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Chinese Physics Letters

Mixed Squeezing for a Pair of Two-Mode Squeezed States

Fan Hong-Yi, Nai-Le Liu

Published Feb 8, 2001• 25 citations
Publisher

Abstract

Based on the neat ⟨η| representation of the two-mode squeezing operator which entangles signal-mode and idle-mode, where ⟨η| is the common eigenvector of the relative position of two particles and the total momentum exhibiting a maximal entanglement between the two modes, we study some kind of squeezing mixing 1-3 modes and 2-4 modes for a pair of two-mode (1-2 modes and 3-4 modes) squeezed states. The explicit form of such mixed squeezed states is derived and the new entanglement is analysed.

DOI
10.1088/0256-307x/18/3/304

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Based on the neat ⟨η| representation of the two-mode squeezing operator which entangles signal-mode and idle-mode, where ⟨η| is the common eigenvector of the relative position of two particles and the total momentum exhibiting a maximal entanglement between the two modes, we study some kind of squeezing mixing 1-3 modes and 2-4 modes for a pair of two-mode (1-2 modes and 3-4 modes) squeezed states. The explicit form of such mixed squeezed states is derived and the new entanglement is analysed.
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Two-mode entangled-state wavefunctions and with complex variables z and y are introduced and investigated. They are direct analogues of the wavefunctions and in the single-mode case or are linearly related to each other by two-dimensional Fourier transformation. The states and are eigenstates of two pairs of commuting operators ( Z , Z † ) (or ( Q + , P − )) and ( Y , Y † ) (or ( P + , Q − )) to eigenvalues ( z , z * ) and ( y , y * ), respectively, and are normalized by means of the two-dimensional delta function. The entangled states and are represented as two limiting cases of two-mode squeezed coherent states. Different representations of these states, in particular, the analogue of the Agarwal–Simon representation of squeezed vacuum states, are derived and the properties of these states are discussed. The transition from the single-mode to the two-mode case is made using the common property of the squeezing operators to belong to different realizations of the abstract SU (1,1) group. The Wigner quasiprobability in representation of the states and is discussed and is explicitly calculated for two-mode squeezed vacuum (and squeezed coherent) states.