Semiclassical interaction of moving two-level atoms with a cavity field: From integrability to Hamiltonian chaos

Prants, S. V.; Kon’kov, L. E.; Kirilyuk, I. L.

doi:10.1103/physreve.60.335

Cited by 29 publications

(12 citation statements)

References 22 publications

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“…They are small under usual conditions. Trying to find another mechanism of local instability in the Hamiltonian atom-photon dynamics without pump and losses, the authors of [20,21] proposed the semiclassical model with atoms moving through a standing-wave cavity in a direction along which the cavity sustains a space-periodic field. The standing wave modulates the atom-field coupling providing in a certain range of the system's parameters intermittent Rabi oscillations.…”

Section: Introductionmentioning

confidence: 99%

Chaos and flights in the atom-photon interaction in cavity QED

2002

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We study dynamics of the atom-photon interaction in cavity quantum electrodynamics (QED), considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinearHamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including Lévy flights and chaotic walkings of an atom in a cavity. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning δ and atomic recoil frequency α. It is demonstrated how the atom-photon dynamics with a given value of α depends on the values of δ and initial conditions. Two types of Lévy flights, one corresponding to the ballistic motion of the atom and another one corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincaré recurrences and moments of the atom position x. The simulation shows different regimes of motion, from slightly abnormal diffusion with < x 2 >∼ τ 1.13 at δ = 1.2 to a superdiffusion with < x 2 >∼ τ 2.2 at δ = 1.92 that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning δ.

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Section: Introductionmentioning

confidence: 99%

Chaos and flights in the atom-photon interaction in cavity QED

2002

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“…where the momentump and positionx operators satisfy the standard commutation relation [x,p] = i , and the Pauli operators are connected with R operators (19) as follows:σ z = 2R 0 ,σ ± = R ± . Operators belonging to different degrees of freedom commute with each other at the same time moment.…”

Section: Quantum-classical Hybrids Dynamic Chaos and Fractals With Tmentioning

confidence: 99%

“…In spite of their structural simplicity, these models have been shown to demonstrate rich dynamics from full controllability to dynamic chaos with sensitive dependence of outputs on small variations in the initial conditions and control parameters. Atoms in optical lattices and high-quality cavities are ideal objects to study a variety of phenomena in the atom-field interaction, including dynamic symmetries [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and dynamic chaos [13,[18][19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Prants

2015

J Russ Laser Res

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We consider dynamic symmetry, quantum control, and dynamic chaos of atoms moving in high-quality cavities. We review the group-theoretical approach to solve the evolution equations in the cavity quantum electrodynamics and control the quantum evolution in a micromaser device. Taking into account the photon recoil effect, we study nonlinear dynamics of the fundamental interactions between two-level atoms and a quantized cavity field. The strongly coupled atom-field system is treated as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. Interaction of the purely quantum atom-field system with the classical translational atomic degree of freedom results in emergence of classical dynamic chaos from quantum electrodynamics. That chaos is shown to manifest itself in some ranges of the control parameters in the exponential sensitivity of quantum atomic variables to small variations in the initial conditions and in the appearance of dynamic atomic fractals. We discuss how to observe this effect in real experiments. Our findings establish a quantum-classical correspondence in the cavity quantum electrodynamics.

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“…Detector initially in excited state (3,15), (4,14), (5,13), (6, 11), (7,8), (7,9), (8, 2), (8, 3), (8, 4)}. For the initially excited detector, the number expectation values are underestimated only for those modes with associated energies that are close to the detector's gap for low accelerations; for higher accelerations this will get shifted in l direction mainly due to the Doppler shift.…”

Section: Validity Of Non-relativistic Approximationmentioning

confidence: 99%

Relativity and quantum optics: accelerated atoms in optical cavities

Lopp¹,

Martín-Martínez²,

Page³

2018

Class. Quantum Grav.

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We analyze the physics of accelerated particle detectors (such as atoms) crossing optical cavities. In particular we focus on the detector response as well as on the energy signature that the detectors imprint in the cavities. In doing so, we examine to what extent the usual approximations made in quantum optics in cavities (such as the single-mode approximation, or the dimensional reduction of 3+1D cavities to simplified 1+1D setups) are acceptable when the atoms move in relativistic trajectories. We also study the dependence of these approximations on the state of the atoms and the relativistic nature of the trajectory. We find that, on very general grounds, and already in the weak coupling limit, single-and few-mode approximations, as well as 1+1D dimensional reductions, yield incorrect results when relativistic scenarios are considered.

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Semiclassical interaction of moving two-level atoms with a cavity field: From integrability to Hamiltonian chaos

Cited by 29 publications

References 22 publications

Chaos and flights in the atom-photon interaction in cavity QED

Chaos and flights in the atom-photon interaction in cavity QED

Dynamic Symmetries, Control, and Chaos with Moving Atoms in High-Quality Cavities

Relativity and quantum optics: accelerated atoms in optical cavities

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