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Quantum Optics Journal of the European Optical Society Part B

Higher-order squeezing for even- and odd-displaced squeezed states

Hong-Yi Fan, Zhongxi Zhang

Published Oct 1, 1994• 8 citations
Publisher

Abstract

We study even- and odd-displaced squeezed states, which were proposed by us as 1/N e (D(z)+D(-z))S(r) mod 0) and 1/N 0 (D(z)-D(-z))S(r) mod 0). We find: (i) when z is real, the 2Nth moments in both states are larger than in the ordinary squeezed state; (ii) for the same z= mod z mod , the two states can not exhibit stronger squeezing than the squeezed state in the same order; (iii) under the condition mod z mod e -r square root 2>>1, the even (odd)-displaced squeezed state can respectively exhibit stronger (4k-2) (4k)-order (k=1,2,3,...) squeezing than the squeezed state.

DOI
10.1088/0954-8998/6/5/004

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Modern Physics Letters B•Jul 10, 2000•1 citation
We study even- and odd-displaced squeezed states, which were proposed by us as 1/N e (D(z)+D(-z))S(r) mod 0) and 1/N 0 (D(z)-D(-z))S(r) mod 0). We find: (i) when z is real, the 2Nth moments in both states are larger than in the ordinary squeezed state; (ii) for the same z= mod z mod , the two states can not exhibit stronger squeezing than the squeezed state in the same order; (iii) under the condition mod z mod e -r square root 2>>1, the even (odd)-displaced squeezed state can respectively exhibit stronger (4k-2) (4k)-order (k=1,2,3,...) squeezing than the squeezed state.
The one- and two-mode combination squeezed states are constructed by applying the operator U identical to exp(-i lambda (erQ1P2+e-rQ2P1)) or W identical to exp(-i lambda (erQ1Q2-e-rP1P2)) (where lambda , r are real; Qi, Pi, i=1, 2 are coordinate and momentum operators, respectively) to the vacuum state. When the condition tanh lambda <1/(1+cosh r) is satisfied, such states can have less fluctuations in one quadrature phase than the usual two-mode squeezed state. Here, the authors examine the higher-order squeezing properties for such states. The result shows that under the same conditions, these states can exhibit a stronger form of higher-order squeezing than the usual two-mode squeezed state.
In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.