Wehrl information entropy and phase distributions of Schrödinger cat and cat-like states

Abstract

Abstract. The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schrödinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schrödinger cats (including even, odd and Yurke-Stoler coherent states), as well as the cat-like states generated in Kerr medium are analyzed in detail. It is shown that, in contrast to the Wehrl entropy, the Wehrl phase distribution properly distinguishes between different superpositions of unequally-weighted states in respect to their number and phasespace configuration.

Quasi-Bell states in a strongly coupled qubit–oscillator system and their delocalization in the phase space

“…V.A. In the presence of a Kerr-type of nonlinear Hamiltonian an initial coherent state is known to evolve [30][31][32][33], at specified times, to discrete superposition of coherent states. We will discuss the similarities and dissimilarities of these results with that of the present example in Subsec.…”

“…In its region of validity the leading terms in the theta function structure provides simple estimates, say, for the revival time for the off-diagonal qubit matrix element. Analysing the Q-function in the Kerr-like nonlinear self-interacting photonic models it has been observed [30][31][32][33] that an initial coherent state therein evolves, at certain specified times, to macroscopic superposition of coherent states popularly known as 'kitten' states. In the current qubit-oscillator interacting model the reduced density matrix of the oscillator shows similar properties with, however, an important distinction that stems from the existence of interaction-generated multiple time scales.…”

Interplay of information quantifiers and the modified Jaynes-Cummings model

“…We can specialize things by recourse to the Wehrl phase distribution (Wehrl PD), defined to be the phase density of the Wehrl entropy [18,19,22], i.e.,…”

“…As a consequence, we are led to the concept of Wehrl phase distribution (WPD), that has been extensively developed and shown to be a successful indicator of both noise (phase-space uncertainty) and phase randomization [18,19]. Furthermore, the FWE has been fruitfully applied to dynamical systems.…”

“…In this respect we must mention that the FWE-time evolution in the case of the Jaynes-Cummings model has been thoroughly investigated in [17,20,21]. The FWE i) turns out to be more apt for distinguishing amongst states than the NE [18,19] and ii) is known to yield helpful information on atomic inversion processes. Indeed, FWE-studies of the canonical setting in which a single-trapped ion interacts with a laser field (with different field configurations) have been considered in [22].…”