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Physical Review Letters

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

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

Published Apr 29, 1996• 45 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.76.3304

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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 \ensuremathτcr{\ensuremath{\tau}}_{\mathrm{cr}}\ensuremathτcr​. A classical analysis of nonlinear resonances shows that resonance overlap occurs at \ensuremathτcr{\ensuremath{\tau}}_{\mathrm{cr}}\ensuremathτcr​, 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.
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.
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.
We report an experimental and theoretical study of momentum transfer from a modulated standing wave of light to a sample of ultracold atoms. This system is a quantum realization of the periodically driven rotor where the underlying classical phase space goes from stable to chaotic as a control parameter is varied. Our experimental results are in good absolute agreement with a quantum Floquet analysis and with a quantum simulation. We relate the quantum evolution to the underlying classical dynamics in this mixed phase space regime.
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 study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.