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Computational Methods in Science and Technology

Cellular Automata Simulations for the System of Two-Level Atoms Placed in Two-Dimensional Cavity

T.V. Nguyen, Dieu Tien Bui, Van Cao Long, W. Leoński

Published Dec 30, 2013• 1 citation
Publisher

Abstract

In this paper, using one of the most effective simulation methods, namely the cellular automata formalism, we simulate the dynamics of a system which is composed of a large number of two-level atoms placed in a two-dimensional cavity.We suppose additionally that the cavity is confined by four semi-transparent "mirrors".We show that similarly to the one-dimensional case, several interesting effects including the molasses effect occur in the considered system.

DOI
10.12921/cmst.2013.19.04.189-194

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In this paper, using one of the most effective simulation methods, namely the cellular automata formalism, we simulate the dynamics of a system which is composed of a large number of two-level atoms placed in a two-dimensional cavity.We suppose additionally that the cavity is confined by four semi-transparent "mirrors".We show that similarly to the one-dimensional case, several interesting effects including the molasses effect occur in the considered system.
We propose to adapt the cellular automata approach as a tool for investigation of quantum optical systems. As an example we propose a model comprising a cavity filled with a one dimensional chain of identical two level atoms. To simulate the probabilistic character of a single atom evolution we use the Monte Carlo algorithm. We assume that the cavity is confined by mirrors of the reflectivity r. This fact allows simulation of the cavity losses. In this communication we shall show the influence of the probabilities of photon absorption by a single atom inside the cavity, on the system dynamics.
Recently, strong coupling dominating dissipative and decoherence effects between the atom and a quantum cavity has been investigated experimentally. In this paper, we study the entanglement dynamics of two two-level atoms coupling to a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. We consider the effects of both Markovian dynamics and non-Markovian dynamics on the entanglement evolution of the two central atoms. Our results show that the steady entanglement can be generated between the two central atoms whether the system is under the Markov regime or non-Markov regime when the number of atoms of the atomic mirrors is finite. When the number of the atomic mirrors is large enough, the entanglement of two central atoms takes oscillating behavior without a stable value. The effect of detuning and dissipation on entanglement dynamics is also discussed and the results imply that the detuning plays an important role in improving the entanglement amplitude.
We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
It has great meaning to study the effect of a moving mirror in a cavity on the dynamic behavior of a two-level atom injected in the cavity. In this paper, for a system composed of a two-level injected atom and a single-mode field and a moving mirror in the cavity (the moving mirror to be regarded as a quantum harmonic oscillator with frequency ωm), the time-evolution of its state is obtained by means of complete quantum theory in the interaction picture. The time-evolution of the atomic population is derived on the basis of former investigations. It is found that the atomic population oscillates near its initial value. The result shows that the periodic motion of the mirror has a periodic effect on the atomic population.
The behavior of a two-level atom in a half-cavity, i.e., a cavity with one mirror, is studied within the framework of a one-dimensional model with respect to spontaneous decay and resonance fluorescence. The system under consideration corresponds to the setup of a recently performed experiment [J. Eschner et al., Nature (London) 413,413,413, 495 (2001)] where the influence of a mirror on a fluorescing single atom was revealed. In the present work special attention is paid to the regime of large atom-mirror distances where intrinsic memory effects can not longer be neglected. This is done with the help of delay-differential equations which contain, for small atom-mirror distances, the Markovian limit with effective level shifts and decay rates leading to the phenomenon of enhancement or inhibition of spontaneous decay. Several features are recovered beyond an effective Markovian treatment, appearing in experimentally accessible quantities like the intensity or emission spectra of the scattered light.