Statistical and phase properties of the binomial states of the electromagnetic field

Abstract

We investigate the nonclassical properties of the single-mode binomial states of the quantized electromagnetic 6eld. We concentrate our analysis on the fact that the binomial states interpolate between the coherent states and the number states, depending on the values of the parameters involved. We discuss their statistical properties, such as squeezing (second and fourth order) and sub-Poissonian character. We show how the transition between those two fundamentally diferent states occurs, employing quasiprobability distributions in phase space, and we provide, at the same time, an interesting picture for the origin of second-order quadrature squeezing. We also discuss the phase properties of the binomial states using the Hermitian-phase-operator formalism.

Bell’s inequality violation for entangled generalized Bernoulli states in two spatially separate cavities

“…We analyze the dependance of the correlations on the values of the system variables. Since we are considering singlemode electromagnetic fields of frequency ω inside cavities of volume V , the quantized electric field inside each cavity j (j = 1, 2), at the time t j = 0, can be written aŝ E j (z j ) = ǫ jÊj (z j ), where [20] …”

Nonlocal properties of entangled two-photon generalized binomial states in two separate cavities

“…The quantized electric field inside each single-mode cavity C j (j = 1, 2) of frequency ω and volume V , can be written, at the time t j = 0 and in the center of the cavity, asÊ j (z j ) = e jÊj where [20]…”

Correspondence between generalized binomial field states and coherent atomic states

“…One of their peculiarities is that they are "intermediate" between the number state and the coherent state. Because of their interesting features, BSs have been subject of several studies aimed at determining their properties and possible applications [1,2,4,5,6,7,8,9]. Recently, interest has again arisen about GBSs because of the discover that they can be exploited as reference states within schemes devoted at measuring the canonical phase of quantum electromagnetic fields [10,11].…”

“…They are defined as a finite linear superposition of field number states |n weighted by a binomial counting probability distribution. BSs are characterized by a maximum number of excitations N and a probability of single excitation occurrence p. When they are also characterized by a mean phase φ [2], they are called generalized binomial states (GBSs) [1,3]. One of their peculiarities is that they are "intermediate" between the number state and the coherent state.…”

“…However, most of the properties of BSs and GBSs have been previously obtained by algebraic procedures [1,2,3,4,5,16,17], that often make non intuitive both the determination and interpretation of these properties. In particular, the orthogonality between two GBSs, that plays a fundamental rule in the study of classical-quantum superpositions, has been reported only recently [3].…”