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.
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.
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.
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.
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the delta-kicked rotor, a paradigm in classical chaos theory, and the novel delta-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate delta-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity’s effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential’s effect. Each system’s dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms’ mean kinetic energy on the number and time period of the delta-kicks. The phenomena of dynamical localisation and quantum resonances in the delta-kicked rotor, which have no counterparts in the system’s classical analogue, are observed and investigated. Similar experiments on the delta-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system’s classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a technique for measuring gravity, and a method of preparing atoms in a particular region of phase space. This may allow measurement of quantum phase space stability, and hence investigation of quantum chaos and quantum-classical correspondence.
The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.
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.