Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Delta-kicked rotor experiments with an all-optical BEC

Arif Ullah

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

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.

Related papers

Quantum chaos in atom optics

M. B. d’Arcy

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.

•Jan 1, 2002•2 citations

Manifestation of quantum resonant effects in the atom-optical delta-kicked accelerator

M. Saunders

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.

•Jan 1, 2009•0 citations

Applications of the atom-optical kicked rotor

Rajendra K. Shrestha

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.

•Jan 1, 2013•0 citations

Quantum state manipulation and quantum chaos in an optical lattice

J. F. Kanem

The effects of reversing the sinusoidal potential every q kick periods with q = 0, l, 2,3 are examined numerically with the q = 0, 1, 2 cases being verified experimentally. I have found that when considering the energy absorption of the system the q = 1 case is qualitatively and quantitatively the same as the standard kicked rotor, while the q = 2 case is qualitatively the same as the standard kicked rotor with an effective increase in the scaled dimensionless kick strength parameter, k, of k rarr; k+ p2 .In this thesis I detail the background, implementation and results of two experiments from relatively different fields of study, both of which involve ultra-cold Rubidium atoms trapped in an optical lattice. The first is an analysis of the superpositions of vibrational states of the lattice. This includes a characterization and modelling of the dephasing of the states, an effect inherent to the lattice. It is found that the lattice geometry is a primary factor in the observed dephasing. This geometry results in position-dependent energy eigenstates in the lattice. Modelling this distribution of energies allows the accurate prediction of several experimental observables and provides useful information for future experiments. Several methods of applying pulse echoes to recover the state in the face of this dephasing are demonstrated, characterized and successfully modelled. The second set of experiments centre around using the optical lattice and Rubidium atoms as a delta-kicked rotor system. First I examine quantum resonances in the delta-kicked rotor. These are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances exist when the effective Planck's constant, a parameter that determines how quantum-mechanically the system behaves, has a value of plank; d5;=rs dot;4p, for integers r and s. However only for plank; d5;=r dot;2p are resonances easily observable. Here I report on the first observation of high-order quantum resonances in a non-condensed atomic sample at values of plank; d5;=r16 dot;4p for integers r = 2--6. Quantum numerical simulations suggest that this observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.

•Jan 1, 2007•0 citations

Experimental investigation of early-time diffusion in the quantum kicked rotor using a Bose-Einstein condensate

G. J. Duffy, A. S. Parkins, T. Müller +3 more

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.

arXiv:cond-mat/0401346•Physical Review E•Nov 16, 2004•62 citations

Experimental observation of Loschmidt time reversal of a quantum chaotic system

Arif Ullah, Maarten D. Hoogerland

We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic de Broglie waves. We use ultracold atoms from a Bose-Einstein condensate in a quantum δ-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of "chaotic" evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the kick sequence.

arXiv:0911.4974•Physical Review E•Apr 25, 2011•42 citations
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.
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.
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.
The effects of reversing the sinusoidal potential every q kick periods with q = 0, l, 2,3 are examined numerically with the q = 0, 1, 2 cases being verified experimentally. I have found that when considering the energy absorption of the system the q = 1 case is qualitatively and quantitatively the same as the standard kicked rotor, while the q = 2 case is qualitatively the same as the standard kicked rotor with an effective increase in the scaled dimensionless kick strength parameter, k, of k rarr; k+ p2 .In this thesis I detail the background, implementation and results of two experiments from relatively different fields of study, both of which involve ultra-cold Rubidium atoms trapped in an optical lattice. The first is an analysis of the superpositions of vibrational states of the lattice. This includes a characterization and modelling of the dephasing of the states, an effect inherent to the lattice. It is found that the lattice geometry is a primary factor in the observed dephasing. This geometry results in position-dependent energy eigenstates in the lattice. Modelling this distribution of energies allows the accurate prediction of several experimental observables and provides useful information for future experiments. Several methods of applying pulse echoes to recover the state in the face of this dephasing are demonstrated, characterized and successfully modelled. The second set of experiments centre around using the optical lattice and Rubidium atoms as a delta-kicked rotor system. First I examine quantum resonances in the delta-kicked rotor. These are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances exist when the effective Planck's constant, a parameter that determines how quantum-mechanically the system behaves, has a value of plank; d5;=rs dot;4p, for integers r and s. However only for plank; d5;=r dot;2p are resonances easily observable. Here I report on the first observation of high-order quantum resonances in a non-condensed atomic sample at values of plank; d5;=r16 dot;4p for integers r = 2--6. Quantum numerical simulations suggest that this observation of high-order resonances indicates a much longer spatial coherence than expected from an initially thermal atomic sample.
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.
We have performed an experiment to demonstrate the approximate time reversal of a "chaotic" time evolution of atomic de Broglie waves. We use ultracold atoms from a Bose-Einstein condensate in a quantum δ-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of "chaotic" evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the kick sequence.