Multipartite squeezed states as SU(1, 1) coherent states

Pradip Das

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.

Петер Адам, József Janszky

A. I. Solomon, Jacob Katriel

The authors present the results of an analysis of the squeezing of components of the (conventional) electromagnetic field in quantum group analogues of the Heisenberg-Weyl (HW) coherent state and SU(1,1) squeezed state. They find that squeezing occurs for all finite-q values not equal to unity in the HW q-coherent state, in contrast to the usual case; and also in the SU q (1,1) case, although here less than in the usual (q=1) SU(1,1) squeezed state.

Chon‐Fai Kam, Wei-Min Zhang, D.H. Feng

Christopher C. Gerry, Charles Johnson

We study the time evolution of SU(1,1) coherent states in an exactly solvable model of a single-mode quantized electromagnetic field in a four-photon medium that has previously been shown to give squeezed states from ordinary coherent states. If the SU(1,1) coherent state initially exhibits squeezing in the ${X}_{1}$ quadrature, the squeezing is revoked. We also show that for certain choices of phase in the initial state, enhanced squeezing may appear in the ${X}_{2}$ quadrature. Numerical results are also presented for the case when the model is not exactly solvable.