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Phase Noise in the Delta Kicked Rotor: From Quantum to Classical

D. H. White, S. K. Ruddell, M D Hoogerl

Published Aug 17, 2016• 22 citations
OpenAlex

Abstract

We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.

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We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.

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European Quantum Electronics Conference (EQEC)•Jan 1, 2003•0 citations
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.
The effect of pulse train noise on the quantum resonance peaks of the atom optics kicked rotor is investigated experimentally. Quantum resonance peaks in the late time mean energy of the atoms are found to be surprisingly robust against all levels of noise applied to the kicking amplitude, while even small levels of noise on the kicking period lead to their destruction. The robustness to amplitude noise of the resonance peak and of the fall-off in mean energy to either side of this peak are explained in terms of the occurrence of stable, epsilon classical dynamics [Nonlinearity 16, 1381 (2003)]] around each quantum resonance.
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.
We study analytically the effect of amplitude noise on the quantum resonances of an atom optics realization of the δ-kicked rotor. Noise is shown to add a time growth to the ‘deterministic’ energy and to induce a time increasing spreading in the momentum distribution; exact results are given for both effects. The ballistic peaks characteristic of the noiseless distribution for particular initial conditions broaden and eventually vanish, whereas the associated quadratic growth of energy persists; at large times, the survival probability decays as t −1 . Moreover, the nonexponential ‘localization’ linked to different initial conditions is gradually destroyed. Features specific to Gaussian noise, white and coloured, are analysed. The feasibility of experimental tests of these effects is discussed.