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Modern Physics Letters B

HIGHER-ORDER SUCCESSIVE SQUEEZED NUMBER AND COHERENT STATES

Vasile A. Popescu

Published Jul 10, 2000• 1 citation
Publisher

Abstract

The statistical properties of the higher-order squeezed thermal states [V. A. Popescu, Mod. Phys. Lett. B14, 203 (2000)] and of the higher-order squeezed number and coherent states (this paper) can be improved by successive application of the squeeze operator. We compare our method with the usual procedure for higher-order squeezing and with another way for superposition of two squeezed coherent states.

DOI
10.1142/s0217984900000781

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The statistical properties of the higher-order squeezed thermal states [V. A. Popescu, Mod. Phys. Lett. B14, 203 (2000)] and of the higher-order squeezed number and coherent states (this paper) can be improved by successive application of the squeeze operator. We compare our method with the usual procedure for higher-order squeezing and with another way for superposition of two squeezed coherent states.
We have investigated the properties of two-mode squeezed states of various kinds: squeezed coherent states, squeezed number states, squeezed thermal states, and squeezed number-thermal states. The properties studied include characteristic functions, photon number distributions, and high-order moments. We show that a two-mode squeezed coherent state appears in either of its modes as a Glauber-Lachs superposition of a coherent signal with thermal noise; this generalizes the well-known thermofield result that a two-mode squeezed vacuum state behaves like a pure thermal state in either of its modes. We investigate the higher-order squeezing (in the sense of Hong and Mandel) of squeezed coherent-thermal and squeezed number-thermal states. Although the squeezing is found to increase with order in both cases, there are nevertheless interesting differences that can be traced to the fact that the Wigner function has a Gaussian form for the former but not for the latter.
By extending the usual two-mode squeezing operator S2 = exp [iλ (Q1P2 +Q2P1)] to the three-mode squeezing operator S3 = exp {iλ [Q1 (P2 + P3) +Q2 (P1 + P3) +Q3 (P1 + P2)]}, we obtain the corresponding three-mode squeezed coherent state. The state’s higher-order properties, such as higher-order squeezing and higher-order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement comparing with the usual cases. In addition, we examine the violation of Bell-inequality for the three-mode squeezed states by using the formalism of Wigner representation. PACS: 03.65.-W; 03.65.Ud
Much attention has been given in the past to two classes of squeezed states: the squeezed vacuum and coherent states. Here we study the effects of squeezing on number states and on thermal field states. The statistical properties of these various squeezed states are discussed using the second-order correlation functions. The quasiprobabilities of the Wigner, Q, and positive P representations are calculated and compared for the squeezed states. The Glauber P representation for the squeezed thermal state explicitly shows the limit of its applicability. The photon number distributions of the squeezed number and squeezed thermal states are extensively discussed and new interference effects in phase space are shown to lead to highly structured number distributions.
By use of the squeezed-number-state basis, we study several features of the squeezed thermal states. Higher-order squeezing properties are found to be entirely determined by the second-order ones. The photon-number distribution is expressed in closed form in terms of a Legendre polynomial. We point out that at a critical value of the squeeze parameter, pairwise oscillations of the photon-number distribution set in. Finally, a compact analytical expression of the exact lth-order correlation function is derived and examined.