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.

Generalized definition of coherent states and dynamical groups

Abstract: It is shown that coherent states may be defined for an arbitrary dynamical (Hamiltonian) quantum system and the definition is consistent with the requirement that the Hamiltonian commutes with a Lie algebra γ, and γ can be integrated to form a Lie groupG.

Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states: The quantum-classical divide and computational-complexity transitions in linear optics

Abstract: Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.

N-dimensional affine Weyl-Heisenberg wavelets

Abstract: n-dimensional coherent states systems generated by translations, modulations, rotations and dilations are described. Starting from unitary irreducible representations of the n-dimensional affine Weyl-Heisenberg group, which are not square-integrable, one is led to consider systems of coherent states labeled by the elements of quotients of the original group. Such systems can yield a resolution of the identity, and then be used as alternatives to usual wavelet or windowed Fourier analysis. When the quotient space is the phase space of the representation, different embeddings of it into the group provide different descriptions of the phase space.

New photon-added and photon-depleted coherent states associated with inverse q-boson operators: nonclassical properties

Abstract: In this paper, we introduce a new family of photon-added as well as photon-depleted q-deformed coherent states related to the inverse q-boson operators. These states are constructed via the generalized inverse q-boson operator actions on a newly introduced family of q-deformed coherent states (Quesne C 2002 J. Phys. A: Math. Gen. 35 9213) which are defined by slightly modifying the maths-type q-deformed coherent states. The quantum statistical properties of these photon-added and photon-depleted states, such as quadrature squeezing and photon-counting statistics, are discussed analytically and numerically in the context of both conventional (nondeformed) and deformed quantum optics.