Abstract

We revisit the Perelomov ${\rm SU}(1,1)$-displaced coherent states as possible quantum states of light. We disclose interesting statistical aspects of these states in relation to photon counting and squeezing. In the non-displaced case, we discuss the efficiency of the photodetector as inversely proportional to the parameter $\varkappa $ of the discrete series of unitary irreducible representations of ${\rm SU}(1,1)$. In the displaced case, we study the counting and squeezing properties of the states in terms of $\varkappa $ and the number of photons in the original displaced state. We finally examine the quantization of a classical radiation field based on these families of coherent states. The procedure yields displacement operators that might allow to prepare such states in the way proposed by Glauber for standard coherent states.

© 2023 Optica Publishing Group

Lowering the Helstrom bound with non-standard coherent states

Evaldo M. F. Curado, Sofiane Faci, Jean-Pierre Gazeau, and Diego Noguera
J. Opt. Soc. Am. B 38(12) 3556-3566 (2021)

SU(1,1) parity and strong violations of a Bell inequality by entangled Barut–Girardello coherent states

Edwin E. Hach, Richard Birrittella, Paul M. Alsing, and Christopher C. Gerry
J. Opt. Soc. Am. B 35(10) 2433-2442 (2018)

Correlated two-mode SU(1, 1) coherent states: nonclassical properties

Christopher C. Gerry
J. Opt. Soc. Am. B 8(3) 685-690 (1991)

Coherent states, squeezed fluctuations, and the SU(2) am SU(1,1) groups in quantum-optics applications

K. Wodkiewicz and J. H. Eberly
J. Opt. Soc. Am. B 2(3) 458-466 (1985)

Pseudospin approach to the dynamics and squeezing of SU(2) and SU(1, 1) coherent states

P. K. Aravind
J. Opt. Soc. Am. B 5(7) 1545-1553 (1988)