R. Tanaś

Entangled states and collective nonclassical effects in two-atom systems

We propose a review of recent developments on entanglement and nonclassical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

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.

Self-squeezing of light propagating through nonlinear optically isotropic media

Abstract In an isotropic medium in which light self-induces a cubic optical nonlinearity, the light field is shown to be in squeezed states on traversal of the medium. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is derived explicitly. A comparison is made to the photon antibunching effect in the same phenomenon.

Collapses, revivals, and phase properties of the field in Jaynes-Cummings type models

Abstract Phase properties of the field in a coherent state interacting with a two-level atom in a lossless cavity (Jaynes-Cummings models) are studied using the new phase formalism of Pegg and Barnet. The phase density distribution, the expectation values and the variances of the hermitian phase operator are calculated. On a polar diagram, the initial phase distribution is shown to split into two counterrotating satellite distributions. When two satellite distributions overlap, revivals of the atomic inversion occur. Phase properties of the field in a model with an intensity depending coupling, for which the time behavior is exactly periodic, are also discussed.

Phase properties of the two-mode squeezed vacuum states

Abstract The phase properties of the two-mode squeezed vacuum states are re-examined from the point of view of the Hermitian phase formalism introduced by Pegg and Barnett. The joint probability distribution for the phases of the two models is obtained, and the phase properties associated with this distribution are discussed thoroughly.

Squeezing from an anharmonic oscillator model: (a+)2a2 versus (a+a)2 interaction Hamiltonians

Abstract A comparison is made between squeezing obtained from two versions of the anharmonic oscillator model. The periodic revivals of squeezing in the long-time scale are shown to exist in both cases and the differences in this scale are shown explicitly. It is shown that in the short-time scale, for large number of photons, both versions of the model lead to the same results. The approximate formula describing the normally ordered variances in this case is derived and illustrated graphically. Some recent misinterpretations are clarified.

Squeezing in the third-harmonic field generated by self-squeezed light

A new mechanism for producing squeezed states in the third-harmonic field generated in isotropic media is discussed. It is shown that considerable squeezing is obtained if the third-harmonic field is generated by self-squeezed light resulting from a nonlinear propagation process. Analytical formulas describing this novel way of producing squeezed states are derived and illustrated graphically, showing strong correlations of squeezing in the fundamental and the third-harmonic beams.

Quantum fluctuations in the Stokes parameters of light propagating in a Kerr medium

Abstract The quantum theory of light propagation in a nonlinear Kerr medium is applied to calculate the Stokes parameters and their variances in the process of light propagation. Exact quantum formulae are derived for the expectation values of the Stokes operators and thus for the azimuth θ and ellipticity η of the beam. The role of quantum fluctuations in light polarization characteristics is discussed. The periodic behaviour of quantum evolution of the light polarization is revealed explicitly. It is shown that the degree of polarization is diminished at early stages of each period of the evolution but then reverts to its initial state of complete polarization at the end of the period. The variances of the Stokes parameters are also periodic and intensity-dependent; however, they never fall below their coherent state values.

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.

On the Possibility of Almost Complete Self-squeezing of Strong Electromagnetic Fields

The propagation of quantized electromagnetic fields through optically isotropic media with cubic optical nonlinearity is considered. Analytical solutions are presented in closed form showing that the light field can emerge from the medium in a squeezed quantum state. A detailed numerical analysis of the results is performed and presented graphically. Over 90 per cent of the squeezing permitted by quantum-mechanical theory is achieved in this way. The dependence of the squeezing effect on the polarization state of the field and the nonlinear molecular parameters is also discussed.