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arXiv:1210.5656 · Physical Review E

Fidelity of the quantum δ -kicked accelerator

Rajendra K. Shrestha, Sandro Wimberger, Jiating Ni, Wa Kun Lam, G. S. Summy

Published Feb 27, 2013• 17 citations
arXivHTMLPDF

Abstract

The sensitivity of the fidelity in the kicked rotor to an acceleration is experimentally and theoretically investigated. We used a Bose-Einstein condensate exposed to a sequence of pulses from a standing light wave followed by a single reversal pulse in which the standing wave was shifted by half a wavelength. The features of the fidelity "spectrum" as a function of acceleration are presented. This work may find applications in the measurement of temperature of an ultracold atomic sample.

DOI
10.1103/physreve.87.020902

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•Jan 1, 2009•0 citations
The sensitivity of the fidelity in the kicked rotor to an acceleration is experimentally and theoretically investigated. We used a Bose-Einstein condensate exposed to a sequence of pulses from a standing light wave followed by a single reversal pulse in which the standing wave was shifted by half a wavelength. The features of the fidelity "spectrum" as a function of acceleration are presented. This work may find applications in the measurement of temperature of an ultracold atomic sample.
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.
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.
We report measurements of the early-time momentum diffusion for the atom-optical delta-kicked rotor. In this experiment a Bose-Einstein condensate provides a source of ultracold atoms with an ultranarrow initial momentum distribution, which is then subjected to periodic pulses (or "kicks") using an intense far-detuned optical standing wave. We characterize the effect of varying the effective Planck's constant for the system, while keeping all other parameters fixed. The observed behavior includes both quantum resonances (ballistic energy growth) and antiresonances (re-establishment of the initial state). Our experimental results are compared with theoretical predictions.
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.
We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.
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.