M. Kozierowski

Quantum fluctuations in second-harmonic light generation☆

Abstract Second-harmonic light generation (SHLG) is analyzed from the viewpoint of the photon statistics of the fundamental and generated beams versus the path traversed by the two waves in the medium. The calculations lead to an anti-bunching effect for coherent incident light.

Photon Antibunching and Squeezing

The occurrence of photon antibunching and squeezing is strongly connected with nonlinear optical phenomena in general. Recent results are presented for two-atom resonance fluorescence, the anharmonic oscillator, nonlinear propagation of light and higher-harmonic generation.

Dicke model: quantum nonlinear dynamics and collective phenomena

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.

Photon statistics in an N-level (N − 1)-mode system

Abstract The characteristic and photon-number distribution functions, the statistical moments of photon numbers and the correlations of modes are studied. The normally ordered variances of the photon numbers and the cross-correlation functions are calculated.

Many-atom spontaneous emission in a lossless cavity

Applying a perturbation method, constructed in terms of SU(2)-group representations, we investigate the anharmonic dynamics of spontaneous emission of a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially inverted. The phenomenon of collective collapses and revivals is revealed.

On an exactly solvable N-level system coupled to N-1 field modes

The time evolution of level population and photon number operators is found in the rotating wave approximation.

Photon Statistics in Thermal Multiphoton Jaynes-Cummings Models with an Initially Excited Atom

Abstract Analytical expressions for the time evolution of the mean photon number and normally ordered photon number variance for the case of an initially thermal cavity field coupled to an initially excited two-level atom with m-photon transitions are proposed. The emergence of sub-Poissonian field statistics is discussed.

Second-harmonic generation as a source of correlated coherent states☆

Abstract The field of the fundamental mode in the course of second-harmonic generation is shown to be in a correlated coherent state. Optimum squeezing occurs for the uncorrelated field quadrature components. Only then the field of the mode under consideration is in a minimum Heisenbergs uncertainty squeezed state.

Thermal and squeezed vacuum Jaynes–Cummings models with a Kerr medium

Abstract The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

Abstract Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.