We study the resonant interaction of A initially unexcited two-level atoms with single-mode Fock, coherent and thermal cavity fields of arbitrary intensity. Two mechanisms lead to a spread of the eigenfrequencies: one is due to the photon-number distribution in the initial state and the other reflects the cooperativity of the system. Both affect the evolution of the photon number and photon statistics. We present approximate expressions for the eigenvalues and eigenvectors of the system. Its regular dynamical regions are found and the difference in shape of the collapses and revivals connected with the above mechanisms is discussed.

https://iopscience.iop.org/article/10.1088/1355-5111/8/4/003/pdf

Dicke model: quantum nonlinear dynamics and collective phenomena

CQED has been an active field of research for the last three decades, describing the intimacy of the interaction of radiation and matter in small volumes λ3, and have demonstrated that modifies not only the nature of this interaction, but also atomic characteristic that often were thought intrinsic, such as spontaneous emission or the very quantum nature of the interaction. These conditions have acquired quite an importance for the current activity on Quantum computation and Information. However, most of that activity has been developed in the conceptual and experimental framework of atomic systems. There is evidence that such features also occurs in Quantum Dots. We compare the Dicke and Jaynes Cummings dynamics of atoms described by the Hamiltonian of Quantum Dots, and develop the SU(2) perturbative approach in the regimen where the excitation number (atoms + photons) is larger than the number of atoms L. We exhibit the dynamical detuning produced by the Forster interaction.

Comparison of the Dicke model and the Hamiltonian for n quantum dots

A system of N identical two-level atoms interacting with the single mode of the boson field is considered in the rotating-wave approximation. The solution of the Schrodinger equation with the initial condition of all atoms excited and the field in the coherent state is discussed. The resulting state is interpreted as an amplified state of the field correlated with the state of the system of atoms. The system of atoms is interpreted as an example of a nonlinear quantum amplifier. The algorithm to calculate the amplitude of the field at the output and its uncertainty is described. The relation of the mean value of the output field to the input one is interpreted as the amplification coefficient. The uncertainty of the output field is interpreted in terms of the noise of the amplifier. The dependencies of the noise on the amplification coefficient are plotted for several values of N. The noise is compared with the noise of an ideal linear amplifier of the same amplification coefficient. Conditions at which the nonlinear amplifier has less noise than the linear amplifier are found. Uncertainties of quadrature components which correspond to the amplitude and phase of the field are calculated. It is shown that only one of them has an uncertainty less than the uncertainty in the case of the ideal linear amplifier. Another definition of the amplification coefficient of the nonlinear quantum amplifier is suggested. The differential amplification coefficient gives the simple lower bound of the noise of the nonlinear amplifier. It prohibits the construction of a nonlinear amplifier with a signal-to-noise ratio better than that of an ideal linear amplifier. General bounds of the minimal noise in nonlinear amplifiers are compared with results for a particular amplifier.

S.M. Chumakov

Papers

Atomic coherence versus field incoherence : interaction of many atoms with a thermal quantized cavity field