Quantum kicked rotor and its variants: Chaos, localization and beyond

Santhanam, M. S.; Paul, Sanku; Kannan, J. Bharathi

doi:10.1016/j.physrep.2022.01.002

Cited by 38 publications

(13 citation statements)

References 487 publications

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“…If β = 0 and τ = 4π, we see immediately that the Floquet operator only consists of the kicks without any phase evolution. This is the so-called quantum resonant regime of the kicked rotor [24][25][26]. In this regime the evolution well approximates an ideal quantum walk as suggested in [27] and subsequently realised in [19][20][21], in particular for kick strengths of the order k ≈ 1.5, for which the kicks dominantly couple nearest-neighbor momentum states.…”

Section: The Experimental Setupmentioning

confidence: 66%

“…with three real parameters α, γ and χ (the "Euler" angles of the spin-state rotation) and is realized with microwave radiation addressing the hyperfine levels of rubidium. In contrast to [15] we do not study an ideal quantum walk with exclusively nearest-neighbor couplings but a realisation based on the quantum kicked rotor [24][25][26] with a Bose-Einstein condensate subject to time-periodic kicks from a standing-wave laser [19][20][21].…”

Section: The Experimental Setupmentioning

confidence: 99%

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Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

2022

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We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo’s paradox). In particular, we have in mind an experimental realization with a Bose–Einstein condensate in which the walker’s space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analyzed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo’s paradox for experimentally available time scales of up to a few hundred steps of the walk.

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Section: The Experimental Setupmentioning

confidence: 66%

Section: The Experimental Setupmentioning

confidence: 99%

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

2022

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“…On the other hand, if

, we expect the wave packet to encompass the full extent of the momentum space before any interference effects might stop the diffusion. The transition from the dynamically localized regime to the fully delocalized ergodic regime has been extensively studied in the quantum kicked rotor system (see the review articles [ 41 , 42 ]), billiard systems [ 37 , 38 , 39 , 43 , 44 , 45 , 46 , 47 , 48 ], Dicke model [ 49 ], etc. In particular, our previous studies of DL in the stadium billiard [ 45 ] show the functional dependence of the localization measures and level repulsion exponents on the ratio

.…”

Section: Introductionmentioning

confidence: 99%

Spectral Form Factor and Dynamical Localization

Lozej

2023

Entropy

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Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical transport time of the momentum diffusion is greater than the Heisenberg time. The transport time is typically computed from the corresponding classical dynamics. In this paper, we present an alternative approach based purely on the study of spectral fluctuations of the quantum system. The information about the transport times is encoded in the spectral form factor, which is the Fourier transform of the two-point spectral autocorrelation function. We compute large samples of the energy spectra (of the order of 106 levels) and spectral form factors of 22 stadium billiards with parameter values across the transition between the localized and extended eigenstate regimes. The transport time is obtained from the point when the spectral form factor transitions from the non-universal to the universal regime predicted by random matrix theory. We study the dependence of the transport time on the parameter value and show the level repulsion exponents, which are known to be a good measure of dynamical localization, depend linearly on the transport times obtained in this way.

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“…On the other hand, if t T < t H we expect the wave packet to encompass the full extent of the momentum space before any interference effects might stop the diffusion. The transition from the dynamically localized regime to the fully delocalized ergodic regime has been extensively studied in the quantum kicked rotor system (see the review articles [35,36]), billiard systems [31][32][33][37][38][39][40][41][42], the Dicke model [43] etc. In particular, our previous studies of DL in the stadium billiard [39] show the functional dependence of the localization measures and level repulsion exponents on the ratio α = t H /t T .…”

Section: Introductionmentioning

confidence: 99%

Spectral form factors and dynamical localization

Lozej¹

2023

Preprint

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Quantum dynamical localization occurs when quantum interference stops the diffusion of wave packets in momentum space. The expectation is that dynamical localization will occur when the typical transport time of the momentum diffusion is greater than the Heisenberg time. The transport time is typically computed from the corresponding classical dynamics. In this paper, we present an alternative approach based purely on the study of spectral fluctuations of the quantum system. The information about the transport times is encoded in the spectral form factor, which is the Fourier transform of the two-point spectral autocorrelation function. We compute large samples of the energy spectra (of the order of 10 6 levels) and spectral form factors of 22 stadium billiards with parameter values across the transition between the localized and extended eigenstate regimes. The transport time is obtained from the point when the spectral form factor transitions from the non-universal to the universal regime predicted by random matrix theory. We study the dependence of the transport time on the parameter value and show the level repulsion exponents, that are known to be a good measure of dynamical localization, depend linearly on the transport times obtained in this way.

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Quantum kicked rotor and its variants: Chaos, localization and beyond

Cited by 38 publications

References 487 publications

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

Spectral Form Factor and Dynamical Localization

Spectral form factors and dynamical localization

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