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Showing papers on "Coherent states in mathematical physics published in 2017"


Journal ArticleDOI
TL;DR: In this paper, the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface were derived as eigenstates of the annihilation operator with complex eigenvalues.
Abstract: In this paper we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.

39 citations




Journal ArticleDOI
TL;DR: In this article, a two-body squeezing operator was introduced to represent the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states.
Abstract: Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin, Moore-Read and Read-Rezayi wavefunctions, belong to a special class of orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant). This fundamental observation allows to point out two different recurrence relations for the coefficients of the permanent (Slater) decomposition of the bosonic (fermionic) states. Here we provide an explicit Fock space representation for these wavefunctions by introducing a two-body squeezing operator which represents them as a Jastrow operator applied to reference states, which are in general simple periodic one dimensional patterns. Remarkably, this operator representation is the same for bosons and fermions, and the different nature of the two recurrence relations is an outcome of particle statistics.

8 citations


Journal ArticleDOI
TL;DR: Dehghani et al. as discussed by the authors proposed a scheme to generate new class of even(odd) compass states (specific superpositions of Wigner cat states), in the presence of the parity deformed Jaynes-Cummings Hamiltonian.
Abstract: We proposed a scheme to generate new class of even(odd) compass states (specific superpositions of Wigner cat states [A. Dehghani et al., Ann. Phys. 362, 659 (2015)]), in the presence of the parity deformed Jaynes–Cummings Hamiltonian [A. Dehghani et al., Sci. Rep. 6, 38069 (2016)] describing a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. Particular attention was given to analyze their non-classical properties through of the Mandel’s parameter and quadrature squeezing. The Wigner compass states (WCSs) are compared with the ordinary ones, when the Wigner parameter becomes zero. Meanwhile generalized photon added compass states (PAWCSs) were introduced, by excitations of a newly introduced WCSs. Along with statistical analysis of latter case, a new theoretical framework for preparing them is suggested.

8 citations


Journal ArticleDOI
TL;DR: In this article, a quantum system with variables in Z (d ) is considered, and coherent density matrices and coherent projectors of rank n are introduced, and their properties (e.g., the resolution of the identity) are discussed.

8 citations


Posted Content
TL;DR: A brief review of various families of coherent and squeezed states for a charged particle in a magnetic field can be found in this article, where the main attention is paid to the Gaussian states, but various non-Gaussian states are also discussed.
Abstract: This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided.

8 citations


Journal ArticleDOI
Erik Fuchs1
TL;DR: In this article, the authors construct a quantum gauge phase space with singularities and its quantum counterpart by the tool of Kahler quantization, where the reduced phase space is a stratified Kahler space, and a corresponding costratification on the quantum level consists of a family of Hilbert subspaces corresponding to the strata in the classical phase space stratification.

4 citations


Journal ArticleDOI
O. Abbasi1, A. Jafari1
TL;DR: In this paper, the authors introduced the notion of four-photon nonlinear coherent states (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator A4.
Abstract: We have introduced the notion of ‘four-photon nonlinear coherent states’ (FPNCSs) as right eigenstates of the fourth power of the generalized annihilation operator A4. It has been shown that there are four possible sets of such states which all can be expressed as the deformed Schrodinger cat type states derived from the superposition of four nonlinear coherent states (NCSs) which are π/2 out of phase. The nonclassical properties of the FPNCSs would be studied for two well-known quantum systems, a Kerr-like medium and a trapped laser-driven ion far from the Lamb-Dicke regime. We have found that the depth or the domain of the nonclassical features of FPNCSs in terms of sub-Poissonian photon statistics, higher order squeezing as well as amplitude-squared squeezing are higher than the corresponding standard states. Specifically, the proposed states in this paper exhibit sub-Poissonian statistics over an extensive range of real amplitudes which is in contrast with the lower level of sub-Poissonian characteris...

2 citations


Posted Content
TL;DR: In this paper, the Schrodinger cat states, constructed from Glauber coherent states and applied for description of qubits, are generalized to the kaleidoscope of coherent states related with regular n-polygon symmetry and the roots of unity.
Abstract: The Schr\"odinger cat states, constructed from Glauber coherent states and applied for description of qubits, are generalized to the kaleidoscope of coherent states related with regular n-polygon symmetry and the roots of unity. The cases of the trinity states and the quartet states are described in details. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry. We show that for an arbitrary $n$, these states can be generated by the Quantum Fourier transform and can provide qutrits, ququats and in general, qudit units of quantum information. Relations with quantum groups and quantum calculus are discussed.