Exponential of a Quadratic in Boson Operators and Squeezed States

Anil Roy, C. L. Mehta

Xiaotong Ni, Yu-xi Liu, L. C. Kwek +1 more

Using exponential quadratic operators, we present a general framework for studying the exact dynamics of system-bath interaction in which the Hamiltonian is described by the quadratic form of bosonic operators. To demonstrate the versatility of the approach, we study how the environment affects the squeezing of quadrature components of the system. We further propose that the squeezing can be enhanced when parity kicks are applied to the system.

Gerhart Schroff

Xiang‐Bin Wang, Yong-de Zhang, Jian-Wei Pan

A general approach to antinormally ordering the boson exponential quadratic operators (EQOs) is presented. By the approach, some important EQOs, including squeezed operator of one mode and two mode, linear quantum transformation operator, Bogolubov transformation operator are antinormally ordered.

Bogdan Mielnik

Xu Xiu-Wei, Ren Ting-Qi, Liu Shu-Yan +2 more

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.