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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Problems of reversibility and exact solution in the cooperative interaction of four radiators with the quantum cavity field

N. A. Enaki, Tudor Roşca

Published Sep 12, 2010• 0 citations
Publisher

Abstract

An exact analytical approach for studying the time evolution of equidistant system of radiators prepared in a superposition of states in interaction with single cavity mode it is proposed. This method gives us the possibility to find the analytical representation of wave function for a large system of atoms. Exact solution for interaction of four radiators with quantum cavity field is presented. The representation of cavity field is studied as function of the number of atoms in the system. For odd numbers of radiators was established the following role: one atom have one quantum Rabi frequency, three atoms have two frequencies; fife atoms- thee nonzero frequencies. The zero value Rabi frequencies in the system is absent. For even atomic numbers the zero value of Rabi frequencies appear: two, four, six and so one. In the last case the number of collective level in the system is odd and the trapping states of the atoms in the cavity are possible.

DOI
10.1117/12.885003

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An exact analytical approach for studying the time evolution of equidistant system of radiators prepared in a superposition of states in interaction with single cavity mode it is proposed. This method gives us the possibility to find the analytical representation of wave function for a large system of atoms. Exact solution for interaction of four radiators with quantum cavity field is presented. The representation of cavity field is studied as function of the number of atoms in the system. For odd numbers of radiators was established the following role: one atom have one quantum Rabi frequency, three atoms have two frequencies; fife atoms- thee nonzero frequencies. The zero value Rabi frequencies in the system is absent. For even atomic numbers the zero value of Rabi frequencies appear: two, four, six and so one. In the last case the number of collective level in the system is odd and the trapping states of the atoms in the cavity are possible.
An exact analytical approach to study the time evolution of the interaction between a system of N two-level atoms with a single-mode cavity field is proposed. Supposing that at the initial moment the system of radiators is prepared in a superposition of states, the wave functions of the atom–field interaction for three and four atoms are presented exactly. In the case of an odd number of atoms in the cavity, the quantum Rabi frequencies have non-zero values; otherwise one zero value of the quantum Rabi frequency is characteristic of the even number of atoms. It was shown that with an increase of the odd number of atoms the non-zero quantum Rabi frequencies in the system increase too. It was established that a single atom has one quantum Rabi frequency, three atoms have two frequencies and five atoms have three. For the even number of atoms, a zero value of eigenstates of radiators in the interaction with a single cavity mode is observed. In this case the number of collective levels in the system is odd and the trapping states of atoms in the cavity are possible. From analytical solutions it follows that it is possible to realize the micro-maser regimes for three atoms choosing the flying time for which the radiators pass totally in the ground state. The dependence of the flying time on the number of atoms is established as well as the cavity state for which the atomic ensemble comes back to its initial state. The behavior of quantum fluctuations of photon numbers and atomic inversion during collective absorption and radiation is exactly analytically and numerically studied. The exact quantum solutions for these qubits, formed from two-level atoms, can be used in quantum processing of information encapsuled in the initial states of the atomic ensemble and the cavity field.
The transferred energy between two (three) radiators localized in two (three) cavities in interaction through an evanescent field is investigated. In the good-cavity limit the exact solution of the Schrödinger equation for this system is obtained. An interesting problem appears when the located excitation in one atom from one distinguished cavity is transferred to a second atom from another cavity. We analyze analytically and numerically the dynamics of the transferred energy as a function of the coupling constant between the cavities. Another interesting problem is the trapping condition for two atoms flying through different coupled cavities. For subsystems consisting of two atomic levels, we know that, only a dynamic trapping condition can be found. In this paper, we show that due to the coupling of the cavities, the trapping condition for two atoms flying through different cavities becomes possible. This effect depends on the coupling constants between the cavities and the dipole interaction between the radiators and cavity modes. A similar problem is studied in the bad-cavity limit, when the lifetime of photons in the cavity is smaller than the decay time of excited atoms. In this case, we write the analytical solution of the master equation and show its entanglement. We obtain that entangled states arise from non-entangled initial states of the atoms. The exact description of such a system opens up new possibilities for the processing of quantum information with two optical cavities.
In this paper the dynamics of wave fields in a cavity with one sinusoidally moving mirror are investigated. The wave equation is solved approximately using the method of multiple time scales. Frequency shifts as well as amplitude and phase modulations of cavity modes are given. In all cases when it is possible, an approximate effective field Hamiltonian operator is derived. In the adiabatic case it is then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic motion of a mirror can lead to suppression of the Rabi oscillations of atomic inversion.
The exact solution of the system consisted from two or three q-bits doped in coupled cavities is discussed. The problem of indistinguishable between the excited radiators and photons is analyzed using the intrinsic symmetry of the system. It is demonstrated that the solution is drastically simplified when the radiators and photons are considered as a new polariton excitations. The exact solution of Schrodinger equation is obtained for single and two excitations in each cavity taking into consideration the indistinguishable principle. This approach opens new possibilities in the interpretation of quantum entangled states in comparison with the traditional distinctive situation (see for example [1,2]) due to the decreasing of the number of degrees of freedoms in the system. Considering that the energies of coupling between the radiators and photons is larger than the coupling with external vacuum field, we have found the master equation for the dumping of collective excitations of the system of coupled radiators through the cavity fields. The time-dependence of population for new dressed quasi-levels of energy is obtained solving analytically and numerically the master equation.
Abstract The restoration of the initial state in the Raman interaction of the two atoms with the quantified pump and Stokes (anti-Stokes) cavity modes is analytically obtained. For this the su (2) symmetry representation of the bimodal field and a system of two atoms in scattering interaction is proposed for the simplification of the problem. Using the proprieties of the generators su (2) algebra the exact non-stationary solution of the system of two atoms in interaction with the bimodal field is found, taking into consideration the initial disentangled state between the atomic and field superposition. It is demonstrated that after this collapse and revivals of the inversion of flying atoms in the processes of absorption and emission of the photons from Stokes and pump modes the system atoms and field becomes entangled. The conditions of the restoration of the initial state of the atom-field system were established as a function of the flying time through the resonator possible. A set of discrete flying time intervals for the restoration of the initial disentangled state was found.
The quantum mechanical analysis for a non-resonant case of a single radiation mode interacting with a two-level atom in a cavity is studied. Expressions for the mean value of photon number and the time evolution of the atomic motion are given. The frequency of exchange energy between the atomic levels and the radiation field systems for non- resonant and resonant interactions is obtained. Results for all initial states of the atom-radiation field are presented. Results for resonant and non-resonant interactions are compared.