Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

Макаров, Денис В.; Kon’kov, L. E.

doi:10.1088/0031-8949/90/3/035204

Cited by 7 publications

(4 citation statements)

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“…Here ξ(t) is Gaussian complex-valued white noise with ξ(t) = 0, ξ(t)ξ * (t ′ ) = δ(t − t ′ ). If γ ≪ Ω, then η(t) can be fairly approximated by the complex-valued harmonic noise introduced in [48][49][50][51][52].…”

Section: The Modelmentioning

confidence: 99%

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

Alliluev¹,

Макаров²

2021

Preprint

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We consider dynamics of a quantum nonlinear oscillator subjected to non-Markovian pumping. Models of this kind can describe formation of exciton-polariton Bose-Einstein condensates in course of stimulated scattering and relaxation of reservoir excitons. Using the Markovian embedding techniques, we obtain stochastic differential equations of motion with an additional degree of freedom corresponding to dynamical memory. It is shown that the oscillator asymptotically tends to the intrinsically non-Markovian stable fixed point corresponding to constant product of oscillator amplitude and modulo of the memory variable. The state corresponding to this point exhibits unlimited growth of population, with the growth rate that decreases with time. Our results show that the Markovian behavior could be observed only within some limited early stage of oscillator evolution provided that decay of dynamical memory is sufficiently fast. Transition from the Markovian regime to non-Markovian one with increasing time is linked to phase shift of the pumping term. Coherence properties of the oscillator are studied. It was found that interaction between particles delimits growth of condensate population, thereby impeding formation of Bose-Einstein condensate.

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Section: The Modelmentioning

confidence: 99%

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

Alliluev¹,

Макаров²

2021

Preprint

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“…Noisy 1D OLs have been used to destruct dynamical barriers in the classical phase space and create directed atomic transport [48]. There may arise also in such OLs a partial suppression of chaos due to quantum corrections, so called dynamical localization [49]. New opportunities to control atomic transport appear in superlattices with an additional phase-modulated OL imposed on the main one [50].…”

Section: Cold Atoms In Optical Latticesmentioning

confidence: 99%

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Prants

2017

Phys. Scr.

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This paper is a review article on some aspects of quantum–classical correspondence in chaotic dynamics of cold atoms interacting with a standing-wave laser field forming an optical lattice. The problem is treated from both (semi)classical and quantum points of view. In both approaches, the interaction of an atomic electic dipole with the laser field is treated quantum mechanically. Translational motion is described, at first, classically (atoms are considered to be point-like objects) and then quantum mechanically as a propagation of matter waves. Semiclassical equations of motion are shown to be chaotic in the sense of classical dynamical chaos. Point-like atoms in an absolutely deterministic and rigid optical lattice can move in a random-like manner demonstrating a chaotic walking with typical features of classical chaos. This behavior is explained by random-like ‘jumps’ of one of the atomic internal variable when atoms cross nodes of the standing wave and occurs in a specific range of the atom-field detuning. When treating atoms as matter waves, we show that they can make nonadiabatic transitions when crossing the standing-wave nodes. The point is that atomic wave packets split at each node in the same range of the atom-field detuning where the classical chaos occurs. The key point is that the squared amplitude of those semiclassical ‘jumps’ equal to the quantum Landau–Zener parameter which defines the probability of nonadiabatic transitions at the nodes. Nonadiabatic atomic wave packets are much more complicated compared to adiabatic ones and may be called chaotic in this sense. A few possible experiments to observe some manifestations of classical and quantum chaos with cold atoms in horizontal and vertical optical lattices are proposed and discussed.

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“…In equation (38), superscript j labels the realizations of harmonic noise, and N r is total number of realizations. We calculate Z ¯for initial conditions (23). In the absence of noise, it can be easily found from (28…”

Section: Dominance Of the Statementioning

confidence: 99%

“…Lattice fluctuations can be incorporated into the Hamiltonian by means of the replacement [21][22][23] t t…”

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confidence: 99%

Zitterbewegung with spin–orbit coupled ultracold atoms in a fluctuating optical lattice

Argonov¹,

Макаров²

2016

J. Phys. B: At. Mol. Opt. Phys.

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Dynamics of non-interacting ultracold atoms with artificial spin-orbit coupling is considered. Spin-orbit coupling is created using two moving optical lattices with orthogonal polarizations. Our main goal is to study influence of lattice noise on Rabi oscillations. Special attention is paid to the phenomenon of the Zitterbewegung being trembling motion caused by Rabi transitions between states with different velocities. Phase and amplitude fluctuations of lattices are modelled by means of the two-dimensional stochastic Ornstein-Uhlenbeck process, also known as harmonic noise. In the the noiseless case the problem is solved analytically in terms of the momentum representation. It is shown that lattice noise significantly extends duration of the Zitterbewegung as compared to the noiseless case. This effect originates from noise-induced decoherence of Rabi oscillations.

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Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

Cited by 7 publications

References 50 publications

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

Quantum–classical correspondence in chaotic dynamics of laser-driven atoms

Zitterbewegung with spin–orbit coupled ultracold atoms in a fluctuating optical lattice

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