Control of dynamical localization by an additional quantum degree of freedom

Riedel, K.; Törmä, Païvi; Savichev, V. I.; Schleich, Wolfgang P.

doi:10.1103/physreva.59.797

“…The study of quantum chaos based on quantum gate networks has so far been proposed e.g. by implementing quantum baker's map on a 3-qubit NMR quantum computer [11], by realizing a quantum-mechanical delta-kicked harmonic oscillator or a harmonically driven oscillator in an ion trap [12,13], and by showing quantum-mechanical localization of an ion in a trap [14,15]. In all these cases some sort of sensitivity has been predicted with respect to parameters specifying the dynamics (e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos in small quantum networks

Kim

¹

,

Mahler

²

2000

Journal of Modern Optics

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We study a 2-spin quantum Turing architecture, in which discrete local rotations {α m } of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input {α m } leads to a chaotic dynamics in the entire Hilbert space. The instability of periodic orbits on the Turing head and 'chaos swapping' onto the Turing tape are demonstrated explicitly as well as exponential parameter sensitivity of the Bures metric.

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“…The study of quantum chaos based on quantum gate networks has so far been proposed e.g. by implementing quantum baker's map on a 3-qubit NMR quantum computer [11], by realizing a quantum-mechanical delta-kicked harmonic oscillator or a harmonically driven oscillator in an ion trap [12,13], and by showing quantum-mechanical localization of an ion in a trap [14,15]. In all these cases some sort of sensitivity has been predicted with respect to parameters specifying the dynamics (e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos in small quantum networks

Kim

¹

,

Mahler

²

2000

Journal of Modern Optics

View full text Add to dashboard Cite

We study a 2-spin quantum Turing architecture, in which discrete local rotations {α m } of the Turing head spin alternate with quantum controlled NOT-operations. We show that a single chaotic parameter input {α m } leads to a chaotic dynamics in the entire Hilbert space. The instability of periodic orbits on the Turing head and 'chaos swapping' onto the Turing tape are demonstrated explicitly as well as exponential parameter sensitivity of the Bures metric.

show abstract

“…For more experiments on decoherence in dynamical localization we refer to (Ammann 1997). Moreover, there exists an extensive literature on the influence of spontaneous emission on dynamical localization, see for example , Goetsch 1996, Dyrting 1996, Riedel 1999.…”

Section: Dynamical Effects and Decoherencementioning

confidence: 99%

Classical and quantum chaos in atom optics

Saif

¹

2005

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The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.

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Control of dynamical localization by an additional quantum degree of freedom

Cited by 9 publications

References 34 publications

Quantum chaos in small quantum networks

Quantum chaos in small quantum networks

Quantum chaos in small quantum networks

Classical and quantum chaos in atom optics

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