Search results for "coherent state"
showing 10 items of 95 documents
Bi-squeezed states arising from pseudo-bosons
2018
Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered.
Coherent states: a contemporary panorama
2012
Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schr?dinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably…
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…
Unitary Representations of Quantum Superpositions of two Coherent States and beyond
2013
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results are briefly outlined.
A Swanson-like Hamiltonian and the inverted harmonic oscillator
2022
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the eigensystem of the Hamiltonian $H$ of the inverted quantum harmonic oscillator can be deduced from that of $H_\theta$. We show that there is no need to introduce a different scalar product using some ad hoc metric operator, as suggested by other authors. Indeed we prove that a distributional approach is sufficient to deal with the Hamiltonian $H$ of the inverted oscillator.
Strong vacuum squeezing from bichromatically driven Kerrlike cavities: from optomechanics to superconducting circuits
2015
AbstractSqueezed light, displaying less fluctuation than vacuum in some observable, is key in the flourishing field of quantum technologies. Optical or microwave cavities containing a Kerr nonlinearity are known to potentially yield large levels of squeezing, which have been recently observed in optomechanics and nonlinear superconducting circuit platforms. Such Kerr-cavity squeezing however suffers from two fundamental drawbacks. First, optimal squeezing requires working close to turning points of a bistable cycle, which are highly unstable against noise thus rendering optimal squeezing inaccessible. Second, the light field has a macroscopic coherent component corresponding to the pump, ma…
Quantum dynamics of the intensity-dependent Tavis-Cummings model
1999
An exactly solvable generalization of the intensity-dependent Jaynes-Cummings model to the case of N0 atoms is introduced together with its solution. The quantum dynamics of the model including the squeezing properties of the su(1,1) Perelomov and Glauber coherent states is investigated. The cases of one and two atoms present in the cavity are analysed in detail. These two cases are compared in the situation when the atomic subsystem is initially prepared in the ground state, the Dicke state and the state of thermal equilibrium.
A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states
2007
Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a \underline{bounded} operator related to an annihilation-like operator. We use this bounded operator to construct a sort of modified harmonic oscillator and we analyze the dynamics of this oscillator from an algebraic point of view.
Ground state properties of SmB6
2002
Abstract We have studied the ground state properties of the intermediate valence narrow-gap semiconductor SmB 6 by means of point-contact (PC) spectroscopy and specific heat measurements. The density of states derived from PC tunneling spectra could be decomposed into two energy-dependent parts with E g =21 meV and E d =4.5 meV wide gaps, and a finite residual density of states at the Fermi level. The specific heat of SmB 6 is enhanced below about 2 K, more pronounced for the sample with less impurities. This behavior can be attributed to the formation of a coherent state within the residual density of states in the energy gap.
Quantizations from reproducing kernel spaces
2012
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.