Quantum Chaos

We present experimental measurements of the mean energy in the vicinity of the first and second quantum resonances of the atom optics kicked rotor for a number of different experimental parameters. Our data is rescaled and compared with the one parameter ǫ-classical scaling function developed to describe the quantum resonance peaks. Additionally, experimental data is presented for the "classical" resonance which occurs in the limit as the kicking period goes to zero. This resonance is found to be analogous to the quantum resonances, and a similar one-parameter classical scaling function is derived, and found to match our experimental results. The width of the quantum and classical resonance peaks is compared, and their Sub-Fourier nature examined.

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“…As with the atom-optics kicked rotor, both of the latter systems may be readily realized in laboratory experiments [29,30].…”

Section: Discussionmentioning

confidence: 99%

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

et al. 2005

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“…However, it often happens that quantum eigenstates exhibit an increased probability density in the vicinity of unstable periodic orbits. This scarring phenomenon is nowadays relatively well understood, and the interested reader may consult references [81,82].…”

Section: Scarsmentioning

confidence: 99%

“…This is not unexpected, as semiclassics should fail when the area of the resonance island is comparable toh, compare eq. (82). In this weak driving regime, the pendulum approximation can be used to produce more accurate estimates of the energy levels.…”

Section: Realistic Three-dimensional Atommentioning

confidence: 99%

“…Here, the agreement is worse than for smaller values of N, and is observed only for large F 0 and large p. This confirms the picture that the validity of the semiclassical approach outlined here is directly related to the size, eqs. (71,82), of the resonance island in (Î,θ) space (see also the discussion in section 8.3).…”

Section: Realistic Three-dimensional Atommentioning

confidence: 99%

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Non-dispersive wave packets in periodically driven quantum systems

2002

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With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

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“…On the other hand, the manifestations of chaotic motion in quantum mechanics, though widely studied [1,2], remain somehow not so clearly understood, both from the mathematical as well as from the physical point of view.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos, dynamical stability and decoherence

Casati

Prosen

2005

Braz. J. Phys.

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We discuss the stability of quantum motion under system's perturbations in the light of the corresponding classical behavior. In particular we focus our attention on the so called "fidelity" or Loschmidt echo, its relation with the decay of correlations, and discuss the quantum-classical correspondence. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.

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Quantum Chaos

Cited by 1,000 publications

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Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

Experimental verification of a one-parameter scaling law for the quantum and “classical” resonances of the atom-optics kicked rotor

Non-dispersive wave packets in periodically driven quantum systems

Quantum chaos, dynamical stability and decoherence

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