Multi-headed symmetrical superpositions of coherent states

TL;DR

This paper introduces and compares multi-headed superposition states of coherent states with phase-space symmetry, analyzing their quantum properties and identifying unique squeezing behavior in specific cases.

Contribution

It proposes N-headed incoherent and coherent superposition states based on roots of complex numbers, expanding the understanding of symmetric superpositions in quantum optics.

Findings

Only 2HCSS exhibits quadrature squeezing.

Different superposition states have distinct photon number and Wigner function characteristics.

Theoretical results serve as a reference for future research in quantum state engineering.

Abstract

Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated with N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. Among all these states, only 2HCSS (i.e., Schrodinger cat state) presents quadrature-squeezing effect. Our theoretical results can be used as a reference for researchers in this field.