Robust atomic interferometer

Abstract

The present disclosure relates to an inertial sensor for measuring an amount of inertia along a sensing axis. The sensor includes an atom interferometer including a pulse generator for generating one or more pulsed light beams defined by respective pulse durations to place atoms in superposition and recombine the atoms to measure interference of the atoms, the one or more pulsed light beams being configured to generate one or more pulsed light beams, the one or more pulsed light beams being defined by respective pulse durations, the one or more pulsed light beams being defined by respective pulse durations, and the one or more pulsed light beams being defined by respective pulse durations, the one or more pulsed light beams being defined by respective pulse durations. And calculating the amount of inertia based on the measured interference. The sensor further includes an auxiliary acceleration sensor configured to measure acceleration transverse to one or more of the pulsed light beams; and a control system configured to calculate a lateral offset of the atoms relative to the pulsed light beam caused by the measured acceleration transverse to the one or more of the light beams, increase the pulse duration, and adjusting the pulse timing to compensate for a reduced beam strength applied to the atoms due to the lateral offset.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to PCT application PCT / AU2023 / 050659, filed on July 19, 2023, the contents of which are incorporated herein by reference in their entirety. Technical Field

[0003] This disclosure relates to the use of atomic interferometers to measure inertial quantities, such as acceleration and rotation. Background Technology

[0004] Compared to state-of-the-art classical sensors, quantum accelerometers and gyroscopes based on atomic interferometry may offer higher sensitivity and stability. In many atomic interferometer sensors, the pulsed interaction between a laser beam and an expanding, free-falling cloud of atoms is used to form equivalents of mirrors and beam splitters for atomic matter waves. These pulses are then applied to an interferometer sequence to separate, reflect, and interfere with the atomic matter waves. Despite their inherently high sensitivity to acceleration and rotation, these devices currently have limited applications outside of controlled laboratory environments.

[0005] Atomic interferometers utilize the quantum mechanical wave nature of atoms by measuring the interference between atomic matter waves, which are separated by a beam splitter's matter wave equivalent and propagate along individual paths. Because atoms possess multiple internal and external degrees of freedom (which can be precisely manipulated using light fields) and are sensitive to inertial, electromagnetic, and gravitational effects, they offer excellent uniformity for testing quality. Applications of atomic interferometers include: state-of-the-art measurements of fine structures and the gravitational constant; equivalence principle experiments; exploration of new physics; geophysics; civil engineering; and inertial navigation.

[0006] Any discussion of documents, actions, materials, devices, articles, or the like included in this specification shall not be construed as an admission that any or all of these matters constitute part of the prior art or common knowledge in the field relating to this disclosure prior to the priority date of each appended claim.

[0007] Throughout this specification, the word “comprise” or variations such as “comprises” or “comprising” shall be understood to imply inclusion of the stated elements, integers or steps, or groups of elements, groups of integers or groups of steps, but not to exclude any other elements, integers or steps, or groups of elements, groups of integers or groups of steps. Summary of the Invention

[0008] An inertial sensor for measuring inertial quantities along a sensing axis, the sensor comprising:

[0009] An atomic interferometer includes a pulse generator for generating one or more pulse beams defined by corresponding pulse durations to place atoms into a superposition and rearrange the atoms to measure the interference of the atoms and calculate the inertial quantity based on the measured interference.

[0010] An auxiliary accelerometer, configured to measure acceleration transverse to one or more pulse beams in a pulse beam; and

[0011] The control system is configured to:

[0012] Calculate the lateral displacement of atoms relative to the pulsed beam caused by the measured acceleration of one or more beams transverse to the beam;

[0013] Increase pulse duration to compensate for the reduced beam strength applied to atoms due to lateral offset; and

[0014] Adjust the pulse timing to reduce phase shift caused by the initial longitudinal velocity of the atoms.

[0015] Adjusting the pulse timing can reduce phase shift caused by the initial atomic velocity distribution, which is an advantage. Therefore, the performance degradation caused by increasing the pulse duration to compensate for the reduced beam strength is mitigated.

[0016] In some embodiments, the atomic interferometer includes an atomic source for providing atoms that are moved relative to a sensing axis; a pulsed beam configured to place the atoms in a superposition of a first state and a second state, wherein the first state is associated with a first path and the second state is associated with a second path; a mirroring operation is applied to the atoms between placement and recombination, and the first and second states are recombinated to produce interference between the first and second states; a measurement system for measuring physical effects indicative of the interference; and a processor for calculating an inertial quantity based on the measured physical effects.

[0017] In some embodiments, the inertial quantity is linear acceleration or rotation.

[0018] In some embodiments, measuring the physical effect includes measuring the number of atoms in different superposition states.

[0019] In some embodiments, increasing the pulse duration includes applying an upper limit to the pulse duration.

[0020] In some embodiments, the atom has a velocity distribution, and the upper limit is related to the pulse duration, which still allows the pulse to interact with a threshold number of atoms for the pulse duration.

[0021] In some embodiments, the upper limit is set by the peak two-photon Rabi frequency of the sensor and the longitudinal velocity width of the atom.

[0022] In some embodiments, increasing the pulse duration includes calculating attenuation as one or more pulse adjustment factors, which correlate the ideal interaction of the atom with the pulse beam with the predicted interaction of the atom with the pulse beam at the lateral offset; and increasing the pulse duration by the one or more adjustment factors.

[0023] In some embodiments, the ideal interaction and the predicted interaction are represented by the corresponding two-photon Rabi frequencies.

[0024] In some embodiments, the pulse duration is increased differently for each pulse in the pulse beam by calculating attenuation based on time.

[0025] In some embodiments, the decay is based on the probing time.

[0026] In some embodiments, the auxiliary accelerometer is configured to measure the acceleration of one or more pulse beams transverse to the pulse beam multiple times during the atomic travel through the atomic interferometer; and the control system is configured to use the corresponding measured acceleration to compensate for the attenuation at each pulse beam in the pulse beam.

[0027] In some embodiments, the pulsed beam places atoms into a superposition and reassembles the atoms by exciting Bragg or Raman transitions.

[0028] In some embodiments, superposition is the superposition of two states with different momentum, separated by an integer number of two-photon recoils.

[0029] In some embodiments, the control system is further configured to adjust pulse characteristics other than pulse duration to allow for arbitrary further manipulation of the motion state of the atoms.

[0030] In some embodiments, the control system is further configured to adjust the pulse timing by increasing or decreasing the amount of time between any two or more pulses to compensate for the reduced beam strength applied to the atom due to lateral offset.

[0031] In some embodiments, the increase in time between pulses is calculated using the difference between the reciprocal two-photon Rabi frequencies of the first and second beamsplitters, respectively.

[0032] In some embodiments, adjusting pulse timing includes maintaining the duration and timing of pulses that place atoms into a superimposed array, and adjusting the duration and timing of pulses that apply mirror operations and recombine the first and second states.

[0033] In some embodiments, the control system is further configured to adjust the intensity of one or more beams to compensate for the reduced beam intensity applied to the atoms due to lateral offset.

[0034] A method for measuring inertial quantities along a sensing axis, the method comprising:

[0035] Generate atomic clouds;

[0036] One or more pulse beams are generated, defined by corresponding pulse durations, to place atoms into a superposition and recombine them;

[0037] An auxiliary accelerometer is used to measure the acceleration of one or more pulse beams transverse to the pulse beam;

[0038] Calculate the lateral displacement of atoms relative to the pulse beam caused by the measured acceleration of one or more pulse beams transverse to the pulse beam; and

[0039] Increase the pulse duration of the pulsed beam to compensate for the reduced beam strength applied to atoms due to lateral offset;

[0040] Adjust the pulse timing to reduce phase shift caused by the initial longitudinal velocity of the atoms;

[0041] Measuring the interference of atoms; and

[0042] The inertial quantity is calculated based on the measured interference.

[0043] A computer-implemented method for controlling an atomic interferometer, the computer-implemented method comprising:

[0044] Accelerometer data indicating acceleration transverse to one or more of a plurality of pulse beams, defined by corresponding pulse durations, is received from an auxiliary accelerometer to place atoms in a superposition and rearrange atoms to measure atomic interference.

[0045] Calculate the lateral displacement of atoms relative to the pulse beam caused by the measured acceleration of one or more pulse beams transverse to the pulse beam;

[0046] Increase the pulse duration of the pulsed beam to compensate for the reduced beam intensity applied to atoms due to lateral offset; and

[0047] Adjust the pulse timing to reduce phase shift caused by the initial longitudinal velocity of the atoms. Attached Figure Description

[0048] The following example will now be described with reference to the attached figures:

[0049] Figure 1 The working principle of an atomic interferometer under arbitrary acceleration is demonstrated.

[0050] Figure 2 The diagram depicts the trajectories of two possible free-fall atomic clouds under a) no transverse plateau acceleration and b) constant transverse plateau acceleration. Gaussian intensity curves of the interferometric beam are also shown. If the atoms are accelerated to a position within the beam with lower intensity during interferometry, the pulse area condition disclosed herein no longer satisfies, and the contrast of the fringes decreases.

[0051] Figure 3: a) Regarding the situation Direction affected Constant lateral acceleration Two-photon Rabi frequency multiplier of an extended ensemble of atoms The simulation of the expected changes. Here, It is a space-dependent beam intensity curve. Peak intensity ,and These are classic trajectories of atoms changing over time. Different atoms in a cloud have different initial positions and velocities, and therefore different trajectories. The shaded area shows the full range of variations caused by different atomic trajectories throughout the interferometer with a 15 ms interrogation time. b) depicts the distribution of the two-photon Rabi frequency multiplier during each pulse. The solid black line indicates the use of... Calculated kinematic estimates of the average two-photon Rabi frequency multiplier. For both a) and b), the transverse temperature of the atom is 5. Furthermore, the initial atomic cloud has a Gaussian spatial distribution with a standard deviation of 1 mm, and its center is located on the beam axis. The expected change is achieved by solving the motion formula for each atom and assuming the Gaussian beam has a diameter of 20 mm. It is calculated based on the radius.

[0052] Figure 4a The simulated interferometer fringe contrast is shown. Figure 4b This demonstrates the longitudinal sensitivity (defined by Equation 8) under a series of constant lateral accelerations, with and without software gimbal control (gimbal control) and without gimbal control (conventional). We assume the peak two-photon Rabi frequency of the Raman pulse is 100 kHz and the standard deviation of the longitudinal momentum distribution of the atomic cloud is 0.125. To determine the fringe contrast at each acceleration, we calculated the state after simulating the entire pulse sequence and changing the phase of the last pulse. and The difference in quantity between them. Contrast is defined as the difference between quantities exceeding [a certain threshold]. The amplitude of the stripes is obtained by averaging the values ​​of individual atoms, whose initial positions and velocities are randomly selected from their respective distributions. The interrogation time is 25 ms. The standard deviation of the initial (Gaussian) cloud is 1 mm, and the (Gaussian) beam... The radius is 20 mm, and the transverse temperature is 5. The maximum duration scaling factor is... Our model takes into account ballistic expansion effects, which are used to calculate the two-photon Rabi frequency within each time slice.

[0053] Figure 5 An inertial sensor for measuring inertial quantities such as linear acceleration or rotation is demonstrated.

[0054] Figure 6 A method for measuring inertial quantities is demonstrated.

[0055] Figure 7a This paper presents simulated interferometer fringe contrast under a series of constant lateral accelerations, with and without software gimbal control (GAC). Gimbal control is depicted with and without pulse timing adjustment (GAC: duration and GMC: duration and timing, respectively). Pulse timing adjustment is calculated for each value of lateral acceleration to minimize the interferometer phase dependence on longitudinal atomic momentum. We assume a peak two-photon Rabi frequency of 50 kHz and a standard deviation of 0.25 ħk for the longitudinal momentum distribution of the atomic cloud. eff。 To determine the fringe contrast at each acceleration, we calculated the state after simulating the entire pulse sequence and changing the phase of the last pulse. and The difference in quantity between them. Contrast is defined as the difference between quantities exceeding [a certain threshold]. The amplitude of the stripes is obtained by averaging the values ​​of individual atoms, whose initial positions and velocities are randomly selected from their respective distributions. The interrogation time is 30 ms. The standard deviation of the initial (Gaussian) cloud is 1 mm, and the (Gaussian) beam is 1 / e. 2 The radius is 10 mm and the lateral temperature is 1 μK. The maximum duration scaling factor is 10. Our model considers ballistic expansion effects, which are used to calculate the two-photon Rabi frequency within each time slice.

[0056] Figure 7bThis paper presents simulated interferometer fringe phase shifts under a series of constant offsets in the longitudinal momentum distribution (asymmetric longitudinal momentum distribution) with and without software gimbal control (GAC). A constant transverse acceleration amplitude of 0.5g is assumed in the model. Gimbal control with and without pulse timing adjustment is depicted (GAC: duration and GMC: duration and timing, respectively). The horizontal black dashed line is used only to guide the line of sight. Pulse timing adjustment is calculated to minimize the interferometer phase dependence on longitudinal atomic momentum caused by pulse duration adjustment in response to transverse acceleration. We assume a peak two-photon Rabi frequency of 50 kHz and a standard deviation of 0.25 ħk for the longitudinal momentum distribution of the atomic cloud. eff To determine the fringe phase under each acceleration, we calculated the magnitude difference between states |1> and |2> after simulating the entire pulse sequence and changing the phase of the last pulse. The interferometer phase shift was defined as the difference between states |1> and |2> exceeding 5. 10 4 The phase of the stripes is sinusoidally fitted after averaging the values ​​of individual atoms. The initial positions and velocities of these atoms are randomly selected from their respective distributions. The interrogation time is 30 ms. The standard deviation of the initial (Gaussian) cloud is 1 mm, and the (Gaussian) beam is 1 / e. 2 The radius is 10 mm and the lateral temperature is 1 μK. The maximum duration scaling factor is 10. Our model considers ballistic expansion effects, which are used to calculate the two-photon Rabi frequency within each time slice.

[0057] Figure 8 The Bloch sphere is used in the working principle of an idealized atomic interferometer.

[0058] Figures 9a to 9c The proposed pan-tilt control scheme, which adjusts the pulse duration and timing, is demonstrated. Detailed Implementation

[0059] Figure 1 An optical pulsed atomic interferometer sensor 100 (also referred to simply as an "atomic interferometer") comprising an atomic source 101 is demonstrated. This atomic source is typically cooled and / or velocity-selectively brought to a temperature of a few microKelvin or lower and prepared into a single ground-state electronic atomic state. The electronic state is defined by the electron configuration of the system and the quantum number of each electron constituting that configuration. Each electronic state corresponds to an energy level within the energy levels of an atom.

[0060] In some cases, alkali metal atoms (e.g.) are used However, other alkali metal atoms can also be used, in which case magneto-optical traps (MOTs) and optical traps can be used to achieve trapping and laser cooling. In other examples, ultracold atomic samples (such as Bose-Einstein condensates) are used as the atomic source. Subsequently, a series of optical pulses and / or microwave pulses can be used to velocity-select the atoms along the interferometric beam axis and prepare them into a single magnetically insensitive ground-state hyperfine structure.

[0061] After the atomic source is properly prepared according to the method described above (or other methods), the atomic source is subjected to a series of optical interferometry pulses. More specifically, the first pulse 102 acts as a beam splitter (BS1) in the sense that the pulse places the atoms from source 101 into a superposition of the first and second states. The two states have different momentum and are therefore spatially separated along the interferometry beam axis. The second pulse 103 exchanges the states of each part of the atomic superposition produced after the first pulse 102, which is why the second pulse 103 is also called a mirror (M). Finally, the third pulse 104 recombines the atoms in the superposition to produce interference, which is also called the second beam splitter (BS2). A counter counts the number of atoms in each state after the third pulse 104. In a perfectly functioning atomic interferometer, without any acceleration, there should be no relative phase shift between states, meaning that all atoms should be in the same state after interference.

[0062] However, in the presence of acceleration with a non-zero component along the z-direction, the phase shift accumulated by atoms along each path will differ. This means that after the third pulse 104, the state of some atoms will be different from that without acceleration. This difference in quantity can be "read out" using the basic principles of interferometry. If the states are the same, the matter waves undergo constructive superposition and contribute the most to the optical detection signal. On the other hand, if the states differ in phase... If the phase shifts are such that they cancel each other out, the optical signal is minimized. Any phase shift between these extrema represents a continuously changing measurement result.

[0063] This principle can also be explained using a single atom. A single atom is placed into a superposition of two states by a first pulse 102. With zero acceleration in the longitudinal direction, a third pulse 103 places the atom into a single state. However, under the influence of acceleration, the states in the superposition accumulate non-zero relative phases before the third pulse is applied. Therefore, the third pulse 104 places the atom inaccurately in the ground state. In other words, there is a non-zero probability of measuring the atom in a different state. Therefore, if this experiment is repeated with many atoms, some atoms will be observed to be in different states, a physical phenomenon indicating the acceleration experienced by the atom.

[0064] Interferometers are sensitive to acceleration along the interferometer beam axis (called the longitudinal z-direction). Vertical ( The plane is called the transverse plane, and the acceleration within this plane is called transverse acceleration.

[0065] In some examples, atoms can move freely along the interferometer beam axis. In others, atoms can also move freely within the transverse plane (called "unguided" atomic interferometers), causing the atomic source to expand ballistically without external force. In still others, the dynamics of the atoms in the transverse plane can be altered by means of light fields, etc.; these are called "guided" atomic interferometers. In yet another example, atoms are counteracted by gravity, for example, through Bloch oscillations or extended pulse sequences.

[0066] Atomic interferometry pulses of 10², 10³, and 10⁴ typically induce two-photon Bragg or Raman transitions. These atom-light interactions occur at frequencies of... The two interferometric beams (representing two beams, where c is the speed of light in vacuum) cause a recoil of two photons with momentum differences that are integer multiples of each other. The two motion states are coupled together. In other words, and These are the wavenumbers of the two beams, which also define the propagation direction. For simplicity, this disclosure provides an example of atomic interferometry utilizing two-photon Raman transitions, where the electron is in an electronic state. and momentum Atoms in wave numbers are respectively and Two counter-propagating beams are coupled to a wave with momentum. Different electronic states This makes the effective momentum transferred by the pulse equal to However, the techniques disclosed here can be readily applied to atomic interferometry with other atom-light interactions, such as multiphoton Bragg transitions.

[0067] Resonant two-photon Raman transitions are described by unitary matrices

[0068] (1)

[0069] in, It is the pulse area. It is the time of atom-light interaction. It is the two-photon Rabi frequency, which represents a given time. The intensity of the atom-optical coupling is proportional to the intensity of the interferometric measurement beam. It refers to the relative phase of the light beam. This is determined by selecting the pulse area. It can realize the atomic-optical equivalent of a 50 / 50 beam splitter:

[0070] (2a)

[0071] (2b)

[0072] pulse area Mirroring operation was implemented:

[0073] (3a)

[0074] (3b)

[0075] For duration A rectangular pulse with constant intensity, phase, and frequency, and a pulse area of... Therefore, the conditions for the beam splitter (BS) pulse and the mirror (M) pulse are:

[0076] (4)

[0077] (5)

[0078] In a three-pulse Mach-Zehnder interferometer configuration (BS1-M-BS2), the possible acceleration measurement procedure using a cold atom interferometer is as follows. The first beam splitter pulse acts on the state... The initial atomic cloud in the middle places each atom in and The 50 / 50 atomic superposition. 50 / 50 superposition means that if you measure the state of any given atom, there is a 50% probability that the atom is in state 50 / 50. or .

[0079] After a period of inquiry After the light is turned off during this period, the two parts of the mirror pulse are redirected and superimposed, resulting in the second interrogation time... They then overlap spatially. A second beamsplitter pulse subsequently reassembles the two states, and measurements are then taken of the inner state. and The number of atoms (respectively) and The acceleration component parallel to the backpropagation beam (defining the interferometric beam axis) immediately causes a relative phase shift between the two internal states before the second beam splitter. This affects the measured quantity difference in the following ways:

[0080] (6)

[0081] in It is the total number of atoms, and This refers to fringe contrast. In the limiting case where the pulse duration is much shorter than the interrogation time and the acceleration is constant, the phase shift and acceleration... The relationship is:

[0082] (7)

[0083] Without loss of generality, the beam is aligned with the acceleration here, making ,in and .

[0084] We define sensitivity as the minimum measurable constant acceleration. For a single interferometer operating under the shot noise limit, its value is:

[0085] (8)

[0086] Sensitivity depends on interrogation time stripe contrast ,Light Momentum transferred to atoms and the number of atoms If the pulse area condition (Equations (4) and (5)) is not satisfied for each pulse, resulting in suboptimal beam splitting and / or reflection, then both contrast and sensitivity will be reduced.

[0087] Challenges to be solved

[0088] One challenge in achieving high-precision cold atom acceleration measurements on a mobile platform is that the efficiency of the beam splitter and mirrors is significantly reduced due to platform motion. If the platform acceleration is non-zero in the plane transverse to the interferometric beam, it typically alters the trajectory of the atoms relative to the platform, such as… Figure 2 As shown. It is important to note that for certain types of measurements, such as gravitational measurements, unguided atoms will be treated as "free fall." More generally, "unguided" means that the atom is not subjected to forces transverse to the interferometer's principal sensitivity direction generated by the sensor system. It should be noted that this applies to unguided atom interferometers, but also to some guided atom interferometers where the transverse acceleration is large enough to overcome any guiding force.

[0089] Because interferometric beams have spatially correlated curves, if the positions of atoms within the beam change due to lateral acceleration, the atomic cloud will experience different peak intensities (and therefore different peak two-photon Rabi frequencies) during the initial beam splitter, central mirror, and final beam splitter pulses. For Gaussian beam profiles (such as...),... Figure 2As shown, the farther the atom is from the beam axis, the lower the intensity, and therefore the lower the two-photon Rabi frequency. This lower-than-expected two-photon Rabi frequency alters the pulse area, causing it to deviate from the ideal required for a perfect beam splitter and mirror. and This will significantly reduce the stripe contrast and thus the sensitivity to acceleration along the Raman beam axis (Equation (8)).

[0090] Using the resonant Raman model provided by formula (1), it can be demonstrated how imperfect beam splitting and reflection cause contrast attenuation; assuming the atoms are initially located on the axis ( If the non-zero lateral acceleration only affects the pulse area of ​​the mirror and the second beam splitter, then the output state is...

[0091] (9)

[0092] Calculate the quantity and We got

[0093] (10)

[0094] Let us assume a rectangular pulse with durations given by equations (4) and (5) and lateral accelerations that cause the peak intensities of the mirror and the second beam splitter to decrease by 60% and 90%, respectively. Then, and ,produce The contrast is reduced by 20 times compared to ideal operation.

[0095] Given that the contrast of the interference fringes of an atomic interferometer is directly proportional to the signal-to-noise ratio of the measurement and inversely proportional to the minimum detectable change in acceleration, maintaining high-contrast fringes is ideal for all interferometer sensors, especially for high-performance operation in field-based dynamic environments.

[0096] Reduce contrast loss

[0097] This disclosure provides an adaptive software gimbal technique for reducing contrast loss due to lateral platform acceleration. The disclosure proposes combining a quantum measurement of longitudinal acceleration with at least one classical measurement of platform acceleration in a lateral plane (perpendicular to the Raman beam axis) by an auxiliary accelerometer. This measurement can be performed using a classical accelerometer (e.g., a microelectromechanical system (MEMS) device). Furthermore, a classical gyroscope can be used to determine the variation in the orientation of the interferometer's sensitivity axis relative to a specific coordinate system (e.g., a coordinate system defined by local gravity and the Earth's surface). In this case, rotational measurements can be used to determine the component of gravitational acceleration acting on atoms in the lateral plane. More generally, the disclosed method enables the association of the subject's coordinate system with a fixed inertial coordinate system (or navigation coordinate system, if applicable, such as in the case of cold atom sensors used in navigation applications) using a gyroscope.

[0098] By combining this classical measurement with knowledge of the initial position of the atomic cloud in the beam and the shape of the beam intensity profile, the control system can calculate the expected change in the average two-photon Rabi frequency between pulses, as depicted in Figure 3. This allows the system to feedforward adjust the pulse shape (e.g., duration and / or amplitude) of the three pulses to maintain the pulse area requirement for each of the three interferometric pulses. In common scenarios, most lateral acceleration will move the atoms to a lower intensity position in the beam, meaning that the pulse duration or amplitude needs to be increased.

[0099] The following outlines how the adaptive software gimbal method works using rectangular Raman pulses in an exemplary measurement cycle (steps 2 through 5 are the software gimbal procedure):

[0100] 1. Cooling, trapping, releasing, and preparing atoms

[0101] 2. Use at least one classical accelerometer and / or gyroscope fixed to the device platform to determine the lateral direction ( acceleration Classical measurements of transverse acceleration can be performed once during interferometry (in which case it is assumed that the transverse acceleration in a single measurement is constant), or multiple measurements can be performed to more accurately calculate the position of the atomic cloud in the beam.

[0102] 3. By solving for the center of mass of the atomic cloud in ( )flat The formula for the motion within is used, and the expected average two-photon Rabi frequency during each pulse is calculated using the measured beam intensity curve. For example, in the case of an interferometric beam with Gaussian intensity, this provides...

[0103] (11)

[0104] here, On the beam center axis ( The peak two-photon Rabi frequency obtained at (corresponding to the maximum beam intensity) ), It is the cloud center relative to the beam ( The radial displacement of the axis, and It was determined through experiments. Beam radius. The intensity profile is not limited to a Gaussian shape, and the disclosed techniques are applicable to any measurable and / or known beam profile.

[0105] 4. Select the duration of each pulse ( This makes the pulse area close to its ideal value:

[0106] (12)

[0107] in This is the ideal pulse duration without lateral acceleration (e.g., formulas (4) and (5) for rectangular pulses). The ideal case refers to the pulse area that maximizes the interferometer's contrast. The "ideal" pulse area for non-rectangular (e.g., composite) beam splitters and mirror pulses is not limited to a specific value. and It should be noted that the rectangular pulse is activated for BS1 at time t=0, for M at t=T, and for BS2 at t=2T (left edge).

[0108] 5. Applications with correction pulse duration Interferometric sequence

[0109] 6. Measure the quantitative difference between the two states.

[0110] In one example, the system uses an upper limit on the duration scaling (i.e., This is to avoid excessive velocity selectivity of the pulse in the longitudinal dimension (typically, longer pulse durations resonate with narrower atomic velocity levels). This upper limit is set by the peak two-photon Rabi frequency of the experiment and the longitudinal momentum width of the atomic source: the maximum scaling can be set so that a pulse with maximum length scaling can still interact with all atoms in a velocity distribution with high fidelity.

[0111] Although a rectangular pulse shape is used in this disclosure, the software gimbal technology can be applied to devices with variable pulse shapes without modification. The pulse shape definition also applies to a more general definition of "pulse shape" that includes other control parameters such as laser beam frequency and phase. For example, the total duration or amplitude of Gaussian pulses, composite pulses, and pulses designed using robust control techniques can also be scaled to meet pulse area requirements. As another example, in the case of some composite pulses, the time-varying scans of both the pulse amplitude and the laser frequency can be scaled to meet the resonance conditions and pulse area requirements needed for high-efficiency operation.

[0112] It is important to note that this method is applicable to any interferometer sensor architecture that uses atoms that can move freely in a plane perpendicular to the interrogation beam (e.g., “unguided” atomic interferometers), including: rotation sensors, multi-axis accelerometers, and gravitational gradiometers. It is also applicable to interferometers using different types of atoms and alternative atom-light interactions such as single-photon transitions and two-photon Bragg transitions. In the case of Bragg pulses, it is difficult to compensate for variations in the pulse area by scaling the duration using Equation (12). Instead, the disclosed adaptive software gimbal technique achieves this by providing a lookup table that allows the user to select a pre-optimized pulse shape in real time. The selected Bragg pulse can be optimized for the two-photon Rabi frequency calculated in Equation (11).

[0113] advantage

[0114] One advantage of the disclosed software gimbal technique is the significant reduction in fringe contrast attenuation caused by the lateral acceleration of the device platform. Without this compensation, contrast attenuation due to probing atoms in regions with lower beam intensity could degrade the device's sensitivity. To demonstrate this quantitatively, we performed Monte Carlo simulations of the entire unguided interferometry sequence using rectangular Raman pulses from both the disclosed and undisclosed software gimbal techniques. Our simulations include the effects of cloud expansion and use a piecewise constant approximation of the Raman Hamiltonian for quantum state evolution. The results are depicted in Figure 4.

[0115] In the simulation, we assume that the initially prepared atomic source has an initial Gaussian spatial distribution with a standard deviation of 1 mm, and that during an unguided interferometric measurement sequence with an interrogation time of 25 ms, due to... The lateral temperature causes the atomic source to expand. We also assume that the peak two-photon Rabi frequency is... Furthermore, the standard deviation of the longitudinal momentum distribution of atomic clouds (e.g., Gaussians) is 0.125. For our software gimbal algorithm, we set the upper limit of pulse length scaling to... We found that software gimbal technology significantly reduces contrast degradation caused by lateral acceleration, which means that for images larger than [a certain size], [the contrast is reduced]. The sensitivity is improved tenfold for lateral acceleration. We emphasize that although the simulation range for lateral acceleration is large, even small accelerations can lead to a significant decrease in contrast when the interrogation time is increased without applying a software gimbal method; therefore, this technique is suitable for smaller lateral accelerations.

[0116] In summary, this disclosure provides an adaptive software gimbal technique designed to reduce contrast loss in atomic interferometer quantum sensors caused by platform acceleration perpendicular to the quantum measurement axis. The disclosed technique uses at least one adjacent classical auxiliary sensor to simultaneously measure platform acceleration. Using this measurement, we calculate the expected trajectory of the atomic cloud within the interferometric beam and thus estimate the variations in laser intensity and two-photon Rabi frequency during the interferometer pulse sequence. This result is used for feedforward adjustment of the pulse length or pulse shape. This allows the pulse area of ​​the beam splitter and mirrors to be restored to the size required for efficient beam splitting and reflection, and thus maintains high-contrast interference fringes. Therefore, this technique should improve the stability and sensitivity of atomic interferometers operating in dynamic sensing environments.

[0117] Figure 5 An inertial sensor 500 is shown for measuring inertial quantities along sensing axis 501. Sensor 500 includes an atomic interferometer 502, which includes a pulse generator 503 for generating one or more pulse beams 504, 505, 506 defined by corresponding pulse characteristics to place atoms into a superposition and rearrange the atoms to measure the interference of the atoms, and to calculate the inertial quantity based on the measured interference. Here, the interference is measured in the form of atomic counts provided by counters 507 / 508.

[0118] In addition, an auxiliary acceleration sensor 510 (such as a MEMS or fiber optic sensor) is provided, which is configured to measure acceleration transverse to pulse beams 504, 505, 506. The control system 511 is configured to increase the pulse duration of pulse beams 504, 505, 506 to compensate for placement and recombination attenuation caused by the measured acceleration transverse to one or more beams in the beam.

[0119] Figure 6A method 600 for measuring inertial quantities along a sensing axis as described above is presented. The method includes: generating 601 an unguided cloud of atoms; and generating 602 one or more pulsed beams defined by corresponding pulse characteristics to place atoms into a superposition and recombination arrangement. Method 600 then measures 603 the interference of the atoms and calculates 604 the inertial quantity based on the measured interference. To improve sensitivity, method 600 uses an auxiliary accelerometer to measure 605 the acceleration of one or more pulsed beams transverse to the pulsed beams and increases 606 the pulse duration of the pulsed beams to compensate for attenuation in placement and recombination caused by the measured acceleration of one or more beams transverse to the beams. It should be noted that the steps in method 600 do not need to be performed in a given order. For example, acceleration can be measured in step 605 before generating atoms in step 601, and then the pulse duration can be increased 606.

[0120] It should be noted that the examples in this paper involve a three-pulse BS1-M-BS2 Mach-Zehnder interferometer setup, but many other atomic interferometry schemes exist that can use different numbers of pulses and non-standard splitting ratios. In these cases, acceleration transverse to the beam can also be measured, and the pulse duration of the beam can be increased to compensate for placement and recombination attenuation caused by the measured acceleration.

[0121] Adjusting the timing

[0122] As mentioned above, the pulse duration can be adjusted to compensate for the effects of lateral acceleration. However, it has been found that increasing the pulse duration exacerbates the device symmetry problem. More specifically, as... Figure 9a As shown, the time-varying two-photon Rabi frequency of the entire interferometer sequence is time-symmetric about the midpoint time of the interferometer. Time symmetry also exists between beam splitter 102 and mirror 103, and between mirror 103 and the second beam splitter 104.

[0123] Figure 8 The steps of an idealized interferometer utilizing pulses of infinitely short duration are illustrated with a Bloch sphere 800, and the importance of using a time-symmetric interferometer sequence is explained. Atoms are initially prepared in |1> at the poles of the Bloch sphere 801, and a first beam splitter 102 applies a rotation (i.e., a superposition state) to the equator 802. During the free precession time, this state rotates along the equator to state 803. The rotation angle along the equator depends on the free precession time (which can be chosen relatively arbitrarily) and the longitudinal atomic velocity.

[0124] Mirror pulse 103 then applies a π rotation about an axis in the equatorial plane to state 804, and then, in the next free precession cycle, the state rotates back to state 802 along the equator. In the absence of longitudinal acceleration, the rotation angles are equal because the first free precession time equals the second free precession time, meaning the state should arrive exactly at 802. When non-zero longitudinal acceleration is present, the azimuth rotation angle differs from the case of zero longitudinal acceleration because the atomic velocities change during the interferometer operation. Therefore, the state does not arrive exactly at 802, but rather at an azimuth angle that differs from 802 by a quantity given by Equation 7. In both cases, the final angle is independent of the longitudinal atomic velocity because the first free precession time equals the second free precession time. Finally, at the end of the second free precession, the second beam splitter 104 rotates the final state 90 degrees about an axis in the equatorial plane. The interference (i.e., the number of atoms in state 801) at this point indicates the acceleration of the device.

[0125] In a practical interferometer with pulses of finite duration, additional azimuth precessions (rotations about the z-axis of the Bloch sphere) exist during the first beamsplitter pulse 102 and the second beamsplitter pulse 104, respectively. These additional precessions depend on the two-photon Rabi frequency, pulse duration, and longitudinal atom velocity during each pulse. In a time-symmetric interferometer, the precession during the first beamsplitter 102 cancels out the precession during the final beamsplitter 104. However, it has been found that when the two-photon Rabi frequencies during pulses 102 and 104 are not equal, these precessions no longer cancel each other out, meaning the interferometer phase will depend on the initial longitudinal atom velocity.

[0126] As mentioned above, extending any or all pulses according to the lateral acceleration helps compensate for the reduced beam strength and provides ideal rotation. However, it has been found that extending the pulses increases temporal asymmetry. More specifically, the length of the first beamsplitter pulse 102 is different from the length of the second beamsplitter pulse 104. Therefore, the azimuth precession during pulse 102 will not cancel out the azimuth precession occurring during pulse 104, meaning that the interferometer will accumulate additional phase. This phase depends on the initial atomic velocity and will introduce a bias in inertial measurements. We call this phase the bias phase.

[0127] This time asymmetry degrades the performance of the interferometer in two ways:

[0128] • It reduces fringe contrast. The velocity distribution of the atomic cloud is non-uniform, so each atom in the cloud accumulates a different velocity-dependent phase shift at the interferometer's output. When the number at the output is measured, this phase shift is averaged, thus reducing fringe contrast.

[0129] • It can lead to unknown systemic biases, thereby reducing the accuracy of acceleration measurements.

[0130] Increasing the duration of each pulse to compensate for the decrease in laser intensity increases the pulse area, thereby maximizing the fidelity of each pulse. However, this does not restore the interferometer's temporal asymmetry; in fact, it significantly exacerbates it. Therefore, increasing the pulse duration of each pulse is insufficient to restore the peak interferometer's performance.

[0131] It has been found that adjusting the timing of interferometer pulses can resolve the problem exacerbated by increasing pulse duration by reducing (or completely eliminating) the bias phase related to atomic velocities. Timing adjustment can also be described as restoring the symmetry of the interferometer.

[0132] Therefore, this study employs both increasing pulse duration and adjusting pulse timing to maintain insensitivity to initial atomic velocities while mitigating the reduction in laser intensity caused by lateral displacement of atoms in the beam.

[0133] In other words, besides changing the pulse duration to compensate for the variation in the two-photon Rabi frequency amplitude, the pulse timing can also be adjusted to improve the interferometer's contrast. Figure 7a ), and reduce unnecessary phase shifts caused by changes in the initial longitudinal velocity of the atomic cloud ( Figure 7b This can also be used to control the measurement scaling factor of a cold atom sensor, where the measurement scaling factor is defined as the ratio between the measured phase of the interference fringes (Equation (7)) and the longitudinal acceleration a (or the inertial quantity that the atomic interferometer is configured to measure).

[0134] For example, the time increment dt between the first interferometer pulse and the second interferometer pulse can be used, where dt depends on the laser intensity curve and the transverse acceleration a measured by the classical auxiliary sensor. ┴ (t). This is calculated using the average two-photon Rabi frequency during each pulse (Equation (11)). Specifically, ,in These are the amplitudes of the two-photon Rabi frequencies during the first and second beamsplitter pulses, calculated using formula (11), respectively. This pulse timing adjustment was chosen to minimize the interferometer phase as a function of the longitudinal atomic momentum p. z Changes in the function ( Figure 7b This improves the contrast of the interferometer. Figure 7a This is because atoms with different longitudinal momentum leave the interferometer at the same phase, thus preventing the interference fringes from "fading." Another advantage of this method is that it provides robustness to changes in the initial longitudinal atomic momentum and any asymmetry in their longitudinal velocity distribution.

[0135] Another way to explain the importance of pulse timing adjustments is that they increase the spatial overlap between atomic wave packets at the end of the last pulse in the interferometer sequence. Increasing the pulse duration without adjusting the pulse timing reduces the spatial overlap between atomic wave packets at the end of the interferometer pulse sequence. Pulse timing adjustments are necessary to address this problem.

[0136] Figure 9 illustrates the proposed gimbal control scheme through pulse duration and timing adjustment. (a) Depicts the ideal three-pulse interferometer sequence ( All three pulses have the same two-photon Rabi frequency amplitude. And has equally spaced time midpoints. , making (b) Depicts a conventional interferometer sequence of attenuation, where the lateral displacement of atoms causes the two-photon Rabi frequency amplitude of each pulse in the pulse ( (c) Describes the proposed gimbal control scheme by adjusting the pulse timing and duration. By adjusting the midpoint of the time ( ) makes And adjust the duration of the pulse ( The disclosed method can mitigate the lateral displacement of atoms. This scheme improves the contrast of interference fringes and ensures that the interferometer remains insensitive to the initial longitudinal velocity of atoms.

[0137] We can quantify the effect of interferometer asymmetry through analytical methods. In the limit where two-photon detuning is much smaller than the two-photon Rabi frequency, The interferometer bias phase of a single atom at the end of the pulse sequence can be written as:

[0138] (13)

[0139] in, The two-photon Rabi frequency of the first and second beamsplitter pulses (proportional to the laser intensity felt by the atoms during these pulses). For velocity-dependent two-photon detuning, and time interval Given by the following formula

[0140] (14)

[0141] The durations of the first and second beam splitter pulses are typically the same under normal conditions without pan-tilt control. The duration of the central mirror pulse, and The midpoint of the time interval for each pulse. Any asymmetry in the pulse timing is quantified and is typically set to zero; it can be made non-zero by adjusting the pulse duration and / or pulse timing. Product (For i = BS1, M, or BS2) is the pulse area of ​​a given pulse. Ideally, for two beam splitters (BS1, BS2), it should be... And for mirror (M) it should be .

[0142] First, assume that the time interval between the midpoints of BS1 and M is equal to the time interval between the midpoints of M and BS2. Then, if the two-photon Rabi frequency and pulse duration of each beam splitter pulse are the same, then... Furthermore, there is no bias phase. However, due to the reduced intensity of light applied to the atoms caused by the lateral displacement of atoms between pulses, the two-photon Rabi frequencies of the first and second beamsplitter pulses will no longer be equal. This means that the interferometer bias phase is no longer zero and depends on the two-photon detuning. This, and therefore affects the atomic velocity.

[0143] This velocity-dependent bias phase can reduce the interferometer's contrast. This is because the interferometer's output is determined by... Given, among which It's contrast, and This represents the average value taken over the entire atomic cloud, which contains atoms with velocity distributions and therefore biased phases. Averaging sinusoidal signals with different phases yields a sinusoidal signal with reduced amplitude.

[0144] Increasing the duration of each pulse will restore the pulse area of ​​each beam splitter to its original value. This improves pulse fidelity, but at the cost of increasing the amplitude of the bias phase, becoming...

[0145] ,

[0146]

[0147] (15)

[0148] However, if we take the pulse End and Pulse Increase the time between starts This timing adjustment will then cancel out the bias phase of all atoms.

[0149] It is important to note that adjusting pulse timing implies changing the start or end of the pulse, or both. For example, as mentioned above, adjusting pulse timing may involve time-displacement of the pulse by moving the midpoint of the time along the time axis while keeping the pulse duration constant. An equivalent result, the free precession time, can be obtained by calculating the time difference between the previous pulse and the current pulse and adjusting that time difference by displacing one or both pulses. In this sense, the method can be said to involve adjusting the free precession time of atoms between pulse beams to reduce phase shift caused by changes in the initial longitudinal velocity of the atoms. As shown herein, the first free precession time between the first beam splitter and the mirror differs from the second free precession time between the mirror and the second beam splitter. In some embodiments, the first free precession time is shorter than the second free precession time.

[0150] In one example, the method involves keeping the first beam splitter pulse (timing and duration) constant and adjusting the duration and timing of the mirror pulse and the second beam splitter pulse. It is important to note that the calculation of the above time adjustment is independent of the Rabi frequency of the mirror pulse, because errors in the intermediate pulses simply mean that inaccurately reflected atoms were not detected.

[0151] Adjust laser intensity

[0152] The laser intensity can be adjusted during each pulse to compensate for the effects of the transverse motion of atoms in the laser beam. As shown in Equation (11), the amplitude of the two-photon Rabi frequency varies with time due to transverse acceleration. By calculating this reduction during each pulse, the peak laser intensity I0 can be tilted upwards during each pulse, keeping the amplitude of the two-photon Rabi frequency constant. This will maintain the temporal symmetry and fidelity of each optical pulse and minimize unwanted interferometer phase shifts caused by intensity variations during each pulse.

[0153] Computer implementation

[0154] It should be noted that the methods disclosed herein can be implemented by computer systems, which may include edge computing, cloud computing, local (desktop / laptop / tablet) computing, computing performed by remote or local servers, virtual machines, and hardware solutions such as field-programmable gate arrays, application-specific circuits, and other platforms.

[0155] In this sense, a computer system may include a processor (as described above) that receives accelerometer data from an auxiliary accelerometer indicating accelerations transverse to one or more of a plurality of pulse beams. The pulse beams are defined by corresponding pulse characteristics to place atoms into a superposition and rearrange atoms to measure atomic interference. The processor then increases the pulse duration of the pulse beams and / or adjusts the timing and intensity to compensate for attenuation caused by the measured accelerations transverse to one or more beams in the beam.

[0156] Those skilled in the art will understand that many changes and / or modifications can be made to the embodiments described above without departing from the broad overall scope of this disclosure. Therefore, these embodiments should be considered illustrative rather than restrictive in all respects.

Claims

1. An inertial sensor for measuring an inertial quantity along a sensing axis, the sensor comprising: an atomic interferometer comprising a pulse generator for generating one or more pulsed light beams defined by respective pulse durations to place atoms into a superposition and recombine the atoms to measure an interference of the atoms and compute the inertial quantity based on the measured interference; an auxiliary acceleration sensor configured to measure an acceleration transverse to one or more of the pulsed light beams; and a control system configured to: compute a transverse shift of the atoms relative to the pulsed light beams caused by the measured acceleration transverse to the one or more of the light beams; increase the pulse durations to compensate for a reduced beam intensity applied to the atoms due to the transverse shift; and adjust pulse timing to reduce a phase shift caused by an initial longitudinal velocity of the atoms.

2. The sensor of claim 1, wherein the atomic interferometer comprises: an atomic source for providing the atoms moving relative to the sensing axis; the pulsed light beams are configured to: place the atoms into a superposition of a first state and a second state, wherein the first state is associated with a first path and the second state is associated with a second path; apply a mirror operation to the atoms between the placing and the recombining; and recombine the first state and the second state to produce an interference between the first state and the second state; a measurement system for measuring a physical effect indicative of the interference; and a processor for computing the inertial quantity based on the measured physical effect.

3. The sensor of any preceding claim, wherein the inertial quantity is a linear acceleration or a rotation.

4. The sensor of any preceding claim, wherein measuring the physical effect comprises measuring a number of atoms in different superposition states.

5. The sensor according to any one of the preceding claims, wherein, Increasing the pulse durations comprises applying an upper limit to the pulse durations.

6. The sensor of claim 5, wherein the atoms have a velocity distribution and the upper limit is related to a pulse duration for which a threshold number of the atoms can still interact with the pulse.

7. The sensor of claim 5 or 6, wherein the upper limit is set by a peak two-photon Rabi frequency of the sensor and a longitudinal velocity width of the atoms.

8. The sensor of any preceding claim, wherein increasing the pulse durations comprises: computing an attenuation as one or more pulse adjustment factors relating an ideal interaction of the atoms with the pulsed light beams to a predicted interaction of the atoms with the pulsed light beams under the transverse shift; and increasing the pulse durations by the one or more adjustment factors.

9. The sensor of claim, wherein the ideal interaction and the predicted interaction are represented by corresponding two-photon Rabi frequencies.

10. The sensor of any one of the preceding claims, wherein the pulse duration is increased differently for each of the pulsed light beams by calculating the attenuation as a function of time.

11. The sensor of any one of the preceding claims, wherein the attenuation is a function of the interrogation time.

12. The sensor of any one of the preceding claims, wherein the auxiliary acceleration sensor is configured to measure the acceleration transverse to one or more of the pulsed light beams multiple times during the atom’s travel through the atomic interferometer; and the control system is configured to use the corresponding measured accelerations to compensate for attenuation at each of the pulsed light beams.

13. The sensor of any one of the preceding claims, wherein the pulsed light beams place the atom into the superposition and recombine the atom by exciting a Rabi or Raman transition.

14. The sensor of any one of the preceding claims, wherein the superposition is a superposition of two states with different momenta, the two states being separated by an integer number of two-photon recoil intervals.

15. The sensor of any one of the preceding claims, wherein the control system is further configured to adjust pulse characteristics other than pulse duration to perform arbitrary further manipulations of the atom’s motional state.

16. The sensor of claim 15, wherein the control system is further configured to adjust the pulse timing by increasing or decreasing the amount of time between any two or more pulses to compensate for the reduced beam intensity applied to the atom due to the transverse offset.

17. The sensor of claim 16, wherein the increase in the amount of time between the pulses is calculated using a difference between inverse two-photon Rabi frequencies of a first beam splitter and a second beam splitter, respectively.

18. The sensor of claim 16 or 17, wherein adjusting the pulse timing includes maintaining the duration and timing of the pulses that place the atom into the superposition and adjusting the duration and timing of the pulses that apply the mirror operation and recombine the first and second states.

19. The sensor of any one of the preceding claims, wherein, the control system is further configured to adjust the intensity of the one or more light beams to compensate for the reduced beam intensity applied to the atom due to the transverse offset.

20. A method for measuring an inertial quantity along a sensing axis, the method comprising: generating a cloud of atoms; generating one or more pulsed light beams, the one or more pulsed light beams being defined by respective pulse durations to place the atoms into a superposition and recombine the atoms; measuring an acceleration transverse to one or more of the pulsed light beams using an auxiliary acceleration sensor; calculating a transverse offset of the atoms relative to the pulsed light beams caused by the measured acceleration transverse to the one or more of the pulsed light beams; and increasing the pulse duration of the pulsed light beams to compensate for reduced beam intensity applied to the atoms due to the lateral shift; adjusting pulse timing to reduce phase shifts caused by initial longitudinal velocity of the atoms; measuring interference of the atoms; and calculating the inertial mass based on the measured interference.

21. A computer-implemented method for controlling an atomic interferometer, the method comprising: receiving, from an auxiliary acceleration sensor, acceleration sensor data indicative of acceleration transverse to one or more of a plurality of pulsed light beams, the one or more pulsed light beams defined by respective pulse durations to place the atoms into superposition and recombine the atoms to measure interference of the atoms; calculating a lateral shift of the atoms relative to the pulsed light beams caused by the measured acceleration transverse to the one or more of the light beams; increasing the pulse duration of the pulsed light beams to compensate for reduced beam intensity applied to the atoms due to the lateral shift; and adjusting pulse timing to reduce phase shifts caused by initial longitudinal velocity of the atoms.

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