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Physica Scripta

Even and odd superposition of bilayer graphene coherent states and their non-classical properties

Amin Motamedinasab, Azam Anbaraki

Published Mar 11, 2021• 3 citations
Publisher

Abstract

Abstract Using exfoliation of graphite, bilayer graphene which is composed of two monolayers of carbon atoms can be obtained. Defining annihilation operator, coherent states for charge carrier of bilayer graphene in a perpendicular magnetic field can be calculated. In this paper, introducing even and odd superposition of bilayer graphene coherent states, we investigate their non-classical properties including entanglement, statistical properties and squeezing. With the use of Concurrence, we have found that these states are entangled and the entanglement goes to zero for large values of coherency parameter. Also, using Mandel parameter and second coherence function, we have realized that only odd states represent sub-Poissonian statistics in some ranges of coherency parameter. In addition, our squeezing considerations show that none of the states exhibits squeezing in quadrature operators. The results of these properties for bilayer graphene coherent states, are different from the similar calculations for monolayer ones.

DOI
10.1088/1402-4896/abede3

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Abstract Using exfoliation of graphite, bilayer graphene which is composed of two monolayers of carbon atoms can be obtained. Defining annihilation operator, coherent states for charge carrier of bilayer graphene in a perpendicular magnetic field can be calculated. In this paper, introducing even and odd superposition of bilayer graphene coherent states, we investigate their non-classical properties including entanglement, statistical properties and squeezing. With the use of Concurrence, we have found that these states are entangled and the entanglement goes to zero for large values of coherency parameter. Also, using Mandel parameter and second coherence function, we have realized that only odd states represent sub-Poissonian statistics in some ranges of coherency parameter. In addition, our squeezing considerations show that none of the states exhibits squeezing in quadrature operators. The results of these properties for bilayer graphene coherent states, are different from the similar calculations for monolayer ones.
In this paper we consider the interaction of electrons in bilayer graphene with a constant homogeneous magnetic field which is orthogonal to the bilayer surface. Departing from the energy eigenstates of the effective Hamiltonian, the corresponding coherent states will be constructed. For doing this, first we will determine appropriate creation and annihilation operators in order to subsequently derive the coherent states as eigenstates of the annihilation operator with complex eigenvalue. Then, we will calculate some physical quantities, as the Heisenberg uncertainty relation, the probabilities and current density as well as the mean energy value. Finally, we will explore the time evolution for these states and we will compare it with the corresponding evolution for monolayer graphene coherent states.
In this paper we consider the interaction of electrons in bilayer graphene with a constant homogeneous magnetic field which is orthogonal to the bilayer surface. Departing from the energy eigenstates of the effective Hamiltonian, the corresponding coherent states will be constructed. For doing this, first we will determine appropriate creation and annihilation operators in order to subsequently derive the coherent states as eigenstates of the annihilation operator with complex eigenvalue. Then, we will calculate some physical quantities, as the Heisenberg uncertainty relation, the probabilities and current density as well as the mean energy value. Finally, we will explore the time evolution for these states and we will compare it with the corresponding evolution for monolayer graphene coherent states.
Abstract The multiphoton coherent states, a generalization to coherent states, are derived for electrons in bilayer graphene placed in a constant homogeneous magnetic field which is orthogonal to the bilayer surface. For that purpose a generalized annihilation operator is constructed in order to determine the multiphoton coherent states as eigenstates of such operator with complex eigenvalue. In addition, some physical quantities are calculated for these states, as the Heisenberg uncertainty relation, the probability density and the mean energy value. Finally, in order to study the dynamics of the system the time evolution is explored and the time-correlation function is computed.
In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.
Abstract Two-mode nonlinear semi-coherent states and their even and odd superpositions are defined. Their non-classical properties, including photon statistics and squeezing, are then evaluated. We use the Mandel parameter and the second-order coherence function to study sub-Poissonian photon statistics and the photon antibunching effect. By calculating the variance of two-mode quadrature operators, we evaluate the squeezing effect for the introduced states. Next, we examine entanglement using concurrence. We have found that all states display non-classical properties within certain ranges of the parameters involved. The calculation of concurrence demonstrates that all states are entangled within specific ranges of parameters.