Invariances for states of light and their quasi-distributions

Soumyabrata Paul, V. Balakrishnan, S. Ramanan +1 more

Octavio Castaños, Julio A. López-Saldívar

A review of the definition of Crystallized Schrödinger cat states and their statistical properties is presented. The associated Wigner and Husimi quasi-probability distribution functions are also calculated together with the second moment of the Husimi function. The Hamiltonian formulation of the Nöther's theorem is used to get the linear time dependent invariants of until general quadratic Hamiltonians in the quadratures of the electromagnetic field. By means of these invariants, the evolution of Crystallized Schrödinger cats is studied, thus we have explicit time dependent expressions for the means and dispersions of the quadratures of the electromagnetic field together with the corresponding Wigner and Husimi functions. By means of these results, we establish some conditions on the parameters of the Crystallized cat states to have the description of non-classical light.

Peter Michler, Simone Luca Portalupi

V. P. Karassiov, Vladimir Leonardovich Derbov, Sergue Il'ich Vinitsky

Polarization coherent states (PCS) are considered as generalized coherent states of SU(2)p group of the polarization invariance of the light fields. In terms of PCS the polarization quasi probability functions are defined, which determine the quasi classical description of the statistical polarization properties of quantum light fields. The geometric phases of PCS are introduced in a way analogous to that used in the classical polarization optics.

Arne Skov Jensen

B. M. Garraway, P. L. Knight

The probability distribution for finding a quantum state of the light field with a particular phase can be described by a number of theoretical methods. One of the most frequently used in quantum optics is the Pegg–Barnett phase distribution which identifies the phase distribution as the (necessarily positive) modulus square of the overlap of the quantum state with the relevant phase state. Other phase distributions have been proposed which employ the phase-sensitivity of various quantum quasi-probabilities such as the Wigner function. In this paper we discuss the connections between these approaches and illustrate their similarities and important differences for a number of pertinent quantum states of light. For some of these states, quantum interference can generate significant regions of phase space for which the Wigner quasi-probability is negative, and as we show, this may render the quasi-probability phase distribution negative. We discuss the general significance of this phenomenon.