Statistical properties of the squeezed displaced number states

Abstract

Squeezed Displaced Number States of the light w ere introduced in the recent literature. They exhibit various nonclassical properties as sub-Poissonian statistics, squeezing and oscillations in the photon-number distribution. Here we i n vestigate other properties of these elds, as waiting-time and photoelectron-counting distributions. We considerably simplify previous calculations in the literature while showing that these states constitute a uni ed approach for number, coherent, and squeezed states. I IntroductionIn recent y ears, many authors have i n vestigated new quantum states of the electromagnetic eld. The squeezed state can be considered as one of the most studied state 1 . It is characterized by the fact that the indetermination in one of the two quadraturecomponents of the electromagnetic eld is smaller than in the usual coherent states. It is of great importance, as in optical communication and interferometry 2 . Special attention is given to three classes of squeezed states: i squeezed vacuum states, ii squeezed coherent states and iii squeezed number states.Here we will study a new class of squeezed states, called Squeezed Displaced Number State SDNS , recently introduced in the literature 3 . We show that this class contains, as particular cases, various states already studied in the literature, such as the squeezed coherent states 4 , squeezed number states 5 , displaced number states 6 , including the coherent state and number states. The photoelectron-counting distribution P m; T and the distribution of waiting-time intervals ! ; between the arrivals of successive photons, are analyzed as a function of various parameters. Depending on the values of the parameters characterizing a particular realization of the SDNS, it may exhibit sub-Poissonian or super-Poissonian statistics, which i s analyzed in terms of Mandel's Q -parameter. As a consequence, it exhibits photon bunching or photon antibunching, which is analyzed in terms of the distribution ! .This paper is organized as follows: In Section II we introduce the SDNS and analyze the photon number distribution Pj, including variances of number operatorn = a +â and quadrature operators b X 1 = a+â y =2 and b X 2 = a ,â y =2i, whereâ y â is the creation annihilation operator for photons in a single-mode state. In Section III we analyze the photoelectron-counting distribution Pm; T and in Section IV we discuss the behavior of waiting-time distribution ! : Finally, Section V contains a summary of results and conclusion.

Squeezing metrology: a unified framework

“…For a quadrature squeezed displaced state we find X = √ 2Re(α), and ∆P = e −ξ / √ 2, where α and ξ are the displacement and squeezing parameters and where we choose real ξ (the only interesting case here). Since H = |α| 2 + sinh 2 |ξ| [44], it is clear that the good strategies (the ones which do not waste energy) are the ones where α sq and α cl are real. For these, ∆φsq (15) where the last equality holds for large squeezing |ξ| 1 and for the optimal classical strategy that, again, is for a † a = ∆H = ∆H 2 = α 2 cl = 1.…”