Squeezed States: Basic Principles

Xu Jing-Bo, Tiezheng Qian, Xiao-Chun Gao

Óscar Rosas-Ortiz

John R. Klauder

Kazuyuki Fujii, Hiroshi Ôike

In this paper, we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states {|α, β〉|α, β ∈ C} makes a real four-dimensional surface in the Fock space ℱ (which is of course not flat), we can calculate its metric. On the other hand, we know that coherent-squeezed states satisfy the minimal uncertainty of Heisenberg under some condition imposed on the parameter space {α, β}, so that we can study the metric from the viewpoint of uncertainty principle. Then, we obtain a surprising simple form (at least to us). We also make a brief review on Holonomic Quantum Computation by use of a simple model based on nonlinear Kerr effect and coherent-squeezed operators.

A. D. Jannussis, E. Vlahos, Vasileios Bartzis

Yixiao Huang, Heng-Na Xiong, Wei Zhong +2 more

Abstract SU(1, 1) coherent and squeezed states have been widely studied in optical, hybrid atom–light, and spinor Bose–Einstein condensate experiments. Traditionally, the definition of SU(1, 1) squeezing refers to the uncertainty relationship, which implies that the SU(1, 1) coherent state is already squeezed if it is placed in an appropriate system of coordinates. In this report we investigate the basic concept of SU(1, 1) squeezing and discuss the principle for the generation of squeezed states. We establish a new definition of the squeezing criterion for the SU(1, 1) states. We study the dynamical properties in an atom–molecule system and show that the SU(1, 1) squeezed state can be generated with a nonlinear atomic interaction, which is similar to the one-axis twisting mechanism in spin squeezing. We also discuss the effect of the atomic number on squeezing, and show that the optimal squeezing and optimal squeezing angle exhibit a sudden transition at a fixed atomic number value.