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Journal of Physics B Atomic Molecular and Optical Physics

Effects of finite momentum width on the reversal dynamics in a BEC based atom optics δ -kicked rotor

Jay Mangaonkar, Chetan Vishwakarma, S. Sagar Maurya, Sumit Sarkar, Jamie MacLennan, Pranab Dutta, Umakant D. Rapol

Published Oct 7, 2020• 9 citations
Publisher

Abstract

Abstract This experimental work demonstrates the importance of finite-width effects in the evolution of a quantum system, where the results deviate considerably from the plane wave approximation even for an initial state with a very narrow momentum width i.e a Bose–Einstein condensate. The system under consideration is an atom optics δ -kicked rotor for which a fidelity based measurement has been proposed to possess a rapid scaling of sensitivity ( N −3 ) with pulse number N . Although attractive, we demonstrate that this scaling does not hold in the regime where the momentum selectivity of the pulse sequence becomes significantly smaller than the momentum width of the initial state. Additionally, the momentum distribution post kicking shows a lattice-phase dependent intra-order and inter-order asymmetry in the diffracted orders. The intra-order asymmetry, in which no net momentum current is present, is a previously unreported type of effect. For a two pulse case, the inter-order asymmetry signal is found to be about five times more sensitive to the resonance than the initial state fidelity. Both of these asymmetries provide a zero-crossing signal which can be used to diagnose any undesirable lattice phase offset at resonant and off-resonant pulse periods.

DOI
10.1088/1361-6455/abbf43

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Abstract This experimental work demonstrates the importance of finite-width effects in the evolution of a quantum system, where the results deviate considerably from the plane wave approximation even for an initial state with a very narrow momentum width i.e a Bose–Einstein condensate. The system under consideration is an atom optics δ -kicked rotor for which a fidelity based measurement has been proposed to possess a rapid scaling of sensitivity ( N −3 ) with pulse number N . Although attractive, we demonstrate that this scaling does not hold in the regime where the momentum selectivity of the pulse sequence becomes significantly smaller than the momentum width of the initial state. Additionally, the momentum distribution post kicking shows a lattice-phase dependent intra-order and inter-order asymmetry in the diffracted orders. The intra-order asymmetry, in which no net momentum current is present, is a previously unreported type of effect. For a two pulse case, the inter-order asymmetry signal is found to be about five times more sensitive to the resonance than the initial state fidelity. Both of these asymmetries provide a zero-crossing signal which can be used to diagnose any undesirable lattice phase offset at resonant and off-resonant pulse periods.
This thesis deals with an investigation of the chaotic dynamics of an atom optics δ-kicked rotor (AOKR) system, a paradigm of classical and quantum chaos. The AOKR rotor is realized by subjecting a Bose-Einstein condensate (BEC) of ⁸⁷Rb atoms to a periodic potential. The potential in the form of a standing wave, obtained from a far detuned laser beam is turned on and off periodically in time, producing short pulses (kicks) of laser light. For certain values of the period between the kicks, resonant effects known as quantum resonances are observed that are purely quantum effects. Quantum resonances have been examined in the AOKR for a series of kicks. For large number of kicks, the width of these resonances have been shown to become narrow. Higher order resonances corresponding to fractional Talbot times have been observed in the system. These quantum resonant effects have been found to depend sensitively on the initial velocity of the atoms. The first three primary resonances have been studied in detail, by measuring the momentum distribution and the kinetic energy of the atoms, for two and four kicks. A sinusoidal dependence of the energy on the initial momentum has been observed for two kicks. By increasing the number of kicks, the system becomes extremely sensitive to the initial momentum of the atoms. For four kicks, a more complex behavior is observed in the system energy. A scheme for investigating Loschmidt time reversal of chaotic dynamics of the atomic deBroglie waves have been described in the AOKR system. It has been demonstrated that the initial wave function of an ensemble of ultracold atoms is restored, after a series of delta-kicks in what is essentially a multiple beam interferometry experiment. During the process, the evolution of the system for a fraction of the atoms with a very small initial momentum is reversed, which results in a narrowing of the momentum distribution. It is hoped that the research presented in this thesis will significantly contribute to the understanding of the connection between the classical and quantum worlds.
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 experimentally investigate the sub-Fourier behavior of a δ-kicked-rotor resonance by performing a measurement of the fidelity or overlap of a Bose-Einstein condensate exposed to a periodically pulsed standing wave. The temporal width of the fidelity resonance peak centered at the Talbot time and zero initial momentum exhibits an inverse cube pulse number (1/N3)-dependent scaling compared to a 1/N2 dependence for the mean energy width at the same resonance. A theoretical analysis shows that for an accelerating potential the width of the resonance in acceleration space depends on 1/N3, a property which we also verify experimentally. Such a sub-Fourier effect could be useful for high precision gravity measurements.
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.
We investigate analytically and numerically early-time momentum diffusion rates for the delta-kicked rotor across the quantum to classical transition, i.e., as increased total system action produces more macroscopic dynamics. For sufficiently narrow initial momentum distributions we find a rich structure of resonances in these diffusion rates as a function of the effective Planck's constant. Our study is set in the physical context of the atom optics kicked rotor, and numerical simulations confirm that the resonances persist with kicks of finite duration and with other typical experimental imperfections, such as spontaneous emission noise. Our results should be testable in experiments where narrow initial momentum distributions are prepared using, for example, velocity selective Raman transitions or Bose-Einstein condensates.
This thesis reports on the experimental investigation of several applications of the atom-optical quantum kicked rotor (AOQKR) using a Bose-Einstein condensate (BEC) of 87Rb atoms. The AOQKR was achieved by exposing a BEC to short periodic pulses from a horizontal optical standing wave formed from the interference of two off-resonant laser beams. In the first set of experiments the fidelity or overlap between the kicked rotor states with a reference state was studied. The fidelity resonance widths in pulse period and in acceleration were found to scale as the inverse cube of the kick numbers, a sub-Fourier behavior with possible application in precision measurement experiments. The sensitivity of the fidelity to acceleration was experimentally and theoretically investigated and found to depend on the magnitude and direction of the applied acceleration. The asymmetry between positive and negative acceleration was found to be related to the temperature of the atomic sample. In the second set of experiments, the phenomenon of a quantum ratchet (which is manifested by a directed current of particles in the absence of a net bias force) both at resonance and away from resonance was studied. It was confirmed that the current direction can be controlled by changing experimental parameters which leave the underlying symmetries of the system unchanged. It was demonstrated that this behavior can be understood using a single variable containing many of the experimental parameters. These experiments confirmed that such a ratchet behavior can under certain circumstances be the same in both the true classical and quantum regimes. The final application of the AOQKR discussed in this thesis is the quantum accelerator mode. Both the formation and decay mechanism of these modes were studied.