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arXiv:quant-ph/0307034 · Physical Review E

Decoherence as a probe of coherent quantum dynamics

M. B. d’Arcy, R. M. Godun, Gil S. Summy, Italo Guarneri, Sandro Wimberger, Shmuel Fishman, Andreas Buchleitner

Published Feb 26, 2004• 34 citations
arXivHTMLPDF

Abstract

The effect of decoherence, induced by spontaneous emission, on the dynamics of cold atoms periodically kicked by an optical lattice is experimentally and theoretically studied. Ideally, the mean energy growth is essentially unaffected by weak decoherence, but the resonant momentum distributions are fundamentally altered. It is shown that experiments are inevitably sensitive to certain nontrivial features of these distributions, in a way that explains the puzzle of the observed enhancement of resonances by decoherence [Phys. Rev. Lett. 87, 074102 (2001)]. This clarifies both the nature of the coherent evolution, and the way in which decoherence disrupts it.

DOI
10.1103/physreve.69.027201

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•Jan 1, 2004•0 citations
The effect of decoherence, induced by spontaneous emission, on the dynamics of cold atoms periodically kicked by an optical lattice is experimentally and theoretically studied. Ideally, the mean energy growth is essentially unaffected by weak decoherence, but the resonant momentum distributions are fundamentally altered. It is shown that experiments are inevitably sensitive to certain nontrivial features of these distributions, in a way that explains the puzzle of the observed enhancement of resonances by decoherence [Phys. Rev. Lett. 87, 074102 (2001)]. This clarifies both the nature of the coherent evolution, and the way in which decoherence disrupts it.
In this manuscript I present an experimental investigation of the dynamics of an ultracold gas of bosonic ytterbium loaded into optical lattices and exposed to resonant light. The interaction between atoms and light makes it possible to study the coherence properties of the gas. The resonant driving is performed on the relevant optical transitions featured by ytterbium. On the one hand, I demonstrate the coherent driving of the internal state of the atoms on the clock transition, the excited state of which is metastable and can not spontaneously decay, thus preserving the coherence of the gas. The temporal internal dynamics in a deep lattice allows me to measure the collisional properties at low temperature for both clock states. On the other hand, I use the spontaneously emitted photons of the intercombination transition excited level to induce a coupling to the atomic external degrees of freedom. I present the momentum diffusion of a superfluid excited on this transition. Strong interactions between atoms slow down the decoherence and lead to an anomalous sub-diffusive relaxation. A simple model comprising atomic motion, interactions and dissipation accounts for our observations. A theoretical study of the dissipative dynamics in optical lattices sheds light on complementary phenomena such as induced dipole-dipole interactions or collective effects in spontaneous emission.
The possibility of experimental observation of chaotic motion of cold atoms in a one-dimensional rigid optical lattice without any modulation of its parameters and additional impact is demonstrated theoretically and numerically. This effect of deterministic chaos arises near the optical resonance due to the nonlinear coupling of electronic and mechanical degrees of freedom in the atom. In a certain range of resonance detunings, at each crossing of the lattice-forming standing wave node by the atom, the atomic dipole moment changes pseudorandomly in a step-like manner, accompanied by an appropriate change in the atom momentum. This leads to the effect of chaotic wandering of atoms, possessing the properties of the classical deterministic chaos, namely, to the exponential sensitivity of atomic trajectories to small variations of the initial conditions and/or the control parameters. With time, part of atoms from the initial cloud changes the direction of their motion to the opposite one, which can be detected in a real experiment. Numerical experiments with lithium atoms with the spontaneous emission taken into account show that by varying the laser radiation intensity (normalised detuning of resonance) in the rigid optical lattice, one can implement the transition from the regular regime of the atomic motion to the chaotic wandering in a real experiment.
Quantum systems upon interaction with the environment undergo decoherence or decay towards classical states. The dynamics of the quantum coherence at the borderline between quantum and classical world is not fully understood yet. The quantum coherence is generally known to exponentially decay in time so that macroscopic quantum superpositions are not sustained for a long time. In many practical applications, it is necessary to maintain quantum coherences for as long as possible. In this work, we use the experimental test-bed of cold atoms in a pulsed one-dimensional optical lattice to realise an atom-optics kicked rotator. We manipulate the waiting time between consequent kicks in this system by taking it as a random variable from a L\'{e}vy distribution. In this noisy scenario, we show that coherence can be made to decay slower than an exponential form. This manifests in the form of quantum subdiffusion that can be controlled through the L\'{e}vy exponent. The experimental results are in good agreement with the analytical expressions and numerical simulations for the mean energy growth of atom-optics kicked rotor.
The quantum resonances occurring with δ-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analysed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by spontaneous emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling laws describing the shape of the resonant peaks are obtained. Such analytical results are supported by extensive numerical simulations, and explain some recent surprising experimental observations.
The influence of spontaneous emission on the dynamical localization in atomic momentum transfer observed in recent experiments is investigated. Our numerical and analytical results indicate that contrary to previous expectation quantum diffusion due to decoherence by spontaneous emission is non-negligible in the experimental regime and may actually be visible in the measured data. Modifications of the experiments to strengthen this point are proposed. \textcopyright{} 1996 The American Physical Society.
This thesis investigates quantum transport in the energy space of two paradigm systems of quantum chaos theory. These are highly excited hydrogen atoms subject to a microwave field, and kicked atoms which mimic the delta-kicked rotor model. Both of these systems show a complex dynamical evolution arising from the interaction with an external time-periodic driving force. In particular two quantum phenomena, which have no counterpart on the classical level, are studied: the suppression of classical diffusion, known as dynamical localisation, and quantum resonances as a regime of enhanced transport for the delta-kicked rotor. The first part of the thesis provides new support for the quantitative analogy between energy transport in strongly driven highly excited atoms and particle transport in Anderson-localised solids. A comprehensive numerical analysis of the atomic ionisation rates shows that they obey a universal power-law distribution, in agreement with Anderson localisation theory. This is demonstrated for a one-dimensional model as well as for the real three-dimensional atom. We also discuss the implications of the universal decay-rate distributions for the asymptotic time-decay of the survival probability of the atoms. The second part of the thesis clarifies the effect of decoherence, induced by spontaneous emission, on the quantum resonances which have been observed in a recent experiment with delta-kicked atoms. Scaling laws are derived, based on a quasi-classical approximation of the quantum evolution. These laws describe the shape of the resonance peaks in the mean energy of an experimental ensemble of kicked atoms. Our analytical results match perfectly numerical computations and explain the initially surprising experimental observations. Furthermore, they open the door to the study of the competing effects of decoherence and chaos on the stability of the time evolution of kicked atoms. This stability may be characterised by the overlap of two identical initial states which are subject to different time evolutions. This overlap, called fidelity, is investigated in an experimentally accessible situation.