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Quantum Accelerator Modes in the Absence of Gravity

Oded Barash, Itzhack Dana

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The experimental study of cold atoms kicked by a pulsed optical standing wave and falling under gravity has led to the important discovery of the accelerator modes (QAMs). It is shown that QAMs in the absence of gravity can feature a rotational quasiregularity which cannot be found in the usual QAMs. Thus, QAMs with non-accelerating quasiregular segments may be used to control the quantum motion of atoms in a way which is not possible in the presence of gravity. Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved.

Related papers

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This thesis is devoted to the study of some theoretical aspects of the problem of Quantum Accelerator Modes (QAMs), which has received considerable interest in recent years both by experimentalists and theorists in the fields of Quantum Chaos, Quantum Optics and cold-ultracold atomic physics.\nQAMs, recently observed in cold atom optics, are formed by exposing cold alkali atoms to periodic kicks in the direction of the gravitational field. The kicks are generated by a pulsed standing wave of light. A QAM is characterized by a momentum transfer, which increases linearly with the number of pulses, to a substantial fraction of the atoms. QAMs arise for values of the pulse period close to a integer multiple of half of a characteristic time TB (the Talbot time), typical of the kind of atoms used.\nA detailed theoretical explanation of this quantum effect is presented. The system can be modelled by a variant of the well-known quantum Kicked Rotator, in which the effects of a static force, produced by the earth gravitational field, are taken into account. A pseudo-classical theory has been formulated, in which the role of Planck constant is played by the detuning of the kicking period from the resonant value: in the asymptotic limit for a vanishing detuning, QAMs are described by the stable periodic orbit of a “formally” classical map on the 2-torus. An analysis of parametric dependence of the map is performed perturbatively; the parameter regions where the motion is stable and periodic exhibit Arnol’d tongues-like structures. The ordering of Arnol’d tongues and hence the classification of experimentally observed accelerator modes is provided by a number-theoretic construction known as the Farey Tree.\nQuantum decay of the modes from classical stable islands immersed in a chaotic sea is analysed and its relations to the famous Wannier-Stark problem are investigated. Theoretical estimates for the lifetimes of the metastable states as a function of the effective Planck constant are obtained.\nQAM dynamics in a Bose-Einstein condensate is then considered. Modifications on transport phenomena, imposed by nonlinearities of Gross-Pitaevskii type, which describe the atomic interactions in a mean-field approach, are examined by computer-assisted analysis.\nFinally, the problem of QAMs in the vicinity of a generic quantum resonance, namely for kicking period sufficiently close to any rational multiple of the Talbot time, is studied.\nThe theoretical framework is nontrivially generalized in terms of spinor dynamics: an ansatz of the Born-Oppenheimer type allows to decouple the dynamics of spinor and orbital degrees of freedom and a description of the orbital motion by means of “formally” classical equations is achieved. New rich families of experimental observable QAMs are predicted.

•Jan 1, 2008•0 citations

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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
The experimental study of cold atoms kicked by a pulsed optical standing wave and falling under gravity has led to the important discovery of the accelerator modes (QAMs). It is shown that QAMs in the absence of gravity can feature a rotational quasiregularity which cannot be found in the usual QAMs. Thus, QAMs with non-accelerating quasiregular segments may be used to control the quantum motion of atoms in a way which is not possible in the presence of gravity. Copyright © 2007 Praise Worthy Prize S.r.l. - All rights reserved.
This thesis is devoted to the study of some theoretical aspects of the problem of Quantum Accelerator Modes (QAMs), which has received considerable interest in recent years both by experimentalists and theorists in the fields of Quantum Chaos, Quantum Optics and cold-ultracold atomic physics.\nQAMs, recently observed in cold atom optics, are formed by exposing cold alkali atoms to periodic kicks in the direction of the gravitational field. The kicks are generated by a pulsed standing wave of light. A QAM is characterized by a momentum transfer, which increases linearly with the number of pulses, to a substantial fraction of the atoms. QAMs arise for values of the pulse period close to a integer multiple of half of a characteristic time TB (the Talbot time), typical of the kind of atoms used.\nA detailed theoretical explanation of this quantum effect is presented. The system can be modelled by a variant of the well-known quantum Kicked Rotator, in which the effects of a static force, produced by the earth gravitational field, are taken into account. A pseudo-classical theory has been formulated, in which the role of Planck constant is played by the detuning of the kicking period from the resonant value: in the asymptotic limit for a vanishing detuning, QAMs are described by the stable periodic orbit of a “formally” classical map on the 2-torus. An analysis of parametric dependence of the map is performed perturbatively; the parameter regions where the motion is stable and periodic exhibit Arnol’d tongues-like structures. The ordering of Arnol’d tongues and hence the classification of experimentally observed accelerator modes is provided by a number-theoretic construction known as the Farey Tree.\nQuantum decay of the modes from classical stable islands immersed in a chaotic sea is analysed and its relations to the famous Wannier-Stark problem are investigated. Theoretical estimates for the lifetimes of the metastable states as a function of the effective Planck constant are obtained.\nQAM dynamics in a Bose-Einstein condensate is then considered. Modifications on transport phenomena, imposed by nonlinearities of Gross-Pitaevskii type, which describe the atomic interactions in a mean-field approach, are examined by computer-assisted analysis.\nFinally, the problem of QAMs in the vicinity of a generic quantum resonance, namely for kicking period sufficiently close to any rational multiple of the Talbot time, is studied.\nThe theoretical framework is nontrivially generalized in terms of spinor dynamics: an ansatz of the Born-Oppenheimer type allows to decouple the dynamics of spinor and orbital degrees of freedom and a description of the orbital motion by means of “formally” classical equations is achieved. New rich families of experimental observable QAMs are predicted.
We describe measurements of the mean energy of an ensemble of laser-cooled atoms in an atom optical system in which the cold atoms, falling freely under gravity, receive approximate delta-kicks from a pulsed standing wave of laser light. We call this system a "delta-kicked accelerator." Additionally, we can counteract the effect of gravity by appropriate shifting of the position of the standing wave, which restores the dynamics of the standard delta-kicked rotor. The presence of gravity (delta-kicked accelerator) yields quantum phenomena, quantum accelerator modes, which are markedly different from those in the case for which gravity is absent (delta-kicked rotor). Quantum accelerator modes result in a much higher rate of increase in the mean energy of the system than is found in its classical analog. When gravity is counteracted, the system exhibits the suppression of the momentum diffusion characteristic of dynamical localization. The effect of noise is examined and a comparison is made with simulations of both quantum-mechanical and classical versions of the system. We find that the introduction of noise results in the restoration of several signatures of classical behavior, although significant quantum features remain.
Using a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett. 89, 084101 (2002)]]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin.
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.