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.

On detection of quasiclassical states

Abstract: We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a single operator.

Tomographic probability representation for states of charge moving in varying field

Abstract: The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the tomographic probability representation of quantum mechanics. The states are expressed in terms of quantum tomograms. The coherent states tomograms are shown to be described by normal distributions with varying dispersions and means. The Fock state tomograms are given in the form of probability distributions described by multivariable Hermite polynomials with time-dependent arguments.

Generation of nonlinear motional trio coherent states and their nonclassical properties

Abstract: Using the nonlinear coherent states approach, a general formalism for the construction of various classes of nonlinear trio coherent states in the context of multi-mode quantum states has been proposed. In particular, taking into account the most popular nonlinearity function associated with f-deformed coherent states, i.e. the nonlinearity function of the centre-of-mass motion of a trapped ion, it is illustrated that the corresponding trio coherent state possesses some interesting nonclassical properties. To establish this observation, sub-Poissonian statistics, three-mode squeezing, the behaviour of Vogel's characteristic function and the existence of entanglement are investigated. Due to the intrinsic non-classicality nature of the considered three-mode states, their physical production may be of high interest in the quantum optics field. Thus, we have finally demonstrated how nonlinear motional trio coherent states can be generated in three-dimensional anisotropic traps, appropriately.

Effective Casimir Conditions and Group Coherent States

Abstract: Properties of group coherent states can be derived "effectively" without knowing full wave functions The procedure is detailed in this article as an example of general methods for effective constraints The role of constraints in the present context is played by a Casimir condition that puts states within an irreducible representation of a Lie group (or, equivalently, on a quantization of a co-adjoint orbit of the dual Lie algebra) Simplifications implied by a Casimir condition, compared with general first-class constraints, allows one to show that the correct number of degrees of freedom is obtained after imposing the condition When combined with conditions to saturate uncertainty relations, moments of group coherent states can be derived A detailed example in quantum cosmology (cosmic forgetfulness) illustrates the usefulness of the methods