Control of the electric field in a vapor cell

Abstract

Provides control of the electric field in the vapor cell. In one general aspect, a method includes interacting a light beam with vapor in a vapor cell. The vapor cell includes a body defined by stack layers including an electrically conductive layer and an electrically insulating layer. The stack layers are bonded to one another and have first and second end layers at opposite ends of the body. The stack layers also have an intermediate layer between the first and second end layers and defining an internal cavity of the body. Vapor is disposed in the internal cavity. The method includes applying voltages to one or more electrodes to vary an electric field in the internal cavity. The method also includes measuring one or both of an ion signal based on charged particles in the vapor and an optical property of the light beam after interacting with the vapor.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Patent Application No. 17 / 943,796, filed September 13, 2022, the disclosure of which is incorporated herein by reference.

[0002] The following description relates to controlling the electric field in a vapor cell. [Background technology]

[0003] A vapor cell is fabricated by enclosing a vapor or gas in a closed volume. The vapor or gas can be used as a medium that interacts with electromagnetic radiation, affecting the transmission of light through the vapor or gas when irradiated with laser light. Thus, a laser beam propagating through the vapor cell may change its optical properties, which can be used to characterize the electromagnetic radiation. In this case, the vapor cell may be suitable to function as a sensor of electromagnetic radiation. [Brief explanation of the drawings]

[0004] [Figure 1A] FIG. 1 is a schematic diagram of an exemplary vapor cell having a body defined by stack layers. [Figure 1B] 1A and 1B are schematic perspective and cross-sectional views of an exemplary vapor cell in which the first and second end layers are conductive layers. [Figure 1C] 1A and 1B are schematic perspective and cross-sectional views of an exemplary vapor cell in which the first and second end layers are electrically insulating layers. [Figure 2A] 1A and 1B are schematic perspective and cross-sectional views of a second exemplary vapor cell having a body defined by stack layers. [Figure 2B] FIG. 1 is an image of a subset of intermediate layers showing an exemplary internal cavity having first and second portions. [Figure 3A] 1 is a graph of three longitudinal profiles of different electric fields generated by applying voltage profiles to the conductive layer of a simulated vapor cell. [Figure 3B] 3B is a schematic perspective and cross-sectional view of the simulated vapor cell of FIG. 3A. FIG. [Figure 3C] 3C is a graph of three exemplary transverse profiles for various electric fields generated by the simulated vapor cell of FIG. 3B. [Figure 3D] 3C is a graph of an exemplary gradient for the electric field generated by the simulated vapor cell of FIG. 3B. [Figure 4A] FIG. 2 is a schematic diagram of an exemplary conductive layer divided into quadrants defining each segment of a segmented electrode. [Figure 4B] FIG. 4B is a schematic diagram of two instances of the exemplary conductive layer of FIG. 4A separated by a distance along a central axis. [Figure 5] 1 is a schematic perspective view of a portion of an exemplary stack of layers of alternating glass and silicon layers; [Figure 6] 1 is a table showing exemplary parameters of an anodic bonding stack of glass and silicon layers. [Figure 7] 1A and 1B are images of two exemplary layer stacks including an interface where alternating layers of silicon (Si) and glass (G) are bonded together. DETAILED DESCRIPTION OF THE INVENTION

[0005] In one general aspect, a vapor cell may include a body defined by stacked layers bonded together, such as stacked or bonded stacked layers. The stacked layers include conductive and insulating layers, which can enable control of the electric field within the body's internal cavity. Control of the electric field strength inside the vapor cell can be important for using states with large principal quantum numbers (n) and large angular momentum (l) for Rydberg atom-based sensing. In other words, control of the electric field can enable the use of Rydberg states with large Stark shifts (e.g., shifts in Rydberg energy levels due to the electric field). Furthermore, a structured time-dependent electric field allows the vapor cell to be used as a time-of-flight spectrometer, thereby enabling ionization detection for Rydberg atom-based sensing and gas sensing. Furthermore, the use of conductive layers (or electrodes) at the ends of the vapor cell allows for measurement of incident charge, especially in the case of radio frequency (RF) electromagnetic fields.

[0006] The stack layers may be configured to define an electrode structure that allows the vapor cell to establish a target electric field profile in the internal cavity. For example, the electrode structure can be used to create a uniform electric field environment for atoms and extract unwanted charged particles in the vapor cell. Sensing low-frequency electric fields is feasible for applications such as over-the-horizon radar, which can rely on large n states and corresponding low-frequency transitions, as well as for sensing DC electric fields using the Stark shift of Rydberg atoms. Creating a gradient electric field can also broaden the bandwidth of the vapor cell, which can operate as a Rydberg atom-based sensor. Furthermore, combining a periodic electric field with a gradient electric field can create separate sensing bands at similar frequencies within the same vapor cell.

[0007] The stack layers may also be configured to include a conductive layer having segments that define segmented electrodes. The segmented electrodes can be implemented to change the direction of the electric field inside the vapor cell. In particular, segmented electrodes can be used to apply a radio frequency electric field to the vapor (or, for example, atoms therein) to change the atomic or molecular interactions within the vapor, or to apply a heterodyne electric field. Applying a time-dependent electric field can also modulate the energy level of the vapor, which can be useful for signal processing.

[0008] The conductive layer may also have tabs extending outward from the body, presenting respective surfaces that may define electrical contacts for wires or the like. Examples of tabs are described in U.S. Pat. No. 11,313,926, "Interlockable Vapor Cells." Vapor cells can also be shaped in three dimensions, using electrodes inside the vapor cell. In variations where the vapor is defined by Rydberg atoms, it may be possible to actively control the electric field inside the vapor cell using spectroscopic signals obtained from the atoms. The electric field strength and its spatial dependence add a dimension to Rydberg atom-based vapor cell sensors, potentially offering other advantages.

[0009] In some applications of Rydberg atom-based sensing, such as over-the-horizon radar and continuously variable sensors, it may be advantageous to control the DC electric field environment at the location of the atoms used for sensing. Rydberg atoms can exhibit large Stark shifts, especially in quantum states with large electron orbital angular momentum l (so-called hydrogen states). Hydrogen states shift linearly in proportion to the electric field and can exhibit high polarizability. Also, to sense the long wavelengths associated with over-the-horizon radar, it may be useful to create states with large principal quantum number n that can couple the target electromagnetic field to energetically close states (e.g., low-energy difference states on the order of tens of MHz). The Stark shift is stronger with larger principal quantum numbers, and n 7As the size of the electron orbit increases, the Rydberg electrons become more sensitive to the external electric field. In such cases, it may be useful to have more precise control over the electric field inside the vapor cell.

[0010] Controlling the electric field in the internal cavity (e.g., at the atom's position) can mitigate negative effects during measurement or detection. However, controlling the electric field inside the vapor cell can also detect the state of Rydberg atoms, and electrodes (or conductive layers) can be designed to detect ions in the vapor cell. The window of the vapor cell (e.g., an end layer of the stack) can serve as an electrode to read out incident charged particles via, for example, an induced current passing through the vapor cell. Controlling the electric field can also ionize Rydberg atoms and generate charged particles (so-called field ionization), which can serve as a precise method for detecting the presence or absence of Rydberg atoms, since the charge can be efficiently read out at the single particle level. Controlling the electric field inside the vapor cell can also control the particle collision energy with the electrode, which affects the quantum efficiency. This quantum efficiency can represent the probability that a charged particle inside the vapor cell is converted into a current that travels through the electrode. The ionization field can also be time-controlled by pulsing the electrodes that generate the electric field at selected locations in the vapor cell. Field gradients and textured fields can also be useful. For example, the use of a gradient electric field can increase the bandwidth of a vapor cell sensor because the Rydberg energy levels change (e.g., shift) with the magnitude of the electric field. A linear gradient across a sample of Rydberg atoms in a vapor cell can create a sensing device in which atoms located in different regions of the vapor cell can resonate with different frequencies of the target electric field.

[0011] Vapor cells can be deployed in a wide range of applications where precise control of the electric field at one or more locations in the vapor is useful. In variations where the vapor is based on Rydberg atoms, these applications can benefit from the large Stark shift that Rydberg atoms undergo in DC electric fields. The use of time-dependent electric fields can also enhance signal detection and manipulate the interactions of the Rydberg atoms. Furthermore, in many applications, it is desirable to adjust the electric field applied to the vapor to cancel out background electric fields. In some applications, the vapor cell may be part of an atomic clock, such as providing a precision spectroscopic signal for an atomic clock.

[0012] FIG. 1A is a schematic perspective view of an exemplary vapor cell 100 having a body 102 defined by stack layers 104. The individual layers of the stack 104 may correspond to a wafer, slab, substrate, film, coating, or some other type of layer. The stack layers 104 include an arrangement of electrically conductive layers 104a and electrically insulating layers 104b bonded together, such as by a lamination process. To facilitate such bonding, the stack layers 104 may include an adhesive layer (not shown) at one or more interfaces of the stack layers 104. The stack layers 104 have first and second end layers 106a, 106b at opposite ends of the body 102. These layers 106a, 106b are optically transparent. For example, the first and second end layers 106a, 106b may be transparent to the target radio frequency (RF) electromagnetic radiation detected by the exemplary vapor cell 100. However, the layers 106a, 106b may be transparent to electromagnetic radiation of other frequencies. The stack layers 104 also include a middle layer 106c between the first and second end layers 106a, 106b that defines an interior cavity 108 of the body 102. The interior cavity 108 extends through the body 102 between the first and second end layers 106a, 106b. A vapor or vapor source is disposed in the interior cavity 108.

[0013] In some variations, the stack layers 104 are configured with alternating conductive layers 104a and electrically insulating layers 104b. However, other configurations are possible. In some variations, one or both of the first and second end layers 106a, 106b are conductive layers 104a. However, in certain cases, one or both of these layers can be electrically insulating layers 104b. For example, FIG. 1B is a schematic perspective view and a schematic cross-sectional view of an exemplary vapor cell 100 in which the first and second end layers 106a, 106b are conductive layers. This figure shows the cylindrical shape of the periphery of the exemplary vapor cell 100 as well as the annular ring electrode structure in the internal cavity 108. The electrode 104a may correspond to an insulating substrate coated with a conductive film or some other structure including a conductive material. The electrically insulating layer 104b can be composed of high-resistivity silicon or silicon nitride.

[0014] In contrast, FIG. 1C shows a schematic perspective view and a schematic cross-sectional view of an exemplary vapor cell 100 in which the first and second end layers 106a, 106b are electrically insulating layers 104b. This view also illustrates the cylindrical shape of the periphery of the exemplary vapor cell 100. The electrodes of the exemplary vapor cell 100 have an annular ring structure surrounding the internal cavity 108. The electrodes 104a may be formed of low-resistivity silicon (e.g., doped silicon) or some other type of conductive material (e.g., aluminum). The electrically insulating layer 104b can be composed of glass or some other type of insulating material (e.g., sapphire, quartz, etc.). The type of junction used to stack the stack layers 104 into the body 102 can be determined by the materials from which the electrodes 104a, the electrically insulating layer 104b, and any coatings (if any) are formed.

[0015] In some variations, at least one of the intermediate layers 106c includes a plurality of holes 110 between the internal cavity 108 and the periphery of the intermediate layer 106c. FIG. 1A illustrates a particular variation in which the plurality of holes 110 extend through all of the intermediate layers 106c. However, other depths (including partial depths through one or more intermediate layers 106c) are possible. In some variations, one or more of the plurality of holes have different shapes. These shapes may vary, such as to create a non-uniform distribution of holes along a direction between the internal cavity 108 and the periphery of the intermediate layer 106c. In some variations, the exemplary vapor cell 100 is configured to detect target electromagnetic radiation. In these variations, each of the plurality of holes 110 may have a maximum dimension equal to or smaller than the wavelength of the target electromagnetic radiation. In this case, the plurality of holes 110 may reduce the interaction volume of the body 102 with the target electromagnetic radiation, thereby reducing absorption and / or scattering of the target electromagnetic radiation when incident on the body 102. Such reduction may improve the detection accuracy of the exemplary vapor cell 100.

[0016] The exemplary vapor cell 100 of FIGS. 1A-1C may be suitable for multiple sensing applications, such as metrology applications. The internal cavity 108 is cylindrical in shape. Furthermore, the conductive layer 104a may be formed of low-resistivity silicon, which can be used as an electrode material for applying an electric field. By setting a voltage across all of the conductive layers 104a of the exemplary vapor cell 100, a high degree of control over the electric field inside the exemplary vapor cell 100 can be achieved. Generally, the more conductive layers 104a there are, the higher the degree of control over the electric field. The electrically insulating layer 104b may be formed of glass, but can also be formed of other types of insulating ceramics (e.g., alumina, sapphire, quartz, etc.). In some variations, the conductive layer 104a may correspond to a coating on the electrically insulating layer 104b. In other variations, one or more of these coatings may be patterned into multiple portions that define segments of a segmented electrode.

[0017] The exemplary vapor cell 100 can be structured in three dimensions by joining layers of two-dimensional structures together. These layers can also be formed with interlocking tabs or connectors to allow for array-like arrangement of multiple instances of the exemplary vapor cell 100. In this manner, arrays or portions of larger aggregate vapor cells of various sizes can be constructed. In this disclosure, the inherent flexibility and practicality of the stacked vapor cell concept is utilized to incorporate electrode structures into the vapor cell. Examples of mechanical interfaces for joining vapor cells into arrays are described in detail in U.S. Pat. No. 11,313,926, entitled "Interlockable Vapor Cells."

[0018] The exemplary vapor cell 100 is configured so that the electric field inside the internal cavity 108 can be controlled at the location of atoms or molecules (e.g., vapor atoms or molecules) used for sensing. In operation, an electric potential can be applied to the conductive layers 104a to generate an electric field inside the exemplary vapor cell 100. When multiple conductive layers 104a are present, the electric field can be more precisely controlled and shaped. For example, in FIGS. 1A-1C, every other layer of the stack layer 104 is conductive, thereby generating a highly uniform electric field inside the internal cavity 108. The conductive layers 104a of the exemplary vapor cell 100 can penetrate to the outside of the body 102 and function as respective electrodes of the exemplary vapor cell 100. Furthermore, each conductive layer 104a includes a contact surface on the exterior surface of the body 102 that can be used as an electrical contact for applying an electric potential to the conductive layer 104a. Adjacent conductive layers 104a are separated by at least one electrically insulating layer 104b so that different potentials can be applied to the conductive layers 104a without shorting.

[0019] The conductive layer 104a and the electrically insulating layer 104b can have different internal and external shapes. For example, the conductive layer 104a can have a smaller-radius through-hole in its center. The conductive layer 104a can also have a larger outer diameter so that a wire can be connected to apply a voltage. Varying the shapes of the individual layers of the stack 104 can be advantageous because they can be determined by the desired electric field profile inside the internal cavity 108. Furthermore, the body 102 can have various shapes as needed to best approximate the ideal electric field. Examples of glass-based electrically insulating layer coatings include oxide semiconductors such as tin oxide, gallium oxide, zinc oxide, indium tin oxide, and indium gallium zinc oxide. Materials that are electrically conductive and transparent to radio frequency waves for Rydberg atom-based sensing can be particularly useful in forming the conductive layer 104a (e.g., coating, film, wafer, etc.).

[0020] In some variations, bonding of layers in the stack 104 can be achieved by using an adhesive layer, such as silicon dioxide, on the conductive layer 104a. The adhesive layer need not cover the entire layer. For example, the adhesive layer can cover only the areas to be bonded to seal the stack layers 104. Alternatively, if electrically insulating, the adhesive layer can cover the portion of the conductive layer 104a that extends into the internal cavity 108. For detecting radio frequency electromagnetic radiation, the exemplary vapor cell 100 can incorporate larger platens and tabs to form an array. The exemplary vapor cell 100 can also implement segmented (e.g., quadrant, sextant, octant, etc.) electrodes to guide ions into the internal cavity 108 or modulate their energy levels by applying electric or RF fields in various directions.

[0021] In some variations, the vapor includes a gas of Rydberg atoms (e.g., a gas of Group IIA atoms). By monitoring the spectrum of the Rydberg atoms in the exemplary vapor cell 100, such as through the principles of a Rydberg atom-based sensor, it may be possible to generate a feedback loop that optimizes the voltage applied to the conductive layer 104a according to a merit function, such as the observed Stark shift and / or the spectral broadening of the Rydberg spectrum. All-optical methods, such as electromagnetically induced transparency, may be used to acquire the spectrum. The feedback loop may use a field-programmable gate array (FPGA) or analog circuitry (e.g., SOC). An FPGA may be useful when adapting the feedback loop. If the first and second end layers 106a, 106b are conductive and thus can function as end electrodes, the electric field can be optimized using ionization readout. In these cases, ions are generated from the Rydberg atoms by field ionization, impact ionization, or blackbody ionization, followed by charge detection. Other physical processes may also be applicable.

[0022] 2A, which is a schematic perspective and cross-sectional view of a second exemplary vapor cell 200 having a body 202 defined by stack layers 204. The stack layers 204 are bonded together, and the individual layers may correspond to wafers, slabs, substrates, coatings, films, or any other type of layer. Furthermore, the individual layers may be formed of single crystalline, polycrystalline (e.g., ceramic), or amorphous (e.g., glass) materials. In many variations, each layer of the stack 204 is a planar configuration (e.g., a planar layer).

[0023] The stack layer 204 includes a conductive layer 204a and an electrically insulating layer 204b. In some variations, the conductive layer 204a is 3For example, one or more of the conductive layers 204a may be formed of a transparent conductive oxide (e.g., SnO2:F, In2O3:Sn, etc.), or may be formed of doped silicon (n + Si, p + In some variations, the electrically insulating layer 204b may be made of a material such as silicon (Si), a metal, or an alloy (e.g., Al, Cu, Au, Pt, Cu-Ag, Pd-Au, etc.). 6 The insulating layers 204a are formed of a material having a resistivity greater than Ω·cm. For example, one or more of the insulating layers 204a may be formed of a glass containing silicon oxide (e.g., vitreous silica, borosilicate glass, aluminosilicate glass, etc.). Other materials are also possible, including ceramics (e.g., alumina, zirconia, etc.) and single crystal materials (e.g., quartz, sapphire, diamond, etc.).

[0024] The stack layers 204 may be ordered in any configuration in which adjacent conductive layers 204a are separated by at least one electrically insulating layer 204b. Furthermore, each conductive layer 104a defines an electrode of the exemplary vapor cell 200 and includes a contact surface 206 on the exterior surface of the body 202. The contact surface 206 may define an electrical contact for the electrode. However, other exterior surfaces of the conductive layer 104a may be used to define the electrical contact (e.g., instead of or in addition to the contact surface 206). In some variations, at least a portion of the stack layers 204 alternate between conductive layers 204a and electrically insulating layers 204b. FIG. 2A illustrates one variation in which the entire stack layers alternate between conductive layers 204a and electrically insulating layers 204b. However, other configurations of these layers 204a, 204b are possible.

[0025] In many embodiments, the individual layers of stack 204 are formed from materials that are transparent to the target electromagnetic radiation (e.g., RF electromagnetic radiation) that exemplary vapor cell 200 measures. These materials enable stack layers 204 to absorb and / or scatter no more than 20% of the target electromagnetic radiation as it passes through body 202. For example, conductive layer 204b may be formed from a material with a bandgap of at least 2 eV. As another example, electrically insulating layer 204b may be formed from a material with a high resistance (e.g., ρ>10 8 The stack layers 204 may be formed of dielectric materials that are considered to have a resistivity of Ω·cm. In some cases, these materials enable the stack layers 204 to absorb and / or scatter no more than 10% of the target electromagnetic radiation as such radiation passes through the body 202. In certain cases, the loss due to such absorption and / or scattering may be, for example, 1% or less.

[0026] In some embodiments, a "transparent" material is one that minimizes absorption and / or scattering of target electromagnetic radiation by body 202. In these embodiments, stack layer 204 can transmit target electromagnetic radiation to the end or into body 202 without significant distortion. In some variations, stack layer 204 has a radar scattering cross section that is smaller than its geometric cross section. Stack layer 204 may absorb and / or scatter less than 20%, and in some variations, less than 10%, of the target electromagnetic radiation. For example, stack layer 204 may be formed in whole or in part from float silicon. Float silicon has a loss tangent of 10 at frequencies up to 400 GHz. -3It is believed to be less than 100%. Certain applications of exemplary vapor cell 200, such as antenna testing, require high transparency to minimize reflections in the test environment and accurately measure power on two or more spatial planes or surfaces. In some cases, the materials forming stack layers 204 may allow the target electromagnetic field inside exemplary vapor cell 200 to fall within a threshold percentage of the incident target electromagnetic field. In some variations, this threshold percentage is 20%. In some variations, this threshold percentage is 10%. In some variations, this threshold percentage is 1%.

[0027] The stack layer 204 includes first and second end layers 208a, 208b on either side of the body 202. These layers 208a, 208b are optically transparent. For example, the first and second end layers 208a, 208b may be transparent to the targeted wireless RF electromagnetic radiation detected by the exemplary vapor cell 200. However, the layers 208a, 208b may be transparent to electromagnetic radiation of other frequencies. In some variations, such as that shown in FIG. 2A , the first and second end layers 208a, 208b are conductive layers and define the first and second end electrodes, respectively, of the exemplary vapor cell 200. The stack layer 204 also includes an intermediate layer 208c between the first and second end layers 208a, 208b that defines the interior cavity 210 of the body 202. An interior cavity 210 extends through the body 202 between the first and second end layers 208a, 208b.

[0028] In some embodiments, the at least one conductive layer 204a includes a substrate (e.g., a planar substrate) and a conductive coating covering at least a portion of the substrate. For example, when disposed on the substrate, the conductive coating can include a first portion exposed to the internal cavity 210 and a second portion defining the contact surface 206 of the conductive layer 204a. The substrate may be formed of an electrically insulating material, such as described above with respect to the electrically insulating layer 204b. Additionally, optionally, the at least one conductive layer 204a includes an electrically insulating coating disposed on the conductive coating and covering at least the first portion. The electrically insulating coating may be inert to the chemical reactivity of the vapor in the internal cavity 210, and thus operable to shield the conductive coating from chemical attack. Examples of electrically insulating coatings include oxide materials (e.g., SiO x , SiO2, ZrO2, etc.), however, other materials are also possible (for example, nitride materials, carbide materials, etc.).

[0029] In some embodiments, the stack of materials 204 includes one or more interior surfaces that bound the internal cavity 210. These surfaces may be associated with the interior surfaces of the first and second end layers 208a, 208b as well as the middle layer 208c. In these embodiments, at least a portion of the one or more interior surfaces is covered with a coating that is chemically inert to the vapors in the internal cavity 210. In certain cases, this portion may include all of the interior surfaces associated with the conductive layer 204a. This coating may be formed of a material similar to those described above with respect to the electrically insulating coating (e.g., oxide material, nitride material, carbide material, etc.). In some variations, this coating is formed of the same material as the electrically insulating coating.

[0030] The exemplary vapor cell 200 also includes a vapor (not shown) disposed in the internal cavity 210 defined by the intermediate layer 208c. The vapor may include components such as an alkali metal atomic gas, a noble gas, a diatomic halogen molecular gas, an organic molecular gas, or any combination thereof. For example, the vapor may include an alkali metal atomic gas (e.g., K, Rb, Cs, etc.), a noble gas (e.g., He, Ne, Ar, Kr, etc.), or both. The presence of alkali metal atoms in the vapor may enable the vapor to function as a Rydberg atomic gas. In another example, the vapor may include a diatomic halogen molecular gas (e.g., F2, Cl2, Br2, etc.), a noble gas, or both. In yet another example, the vapor may include an organic molecular gas (e.g., acetylene), a noble gas, or both. Other combinations of vapors, including other components, are also possible.

[0031] In some embodiments, exemplary vapor cell 200 includes a vapor source. In these embodiments, intermediate layer 208c may define a wall surrounding a first portion of internal cavity 210. The first portion may correspond to a majority of the volume of internal cavity 210. Internal cavity 210 also includes a second portion extending from the first portion into the wall and including the vapor source. The second portion may correspond to a small portion of internal cavity 210 that is in fluid communication with the first portion (e.g., via an opening in the wall, a channel in the wall, etc.). This configuration of exemplary vapor cell 200 may be useful for sealing the vapor source of exemplary vapor cell 200 during fabrication. At some later point, the vapor source may be stimulated by an energy source (e.g., heat from a laser beam) to release vapor (e.g., by melting an outer protective coating, decomposing a chemical precursor, etc.). 2B is an image of a subset of intermediate layer 250 showing an example interior cavity 252 having first and second portions 252a, 252b. In some variations, the vapor source may function in part as a getter.

[0032] The stack layer 204 may include one or more exterior surfaces that define the exterior shape of the body 202 (e.g., an exterior cubic shape, an exterior spherical shape, an exterior rectangular shape, an exterior oval shape, etc.). For example, each layer of the stack 204 may include an outer periphery 212 that defines an exterior cross-section at that layer (e.g., a square cross-section, a circular cross-section, a rectangular cross-section, etc.). The cross-section may remain constant along the stack layer 204, may vary along the stack layer 204, or may be some combination thereof. To achieve the varying cross-section, at least two adjacent layers may each have an outer periphery 212 that differs in shape and / or size. FIG. 2A illustrates the exemplary vapor cell 200 as having an exterior cubic shape with a constant cross-section along the stack layer. However, other shapes are possible.

[0033] In some embodiments, each intermediate layer 208c includes a through-hole that defines a portion of the internal cavity 210 through that intermediate layer 208c. In these embodiments, the through-holes may be selectively configured to define a desired three-dimensional volume for the internal cavity 210 (e.g., a sphere, a frustum, a tilted parallelepiped, etc.) when the intermediate layers 208c are stacked. The through-holes may be configured with any combination of shape, size, and location. Other characteristics are possible. In some variations, each through-hole is identical in shape and size. In these variations, the internal cavity 210 may have a constant cross-section throughout the intermediate layer 208c. In some variations, at least two adjacent intermediate layers 208c each have through-holes that differ from one another in either or both shape and size. In these variations, the internal cavity 210 may have a cross-section that varies at least in part throughout the intermediate layer 114.

[0034] FIG. 2A illustrates an example in which the through-holes are circular, have two alternating diameters, and are aligned along a direction perpendicular to the stack layers 204. The through-holes thus define a cylindrical volume for the internal cavity 210, into which the conductive layer 204a of the intermediate layer 208c protrudes. In FIG. 2A, each intermediate layer 208c includes an inner circumferential surface 214 that defines a portion of the internal cavity 210. The inner circumferential surface 214a of the conductive layer 204a is configured such that the conductive layer 204a can protrude into the internal cavity 210 beyond the inner circumferential surface 214b of the electrically insulating layer 204b (e.g., beyond the layer in the stack 204 adjacent to the conductive layer 204a). In some variations, each intermediate layer 208c includes an outer circumferential surface 212 that defines a portion of the outer surface 216 of the body 202. In these variations, the outer peripheral surface 212 of at least one conductive layer 204a may be configured such that the conductive layer 204a may protrude from the outer surface 216 beyond the layer in the stack 204 adjacent to the conductive layer 204a. Such protrusion may help define the contour of the body 202, while also helping to define the electrical contacts of the exemplary vapor cell 200. The tab may include, for example, the contact surface 206 of the conductive layer 204a.

[0035] Other features of the intermediate layer 208c may be used to define the target three-dimensional volume. For example, two or more intermediate layers 208c (e.g., adjacent intermediate layers) may have different thicknesses. As another example, the through-holes in the intermediate layers may be defined by an inner periphery of the intermediate layer, including an inner periphery surface. The inner periphery surface may be angled, sloped, or rounded to help define the target three-dimensional volume.

[0036] The target three-dimensional volume may be selected to shape the profile formed in internal cavity 210 when electromagnetic radiation is incident on exemplary vapor cell 210. For example, the target three-dimensional volume may be selected to concentrate the incident electromagnetic radiation at the center of internal cavity 210. Such shaping may increase the amplitude (e.g., the amplitude of the electric or magnetic field) of the incident electromagnetic radiation in internal cavity 210, making exemplary vapor cell 200 more sensitive to the incident electromagnetic radiation. The target three-dimensional volume may also be selected to make the profile of the incident electromagnetic radiation more uniform across, for example, a desired region of internal cavity 210. Improved uniformity may increase the amount of vapor interacting with the incident electromagnetic radiation, thereby increasing the detection area within internal cavity 210. The target three-dimensional volume may also be selected to reduce the thickness of the walls surrounding internal cavity 210, thereby making body 202 of exemplary vapor cell 200 more transparent to the incident electromagnetic radiation. Other benefits are also possible.

[0037] Additionally, the target three-dimensional volume may be selected along with the outer shape of body 202. A particular volume and outer shape combination may improve the performance of example vapor cell 200 for a target application. For example, internal cavity 210 may have a spherical volume, and body 202 may have a spherical outer shape. This combination may facilitate easier modeling of the electromagnetic field profile inside and outside example vapor cell 200. This easier modeling may improve the performance of example vapor cell 200 in applications such as metrology. Other examples of example vapor cell 200 shapes are described in U.S. Pat. No. 11,307,233, entitled "Vapor Cells Having Stacks of Layers Defining Target Three-Dimensional Volumes for Internal Cavities."

[0038] In some embodiments, stack layer 204 includes multiple sets of tabs extending outward from one or more outer surfaces of body 202. Each set of tabs can define a mechanical interface that allows exemplary vapor cell 200 to couple (e.g., interlock) with another vapor cell. In some variations, the multiple sets of tabs include one or more tabs that are an integral part of the layer. For example, middle layer 208c can have an inner circumferential surface disposed within the outer circumferential surface. The inner circumferential surface can define through-holes in middle layer 208c, and the outer circumferential surface can define tabs that extend outward from the outer surface of middle layer 208c. In another example, an end layer (e.g., first end layer 208a or second end layer 208b) can have an outer circumferential surface that defines tabs that extend outward from the outer surface of the end layer. In these variations, the one or more tabs can define electrode contact surfaces when the layer corresponds to conductive layer 204a.

[0039] In some embodiments, such as those intended to reduce or prevent helium permeation, stack layer 204 includes layers formed of aluminosilicate or borosilicate glass (e.g., Pyrex®). Stack layer 204 may be coated with a material that exhibits low helium permeation. Various optical coatings (e.g., Bragg mirrors) may also be disposed on first and second end layers 208a, 208b to act as high reflectors and filters for the optical signals used to generate the laser and signal. Wave plates may be used to control polarization in conjunction with polarization-maintaining fiber. Furthermore, the exemplary vapor cell 200 may be optically coupled to a fiber using a GRIN (graded index) lens centered on an end layer (e.g., first end layer 208a or second end layer 208b) of the exemplary vapor cell 200.

[0040] During operation of the exemplary vapor cell 200, one or more optical signals (e.g., laser light) may interact with the vapor in the internal cavity 210. For example, the optical signals may enter the internal cavity 210 through the first end layer 208a and then exit the internal cavity 210 through the second end layer 208b. In another example, the optical signals may enter the internal cavity 210 through the first end layer 208a, reflect off the inner surface of the second end layer 208b, and then exit the internal cavity 210 through the second end layer 208b. When two or more optical signals are used, a forward-pumped or backward-pumped mode of operation may be established. In the forward-pumped mode, each optical signal traverses the internal cavity 210 along the same direction. In the backward-pumped mode, each optical signal traverses the internal cavity 210 along opposite directions. Examples of vapor cell excitation modes, including examples of vapor cell operation, are described in US Pat. No. 10,509,065, entitled "Imaging of Electromagnetic Fields."

[0041] To aid in the propagation of optical signals through the internal cavity 210, the first and second end layers 208a, 208b may include one or more optical coatings. Examples of such optical coatings include reflective coatings, anti-reflective coatings, filter coatings, polarization coatings, etc. In some embodiments, the first end layer 208a includes an inner surface 218a that covers a first opening of the internal cavity 210 adjacent to the first end layer 208a. The first end layer 208a also includes an outer surface 218b opposite the inner surface 218a. In these embodiments, an optical coating may be disposed on one or both of the inner surface 218a and the outer surface 218b. A combination of optical coatings is also possible on the inner surface 218a and the outer surface 218b. In some embodiments, the second end layer 208b includes an inner surface 220a that covers a second opening of the internal cavity 210 adjacent to the second end layer 208b. The second end layer 208b also includes an outer surface 220b opposite the inner surface. In these embodiments, an optical coating is disposed on one or both of the inner surface 220a and the outer surface 220b. A combination of optical coatings is also possible on each of the inner surface 220a and the outer surface 220b.

[0042] In some embodiments, stack layer 204 includes one or more interior surfaces that bound internal cavity 210. In these embodiments, one or more interior surfaces may be at least partially covered by an anti-relaxation coating. The anti-relaxation coating may include a hydrocarbon material, such as a paraffin material, although other materials are possible for the anti-relaxation coating.

[0043] The stack layers 204 may include interfaces 222 between adjacent layers of the stack. In some embodiments, the interface 222 between a pair of adjacent layers in the stack 204 directly bonds the pair of layers. In some embodiments, the interface 222 between a pair of adjacent layers in the stack 204 includes an adhesive layer. The adhesive layer may assist in bonding the pair of adjacent layers to one another. In some variations, the adhesive layer includes silicon oxide. For example, the stack layers 204 may alternate between layers formed of silicon and layers formed of borosilicate glass. One or more of the interfaces 222 may include a silicon oxide (e.g., SiO2, SiO x Adhesion layers, such as silicon dioxide, silicon dioxide, silicon dioxide films ...

[0044] The stack layers 204 may be bonded together by, for example, an anodic bonding process, a contact bonding process, a glass frit bonding process, or some other type of bonding process. A combination of bonding processes is also possible. In some variations, the final bonding process used to bond the layers is a contact bonding process. For example, an anodic bonding process may bond the first end layer 208a and the intermediate layer 208c to each other. A contact bonding process may then bond the second end layer 208b to the intermediate layer 208c, thereby sealing the vapor or vapor source to the internal cavity 210. As part of the contact bonding process, the second end layer 208a may be positioned to cover the opening of the internal cavity 210 after the internal cavity 210 is filled with the vapor or contains the vapor source. Often, the internal cavity 210 is evacuated prior to receiving the vapor or vapor source. The contact bonding process is described in detail in U.S. Patent No. 10,859,981, entitled "Vapor Cells Having One or More Optical Windows Bonded to a Dielectric Body."

[0045] In some embodiments, such as that shown in FIG. 2A , at least one of the intermediate layers 208c includes a plurality of holes 224 between the internal cavity 210 and the periphery of the intermediate layer 208c. The plurality of holes 224 may extend partially or entirely through the intermediate layer 208c. In these embodiments, the exemplary vapor cell 200 may be configured to detect target radiation, and each of the plurality of holes 224 may have a maximum dimension equal to or less than the wavelength of the target radiation. For example, the wavelength of the target radiation may be at least 0.3 mm, and each of the plurality of holes 224 may have a maximum dimension equal to or less than 0.3 mm. In some embodiments, one or more of the plurality of holes 224 may include a vapor source. In these embodiments, the intermediate layer 208c may define a channel (or a portion thereof) that fluidly couples one or more of the holes 222 to the internal cavity 210.

[0046] In operation, voltages may be applied to one or more of the contact surfaces 206 of the conductive layer 204a to control the electric field inside the internal cavity 210, thereby generating an electric field profile. FIG. 3A is a graph of three longitudinal profiles of various electric fields generated by applying voltage profiles to the conductive layers of a simulated vapor cell. The simulated vapor cell is similar to the exemplary vapor cell 200 described with reference to FIG. 2A and is shown in FIG. 3B. The longitudinal profiles correspond to a direction parallel to the central axis of the simulated vapor cell. FIG. 3A illustrates the different electric field profiles that can be achieved in a vapor cell including a conductive layer. For example, the curve represented by the dashed-dotted line illustrates a much more uniform electric field than can be achieved by applying potentials only to the end layers (i.e., the curve represented by the dotted line). The curve represented by the solid line illustrates the profile achieved in a vapor cell by applying a linearly gradient voltage to the conductive layers, demonstrating the variations in the electric field that can be achieved. The simulated vapor cell has a length of 9.1 mm and a layer spacing of 1.3 mm. The electrodes (or conductive layers) are 0.3 mm thick. For the parallel plate simulation, the voltages applied to the first and second end layers are 10 V and 3 V, respectively. For the linear calculation, the applied voltages are 10 V, 9 V, 8 V, 7 V, 6 V, 5 V, 4 V, and 3 V. The optimized voltages are 10 V, 9.11453 V, 8.0437 V, 7.02993 V, 5.97598 V, 4.96491 V, 3.89116 V, and 3 V.

[0047] Figure 3C is a graph of three exemplary transverse profiles for various electric fields generated by the simulated vapor cell of Figure 3B. The transverse profiles correspond to directions perpendicular to the central axis of the simulated vapor cell (e.g., radial directions). The graphs show that a simulated vapor cell with stacked electrodes has a more uniform electric field inside its internal cavity than a vapor cell with electrodes configured at the windows (i.e., edge layers) (e.g., as a parallel plate capacitor). The graphs are shown for the center of the vapor cell, which corresponds to the zero position shown in Figure 3A.

[0048] FIG. 3D is a graph of an exemplary gradient of the electric field generated by the simulated vapor cell of FIG. 3B. The gradient is plotted along a direction parallel to the central axis (e.g., z-axis) of the simulated vapor cell and is quadratically related to the voltage applied to the electrodes (or conductive layers). The voltages applied to the electrodes are 10 V, 9.9 V, 9.6 V, 9.1 V, 8.4 V, 7.5 V, 6.4 V, and 5.1 V, respectively, relative to the voltages listed in FIG. 3A. The voltage selection produces a nearly linear electric field gradient. While deviations from a linear field gradient are observed near the edges of the simulated vapor cell (e.g., where the first and second end layers are located), these deviations can be improved by adjusting the voltage.

[0049] Referring again to FIG. 2A , a method of operating exemplary vapor cell 200 may include interacting a light beam with vapor in internal cavity 210. Optionally, first and second light beams may interact with different electronic transitions of the vapor. The method also includes applying voltages to one or more electrodes (e.g., one or more conductive layers 204 a) to vary the electric field in internal cavity 210. The voltages (or a subset thereof) may be varied over time (e.g., periodically over time). Often, the voltages are applied to all electrodes of exemplary vapor cell 200. The method also includes measuring one or both of an ion signal based on charged particles in the vapor and an optical property of the light beam after interacting with the vapor.

[0050] An ion signal may be read from the exemplary vapor cell 200 by measuring the voltage difference between or the current flowing between the first and second end layers 208a, 208b. For example, a reference potential may be applied between the first and second end layers 208a, 208b. The ion signal may be determined by measuring a change in the reference potential when charged particles are generated in the vapor and received by one or both of the first and second end layers 208a, 208b. An optical property of the light beam may be measured using a photodetector optically coupled to one of the first and second end layers 208a, 208b. The optical property may include the amplitude of the light beam, the phase of the light beam, the polarization of the light beam, or any combination thereof. The amplitude may be measured at one or more target frequencies of the light beam.

[0051] In many embodiments, the internal cavity 210 extends between the first and second end layers 208a, 208b along the axis 226. In these embodiments, applying voltages to one or more electrodes may include applying different voltages to two or more electrodes to establish a profile of an electric field along the axis 226. The profile may include a constant magnitude of the electric field. The profile may also include a gradient of the electric field or a periodic variation of the electric field. The profile may also vary over time to generate a series of predetermined profiles over a time interval. Other types of profiles are possible.

[0052] In embodiments in which first and second end layers 208 a, 208 b are conductive layers defining the first and second end electrodes, respectively, of exemplary vapor cell 200, applying respective voltages to one or more electrodes may include displacing targeted charged particles in the vapor toward one or both of the first and second end layers. The targeted charged particles may be generated by a light beam that can be configured to ionize a portion of the vapor in certain instances. Such ionization may produce targeted charged particles having targeted characteristics (e.g., ionization state). However, charged particles may also be generated by an electric field.

[0053] For example, applying voltages to one or more electrodes may include manipulating an electric field to ionize a portion of the vapor to generate charged particles. The electric field may then displace the charged particles to one or both of the first and second end layers 208 a, 208 b. In this case, the method may include measuring the charge of each charged particle incident on one or both of the first and second end layers 208 a, 208 b. The method may also include measuring a current based on the charged particles received by one or both of the first and second end layers 208 a, 208 b over time. The time-of-flight of the charged particles may also be determined based on the time difference between when the charged particles are generated by manipulating the electric field and when they are received by one or both of the first and second end layers 208 a, 208 b.

[0054] In some embodiments, the method includes determining a spectrum of the vapor based on the ion signal, the optical properties, or both. In other embodiments, the method can include monitoring a characteristic of the spectrum over time and varying at least one applied voltage in response to changes in the characteristic of the spectrum. Examples of characteristics include Stark shift and spectral broadening. In some cases, the at least one applied voltage can be varied over time to maintain the characteristic at a target value.

[0055] In operation, the exemplary vapor cell 200 may control the magnitude of the electric field along a direction parallel to the axis 226. However, in certain variations, the exemplary vapor cell 200 may also control the magnitude of the electric field along a direction perpendicular to the axis 226 (e.g., radially). To this end, the exemplary vapor cell 200 may include one or more conductive layers 204a divided into portions that define segments of a segmented electrode. The portions may be electrically isolated from one another, such as by gaps or electrically insulating material. For example, the conductive layer may be divided into gapped quadrants, sextants, octants, etc. The portions may surround the interior cavity 210 along the plane of the conductive layer and may be of any shape and size. In some cases, the portions are equally sized.

[0056] Figure 4A is a schematic diagram of an exemplary conductive layer divided into quadrants that define each segment of a segmented electrode. A voltage can be applied to each of the four quadrants (or segments) to generate an electric field that is in the same plane as the exemplary conductive layer. The electric field can be perpendicular to the axis of the internal cavity, although other directions (e.g., oblique directions) are also possible. The left and right sides of Figure 4A show orthogonal electric fields, respectively.

[0057] The presence of such portions in one or more conductive layers 204a does not prevent them from controlling the magnitude of the electric field along a direction parallel to axis 226. The same voltage may be applied to all portions (or segments) of an individual conductive layer, allowing multiple instances of such a layer to generate an electric field parallel to axis 226. FIG. 4B is a schematic diagram of two instances of the exemplary conductive layer of FIG. 4A separated by a distance along a central axis (e.g., axis 226). The portions of each instance may be at the same potential, defining a common potential for that instance. By holding the two instances at different common potentials, the two instances can generate an electric field along a direction parallel to the central axis.

[0058] In many embodiments, the contact surface 206 of one or more conductive layers 204a may be divided to accommodate multiple segments. For example, the contact surface 206 of the conductive layer 204a may be divided into multiple partial contact surfaces, and each partial contact surface may define an electrical contact for a respective segment. In some embodiments, the multiple partial contact surfaces are each configured to be impedance matched to a radio frequency electromagnetic radiation source.

[0059] 4A and 4B illustrate how electric fields can be canceled through the use of quadrant electrodes. By applying voltages to each portion of a set of stacked segmented electrodes, any electric field can be canceled in a region of space centered about the axis (e.g., axis 226) of the structure between the plates (e.g., first and second end layers 208a, 208b). Similar electric field adjustment is contemplated for an increased number of segmented electrodes. The addition of segmented electrodes provides greater flexibility in adjusting the electric field in the internal cavity of the vapor cell. These examples of segmented electrodes can be integrated as electrode structures in the exemplary vapor cells described herein. Furthermore, stacks of segmented electrodes can be integrated as vapor cells.

[0060] In Rydberg atom-based sensing, there is some motivation to use states with large principal quantum number n. This would result in a higher density of states and larger transition dipole moments. Also, the energy separation between dipole-coupled Rydberg states can be reduced, making this method applicable to long wavelength transitions. Unfortunately, the polarizability of the atom can increase significantly with n (e.g., n 7 (proportional to ).

[0061] This large polarizability can also result in large Stark shifts of atomic energy levels. If the electric field inside the vapor cell is uncontrolled (e.g., non-uniform) or if stray charges are present, the electric field can broaden the spectral features used to detect the target electromagnetic field. Such broadening can also reduce the resolution and dynamic range of the vapor cell. Also, if the electric field is uncontrolled, field ionization of high-n states can occur, creating additional electric fields and further degrading the performance of the vapor cell.

[0062] The ability to generate large Stark shifts can be advantageous for a vapor cell. In this mode of operation, control of the electric field in the vapor cell can allow for continuous modulation of the vapor cell (e.g., via a feedback loop) by adjusting the transitions of the Rydberg atoms. To achieve this mode of operation without compromising sensitivity and traceability, the electric field should be as uniform as possible. Furthermore, it is desirable to know the characteristics of the applied field (e.g., its amplitude as a function of position). It is also possible to modulate the atomic system by applying a time-dependent voltage to the electrodes. Modulation of the atomic energy levels can be used for some signal processing methods.

[0063] Field ionization can be used to read out the population of Rydberg states. In some cases, field ionization can be achieved by using an ionization spectrometer and a charged particle guide. The stack layers described above with respect to FIGS. 1A-2 can allow for various types of spectrometers and charged particle guides to be configured inside the vapor cell, optimizing the charge readout. This charge readout allows for gas detection via the Rydberg states.

[0064] In addition to enabling more continuously tunable sensors, the vapor cells described herein can also help enable over-the-horizon radar applications. These radar systems use extremely low frequencies because the waves can reflect off the atmosphere and reach beyond the horizon. Conventional antennas for radar applications are typically very large due to their long wavelengths. Furthermore, the size of the receiver antennas limits their respective spatial distributions, so they are often not netted, despite the potential for improved performance in netted systems. Rydberg atomic sensors can be small and are not subject to the "size" constraints of conventional antennas. Because the atoms are the sensors, receiver sensors based on the vapor cells described herein can be much smaller in size. The small size of the receiver sensors means they can be more easily deployed as nets that can cooperate to receive weak return signals. The long wavelengths used in these radar systems mean that low-frequency Rydberg transitions (e.g., high-n states) must be used. Therefore, control of the electric field within the vapor cell is highly desirable.

[0065] As shown in Figures 1A-1C and 2, alternating layers of materials can be stacked to form alternating configurations of conductive and insulating layers. Conductive layers, which can function as electrodes, can generate an electric field in the vapor cell's internal cavity upon application of a voltage. Because multiple electrodes are possible in the stack, electric field control is greater than if electrodes were incorporated only in the upper and lower windows. For arrays or larger combinations of vapor cells, tab structures can extend outward relative to the stack layers. When extending outward from the conductive layers, they can serve as electrode contacts for applying a potential via wires or the like. Applying a voltage to the "tabs" applies the voltage to the outer dimensions of the array, so the wires used to supply the voltage can only minimally disrupt sensing performed on the vapor cell array. Electrodes can be ring electrodes or electrodes of different shapes, such as square or circular cross sections. Almost any shape is possible. Similarly, the outer and inner cross sections need not be the same. The electrodes can be segmented into quadrants, sextants, octants, etc., and can be annular or ring-shaped electrodes. The electrodes do not have to be alternating. Also, higher electrode density can be achieved in selected portions of the vapor cell, such as by adjusting the thickness of one or more conductive layers. The electrodes do not have to be uniformly spaced or even constructed of the same material.

[0066] Examples of materials that can be used to construct a laminated vapor cell with electrodes include glass and low-resistivity silicon. The glass can function as an insulator, and the low-resistivity silicon can function as an electrode. Alternatively, a coating such as indium tin oxide (ITO) can be used on the glass piece, or high-resistivity float silicon can be used for the insulating element. The ITO can be coated with silicon dioxide to allow bonding of the interface between layers. Furthermore, the inner surface of the ITO coating can be protected from reaction with alkali atoms in the vapor. A coating on any subset of the body can form a segmented electrode. Electrical connections can be made on the outside of the vapor cell by exposing conductive material. Other types of transparent or conductive coatings are also possible. The electrodes can also be made of semiconductors. Other materials or material ratios are also possible.

[0067] The stacked body configuration allows for three-dimensional structuring of vapor cells and also simplifies the manufacturing requirements for vapor cells. For example, layers can be cut in two dimensions from a large, high-quality wafer. These two-dimensional slices can then be used as electrodes to apply the necessary coatings prior to bonding. The cell bodies can be anodically bonded together or bonded in other ways (depending on the material), such as by frit bonding, contact bonding, or fusion bonding in an oven. Individual vapor cells can also have interlocking tabs that can be used to tilt many cells together and connect voltages to electrodes in the outer regions of the array. The upper and lower windows (i.e., end layers) can be constructed from borosilicate or aluminosilicate glass, among other possibilities. Furthermore, each vapor cell unit can be fiber-coupled, and the windows can be equipped with optical mirrors and filters. The stacked layers allow for flexible designs that enable three-dimensional structuring and efficient manufacturing.

[0068] In some embodiments, the electrodes in the vapor cell define a ring electrode ion guide. This configuration can be used to channel ions from one side of the vapor cell to the other. Ideally, all ions travel along the axis of the vapor cell and avoid contact with the walls. This configuration allows for the detection of ions generated from Rydberg states by collisions or field ionization due to an applied electric field at a subset of the electrodes or at all of the electrodes. Optionally, these ions may be selectively generated by a laser beam passing through the vapor in the vapor cell.

[0069] The use of segmented annular or ring-shaped electrodes allows for three-dimensional control of the electric field. Increasing the number of segments and different electrode shapes also allow for control of the electric field. Using segmented electrodes, radio frequency (RF) fields can be applied. The electrode (e.g., trace width) can be designed to impedance-match the contact to the RF source. RF fields can be used to create ion traps, conveyors, and generally time-dependent potentials for Rydberg atoms and charged particles. RF fields can also be used for RF or DC field tuning of atomic interaction potentials to manipulate Rydberg atom collisions. Furthermore, time-dependent fields can be used to modulate atomic energy levels. Shifting atomic energy levels with an external electric field can detune a laser from resonance, thereby modulating spectroscopic signals.

[0070] As described herein, anodic bonding processes can be used to construct stacked vapor cells. In particular, multilayer wafer stacks can be bonded or laminated in a single anodic step process while minimizing perturbation of mobile ions in the cell structure. Figure 5 shows a schematic perspective view of a portion of an exemplary stack of alternating glass and silicon layers. Four interfaces between five layers are shown, beginning and ending with silicon layers. Five-layer (silicon (Si) / glass (G) / Si / G / Si) and seven-layer (Si / G / Si / G / Si / G / Si) stacks of silicon-glass sandwich wafers have been anodically bonded at 370°C using a sequential hermetic bonding method. The bonds forming these structures are of high quality, high bond strength, and void-free at the interfaces. While it is also possible to bond each interface individually, it is believed to be more efficient to bond the interfaces in a single process. Other types of stack bonding are also possible, such as glass frit bonding, adhesive bonding, and contact bonding.

[0071] To demonstrate this method, the anodic bonding process was performed using standard double-sided polished 1.2 mm thick bare silicon wafers with p-type Si:B<1 0 0> orientation and resistivity between 1 and 15 Ω·cm, and MEMPAX Borofloat glass wafers with a diameter of 4 inches ± 0.005 inches and a thickness of 0.043 inches ± 0.002 inches. The average surface microroughness of the glass wafer, R aThe average ion density (Id) is 0.1–0.5 nm, similar to that of silicon wafers. Glass wafers have high ion mobility and a thermal expansion coefficient well matched to that of silicon. First, silicon and glass wafers were cut into rectangular pieces approximately 1 cm x 2 cm using a dicing saw. After dicing, the silicon and glass substrates were cleaned in Piranha solution (e.g., a 4:1 aqueous mixture of H2SO4:H2O2) for 15 minutes and then rinsed with deionized water (DI water). The wafers were dried with pure nitrogen gas (N2) in a cleanroom environment. Prior to bonding, the silicon and glass substrates were ultrasonically cleaned in DI water, followed by solvent cleaning using methanol (e.g., for 20 minutes) and acetone (e.g., two 15-minute cycles with the bath temperature maintained at 50 °C). After the solvent cleaning, the wafers were rinsed with DI water and then dried with N2 gas. Immediately after drying, the multilayer stacks (5- or 7-layer structures) were manually aligned and pre-bonded in air at room temperature. The stack was then sandwiched between graphite and stainless steel plates, with total thicknesses of 5.6 mm and 7.8 mm for the 5-layer and 7-layer stacks, respectively.

[0072] To complete the anodic bonding process, the pre-bonded multi-stack wafer layers were placed between two plates (anode and cathode) connected to a DC power source. The bonding process parameters were carefully selected based on preliminary optimization tests at various voltages and temperatures. For triple-stack layers (Si / G / Si and G / Si / G), the primary and secondary bonding methods were optimized (e.g., polarity reversal). The resulting bond strengths were 15 MPa and 10 MPa, respectively, as measured using an adhesion tester. In the anodic bonding process, the bottom and top Si layers were connected to the positive and negative electrodes. To increase the mobility of cations in the glass substrate, the stacked wafers were heated to 370 °C. The temperature was then slowly increased in 75 °C steps to avoid residual stress in the pre-bonded wafer layers and undesired wafer bowing. The final temperature was maintained at 370 °C for at least 20 min to ensure temperature uniformity before the application of high voltage. After the temperature stabilized, a DC voltage was applied to the electrodes, and the current was measured as a function of bonding time. The anodic bonding process was completed when the current decayed to a residual value (e.g., 0.008 mA for 3 layers). After the primary bonding was completed, the power supply was turned off and the temperature was maintained at 370°C. After the bonding was completed, the polarity of the DC power supply was switched (secondary bonding process). Similar currents were observed at the completion of the secondary bonding process. The anodic bonding process conditions, parameters, and images of the bonded multilayer stack wafers are shown in the table in Figure 6.

[0073] The bond strength of the wafers was measured by crack opening tests (razorblade tests) and / or dicing and cleaving. Both the 5-layer and 7-layer stacks were investigated by crack opening tests. When a 0.2 mm-thick stainless steel razor blade was inserted into the bonded interface between the glass and silicon, the tip of the razor blade bent spontaneously, indicating a very strong bonded interface. Both bonded substrates were also subjected to diamond saw wafer dicing tests (sample size 1 cm x 1 cm) to evaluate the interface. No cracks, delamination, fractures, or defects were observed. This result indicates that the bond strength is sufficiently high for the fabrication of multilayer sealed vapor cells, as described in Figures 1A-2. Figure 7 shows cross-sectional views of the bonded substrates (5-layer and 7-layer stacks) and their respective interface quality under an optical microscope. The bonded substrates were formed by anodically bonding alternating layers of silicon (Si) and glass (G) to each other using a bonding process such as that described in Figure 6. All bonded interface regions appeared smooth when cut, so they were not polished. As a result, there are no bonding voids (defects, cracks, or peeling) at the bonding interface, indicating excellent bonding quality.

[0074] To create the segmented electrodes, a shadow mask may be used in conjunction with the glass wafer to deposit (e.g., by sputtering) a metal such as chromium or gold. After the chromium or metal is deposited, the wafer can be coated with silicon dioxide by a method such as plasma enhanced chemical vapor deposition (PECVD). The wafer may not be flat at this point due to the embedded electrode structure, but it can be polished to a suitable surface roughness by chemical mechanical polishing (CMP). In this way, almost any electrode pattern can be designed. Other deposition and patterning methods are also possible.

[0075] The vapor cell can be filled with pure Cs either in the vapor cell or in a cavity inside the vapor cell wall, and connected to the cavity through a hole or trench structure. The vapor cell can also be filled with a getter and activated with a laser. Other filling methods (e.g., paraffin-coated alkali metals) can also be used.

[0076] In some embodiments of the present description, the vapor cell can be described by the following example. Example 1. A vapor cell comprising: a body defined by a stack of layers including an electrically conductive layer and an electrically insulating layer, the stack of layers being bonded to one another; first and second end layers at opposite ends of the body, one or both of which are optically transparent; an intermediate layer between the first and second end layers and defining an interior cavity of the body extending through the body between the first and second end layers; and adjacent conductive layers are separated by at least one electrically insulating layer; a body, each conductive layer defining an electrode of the vapor cell and including a contact surface on an exterior surface of the body defining an electrical contact for the electrode; a vapor or vapor source disposed in the interior cavity; A vapor cell comprising: Example 2. A vapor cell as described in Example 1, wherein at least a portion of the stack layers are alternating electrically conductive and electrically insulating layers. Example 3. A vapor cell as described in Example 2, wherein the entire stack layers are alternating electrically conductive and electrically insulating layers. Example 4. The vapor cell of any one of Example 1 or Examples 2-3, wherein the first and second end layers are conductive layers and define first and second end electrodes, respectively, of the vapor cell. Example 5. Each intermediate layer includes an inner periphery defining a portion of an interior cavity; The vapor cell of any one of Example 1 or Examples 2-4, wherein the inner peripheral surface of at least one conductive layer is configured such that the conductive layer can protrude into the internal cavity beyond a layer in the stack adjacent to the conductive layer. Example 6. Each intermediate layer includes an outer peripheral surface that defines a portion of the outer surface of the body; The vapor cell of any one of Example 1 or Examples 2-5, wherein the outer peripheral surface of at least one conductive layer is configured such that the conductive layer can protrude from the outer surface beyond a layer in the stack adjacent to the conductive layer. Example 7. At least one conductive layer is divided into a plurality of portions defining each segment of the segmented electrode; The vapor cell of Example 1 or any one of Examples 2-6, wherein the contact surface of at least one conductive layer is divided into a plurality of partial contact surfaces each defining an electrical contact for a respective segment. Example 8. The vapor cell of Example 7, wherein the sections are electrically isolated from one another. Example 9. The vapor cell of example 7 or 8, wherein the plurality of partial contact surfaces are configured to be each impedance matched to a radio frequency electromagnetic radiation source. Example 10. The vapor cell of Example 1 or any one of Examples 2-9, wherein one or more layers in the stack are planar layers. Example 11. At least one conductive layer is A substrate; a conductive coating covering at least a portion of the substrate and having a first portion exposed to the interior cavity and a second portion defining a contact surface of the conductive layer; The vapor cell of any one of Example 1 or Examples 2-10, comprising: Example 12. The vapor cell of example 11, wherein the substrate is formed of an insulating material. Example 13. At least one conductive layer is The vapor cell of example 11 or example 12, further comprising an insulating coating disposed on the conductive coating and covering at least a first portion thereof. Example 14. The stack layer includes one or more internal surfaces that bound an internal cavity; The vapor cell of Example 1 or any one of Examples 2-13, wherein at least a portion of one or more interior surfaces is covered with a coating that is chemically inert to the vapor. Example 15. The vapor cell of example 14, wherein the portion of the one or more interior surfaces includes all interior surfaces associated with a conductive layer. Example 16. The vapor cell comprises a vapor source; an intermediate layer defining a wall surrounding a first portion of the internal cavity; The vapor cell of Example 1 or any one of Examples 2-15, wherein the interior cavity includes a second portion extending from the first portion into the wall and including the vapor source. Example 17. A body includes a first outer surface and a second outer surface; at least one conductive layer includes first and second tabs extending outwardly from the first and second outer surfaces, respectively; The vapor cell of Example 1 or any one of Examples 2-16, wherein one or both of the first and second tabs define a contact surface of the conductive layer. Example 18. The conductive layer is 10 3 The vapor cell of Example 1 or any one of Examples 2-17, wherein the vapor cell is formed of a material having a resistivity of less than Ω·cm. Example 19. The vapor cell of Example 1 or any one of Examples 2-18, wherein at least one conductive layer is formed of doped silicon. Example 20. The vapor cell of Example 1 or any one of Examples 2-19, wherein at least one conductive layer is formed of a transparent semiconductor oxide. Example 21. The vapor cell of Example 1 or any one of Examples 2-20, wherein at least one conductive layer is formed of a metal or alloy. Example 22. Electrical insulation layer is 10 6 The vapor cell of any one of Example 1 or Examples 2-21, wherein the vapor cell is formed of a material having a resistivity greater than Ω·cm. Example 23. The vapor cell of any one of Examples 1 or 2-22, wherein at least one electrically insulating layer is formed of a glass containing silicon oxide. Example 24. The vapor cell of Example 1 or any one of Examples 2-23, wherein the stack layers include an adhesive layer at the interface between a pair of adjacent layers in the stack. Example 25. The vapor cell of Example 1 or any one of Examples 2-24, wherein one or both of the first and second end layers includes a reflective coating. Example 26. The vapor cell of Example 1 or any one of Examples 2-25, wherein one or both of the first and second end layers includes an anti-reflective coating. Example 27. The stack layer includes one or more internal surfaces that bound an internal cavity; The vapor cell of Example 1 or any one of Examples 2-26, wherein one or more interior surfaces are at least partially covered by an anti-relaxation coating. Example 28. The vapor cell of example 27, wherein the anti-relaxation coating comprises a hydrocarbon material. Example 29. The vapor cell of Example 1 or any one of Examples 2-28, wherein one or both of the first and second end layers includes an inner surface adjacent the end layer and covering the opening of the internal cavity, the inner surface having an optical filter coating disposed thereon. Example 30. The vapor cell of example 1 or any one of examples 1-30, wherein the vapor comprises a gas of Rydberg atoms.

[0077] In some aspects of the present description, a method for operating a vapor cell can be described by the following example. Example 1. Interacting a light beam with a vapor in a vapor cell, the vapor cell comprising: a body defined by a stack of layers including an electrically conductive layer and an electrically insulating layer, the stack of layers being bonded to one another; first and second end layers at opposite ends of the body, one or both of which are optically transparent; an intermediate layer between the first and second end layers and defining an interior cavity of the body extending through the body between the first and second end layers; and adjacent conductive layers are separated by at least one electrically insulating layer; a body, each conductive layer defining an electrode of the vapor cell and including a contact surface on an exterior surface of the body defining an electrical contact for the electrode; a steam generator disposed in the internal cavity; and applying respective voltages to one or more electrodes to vary the electric field in the interior cavity; an ion signal based on charged particles in the vapor; optical properties of the light beam after interacting with the vapor; measuring one or both of A method comprising: Example 2. The method of Example 1, where each voltage is applied to all electrodes of the vapor cell. Example 3. The method of Example 1 or Example 2, wherein applying each voltage to one or more electrodes includes varying at least one applied voltage over time. Example 4. The method of example 3, wherein at least one applied voltage is varied periodically with time. Example 5. The method of Example 1 or any one of Examples 2-4, wherein the first and second end layers are conductive layers and define first and second end electrodes, respectively, of the vapor cell. Example 6. The method of Example 5, wherein applying respective voltages to the one or more electrodes includes displacing target charged particles in the vapor to one or both of the first and second end layers. Example 7. The method of Example 6, wherein interacting the light beam with the vapor includes manipulating the light beam to ionize a portion of the vapor to produce the target charged particles. Example 8. Applying each voltage to one or more electrodes ionizing a portion of the vapor to produce charged particles by manipulating an electric field; displacing charged particles into one or both of the first and second end layers by manipulating an electric field; The method of Example 5, comprising: Example 9. The method of Example 8, including measuring the charge of individual charged particles incident on one or both of the first and second end layers. Example 10. The method of Example 8 or Example 9, including measuring a current based on charged particles received over time in one or both of the first and second end layers. Example 11. The method of any one of Example 8 or Examples 9-10, comprising determining the time of flight of the charged particles based on the time difference between when the charged particles are generated by manipulating the electric field and when the charged particles are received by one or both of the first and second end layers. Example 12. An internal cavity extends along an axis between the first and second end layers; The method of any one of Example 1 or Examples 2-11, wherein applying the voltages to the one or more electrodes comprises applying different voltages to two or more electrodes to establish an electric field profile along the axis. Example 13. The method of example 12, wherein the profile includes a constant magnitude of the electric field. Example 14. The method of example 12 or example 13, wherein the profile includes a gradient of the electric field. Example 15. The method of any one of Example 12 or Examples 13-14, wherein the profile comprises a periodic variation of the electric field. Example 16. At least one conductive layer is divided into a plurality of portions defining each segment of the segmented electrode; a contact surface of at least one conductive layer is divided into a plurality of partial contact surfaces each defining an electrical contact for a respective segment; The method of any one of Example 1 or Examples 2-15, wherein applying each voltage to one or more electrodes comprises applying each voltage to one or more segments. Example 17. An internal cavity extends along an axis between the first and second end layers; 17. The method of Example 16, wherein applying the voltages to the one or more segments comprises applying different voltages to two or more segments to vary the electric field along a direction non-parallel to the axis. Example 18. The method of any one of Examples 1 or 2-17, wherein interacting the light beams includes passing the light beams through the first end layer, the internal cavity, and the second end layer. Example 19. Interacting light beams passing a light beam through the first end layer and the internal cavity; reflecting the light beam off the second end layer and passing it back through the internal cavity and the first end layer; The method of any one of Example 1 or Examples 2-17, comprising: Example 20. The method of any one of Example 1 or Examples 2-19, wherein the optical property comprises an amplitude of the light beam. Example 21. The method of example 21, wherein amplitude is measured at one or more target frequencies of the light beam. Example 22. The method of any one of Example 1 or Examples 2-21, wherein the optical property comprises a phase of the light beam. Example 23. The method of any one of Example 1 or Examples 2-22, wherein the optical property comprises polarization of the light beam. Example 24. The method of any one of Example 1 or Examples 2-23, comprising determining a spectrum of the vapor based on an ion signal, an optical property, or both. Example 25. Monitoring spectral characteristics over time and Varying at least one applied voltage in response to changes in the spectral characteristic; The method of Example 24, comprising: Example 26. The method of example 25, wherein at least one applied voltage is varied over time to maintain the characteristic at a target value. Example 27. The method of example 25, wherein the property is a Stark shift. Example 28. The method of example 25, wherein the characteristic is spectral broadening. Example 29. The method of any one of Example 1 or Examples 2-28, wherein the vapor comprises a gas of Rydberg atoms. Example 30. The method of any one of Example 1 or Examples 2-29, wherein interacting the light beam with the vapor includes interacting first and second light beams with different respective electronic transitions of the vapor.

[0078] While this specification contains many details, these should not be construed as limitations on the scope of the claims, but rather as descriptions of features specific to particular examples. Certain features described herein or illustrated in the context of separate embodiments may also be combined. Conversely, various features that are described or illustrated in the context of a single embodiment may also be implemented in multiple embodiments separately or in any suitable subcombination.

[0079] Similarly, while the figures may depict operations in a particular order, it should not be understood that performing such operations in the particular order depicted, in sequence, or even performing all of the depicted operations is required to achieve desirable results. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the above-described embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems may generally be integrated together as a single product or packaged as multiple products.

[0080] While a number of embodiments have been described, it will be understood that modifications are possible and, therefore, other embodiments are within the scope of the following claims.

Claims

1. interacting a light beam with a vapor in a vapor cell, said vapor cell comprising: a body defined by a stack of layers including an electrically conductive layer and an electrically insulating layer, said stack of layers being bonded to one another; first and second end layers at opposite ends of the body, one or both of which are optically transparent; an intermediate layer between the first and second end layers defining an interior cavity of the body extending through the body between the first and second end layers; and adjacent conductive layers are separated by at least one electrically insulating layer; a body, each conductive layer defining an electrode of the vapor cell and including a contact surface on an exterior surface of the body defining an electrical contact for the electrode; the steam disposed in the internal cavity; and applying voltages to one or more electrodes to vary the electric field in the internal cavity; an ion signal based on charged particles in the vapor; an optical characteristic of the light beam after interacting with the vapor; and measuring one or both of A method comprising:

2. The method of claim 1 , wherein each voltage is applied to all of the electrodes of the vapor cell.

3. The method of claim 1 or 2, wherein applying each voltage to the one or more electrodes comprises varying at least one applied voltage with time.

4. The method of claim 3 , wherein the at least one applied voltage is varied periodically with time.

5. 3. The method of claim 1, wherein the first and second end layers are conductive layers and define first and second end electrodes, respectively, of the vapor cell.

6. The method of claim 5 , wherein applying respective voltages to the one or more electrodes comprises displacing target charged particles in the vapor into one or both of the first and second end layers.

7. The method of claim 6 , wherein interacting the light beam with the vapor comprises manipulating the light beam to ionize a portion of the vapor to produce the target charged particles.

8. applying respective voltages to the one or more electrodes; ionizing a portion of the vapor to generate charged particles by manipulating the electric field; displacing the charged particles into one or both of the first and second end layers by manipulating the electric field; The method of claim 5 , comprising:

9. The method of claim 8 , comprising measuring the charge of individual charged particles incident on one or both of the first and second end layers.

10. The method of claim 8 , comprising measuring a current based on charged particles received over time in one or both of the first and second end layers.

11. 9. The method of claim 8, further comprising determining a time-of-flight of the charged particle based on a time difference between when the charged particle is generated by manipulating the electric field and when the charged particle is received by one or both of the first and second end layers.

12. the internal cavity extends along an axis between the first and second end layers; 3. The method of claim 1, wherein applying voltages to the one or more electrodes comprises applying different voltages to two or more electrodes to establish a profile of the electric field along the axis.

13. The method of claim 12 , wherein the profile comprises a constant magnitude of the electric field.

14. The method of claim 12 , wherein the profile comprises a gradient of the electric field.

15. The method of claim 12 , wherein the profile comprises a periodic variation of the electric field.

16. at least one conductive layer is divided into a plurality of portions defining each segment of the segmented electrode; the contact surface of the at least one conductive layer is divided into a plurality of partial contact surfaces each defining an electrical contact for each of the segments; The method of claim 1 or 2, wherein applying a respective voltage to the one or more electrodes comprises applying a respective voltage to one or more segments.

17. the internal cavity extends along an axis between the first and second end layers; 17. The method of claim 16, wherein applying voltages to the one or more segments comprises applying different voltages to two or more segments to vary the electric field along a direction non-parallel to the axis.

18. The method of claim 1 or 2, wherein interacting the light beam comprises passing the light beam through the first end layer, the internal cavity, and the second end layer.

19. interacting the light beams passing the light beam through the first end layer and the internal cavity; reflecting the light beam off the second end layer and passing it back through the internal cavity and the first end layer; 3. The method of claim 1 or 2, comprising:

20. The method of claim 1 or 2, wherein the optical property comprises the amplitude of the light beam.

21. 22. The method of claim 21, wherein the amplitude is measured at one or more target frequencies of the light beam.

22. The method of claim 1 or 2, wherein the optical property comprises the phase of the light beam.

23. The method of claim 1 or 2, wherein the optical property comprises the polarization of the light beam.

24. The method of claim 1 or 2, comprising determining a spectrum of the vapor based on the ion signal, the optical properties, or both.

25. monitoring a characteristic of the spectrum over time; and Varying at least one applied voltage in response to the change in the characteristic of the spectrum; 25. The method of claim 24, comprising:

26. 26. The method of claim 25, wherein the at least one applied voltage is varied over time to maintain the property at a target value.

27. 26. The method of claim 25, wherein the property is a Stark shift.

28. 26. The method of claim 25, wherein the characteristic is the broadening of the spectrum.

29. The method of claim 1 or 2, wherein the vapor comprises a gas of Rydberg atoms.

30. The method of claim 1 or 2, wherein interacting the light beam with the vapor comprises interacting first and second light beams with different respective electronic transitions of the vapor.

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