Multi-directional higher-order amplitude squeezing

Abstract

Fan-even K-quantum nonlinear coherent states are introduced and higher-order amplitude squeezing is investigated in such states. It is shown that for a given K the lowest order in which an amplitude component can be squeezed is 2K and the squeezing appears simultaneously in K directions separated successively in phase by π/K.

Hillery-type Amplitude Squeezing in Linear and Nonlinear Fan-states

“…But in the case of the driven trapped ion, there are more physical parameters: The Ω 0,1 which are controllable by the driving laser fields and η which is controllable by trapping potential. Using (14)(15)(16) and (27), we can derive the Hillery-type N-powered amplitude squeezing for arbitrary N and k. For the specific nonlinear function f in (27), the simulation shows that for a given k the Hillery-type is squeezed only for N = 2k in some range of the values of ξ 2 and η 2 . In the trapped ion, by controlling the Lamb-Dicke parameter and the pure transition Rabi frequencies, the higher order squeezing in nonlinear fan-states may occur along N directions.…”

“…The second type of higher-order squeezing which is qualitatively different from that by Hong and Mandel, was defined by Hillery [10] and then developed further by many authors (see, e.g., [11][12][13]). The Hong-Mandel-type N -order amplitude squeezing has recently been studied in the fanstates | ξ; 2k, f F which is introduced in [14] as a linear superposition of 2k 2k-quantum nonlinear coherent states in the phase-locked manner. In this paper, we study properties of the Hillery-type N -powered amplitude squeezing in the fan-states.…”