfine ground states. A Mach-Zehnder geometry of nlZ-ii-iilZ pulses was used to split the matter waves into two arms and recombine them to obtain interference fringes. For detection, a standing laser beam was illuminated horizontally through a viewport in the imaging area, consisting of a resonant frequency and a repumping frequency. A photodetector with an imaging lens detected the atoms' fluorescence, with normalized detection implemented by switching the repumping frequency to detect atoms in F=1 and F=2 states separately.

[0126] The experimental results of the magneto-optical trap performance characterized the temperature of the trapped atomic cloud and the number of atoms captured. FIG. 11 A shows a graph plotting atomic cloud width in millimeters versus free-fall time in milliseconds. The data points show the atomic cloud width increasing from approximately 1.65 mm to 1.85 mm as the free-fall time increased from 61 ms to 69 ms. An inset image in the upper right shows a false-color-shaded representation of the atomic cloud, with a 2 mm scale bar for reference.

[0127] The temperature of the atomic cloud was measured using the time-of-flight method, where the width of the atomic cloud was calculated as a function of free-fall time. The temperature T was related to the Gaussian width oft) of the atomic cloud by the equation:o(t)=A / (o02+kBTt2 / m),32HB: 4931-4976-1177.3where G0is the initial Gaussian width of the atomic cloud, kB is the Boltzmann constant, t is the free-fall time, and m is the atomic mass. By fitting the measured cloud widths to this equation, the temperature of the atomic cloud was determined. The experimental results showed the atomic cloud temperature was cooled to approximately 7 K using polarization gradient cooling techniques.

[0128] FIG. 1 IB displays a graph showing atom number versus magneto-optical trap loading time in seconds. The graph contains three separate data sets plotted with error bars and fitted curves. These measurements contained multiple data sets representing different operating conditions. The atom number increased over time before reaching saturation, with the shaded curve reaching the highest final atom number of approximately 9* 106, while the shaded curve saturated at a lower value around 4.5* 106. These measured curves were fit to an exponential growth function:N(t)=N0(l-e-Vr),where N(t) is the atom number at the magneto-optical trap loading time t, Nois the steady-state atom number, and T is the time constant. The different measured curves corresponded to rubidium vapor pressures of 2.7 x 10“9, 3.5 x 10"9, and 7.5 x 10“9Torr in the trapping region, which affected the loading rate and maximum atom number achievable in the magneto-optical trap. The saturated atom number in the free-fall atomic cloud was approximately 1 x io7.

[0129] The dependence of the MOT atom number on the incident cooling laser intensity was characterized. The back-to-back conical mirror MOT was compared with a MOT in a planar mirror assembly having a similar trapping volume, as shown in FIG. 12. The laser beam diameter for the back-to-back conical mirror MOT was approximately 5.4 cm (1 / e2). The laser beam diameter for the planar mirror MOT was approximately 3.6 cm (1 / e2). Each measurement was averaged over five repetitions. The saturation intensity Is of the 87Rb F=2 to F-3 transition with sigma-plus-polarized light is 1.67 mW / cm2. The atom number of the back-to-back conical mirror MOT saturated more quickly as the cooling laser intensity increased, compared with the planar mirror MOT. This behavior was attributed to the conical reflection surfaces focusing the cooling laser toward the center of the trapping volume, thereby increasing the local cooling beam intensity.

[0130] The long-term stability of the magneto-optical trap was investigated over a period of 36 hours. The rubidium vapor pressure during the measurement was approximately 2.5 x 10"9Torr 33HB: 4931-4976-1177.3and the MOT loading time was 1.5 s. The atom number and temperature were simultaneously measured by imaging the freely falling atomic cloud. FIG. 13 A shows the atom number variation plotted against time in hours. FIG. 13B displays the atom temperature variation plotted against time in hours. The average atom number over the 36-hour period was approximately 1.5 x 106. Assuming the atomic clouds had a constant initial Gaussian width, the average temperature of the atomic clouds was approximately 7.4 pK. The peak-to-peak fluctuations of the atom number and temperature were approximately 20%, and were attributed primarily to laser power and polarization drifts of the cooling beam.

[0131] Gravity measurement was demonstrated by forming atom interferometry using a single freely falling cold atomic cloud released from the diamond magneto-optical trap. Atom interferometry was performed as the cold atomic cloud freely fell underneath the cold-atomtrapping mirror assembly. Doppler-sensitive two-photon Raman transitions, driven by two laser beams with wave vectors kl and k2, created atomic superpositions between the 87Rb F=1 and F=2 hyperfine ground states. A Mach-Zehnder geometry was implemented. A TT / 2 pulse placed the atoms into a superposition of two states. A 7t pulse fully transferred atoms between states. A final 7i / 2 pulse combined the superposition states. The three pulses were equally spaced by a pulse separation time T. Because the atoms moved in free fall, they experienced a Doppler-shifted laser frequency. To compensate for this effect, the laser frequency difference between the two beams was linearly ramped with a rate of a.

[0132] The population fractions of the atoms in the two states were used to measure the phase difference Acp between the two interferometer arms according to P = P0 + (C / 2) cos(Acp), where P0 is the normalized background population and C is the contrast. For the gravity measurement, the phase difference was given by Acp = (keff g - a) T2, where keff = kl - k2 is the effective wave vector of the interferometer beams, g is the gravitational acceleration, T is the pulse separation time, and a is the laser frequency chirp rate. Interference fringes were obtained by varying a. FIG. 14 shows the fringe of atom interferometry with a pulse separation time T = 1 ms. The x-axis is the laser frequency chirp rate a in kHz / ms, spanning approximately 24.0 to 26.0 kHz / ms. The y-axis is the atom population ratio between the two superposition states, ranging from approximately 0.5 to 0.7.

[0133] The cosine dependence of the fringes introduced an ambiguity in the gravity measurement. To resolve this ambiguity, a short pulse separation time T of several milliseconds 34HB: 4931-4976-1177.3was first used to obtain a unique but coarse measurement, and finer measurements were then made with progressively longer T values. For each T, the wave vectors were reversed to reduce systematic effects from the magnetic field gradient and the first-order light shift. This procedure was performed automatically at the start of each new measurement. FIG. 15 shows fringes with pulse separation times of T = 1 ms, T = 2 ms, and T = 4 ms. The x-axis is the laser frequency chirp rate a in kHz / ms, spanning approximately 24 to 26 kHz / ms. The y-axis is the atom population ratio between the two superposition states, ranging from approximately 0.4 to 0.7.

[0134] Simulations were conducted to demonstrate the gravimeter's potential capability in mapping mass density changes. FIG. 16A and FIG. 16B depict graphs showing gravity measurements at different positions relative to a sensor. FIG. 16A shows a graph plotting gravity measurements versus position relative to the sensor in meters. The graph contains three curves representing gravity measurements from different positions (Top, Middle, and Bottom). The y-axis shows gravity values in units of 10-8m / s2, while the x-axis shows position from 0 to 15 meters. An inset diagram illustrates the measurement configuration with a cylindrical object and measurement points indicated by shaded dots. The curves show peak gravity values around the 10-meter position, with the Bottom measurement showing the highest peak amplitude. FIG. 16B displays a graph showing gradient and curvature measurements versus position relative to the center of mass in meters. The graph plots the Top Gradient, Bottom Gradient, and Curvature. The left y-axis shows gradient values in units of 10"91 / s2, while the right y-axis shows curve values in units of 10"9l / s2 / m. The x-axis spans from -10 to 10 meters relative to the center of mass. The gradient and curvature measurements show distinct peaks near the zero position, with the curvature measurement exhibiting the sharpest peak features. In these simulations, the gravimeter measured absolute gravity values at three vertical heights separated by 0.3 m, producing two gravity gradient measurements and one curvature measurement. The simulation results showed that compared to absolute gravity values and gravity gradients, the gravity curvature peaked as the density changed, revealing the horizontal structure of the test mass. This simulated sensitivity of third-order gravity derivatives to near subsurface or shallow-density structures suggested that the scalable quantum gravimeter was particularly useful for studying features such as caves, caverns, salt domes, buried fault systems, or other suitable geological features.35HB: 4931-4976-1177.3

[0135] As used herein, "approximately" means within plus or minus 20% of the stated value, unless otherwise specified.

[0136] As used herein, "substantially collimated" refers to a beam whose divergence is sufficiently low that the beam cross-section changes by no more than 20% over the relevant optical path length.

[0137] As used herein, "first axis" refers to the propagation axis of the input light beam.

[0138] Words of orientation or position used in this disclosure, such as "upper," "lower," "above," "below," "top," "bottom," "vertical," "horizontal," "left," "right," "front," "back," and similar terms, refer to relative positions as shown in the figures and described in the detailed description. These terms are used for clarity in describing the exemplary embodiments and should not be construed as implying any particular physical arrangement or orientation of components unless the context clearly indicates otherwise. The described arrangements may be configured in different orientations, and the components may be described using different orientation or positional terms without departing from the scope of the disclosure. The words of orientation and position are used to distinguish between elements in the figures and do not necessarily describe a fixed spatial relationship in all implementations of the disclosed technology.

[0139] As used herein, "comprises," "comprising," and similar terms are non-exclusive and do not exclude additional elements or steps. The order in which steps are described does not imply that the steps are to be performed in that order, unless the context expressly requires it. All ranges disclosed herein include all values and sub-ranges within the stated endpoints. The examples and descriptions in this Detailed Description are nonlimiting, and the claims define the scope of protection sought.

[0140] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.36HB: 4931-4976-1177.3

Claims

CLAIMS1. A device comprising:a cold-atom-trapping mirror assembly comprising:a first set of reflection surfaces oriented toward a light beam input, the first set having a first inclined angle between 45° and 90° relative to a plane perpendicular to a first axis; and a second set of reflection surfaces oriented opposite to the light beam input, the second set having a second inclined angle between 45° and 90° relative to the plane perpendicular to the first axis,wherein the first and second sets of reflection surfaces are arranged parallel to each other and define a central through hole and a cold-atom trapping volume.

2. The device of claim 1, further comprising a magnetic field generator positioned to create a magnetic field within the cold-atom trapping volume.

3. The device of claim 1, further comprising a laser source configured to generate an input light beam having a hollow central core aligned with the central through hole.

4. The device of claim 1, further comprising a retroreflector positioned opposite the light beam input.

5. The device of claim 1, wherein the first and second sets of reflection surfaces are separated by a central gap along the first axis.

6. The device of claim 5, further comprising an access port aligned with the central gap.

7. The device of claim 1, further comprising a plurality of cold-atom-trapping mirror assemblies aligned along the first axis, wherein the cold-atom-trapping mirror assembly is one of the plurality.

8. The device of claim 7, further comprising a sensor positioned to measure a shared detection volume below a lower one of the adjacent cold atom trapping mirror assemblies.

9. The device of claim 1, wherein the first and second sets of reflection surfaces have conical profiles.

10. A gravimeter comprising: a cold-atom-trapping mirror assembly comprising:a first set of reflection surfaces oriented toward a light beam input, the first set having a first inclined angle between 45° and 90° relative to a plane perpendicular to a first axis; and 37HB: 4931-4976-1177.3a second set of reflection surfaces oriented opposite to the light beam input, the second set having a second inclined angle between 45° and 90° relative to the plane perpendicular to the first axis,wherein the first and second sets of reflection surfaces are arranged parallel to each other and define a central through hole and a cold-atom trapping volume;a sensor configured to detect atoms released from the cold-atom trapping volume;a processor coupled to the sensor; andan output configured to provide a gravitational measurement based on signals received from the sensor.

11. The gravimeter of claim 10, further comprising a magnetic field generator positioned to create a magnetic field within the cold-atom trapping volume.

12. The gravimeter of claim 10, further comprising a laser source configured to generate an input light beam having a hollow central core aligned with the central through hole.

13. The gravimeter of claim 10, wherein the cold-atom-trapping mirror assembly comprises a conical mirror assembly having four reflector bodies arranged in a cylindrical configuration, each reflector body including a conical reflective surface oriented at the first inclined angle relative to the first axis.

14. The gravimeter of claim 10, further comprising a retroreflector positioned opposite the light beam input.

15. The gravimeter of claim 10, wherein the first and second sets of reflection surfaces are separated by a central gap along the first axis, and further comprising an access port aligned with the central gap, wherein the sensor is aligned with the access port.

16. The gravimeter of claim 10, further comprising a plurality of cold-atom-trapping mirror assemblies aligned along the first axis, wherein the cold-atom-trapping mirror assembly is one of the plurality, and wherein the processor is configured to receive signals from the sensor corresponding to atoms released from each of the plurality of cold-atom-trapping mirror assemblies and to provide a gravitational measurement for each of the plurality of cold-atom-trapping mirror assemblies.

17. A method comprising:38HB: 4931-4976-1177.3directing a light beam input along a first axis through a central through hole defined by a cold-atom-trapping mirror assembly, such thatthe light beam reflects off a first set of reflection surfaces oriented toward the light beam input, the first set having a first inclined angle between 45° and 90° relative to a plane perpendicular to the first axis and reflects off a second set of reflection surfaces oriented opposite to the light beam input, the second set having a second inclined angle between 45° and 90° relative to the plane perpendicular to the first axis,the first and second sets of reflection surfaces being arranged parallel to each other and defining the central through hole and a cold-atom trapping volume; andgenerating a magnetic field within the cold-atom trapping volume to trap a cold atomic cloud within the cold-atom trapping volume.

18. The method of claim 17, further comprising: releasing the cold atomic cloud from the cold-atom trapping volume; detecting the released cold atomic cloud with a sensor; and generating, by a processor coupled to the sensor, a gravitational measurement based on signals received from the sensor.

19. The method of claim 18, wherein the cold-atom-trapping mirror assembly is one of a plurality of cold-atom-trapping mirror assemblies aligned along the first axis, the method further comprising: trapping a cold atomic cloud within the cold-atom trapping volume of each of the plurality of cold-atom-trapping mirror assemblies; releasing each cold atomic cloud from its respective cold-atom trapping volume; detecting each released cold atomic cloud with the sensor; and generating, by the processor, a gravitational measurement corresponding to each of the plurality of cold-atom-trapping mirror assemblies.39HB: 4931-4976-1177.3

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