In this paper, the mechanism of entanglement between electronic spin states and their spatial degrees of freedom in graphene is reported. From a calculation of the time evolution of von Neumann entropy, as a measure of entanglement, we show that the general behavior is oscillatory with characteristics depending on the external magnetic field, the Rashba spin–orbit coupling and the Landau states. The effect of these agents on the degree of entanglement is also discussed. It is shown that an increase in the magnetic field decreases the degree of entanglement, while an increase in Rashba spin–orbit coupling enhances the entanglement. Furthermore, for higher Landau levels the electronic states become more entangled. The material presented in this paper offers new means of controlling the entanglement of electronic states.
In this paper, the mechanism of entanglement between electronic spin states and their spatial degrees of freedom in graphene is reported. From a calculation of the time evolution of von Neumann entropy, as a measure of entanglement, we show that the general behavior is oscillatory with characteristics depending on the external magnetic field, the Rashba spin–orbit coupling and the Landau states. The effect of these agents on the degree of entanglement is also discussed. It is shown that an increase in the magnetic field decreases the degree of entanglement, while an increase in Rashba spin–orbit coupling enhances the entanglement. Furthermore, for higher Landau levels the electronic states become more entangled. The material presented in this paper offers new means of controlling the entanglement of electronic states.
In this paper we study the entanglement dynamics of spin–subband states for an electron in a quasi-one-dimensional Rashba quantum loop, in a strong perpendicular magnetic field, explicitly including the confining potential and the Rashba spin–orbit coupling into the entropy, which is a measure of entanglement, as a function of time. Our results indicate that the entanglement between the spin states and the structural subbands undergoes periodic oscillations. Furthermore, it is shown that the period of oscillations strongly depends upon the Rashba coupling, while the amplitudes may be optimized by making proper choices of the external magnetic field. It is also shown that the maxima of entanglement, in the long run, oscillate under periodic envelopes, whose characteristics depend upon the magnetic field. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these agents.
Free entanglement—the milestone of any quantum information processing scheme—among the π -electronic spin and its spatial states in graphene, as a function of temperature, is the main concern of the present report. It is assumed that a perpendicular magnetic field generates the Landau levels so that a coupling with the pseudo-spin (sublattice) states is enacted. Moreover, the pseudo-Rashba spin–orbit interaction (SOI), responsible for the coupling of spin and sublattice states, is also taken into account. From the structure of the total Hamiltonian, we introduce a Casimir operator which, in due turn, assists the development of a simple but efficient algorithm for our numerical computation. We then proceed by constructing the thermal density operator, its partially transposed one and, thereby, compute the negativity, the proper measure of free hybrid entanglement, at any temperature. Our results show that the negativity is nonvanishing at absolute zero temperature due to the fact that the ground state is an entangled one. Moreover, our results indicate that the negativity, at certain temperatures, exhibits maxima. The temperatures at which the entanglement (free) is maximal strongly depend on the magnetic field and pseudo-Rashba spin–orbit strength; decreasing the magnetic field and/or increasing the pseudo-Rashba parameter (PRP) enhances the maximal entanglement monotonically. As the temperature increases, however, it is shown that the negativity decreases asymptotically to zero. As a result, there exists distillable entanglement amid the π -electronic spin and its spatial states in graphene at any finite temperature .
The entanglement dynamics of spin–subband states for an electron in a 2D isotropic Rashba quantum dot, with an applied magnetic field of arbitrary strength, is studied. We explicitly include the confining (gate) effects as a two-dimensional isotropic harmonic oscillator. The von Neumann entropy, as a measure of entanglement, is calculated as a function of time, by going to the Fock–Darwin representation. Our results indicate that the period and amplitude of the collapse–revival behavior of the entanglement between the spin states and the structural subbands strongly depend upon the size of the quantum dot (confining length) and choice of heterostructural materials. Our results, thereby, provide means of controlling the degree of entanglement by adjusting these factors.
Abstract In this letter, we have proposed a new model for quantum control of atom photon entanglement in a single layer graphene via von Neumann reduced entropy of entanglement. We consider the effect of terahertz laser field intensity on the degree of entanglement (DEM) in the resonance and off-resonance condition of the applied fields. We also investigate the spatially dependent of the DEM when two applied light becomes standing wave pattern in x and y directions. Our results show that in different parametric conditions, the population of the different states can be controlled and this leads to modifying the DEM of the system.
Tailoring pure valley-Zeeman spin-orbit coupling in WSe2-encapsulated monolayer graphene
Engineering proximity effects in twisted van der Waals heterostructures offers a powerful platform for designing electronic properties. While theoretical predictions of quantum interference in transition metal dichalcogenide-encapsulated graphene can selectively control the spin-orbit coupling component, experimental realizations have remained elusive. Here, we report pure valley-Zeeman spin-orbit coupling in monolayer graphene, achieved by encapsulation between two parallel twisted WSe2 monolayers. We observed a symmetry-enforced reordering of Landau levels, which is driven by the competition between the fixed valley-Zeeman energy and the magnetic-field-dependent cyclotron energy. This reordering is characterized by a transition from symmetry-broken states in the quantum Hall effect to a restored fourfold degeneracy with integer or half-integer quantum Hall sequences. We also demonstrate the ability to completely quench the proximity spin-orbit coupling by tuning the encapsulated geometry.
In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between [Formula: see text] components of magnetic fields acting on each spin, we find several time-dependent coupling functions [Formula: see text] that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.