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arXiv:1907.11023 · Modern Physics Letters A

Entangled states in supersymmetric quantum mechanics

H. P. Laba, V. M. Tkachuk

Published Sep 10, 2020• 3 citations
arXivHTMLPDF

Abstract

We study entanglement of spin degrees of freedom with continuous one in supersymmetric (SUSY) quantum mechanics. Concurrence is determined by mean value of spin and is calculated explicitly for SUSY states. We show that eigenstates of supercharges are maximally entangled. As an example the entanglement of atom state with photon state and SUSY in Jaynes–Cummings model are considered.

DOI
10.1142/s021773232050282x

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We study entanglement of spin degrees of freedom with continuous one in supersymmetric (SUSY) quantum mechanics. Concurrence is determined by mean value of spin and is calculated explicitly for SUSY states. We show that eigenstates of supercharges are maximally entangled. As an example the entanglement of atom state with photon state and SUSY in Jaynes–Cummings model are considered.
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We derive an explicit expression for geometric measure of entanglement for spin and other quantum system. A relation of entanglement in pure state with the mean value of spin is given, thus, at the experimental level the local measurement of spin may allow to find the value of entanglement. The obtained form of the measure is applied to the explicit characterization of bipartite entanglement for nnn-qubit systems in the Werner state, Dicke state, GHZ state and trigonometric states. In particular for Werner-like states the rule of sums is found and it is shown that deviations from the symmetricity of such states diminishes the amount of entanglement. For Dicke states the maximal value of bipartite entanglement is achieved when number of excitations is half of the total number of qubits in these states. For trigonometric states the bipartite entanglement is maximal and does not depend on the number of qubits. We also consider entanglement of discrete-continuous systems on the example of entanglement of spin with continuous variables of electron. The relation of entanglement with the mean value of spin is very useful for calculation of entanglement. With the help of this relation we find in explicit form the entanglement of the one spin with the rest in a spin chain during the evolution determined by the Ising Hamiltonian.
The aim of this work is to define and investigate the generalized Jaynes-Cummings (JC) Hamiltonian by means of supersymmetric (SUSY) quantum mechanics methods. We have considered trigonometric and hyperbolic Pöschl-Teller (PT) potentials as two natural ingredients to modify the standard JC model. We show that these generalized JC Hamiltonians have a list of characteristics in common with the JC Hamiltonian, for example: matrix intertwining, excitation number symmetry, Rabi frequency, formulas for atomic inversion and classical and revival times. Therefore, we conclude that JC Hamiltonians can be considered as one example of a wider a class of generalized Hamiltonians which can be useful in broader interaction problems.
Abstract In this paper, we consider a special type of maximally entangled states namely by entangled SU(1,1) semi coherent states by using SU(1,1) semi coherent states(SU(1,1) Semi CS). The entanglement characteristics of these entangled states are studied by evaluating the concurrence.We investigate some of their nonclassical properties,especially probability distribution function,second-order correlation function and quadrature squeezing . Further, the quasiprobability distribution functions (Q-functions) is discussed.