Saturation of fidelity in the atom-optics kicked rotor

Wimberger, Sandro; Buchleitner, Andreas

doi:10.1088/0953-4075/39/7/l01

Cited by 23 publications

(43 citation statements)

References 26 publications

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“…It has subsequently been extensively utilized in theoretical [19,20,34,35] and experimental studies [35][36][37][38] (for a review see [21]). Most of this research has focused on the difference between chaotic and regular systems.…”

Section: Fidelitymentioning

confidence: 99%

Quantum chaos of a mixed open system of kicked cold atoms

et al. 2011

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The quantum and classical dynamics of particles kicked by a Gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The fidelity (Loschmidt echo) is found to exhibit oscillations that can be determined from classical considerations but are sensitive to phase space structures that are smaller than Planck's constant. Families of quasienergies are determined from classical phase space structures. Substantial differences between the classical and quantum dynamics are found for time-dependent scattering. It is argued that the system can be experimentally realized by cold atoms kicked by a Gaussian light beam.

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Section: Fidelitymentioning

confidence: 99%

Quantum chaos of a mixed open system of kicked cold atoms

et al. 2011

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“…We review here just the result of simple analytical considerations, whose details can be found in [28,33]. The fidelity at a main quantum resonance is considered in two cases: first for the perturbation parameter ∆k = k 2 −k 1 and a fixed quasimomentum β.…”

Section: Quantum Resonant Motion and Saturation Of Fidelitymentioning

confidence: 99%

Applications of fidelity measures to complex quantum systems

Wimberger

2016

Phil. Trans. R. Soc. A.

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We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space.

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“…Our results open the route to future investigations of our system, which fully include the second degree of freedom. This could be done for cold atoms and Bose-Einstein condensates using either internal states of the atoms (an effective spin [15,19,20]) or more than one kick potential with different phases and wavelengths to address independently different momentum classes [21].…”

Section: Introductionmentioning

confidence: 99%

Steering random walks with kicked ultracold atoms

et al. 2015

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A kicking sequence of the atom optics kicked rotor at quantum resonance can be interpreted as a quantum random walk in momentum space. We show how to steer such a random walk by applying a random sequence of intensities and phases of the kicking lattice chosen according to a probability distribution. This distribution converts on average into the final momentum distribution of the kicked atoms. In particular, it is shown that a power-law distribution for the kicking strengths results in a L\'evy walk in momentum space and in a power-law with the same exponent in the averaged momentum distribution. Furthermore, we investigate the stability of our predictions in the context of a realistic experiment with Bose-Einstein condensates.Comment: detailed study of random walks and their implementation with a Bose condensate, 12 pages, 7 figure

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Saturation of fidelity in the atom-optics kicked rotor

Cited by 23 publications

References 26 publications

Quantum chaos of a mixed open system of kicked cold atoms

Quantum chaos of a mixed open system of kicked cold atoms

Applications of fidelity measures to complex quantum systems

Steering random walks with kicked ultracold atoms

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