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arXiv:1810.04218

Mach-Zehnder atom interferometer. Quantum and Doppler corrections caused by the finite pulses' durations

B. Dubetsky

Published Oct 9, 2018• 1 citation
arXivHTMLPDF

Abstract

A new approach to the theory of atoms' interaction with chirped Raman pulses is developed. When the pulses have sufficiently close effective wave lengths, which are smaller than the atomic cloud size, equations for the family of the matrix elements of the atomic density matrix in the Wigner representation are derived. The solution, involving linear (in the pulse duration) phase corrections, is obtained for the rectangular pulse. The interferometric part of the atoms' excitation is calculated.

DOI
10.48550/arxiv.1810.04218

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A new approach to the theory of atoms' interaction with chirped Raman pulses is developed. When the pulses have sufficiently close effective wave lengths, which are smaller than the atomic cloud size, equations for the family of the matrix elements of the atomic density matrix in the Wigner representation are derived. The solution, involving linear (in the pulse duration) phase corrections, is obtained for the rectangular pulse. The interferometric part of the atoms' excitation is calculated.
The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where such quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.
It is proposed to use rectangular Raman pulses for the technique of sequential large momentum transfer. It is shown that the small parameters that make it possible to use this technology for precision atom interferometry can be 40--200 times smaller than in the case of the Bragg regime. It is predicted that in the case of a nonequidistant timing of auxiliary pulses, one can observe oscillations in time of the interference picture with a period inversely proportional to the recoil frequency. Such an observation would be confirmation that Mach-Zehnder atom interference is a phenomenon caused by the quantization of the atomic center-of-mass motion. This effect is calculated for any shape of pulses. One can observe it in the Bragg regime as well. It is proposed to use noncontinuous composite Raman pulses as auxiliary beam splitters so that the effective Rabi frequency remains unchanged for the entire process. The gravity phase of an atomic interferometer is calculated for any shape, duration, and timing of Raman pulses, including the Bragg regime. The phase corrections caused by the finite pulses' durations are also calculated for the rectangular Raman pulse shape.
Light-pulse atom interferometers serve as tools for high-precision metrology and are targeting measurements of relativistic effects. This development is facilitated by extended interrogation times and large-momentum-transfer techniques generating quantum superpositions of both interferometer arms on large distances. Due to the finite speed of light, diffracting light pulses cannot interact simultaneously with both arms, inducing phase perturbations that compromise the accuracy of the sensor -- an effect that becomes progressively important as spatial separations increase. For a consistent framework, we develop a theory for finite-speed-of-light effects in atom interferometers alongside with other relativistic effects such as the mass defect. Our analysis shows that their magnitude depends crucially on the diffraction mechanism and the specific interferometer geometry. We demonstrate that the velocity of the atomic cloud at the mirror pulse of a Mach-Zehnder interferometer is less critical than the precise tuning of the lasers for resonant diffraction. Finally, we propose an experiment to test our predictions based on recoilless transitions and discuss mitigation strategies to reduce the bias in gravimetric applications.
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.
Abstract In this article we present a new representation-free formalism, which can significantly simplify the analysis of interferometers comprised of atoms moving in time-dependent linear potentials. We present a methodology for the construction of two pairs of time-dependent functions that, once determined, lead to two conditions for the closing of the interferometer, and determine the phase and the contrast of the resultant interference. Using this new formalism, we explore the dependency of the interferometer phase on the interferometer time T for different atom interferometers. By now, it is well established that light pulse atom interferometers of the type first demonstrated by Kasevich and Chu (1991 Phys. Rev. Lett. 67, 181–4; 1992 Appl. Phys. B 54, 321–32), henceforth referred to as Mach–Zehnder (MZ) atom interferometers, have a phase scaling as T 2. A few years ago, McDonald et al (2014 Europhys. Lett. 105, 63001) have experimentally demonstrated a novel type of atom interferometer, referred to as the continuous-acceleration bloch (CAB) interferometer, where the phase reveals a mixed scaling which is governed by a combination of T 2 and T 3. Moreover, we have recently proposed a different type of atom interferometer (Zimmermann et al 2017 Appl. Phys. B 123, 102), referred to as the T 3-interferometer, which has a pure T 3 scaling, as demonstrated theoretically. Finally, we conclude that the CAB interferometer can be shown to be a hybrid of the standard MZ interferometer and the T 3-interferometer.
We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.