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arXiv:1906.11420 · Physical Review A

Atom interferometry using δ -kicked and finite-duration pulse sequences

Boris Daszuta, Mikkel F. Andersen

Published Oct 5, 2012• 11 citations
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Abstract

We investigate an atom interferometer in which large momentum differences between the arms are obtained by using quantum resonances in the atom-optics $\ensuremath{\delta}$-kicked rotor. The interferometer can potentially measure the Talbot time (from which $h/m$ can be deduced) and the local gravitational field or can serve as a narrow velocity filter. We present an analytical analysis in the short pulse limit and a numerical investigation for finite pulse durations. The sensitivity of the interferometer is improved by a moderate violation of the short pulse limit. Remarkably simple relations predict the optimal pulse duration and the sensitivity of the interferometer.

DOI
10.1103/physreva.86.043604

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•Jan 1, 2009•0 citations
We investigate an atom interferometer in which large momentum differences between the arms are obtained by using quantum resonances in the atom-optics \ensuremathδ\ensuremath{\delta}\ensuremathδ-kicked rotor. The interferometer can potentially measure the Talbot time (from which h/mh/mh/m can be deduced) and the local gravitational field or can serve as a narrow velocity filter. We present an analytical analysis in the short pulse limit and a numerical investigation for finite pulse durations. The sensitivity of the interferometer is improved by a moderate violation of the short pulse limit. Remarkably simple relations predict the optimal pulse duration and the sensitivity of the interferometer.
We experimentally investigate a uniform pulse sequence in which atom interference is realized using the temporal matter-wave Talbot effect in an atom-optic kicked rotor system. Multi-path interference is obtained in asymmetric configuration with momentum differences up to $\pm$14 ℏk\hbar kℏk, by virtue of Talbot resonance. We experimentally confirm the theoretical limit placed on the performance of this interferometer by the finite momentum distribution of the initial ensemble consisting of a Bose-Einstein condensate (BEC). This limitation on sensitivity, occurring due to the degradation of resonant dynamics is also important in the realization of a one-dimensional continuous-time quantum walk in the implementation of quantum search algorithms.
We investigate the dynamics of the atom-optics δ-kicked rotor in the vicinity of quantum resonance. Although small deviations from resonant conditions lead to a negligible change in the momentum space probability density, they lead to a significant relative phase change between the different momentum states taking part in the dynamics. By adding a tailored pulse to the kicked rotor pulse sequence, one can measure the overlap between the resonant state and any other state, i.e. perform a fidelity measurement. Using this sequence, we predict a narrow peak around quantum resonance with a width that scales as 1/ N 3 with N being the number of pulses in the kicked rotor sequence. This method may be of interest to precision measurements, such as h / M .
We theoretically investigate a proposed scheme to use an atomic $\ensuremath{\delta}$-kicked rotor resonance for high-precision measurements of accelerations and the photon recoil frequency. Although the technique offers rapid scaling of the measurement sensitivity with pulse number, it also features a high sensitivity to initial atomic momentum. We find that for realistic atom sources, the momentum sensitivity significantly limits the achievable precision. We consider several different variations on the technique, but find similar limitations in all cases.
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.
Quantum sensors based upon atom interferometry typically rely on radio-frequency or optical pulses to coherently manipulate atomic states and make precise measurements of inertial and gravitational effects. An advantage of these sensors over their classical counterparts is often said to be that their measurement scale factor is precisely known and highly stable. However, in practice the finite pulse duration makes the sensor scale factor dependent upon the pulse shape and sensitive to variations in control field intensity, frequency, and atomic velocity. Here, we explore the concept of a temporal pulse origin in atom interferometry, where the inertial phase response of any pulse can be parameterized using a single point in time. We show that the temporal origin permits a simple determination of the measurement scale factor and its stability against environmental perturbations. Moreover, the temporal origin can be treated as a tunable parameter in the design of tailored sequences of shaped pulses to enhance scale factor stability and minimize systematic errors. We demonstrate through simulations that this approach to pulse design can reduce overall sequence durations while increasing robustness to realistic fluctuations in control field amplitude. Our results show that the temporal pulse origin explains a broad class of systematic errors in existing devices and enables the design of short, robust pulses which we expect will improve the performance of current and next-generation interferometric quantum sensors.
In this thesis we investigate quantum resonant effects in the atom-optical ὁ-kicked accelerator. Using Floquet analysis, we theoretically study the time evolution of quantum systems which have a classical counterpart that exhibits chaotic dynamics. We introduce quantum resonance and quantum antiresonance features of the quantum ὁ -kicked rotor by setting the pulse period to an integer multiple of the half-Talbot time. The model is generalised to the atom-optical ὁ -kicked accelerator by considering thermal alkali atoms subject to a periodically pulsed standing wave potential formed from counter-propagating laser beams. The dynamics of the momentum distribution is analysed by evaluating the momentum moments and momentum cumulants. We derive analytic solutions for these observables for the ultracold and thermal limiting cases, and observe fractional quantum resonant phenomena. Simulations have been developed to examine the time evolution for individual momentum eigenstates, which we use to construct a non-interacting finite temperature gas, based upon a Monte Carlo method. We investigate the temperature dependence of the ὁ-kicked rotor, neglecting gravitational effects, and show that the atomic dynamics is highly sensitive to the initial momentum width of the gas. A generalisation of the model to quantify the transition between the ultracold and thermal temperature regimes of the atom-optical ὁ -kicked accelerator is examined using linear regression analysis. High order quantum resonance features are found to be sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. We assess the dependence of the ὁ -kicked accelerator upon gravitational acceleration, quantifying the width of the high order quantum resonance features, which we use to assess the prospect for precision measurement using a finite temperature gas.