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arXiv:2003.02042 · Physical Review A

Perturbative operator approach to high-precision light-pulse atom interferometry

Christian Ufrecht, Enno Giese

Published May 8, 2020• 26 citations
arXivHTMLPDF

Abstract

Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like stray magnetic fields or blackbody radiation. Improving the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here we present a systematic operator expansion to obtain phase shift and contrast analytically in powers of a perturbation potential. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects.

DOI
10.1103/physreva.101.053615

Related papers

Reply to “Comment on ‘Perturbative operator approach to high-precision light-pulse atom interferometry' ”

Christian Ufrecht, Enno Giese

Recently, we introduced [C. Ufrecht and E. Giese, Phys. Rev. A 101, 053615 (2020)] a technique to calculate the phase of light-pulse atom interferometers caused by the presence of perturbation potentials and underlined its power by an illustrative example. In the preceding Comment [B. Dubetsky, Phys. Rev. A 102, 027301 (2020)], it was pointed out that other, less idealized situations could have been calculated as well. Our Reply emphasizes that our method is correct, the results from our example can be trivially generalized to other perturbations, and intricate effects of local environments can be even more prominent but also treated by our technique.

Physical Review A•Aug 20, 2020•1 citation

Theoretical approach to high-precision atom interferometry

Christian Ufrecht

The wave properties of matter in quantum mechanics first postulated by de Broglie in 1923 as well as Einstein’s theory of general relativity have radically changed our perception of the world at the beginning of the twentieth century. While each theory is extremely successful and well tested within its range of validity, a unification of both theories has so far resisted any attempt. However, the advances in precision of modern matter-wave interferometers have paved the way to designing experiments at the interface of gravity and quantum mechanics. Indeed, quantum mechanical devices are on the brink of becoming sensitive enough to challenge predictions of general relativity such as the weak equivalence principle or set bounds on alternative gravitational theories. Reaching sensitivities required for these experiments necessitates a careful assessment of deleterious effects some of which might be atom-atom interactions or the influence of the gravitational potential of the laboratory setup itself. Estimation of the size of such effects calls for refined theoretical tools for the description of light-pulse atom interferometry which is the subject of the present thesis.

•Jan 1, 2019•7 citations

Phase shift formulation for N-light-pulse atom interferometers: application to inertial sensing

Malo Cadoret, Nassim Zahzam, Yannick Bidel +4 more

We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift where the leading coefficient in the phase terms up to T^k dependences (k >= 0) in the time separation T between pulses, can be simply expressed in terms of a product between a Vandermonde matrix, and a vector characterizing the two-photon pulse sequence of the interferometer. This simple coefficient dependence of the phase shift reflects very well the atom interferometer's sensitivity to a specific inertial field in the presence of multiple gravito-inertial effects. Consequently,we show that this formulation is well suited when looking for selective atomic sensors of accelerations, rotations, or photon recoil only, which can be obtained by simply zeroing some specific coefficients. We give a theoritical application of our formulation to the photon recoil measurement.

arXiv:1701.04629•Journal of the Optical Society of America B•Jul 25, 2016•11 citations

Beyond the semiclassical approximation in atom interferometry

W. LaRow, Mark Edwards, Charles A. Sackett

We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semiclassical approximation. The calculation benefits from the use of generalized coherent states for a basis. We find that the form of the semiclassical approximation remains valid to first order in the anharmonic perturbation, but that phase differences arise because the trajectory of a quantum wave packet will generally deviate from that of a classical particle. The quantum correction to the phase is a factor ${\ensuremath{\ell}}^{2}/{A}^{2}$ smaller than the semiclassical perturbation itself, where $\ensuremath{\ell}$ is the quantum harmonic-oscillator lengthscale, and $A$ is the classical amplitude of the motion. We provide analytical results for one-dimensional perturbations of power 3 through 6 in the position coordinate.

arXiv:2410.08040•Physical Review A•Mar 19, 2025•1 citation

Analytical framework for dynamic light pulse atom interferometry at short interrogation times

Richard E. Stoner, David L. Butts, Joseph M. Kinast +1 more

High-precision inertial sensing demonstrations with light pulse atom interferometry have typically used Raman pulses having durations orders of magnitude shorter than the dwell time between interferometer pulses. Environmentally robust sensors operating at high-bandwidth will be required to operate at short (millisecond scale) dwell times between Raman pulses. In such an operational mode, the Raman pulse duration becomes an appreciable fraction of the dwell time between pulses. In addition, high-precision inertial sensing applications have typically been demonstrated in mildly dynamic or nondynamic environments having low rate of change of inertial input, ensuring that applied Raman pulses satisfy the Raman resonance condition. Application of nonresonant pulses will be inevitable in sensors registering time-varying inertial input. We present a diagrammatic technique for calculation of atomic output state populations for multipulse atom optics manipulations that explicitly account for the effects of finite pulse duration and finite Raman detuning effects on the laser-induced atomic phase. We analyze several atom interferometer sequences. We report accelerometer and gyroscope phase evolution for fixed Raman laser frequency difference incorporating corrections in powers of the ratio of pulse duration to time interval between interferometer pulses. Our accelerometer result agrees with other published results.

Journal of the Optical Society of America B•Sep 13, 2011•28 citations

Generalized gravity-gradient mitigation scheme

Christian Ufrecht

A major challenge in high-precision light-pulse atom interferometric experiments such as in tests of the weak equivalence principle is the uncontrollable dependency of the phase on initial velocity and position of the atoms in the presence of inhomogeneous gravitational fields. To overcome this limitation, mitigation strategies have been proposed, however, valid only for harmonic potentials or only for small branch separations in more general situations. Here we provide a mitigation formula for anharmonic perturbation potentials including local gravitational effects that vary on length scales much smaller than the spatial extent probed by the atoms and originate, e.g., from buildings that surround the experiment. Furthermore, our results are applicable to general interferometer geometries with arbitrary branch separation and allow for compensation of Coriolis effects in rotating reference frames.

arXiv:2102.02154•Physical Review A•Feb 3, 2021•6 citations
Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like stray magnetic fields or blackbody radiation. Improving the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here we present a systematic operator expansion to obtain phase shift and contrast analytically in powers of a perturbation potential. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects.
Recently, we introduced [C. Ufrecht and E. Giese, Phys. Rev. A 101, 053615 (2020)] a technique to calculate the phase of light-pulse atom interferometers caused by the presence of perturbation potentials and underlined its power by an illustrative example. In the preceding Comment [B. Dubetsky, Phys. Rev. A 102, 027301 (2020)], it was pointed out that other, less idealized situations could have been calculated as well. Our Reply emphasizes that our method is correct, the results from our example can be trivially generalized to other perturbations, and intricate effects of local environments can be even more prominent but also treated by our technique.
The wave properties of matter in quantum mechanics first postulated by de Broglie in 1923 as well as Einstein’s theory of general relativity have radically changed our perception of the world at the beginning of the twentieth century. While each theory is extremely successful and well tested within its range of validity, a unification of both theories has so far resisted any attempt. However, the advances in precision of modern matter-wave interferometers have paved the way to designing experiments at the interface of gravity and quantum mechanics. Indeed, quantum mechanical devices are on the brink of becoming sensitive enough to challenge predictions of general relativity such as the weak equivalence principle or set bounds on alternative gravitational theories. Reaching sensitivities required for these experiments necessitates a careful assessment of deleterious effects some of which might be atom-atom interactions or the influence of the gravitational potential of the laboratory setup itself. Estimation of the size of such effects calls for refined theoretical tools for the description of light-pulse atom interferometry which is the subject of the present thesis.
We report on an original and simple formulation of the phase shift in N-light-pulse atom interferometers. We consider atomic interferometers based on two-photon transitions (Raman transitions or Bragg pulses). Starting from the exact analytical phase shift formula obtained from the atom optics ABCD formalism, we use a power series expansion in time of the position of the atomic wave packet with respect to the initial condition. The result of this expansion leads to a formulation of the interferometer phase shift where the leading coefficient in the phase terms up to T^k dependences (k >= 0) in the time separation T between pulses, can be simply expressed in terms of a product between a Vandermonde matrix, and a vector characterizing the two-photon pulse sequence of the interferometer. This simple coefficient dependence of the phase shift reflects very well the atom interferometer's sensitivity to a specific inertial field in the presence of multiple gravito-inertial effects. Consequently,we show that this formulation is well suited when looking for selective atomic sensors of accelerations, rotations, or photon recoil only, which can be obtained by simply zeroing some specific coefficients. We give a theoritical application of our formulation to the photon recoil measurement.
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semiclassical approximation. The calculation benefits from the use of generalized coherent states for a basis. We find that the form of the semiclassical approximation remains valid to first order in the anharmonic perturbation, but that phase differences arise because the trajectory of a quantum wave packet will generally deviate from that of a classical particle. The quantum correction to the phase is a factor ${\ensuremath{\ell}}^{2}/{A}^{2}$ smaller than the semiclassical perturbation itself, where $\ensuremath{\ell}$ is the quantum harmonic-oscillator lengthscale, and AAA is the classical amplitude of the motion. We provide analytical results for one-dimensional perturbations of power 3 through 6 in the position coordinate.
High-precision inertial sensing demonstrations with light pulse atom interferometry have typically used Raman pulses having durations orders of magnitude shorter than the dwell time between interferometer pulses. Environmentally robust sensors operating at high-bandwidth will be required to operate at short (millisecond scale) dwell times between Raman pulses. In such an operational mode, the Raman pulse duration becomes an appreciable fraction of the dwell time between pulses. In addition, high-precision inertial sensing applications have typically been demonstrated in mildly dynamic or nondynamic environments having low rate of change of inertial input, ensuring that applied Raman pulses satisfy the Raman resonance condition. Application of nonresonant pulses will be inevitable in sensors registering time-varying inertial input. We present a diagrammatic technique for calculation of atomic output state populations for multipulse atom optics manipulations that explicitly account for the effects of finite pulse duration and finite Raman detuning effects on the laser-induced atomic phase. We analyze several atom interferometer sequences. We report accelerometer and gyroscope phase evolution for fixed Raman laser frequency difference incorporating corrections in powers of the ratio of pulse duration to time interval between interferometer pulses. Our accelerometer result agrees with other published results.
A major challenge in high-precision light-pulse atom interferometric experiments such as in tests of the weak equivalence principle is the uncontrollable dependency of the phase on initial velocity and position of the atoms in the presence of inhomogeneous gravitational fields. To overcome this limitation, mitigation strategies have been proposed, however, valid only for harmonic potentials or only for small branch separations in more general situations. Here we provide a mitigation formula for anharmonic perturbation potentials including local gravitational effects that vary on length scales much smaller than the spatial extent probed by the atoms and originate, e.g., from buildings that surround the experiment. Furthermore, our results are applicable to general interferometer geometries with arbitrary branch separation and allow for compensation of Coriolis effects in rotating reference frames.