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Transport and resonances in kicked Bose-Einstein condensates

Ishan Talukdar

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Scope and Method of Study: A purpose of this research was to study the scaling behavior of resonances of a periodically kicked quantum system. Specifically, a model known as a quantum delta-kicked rotor (QDKR) was implemented with a 87 Rb Bose-Einstein Condensate. Two variants of this system, a quantum delta-kicked accelerator (QDKA) and a quantum ratchet, were also realized experimentally and used to study quantum transport. Furthermore, experiments were undertaken to introduce mean-field interactions in these systems through an Optical Feshbach resonance.

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Scope and Method of Study: The purpose of this research was to experimentally study quantum dynamics of systems whose classical dynamics are chaotic. Quantum delta-kicked systems such as kicked rotor and kicked accelerator were used. The cold non condensed atoms were kicked first to realize the kicked accelerator. Among the objectives were the realization of resonances of the kicked accelerator and associated phenomena of quantum accelerator modes using a Bose-Einstein Condensation (BEC). One of the major achievements of the work in this thesis was the creation of the quantum delta-kicked rotor and its associated resonances to realize a quantum ratchet. The properties of the ratchet were studied in detail.

•Jan 1, 2008•1 citation

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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.

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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.

•Jan 1, 2012•1 citation
Scope and Method of Study: A purpose of this research was to study the scaling behavior of resonances of a periodically kicked quantum system. Specifically, a model known as a quantum delta-kicked rotor (QDKR) was implemented with a 87 Rb Bose-Einstein Condensate. Two variants of this system, a quantum delta-kicked accelerator (QDKA) and a quantum ratchet, were also realized experimentally and used to study quantum transport. Furthermore, experiments were undertaken to introduce mean-field interactions in these systems through an Optical Feshbach resonance.
Scope and Method of Study: The purpose of this research was to experimentally study quantum dynamics of systems whose classical dynamics are chaotic. Quantum delta-kicked systems such as kicked rotor and kicked accelerator were used. The cold non condensed atoms were kicked first to realize the kicked accelerator. Among the objectives were the realization of resonances of the kicked accelerator and associated phenomena of quantum accelerator modes using a Bose-Einstein Condensation (BEC). One of the major achievements of the work in this thesis was the creation of the quantum delta-kicked rotor and its associated resonances to realize a quantum ratchet. The properties of the ratchet were studied in detail.
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 study the response of a Bose-Einstein Condensate in a δ-kicked optical lattice ratchet potential, with δ-kicked interactions, at quantum resonances. Our results reveal a strong dependency on the kicking strength K and the interaction parameter g˜. A critical curve in the (K,g˜)-space separating quasi-periodicity from full chaos shows that full chaos can be easily achieved for stronger interactions. In the full chaos regime, large currents including current reversals are generated and the current spectrum symmetry is broken. Outside the stability window, |g˜|≤1, the directed transport is no longer guaranteed. Experiments are possible thanks to recent progress in optical lattices and the possibility of time-modulating Feshbach-resonance.
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.