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Lecture notes in physics

Coherent States

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

Published Jan 1, 2023• 11 citations
Publisher
DOI
10.1007/978-3-031-20766-2

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We discuss the coherence-assisted transformation of pure coherent states under incoherent operations and show that the amount of coherence loss can be reduced with the help of the auxiliary coherent state. Starting with the simplest case i.e., the main coherent state and auxiliary coherent state are both 2×2 dimensional, we compare the change of coherence before and after the transformation and find that the amount of coherence loss can be reduced due to the increase of the coherence of auxiliary coherent state. In general, when the main coherent state and auxiliary coherent state are high-dimensional, the result is also true. For the coherence of auxiliary coherent state is increased, we can get the maximally coherent state at some conditions, this case can be viewed as a new way for the distillation of coherent state. These interesting results of coherence transformation will give us a better understanding of the resource manipulation.
The nonclassical properties of the hybrid coherent state (HCS), which is the superposition state of the coherent state and photon-added coherent (PAC) state, is investigated analytically. We evaluated the photon number statistics, the Wigner-Yanase skew information, the Mandel Q factor and the quadrature squeezing of the HCS to quantify its nonclassicality. This superposition state exhibits more nonclassical properties than the PAC state and even the superposition state of coherent state and single-photon-added coherent (SPAC) state. We reported that the addition of more photons to the PAC state part of the HCS generally quantifies more nonclassicalities. The nonclassical properties of the HCS also depend on the amplitudes of coherent state and the PAC state in the HCS.
In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.