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Journal of Nonlinear Optical Physics & Materials

EVOLUTION OF ATOM-FIELD PROBABILITY IN A COUPLED CAVITY SYSTEM

K. V. PRIYESH, R. B. Thayyullathil

Published Sep 1, 2013• 0 citations
Publisher

Abstract

In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.

DOI
10.1142/s021886351350029x

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In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.
The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated. The exact dynamic solutions in the general condition are obtained via Laplace transform. The simple analytical solutions are obtained in several particular cases, which demonstrate the clear and simple physical picture for the quantum state transition of the system. In the large detuning or hoppling case, the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode. In the large coupling case, the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities. In the case of λ ≈ Δ ≫ g , the quantum states transition of qubits is accompanied by the excitation of the cavity, and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.
In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength ggg and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of ggg and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.
The dynamical evolution of a quantum system composed of two coupled cavities, each containing a two-level atom and a single-mode thermal field, is investigated under different conditions. The entanglement between the two atoms is controlled by the hopping strength and the detuning between the atomic transition and the cavities. We find that when the atomic transition is far off-resonant with both the eigenmodes of the coupled-cavity system, the maximally entangled state for the two atoms can be generated with the initial state in which one atom is in the ground state and the other is in the excited state. When both the two atoms are initially in the excited state, the entanglement exhibits periodical sudden birth and death. By choosing appropriate parameter values, the initial maximal entanglement of the two atoms can be frozen. The relation between the concurrence and the cooperative parameter is calculated.
We study the one-excitation dynamics of a coupled cavity system composed of three cavities, each containing a two-level atom. By adjusting the atom–cavity detuning Δ, cavity–cavity hopping rate v and the initial atomic excitation residential, a wide variety of time-evolution behaviors can be realized. Under certain conditions, the two-atom maximally entangled states and three-atom W states can be obtained. The results provide a theoretical basis for the manipulation of quantum states in such a system and will contribute to the understanding of more complex systems.
We study the dynamics of a ∨-type three-level atom in the cavity employing the dressed state of the system. We consider a ∨-type three-level atom initially in a different state that interacts with two mode photons in a closed cavity. The initial state of the atom and Rabi frequency have a significant effect on the population exchange between excited and ground levels. The numerical results show that the atom-field coupling strength determines the fast and slow periodic oscillation of the probability between the upper and ground states. The highest probability of finding it in the upper and ground states is determined by the initial state conditions of the atom. In general, the initial state conditions of the atom and the atom-field coupling strength have a significant effect on population transfer between the upper and ground states of a ∨-type three-level atom.