Search results for "coherent state"
showing 10 items of 95 documents
Coordinate-free quantization of first-class constrained systems
1996
The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.
Noise-induced effects in nonlinear relaxation of condensed matter systems
2015
Abstract Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuat…
An invariant analytic orthonormalization procedure with applications
2007
We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis.
Squeezed Light Generation via Spatial Symmetry Breaking
2009
The spontaneous spatial symmetry breaking occurring in the transverse section of the light beam emitted by a degenerate optical parametric oscillator is shown to give rise to perfectly squeezed light. Such phenomenon occurs at any operating conditions, unlike conventional squeezing.
Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians
2005
In the spirit of some earlier work on the construction of vector coherent states over matrix domains, we compute here such states associated to some physical Hamiltonians. In particular, we construct vector coherent states of the Gazeau-Klauder type. As a related problem, we also suggest a way to handle degeneracies in the Hamiltonian for building coherent states. Specific physical Hamiltonians studied include a single photon mode interacting with a pair of fermions, a Hamiltonian involving a single boson and a single fermion, a charged particle in a three dimensional harmonic force field and the case of a two-dimensional electron placed in a constant magnetic field, orthogonal to the plane…
Integrated Generation of High-dimensional Entangled Photon States and Their Coherent Control
2017
Exploiting a frequency-domain approach, we demonstrate the generation of high-dimensional entangled quantum states with a Hilbert-space dimensionality larger than 100 from an on-chip nonlinear microcavity, and introduce a coherent control platform using standard telecommunications components.
A note on the Pais-Uhlenbeck model and its coherent states
2011
In some recent papers many quantum aspects of the Pais-Uhlenbeck model were discussed. In particular, several inequivalent hamiltonians have been proposed, with different features, giving rise, at a quantum level, to the fourth-order differential equation of the model. Here we propose two new possible hamiltonians which also produce the same differential equation. In particular our first hamiltonian is self-adjoint and positive. Our second proposal is written in terms of pseudo-bosonic operators. We discuss in details the ground states of these hamiltonians and the (bi-)coherent states of the models.
Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
2017
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.
The quantum relativistic harmonic oscillator: generalized Hermite polynomials
1991
A relativistic generalisation of the algebra of quantum operators for the harmonic oscillator is proposed. The wave functions are worked out explicitly in configuration space. Both the operator algebra and the wave functions have the appropriate c→∞ limit. This quantum dynamics involves an extra quantization condition mc2/ωℏ = 1, 32, 2, … of a topological character.
Susy for non-Hermitian Hamiltonians, with a view to coherent states
2020
We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.