Nonlinear dynamics of the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the interaction of the purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Atomic fractals with self-similar intermittency of smooth and unresolved structures are found in the exit-time scattering function. Tiny interplay between all the degrees of freedom is responsible for dynamical trapping of atoms even in a very short microcavity. Gedanken experiments are proposed to detect manifestations of atomic fractals in cavity quantum electrodynamics.Nonlinear dynamics of the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the interaction of the purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Atomic fractals with self-similar intermittency of smooth and unresolved structures are found in the exit-time scattering function. Tiny interplay between all the degrees of freedom is responsible for dynamical trapping of atoms even in a very short microcavity. Gedanken experiments are proposed to detect manifestations of atomic fractals in cavity quantum electrodynamics.

Kluwer Academic Publishers eBooksJul 28, 20050 citations

Quantum Chaos and Quantum Fractals With Atoms and Photons in a Microcavity

Michael Yu. Uleysky, Sergei V Prants

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical egrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. It manifest itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with a prominent fractal-like behavior and in the quantum atom-filed degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom-field resonance correlate strongly. This result provides a quantum-classical correspondence in a closed physical system.Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality microcavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical egrees of freedom. We show that, even in the absence of any other interaction with environment, the coupling of quantum and classical degrees of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. It manifest itself in the atomic external degree of freedom as a random walking of an atom inside a cavity with a prominent fractal-like behavior and in the quantum atom-filed degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependences of variance of quantum entanglement and of the maximum Lyapunov exponent on the detuning of the atom-field resonance correlate strongly. This result provides a quantum-classical correspondence in a closed physical system.

ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)Jan 1, 20050 citations

Quantum control and quantum chaos in cavity QED

Michael Yu. Uleysky, Sergei V Prants

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.

International Conference Physics and ControlOct 4, 20060 citations

Quantum chaos and fractals with atoms in cavities

Michael Yu. Uleysky, Leonid E. Kon’kov, Sergey V. Prants

We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\\"odinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At large values of detuning $|\\delta|\\gg 1$ , the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep Rabi oscillations that may occur at any large value of $|\\delta|$ to be equal to $|\\alpha p_0|$ , is found numerically and described analytically (with $\\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. In the chaotic regime values of the population inversion $z_{out}$ , measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion $z_{in}$ that the probability of detecting any value of $z_{out}$ in the admissible interval becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\\"odinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At large values of detuning $|\\delta|\\gg 1$, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep Rabi oscillations that may occur at any large value of $|\\delta|$ to be equal to $|\\alpha p_0|$, is found numerically and described analytically (with $\\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. In the chaotic regime values of the population inversion $z_{out}$, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion $z_{in}$ that the probability of detecting any value of $z_{out}$ in the admissible interval becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.

Dec 2, 200210 citations

Atomic Fractals in Cavity QED

Sergei V Prants, Victor Yu. Argonov

We report a clear evidence of atomic fractals in the nonlinear motion of a two-level atom in a standing-wave microcavity. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependencies of outgoing positions and momenta of scattered atoms on their ingoing values and in the dependence of exit times of cold atoms on their initial momenta in the generic semiclassical models of cavity QED (1) with atoms in a far-detuned amplitude (phase)-modulated standing wave and (2) with coupled atomic external and internal degrees of freedom. Tiny interplay between all the degrees of freedom in the second model is responsible for trapping atoms even in a very short microcavity. It may lead simultaneously, at least, to two kinds of atomic fractals, a countable fractal (a set of initial momenta generating separatrix-like atomic trajectories) and a seemingly uncountable fractal with a set of momenta generating infinite walkings of atoms inside the cavity.We report a clear evidence of atomic fractals in the nonlinear motion of a two-level atom in a standing-wave microcavity. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependencies of outgoing positions and momenta of scattered atoms on their ingoing values and in the dependence of exit times of cold atoms on their initial momenta in the generic semiclassical models of cavity QED (1) with atoms in a far-detuned amplitude (phase)-modulated standing wave and (2) with coupled atomic external and internal degrees of freedom. Tiny interplay between all the degrees of freedom in the second model is responsible for trapping atoms even in a very short microcavity. It may lead simultaneously, at least, to two kinds of atomic fractals, a countable fractal (a set of initial momenta generating separatrix-like atomic trajectories) and a seemingly uncountable fractal with a set of momenta generating infinite walkings of atoms inside the cavity.

arXiv:physics/0206005Jun 3, 20020 citations

Entanglement, fidelity, and quantum-classical correlations with an atom moving in a quantized cavity field

Sergei V Prants, Michael Yu. Uleysky, Victor Yu. Argonov

Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics. It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic motion of the atomic center of mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high-finesse cavities.Stability and instability of quantum evolution are studied in the interaction between a two-level atom with photon recoil and a quantized field mode in an ideal cavity, the basic model of cavity quantum electrodynamics. It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic motion of the atomic center of mass in the quantized field of a standing wave in the absence of any kind of interaction with environment. This kind of quantum instability manifests itself in strong variations of reduced quantum purity and entropy, correlating with the respective classical Lyapunov exponent, and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. The connection between quantum entanglement and fidelity and the center-of-mass motion is clarified analytically and numerically for a few regimes of that motion. The results are illustrated with two specific initial field states: the Fock and coherent ones. Numerical experiments demonstrate various manifestations of the quantum-classical correspondence, including dynamical chaos and fractals, which can be, in principle, observed in real experiments with atoms and photons in high-finesse cavities.

arXiv:quant-ph/0511106Physical Review AFeb 9, 200635 citations

|\\delta|\\gg 1

, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep Rabi oscillations that may occur at any large value of

|\\delta|

to be equal to

|\\alpha p_0|

, is found numerically and described analytically (with

\\alpha

to be the normalized recoil frequency and

p_0

the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. In the chaotic regime values of the population inversion

z_{out}

, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion

z_{in}

that the probability of detecting any value of

z_{out}

in the admissible interval becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical for chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.