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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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TL;DR: In this paper, the Bures fidelity for thermal states of a diagonalizable quadratic Hamiltonian in multi-mode Fock space was studied, where two photons are generated and one studies two or more modes.
Abstract: Fidelity, as a measure of the distinguishability of states, is an important concept in quantum mechanics, quantum optics and quantum information theory. Recently, the explicit expressions of fidelity for single-mode squeezed states have been given. However, in experimental studies, especially in non-degenerate parametric down-conversion, two photons are generated and one studies two- or more-mode systems. In this paper we study the Bures fidelity for thermal states of a diagonalizable quadratic Hamiltonian in multi-mode Fock space. To the best of our knowledge, no one has yet attempted to give an explicit general formula of fidelity of mixed states in multi-mode systems.
22 citations
TL;DR: In this article, a formalism for the construction of coherent states associated with inverse bosonic operators and their dual family has been proposed using nonlinear coherent states method and applied to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states.
Abstract: Using the nonlinear coherent states method, a formalism for the construction of the coherent states associated with 'inverse bosonic operators' and their dual family has been proposed. Generalizing the approach, the 'inverse of f-deformed ladder operators' corresponding to the nonlinear coherent states in the context of quantum optics and the associated coherent states have been introduced. Finally, after applying the proposal to a few known physical systems, particular nonclassical features as sub-Poissonian statistics and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been investigated.
22 citations
TL;DR: In this paper, group symmetries can be used to reconstruct quantum states in the context of the two-mode SU(1,1) states of the radiation field, where the input field passes through a nondegenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode.
Abstract: We show how group symmetries can be used to reconstruct quantum states The method we propose is presented in the context of the two-mode SU(1,1) states of the radiation field In our scheme for SU(1,1) states, the input field passes through a nondegenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode The density matrix in the Fock basis is retrieved from the measured data by the least-squares method after singular value decomposition of the design matrix followed by Tikhonov regularization Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered
22 citations
TL;DR: In this article, a specific basis of Fock states was constructed by including a real (continuous) parameter in the generators of the Heisenberg algebra, which formed new bases with respect to harmonic oscillator-like developments.
22 citations
TL;DR: In this paper, the authors investigated the SU(1,1) Lie algebra for the time-dependent quadratic Hamiltonian system and derived exact wave functions for the system.
Abstract: Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.
22 citations