New application of Dirac's representation: N-mode squeezing enhanced operator and squeezed state

2009/03/05 by Xue-xiang Xu, Li-yun Hu, Li-Yun Hu +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.48550/arxiv.0903.0997

8 pages, no figure

arxiv created 2009/03/05 · openalex publication_date 2009/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that exp[i\lamda(Q₁P₁-i/2)] is a unitary single-mode squeezing operator, where Q₁,P₁ are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_n=Exp[i\lamda sum_i=1ⁿ](Q_iP_i+1+Q_i+1P_i))], (Q_n+1=Q₁P_n+1=P₁), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_n's normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

Related

• Squeezing: from numerical to conceptual problems
• Higher power squeezed states, Jacobi matrices, and the Hamburger moment problem
• Squeezed States for General Multiphoton Systems: Towards the displacement-operator formalism
• New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing
• Physical interpretation of generalized two-mode squeezing operator revealed by virtue of the transformation of entangled state representation