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.

Detecting mode entanglement: The role of coherent states, superselection rules, and particle statistics

Abstract: We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such experiments, and we comment on the existence of coherent states in nature. The discussion of coherent states naturally raises questions about the role of particle statistics in this problem. Although the Pauli exclusion principle precludes coherent states with a large number of fermionic particles, we find that a large number of fermionic coherent states, each containing at most one particle, can be used to achieve the same effect as a bosonic coherent state for the purposes of this problem. The discussion of superselection rules arises naturally in this context, because their applicability to a given situation prohibits the use of coherent states. This limitation particularly affects the scenario that we propose for detecting the mode entanglement of fermionic particles.

Elliptic eigenstates for the quantum harmonic oscillator

Abstract: A new family of stationary coherent states for the two-dimensional harmonic oscillator is presented. These states are coherent in the sense that they minimize an uncertainty relation for observables related to the orientation and the eccentricity of an ellipse. The wavefunction of these states is particularly simple and well localized on the corresponding classical elliptical trajectory. As the number of quanta increases, the localization on the classical invariant structure is more pronounced. These coherent states give a useful tool to compare classical and quantum mechanics and form a convenient basis to study weak perturbations.

Optimal local expansion of W states using linear optics and Fock states

Abstract: We derive the maximum success probability of the circuits with passive linear optics for expanding an N-photon W state to an (N + n)-photon W state, by accessing only one photon of the initial W state and adding n photons in a Fock state. We show that the maximum success probability is achieved by a polarization-dependent beamsplitter and n-1 polarization-independent beamsplitters.

Square integrability of group representations on homogeneous spaces. II : Coherent and quasi-coherent states. The case of the Poincaré group

Abstract: The concept of a reproducing triple, developed in the first paper of the series (I), is utilized to give a general definition of a square integrable representation of a group. This definition is applicable to homogeneous spaces of the group, and generalizes earlier attempts at obtaining such notions. Among others, it leads naturally to a notion of equivalence among families of coherent states, and also to the concept of quasi-coherent states, or weighted coherent states. The general considerations are applied to the specific example of the Wigner representation of the Poincare group P+up (1, 1) in one space and one time dimensions. A whole class of equivalent families of coherent states is derived, each of which corresponds to a continuous frame, in the sense of I.

Generalized coherent states and quantum-classical correspondence

Abstract: Gaussian Klauder coherent states are constructed for the harmonic oscillator, the planar rotor, and the particle in a box. The standard harmonic oscillator coherent states are given by expansions in the eigenstates of the Hamiltonian in terms of a complex parameter \ensuremath{\alpha}. When the complex modulus of \ensuremath{\alpha} is large, these states are identical in behavior with a particular choice of Gaussian Klauder coherent state. When the angular momentum of a planar rotor is large compared with Planck's constant, the angle distribution associated with a Gaussian Klauder coherent state for this case remains sharply localized for many rotations. Similarly, for the particle in a box, it is possible to choose parameters in the Gaussian Klauder coherent state so that a localized particle bounces back and forth at constant velocity between the walls of the box for many periods without significant delocalization. Buried in this behavior is the Fourier series for a triangle wave. These examples show how Gaussian Klauder coherent states are of utility in understanding quantum-classical correspondence.