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

Quantum Electronics and Laser Science Conference

Atom optics in nonlinear potentials

Mark G. Raizen, C. F. Bharucha, Kirk W. Madison, F. L. Moore, John C. Robinson, Bala Sundaram, Steven R. Wilkinson

Published Jun 7, 1996• 0 citations
OpenAlex

Abstract

Summary form only given. The study of quantum systems that are chaotic in their classical limit has been the subject of intense research in recent years. Atom optics is an ideal experimental testing ground for this field given the combination of well-defined initial conditions, controlled nonlinear potentials, and absence of dissipative processes. To study nonlinear effects in the simplest setting, we measure momentum transferred from a single pulse of a standing wave of light to a sample of ultracold Na atoms, and observe a sharp increase in the momentum transfer when the pulse duration exceeds a critical value.

Related papers

Experimental tests of quantum nonlinear dynamics in atom optics

W. K. Hensinger, N. R. Heckenberg, Gerard J Milburn +1 more

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck’s constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 ° out of phase with the initial state.

Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•39 citations

Probing mixed phase space dynamics using atom optics

D. Steck, Windell H. Oskay, Mark G. Raizen

Summary form only given. Atom optics has proven to be a fruitful testbed for the experimental study of quantum dynamics in classically chaotic systems. However, the quantum behavior in a mixed classical phase space, where both stable and chaotic regions are present, remains an interesting and challenging subject, with much left to understand. To probe local dynamics in mixed phase space, the atomic sample must be prepared such that it is localized in phase space. To accomplish this, cesium atoms are first prepared in a standard magneto-optic trap. They are then further cooled in a 3-D far-detuned optical lattice. A model system for the study of mixed phase space is realized when the atoms are subjected to an amplitude-modulated standing wave, where the intensity varies as sin/sup 2/ (/spl pi/t/T) (T is the pulse duration). There are three primary resonances in this system; one is at zero momentum, and the other two are located symmetrically about p = 0. As the intensity of the standing wave increases, the resonances overlap, and the resonances appear as islands of stability surrounded by bands of chaos. We have used our method of state preparation to center the atomic distribution at various positions and at the same momentum as one of the "side" resonances. We observe trapping of the atoms in the resonance when the atomic distribution is centered on the island, but not when the atoms are centered away from the resonance, since they instead diffuse through the chaotic region.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations

Can a Single-Pulse Standing Wave Induce Chaos in Atomic Motion?

J. C. Robinson, C. F. Bharucha, Kirk W. Madison +4 more

We measure momentum transferred from a single pulse of a standing wave of light to a sample of ultracold sodium atoms, and observe a sharp increase in the momentum transfer when the pulse duration exceeds a critical value ${\ensuremath{\tau}}_{\mathrm{cr}}$. A classical analysis of nonlinear resonances shows that resonance overlap occurs at ${\ensuremath{\tau}}_{\mathrm{cr}}$, and there is a transition to global classical chaos. These results are a direct experimental test of the ``resonance overlap criteria'' and illustrate that even the turning on and off of a simple spatially periodic interaction can lead to surprising and novel results.

Physical Review Letters•Apr 29, 1996•45 citations

Observation of Dynamical Localization in Atomic Momentum Transfer: A New Testing Ground for Quantum Chaos

F. L. Moore, J. C. Robinson, C. F. Bharucha +2 more

We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.

Physical Review Letters•Nov 28, 1994•390 citations

An experimental realization of the quantum -kicked rotor

Mark G. Raizen, F L Moore, J C Robinson +2 more

We study experimentally quantum effects in atomic motion for a classically chaotic regime. A standing wave is pulsed on periodically in time, and the resulting atomic momentum is measured. Momentum grows diffusively until the quantum break time, after which dynamical localization is observed. Quantum resonances are observed for certain pulse durations.

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Jun 1, 1996•12 citations

Dissipative nonlinear quantum dynamics in atomic optics

Sigurd Dyrting, Gerard J Milburn

It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom's internal state, a band structure, and a time-dependent dissipative process.

Physical Review A•Apr 1, 1995•19 citations
Summary form only given. The study of quantum systems that are chaotic in their classical limit has been the subject of intense research in recent years. Atom optics is an ideal experimental testing ground for this field given the combination of well-defined initial conditions, controlled nonlinear potentials, and absence of dissipative processes. To study nonlinear effects in the simplest setting, we measure momentum transferred from a single pulse of a standing wave of light to a sample of ultracold Na atoms, and observe a sharp increase in the momentum transfer when the pulse duration exceeds a critical value.
Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose–Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck’s constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 ° out of phase with the initial state.
Summary form only given. Atom optics has proven to be a fruitful testbed for the experimental study of quantum dynamics in classically chaotic systems. However, the quantum behavior in a mixed classical phase space, where both stable and chaotic regions are present, remains an interesting and challenging subject, with much left to understand. To probe local dynamics in mixed phase space, the atomic sample must be prepared such that it is localized in phase space. To accomplish this, cesium atoms are first prepared in a standard magneto-optic trap. They are then further cooled in a 3-D far-detuned optical lattice. A model system for the study of mixed phase space is realized when the atoms are subjected to an amplitude-modulated standing wave, where the intensity varies as sin/sup 2/ (/spl pi/t/T) (T is the pulse duration). There are three primary resonances in this system; one is at zero momentum, and the other two are located symmetrically about p = 0. As the intensity of the standing wave increases, the resonances overlap, and the resonances appear as islands of stability surrounded by bands of chaos. We have used our method of state preparation to center the atomic distribution at various positions and at the same momentum as one of the "side" resonances. We observe trapping of the atoms in the resonance when the atomic distribution is centered on the island, but not when the atoms are centered away from the resonance, since they instead diffuse through the chaotic region.
We measure momentum transferred from a single pulse of a standing wave of light to a sample of ultracold sodium atoms, and observe a sharp increase in the momentum transfer when the pulse duration exceeds a critical value ${\ensuremath{\tau}}_{\mathrm{cr}}$. A classical analysis of nonlinear resonances shows that resonance overlap occurs at ${\ensuremath{\tau}}_{\mathrm{cr}}$, and there is a transition to global classical chaos. These results are a direct experimental test of the ``resonance overlap criteria'' and illustrate that even the turning on and off of a simple spatially periodic interaction can lead to surprising and novel results.
We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.
It is proposed that the atomic optical system of an ytterbium atom in a time-dependent optical standing wave be used to experimentally observe quantum nonlinear motion and, in particular, predict the quantum behavior of a system whose classical analog ranges from completely integrable, to near integrable, and finally to globally chaotic motion. We extend previous treatments to include spontaneous emission. From the study of theoretical models of dissipative quantum nonlinear motion, it is known that even small amounts of dissipation can significantly alter the quantum dynamics through the destruction of coherences. In this paper we present some theoretical and numerical results of the effect of spontaneous emission on nonlinear nonintegrable dynamics in atomic optics. When spontaneous emission is included, we show that the nature of the light-atom interaction introduces interesting features not usually investigated in models of dissipative quantum nonlinear dynamics. These include a potential that depends on the atom's internal state, a band structure, and a time-dependent dissipative process.