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arXiv:1309.2419 · Physica Scripta

Collective excitations of atoms and field modes in coupled cavities

N. A. Enaki, Sergiu Bazgan

Published Apr 1, 2014• 2 citations
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Abstract

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.

DOI
10.1088/0031-8949/2014/t160/014010

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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.
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.
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 problem of the coherent generation of the entanglement photon pairs by an ensemble of the two-level atoms passing through the cavity is studied. The dependence of the generation rate of the photon pairs as a function of the coherent states of the atomic stream is established. Considering that the flying time of the atoms passing through the cavity is less than decay time, a new method of the elimination of atomic variables from the system is proposed. The master equation for multimode cavity electromagnetic field is obtained. Using the Fokker–Planck equations, the steady state solution of this master equation is studied. The quantum properties of the multimode electromagnetic field are analyzed, using the non-diagonal P representation for su (1,1) symmetry.
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.