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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 authors extend their previous work on coherent paired states associated with the Lie group SU(1,1) and define new coherent states in terms of two distinct types of bosons or oscillators.
Abstract: The authors extend their previous work on coherent paired states associated with the Lie group SU(1,1). Whereas the earlier states were defined with respect to a single type of canonical boson or (linear) quantum harmonic oscillator, the new states are defined in terms of two distinct types of bosons or oscillators. The new coherent states may again, on the one hand, be viewed as ordinary (Glauber) coherent states in the two-boson Hilbert space spanned by arbitrary numbers of two distinct Bogoliubov quasiparticles associated with the original bosons via a generalised Bogoliubov transformation. Alternatively, expressed wholly in terms of the original bosons these new coherent states are reached from the ordinary coherent states via a unitary (pairing) transformation which is shown to be associated with the entire so-called discrete series of representations of the group SU(1,1). As an important illustration of the use of these states and transformations, they study in detail a rather general class of quantum Lagrangians which includes the damped linear harmonic oscillator. They thereby illustrate their possible usefulness in applications to quantum many-body or field-theoretic processes involving fluctuation-dissipation phenomena in general.
17 citations
TL;DR: In this article, the fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed, and the authors propose and demonstrate the superior cloning of coherent states under the Gaussian assumption.
Abstract: The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and feedforward.
16 citations
TL;DR: The relationships between certain important nonclassical states of the quantized field and the coherent states associated with the SU(2) and SU(1,1) Lie groups and associated Lie algebras is briefly reviewed.
Abstract: The relationships between certain important nonclassical states of the quantized field and the coherent states associated with the SU(2) and SU(1,1) Lie groups and associated Lie algebras is briefly reviewed. As an example of the utility of group theoretical methods in quantum optics, a method for generating maximally entangled photonic states is discussed. These states may be of great importance for achieving Heisenberg-limited interferometry and in beating the diffraction limit in lithography.
16 citations
TL;DR: A path integral written in terms of the group theoretic coherent states by using the Kahler structure of the coherent state manifold with the particular emphasis on the boundary fixing term derivation is considered in this paper.
Abstract: A path integral written in terms of the group theoretic coherent states by using the Kahler structure of the coherent state manifold with the particular emphasis on the boundary‐fixing term derivation is considered herein. The path integral for a propagator of the system with Hamiltonian linear in the SU(2)/SU(1,1) generators is shown to be diagonalized by an appropriate motion in the phase space.
16 citations
TL;DR: In this article, the problem of the time development of coherent states for a Hamiltonian of the type (1) was considered for the case of Hamiltonians of type (2).
16 citations