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Physical review. B./Physical review. B

Long-lived quantum entanglement of multiple qubits: Excitons in strained graphene

Gabriel P. Martins, Oleg L. Berman, Godfrey A. Gumbs, Yu. E. Lozovik

Published Jan 21, 2025• 2 citations
Publisher

Abstract

We investigate the entanglement dynamics of systems consisting of up to five qubits coupled to an optical microcavity. This is depicted by a system of excitons in strained graphene. We numerically calculate the time evolution of multiple entanglement monotones in such systems when subjected to a coherent source of photons (e.g., a laser). We propose a different way of estimating the total amount of quantum entanglement contained within a multipartite system based on the negativity which we refer to as total negativity, and to which we give clear upper and lower bounds for this quantity. We compared the results for a system of excitons in strained graphene along with two other systems which can be described by the same Hamiltonian as that for superconducting qubits coupled to a waveguide, and for trapped Rb atoms. We have shown that, depending on the physical parameters of the system, a reasonable amount of long-living entanglement can be created between the qubits. This entanglement is exempt from decay as long as the systems are being continuously pumped with coherent photons. We have reached the interesting conclusion that freely adding new qubits to the system does not, in general, increase the overall amount of entanglement created by the dynamics: there exist an optimum number of system qubits which depend on the Rabi coupling as well as the cavity decay rate for maximal entanglement. We believe that such systems are good candidates for the generation of resilient sets of long-lived partially entangled states suitable for experiments in entanglement distillation.

DOI
10.1103/physrevb.111.045425

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We investigate the entanglement dynamics of systems consisting of up to five qubits coupled to an optical microcavity. This is depicted by a system of excitons in strained graphene. We numerically calculate the time evolution of multiple entanglement monotones in such systems when subjected to a coherent source of photons (e.g., a laser). We propose a different way of estimating the total amount of quantum entanglement contained within a multipartite system based on the negativity which we refer to as total negativity, and to which we give clear upper and lower bounds for this quantity. We compared the results for a system of excitons in strained graphene along with two other systems which can be described by the same Hamiltonian as that for superconducting qubits coupled to a waveguide, and for trapped Rb atoms. We have shown that, depending on the physical parameters of the system, a reasonable amount of long-living entanglement can be created between the qubits. This entanglement is exempt from decay as long as the systems are being continuously pumped with coherent photons. We have reached the interesting conclusion that freely adding new qubits to the system does not, in general, increase the overall amount of entanglement created by the dynamics: there exist an optimum number of system qubits which depend on the Rabi coupling as well as the cavity decay rate for maximal entanglement. We believe that such systems are good candidates for the generation of resilient sets of long-lived partially entangled states suitable for experiments in entanglement distillation.
We studied the effects arising from a coherent source of photons on the entanglement between excitons in a strained graphene monolayer. The graphene layer was considered to be embedded in an imperfect optical microcavity. In our investigation, we have studied the entanglement dynamics of systems consisting of up to five excitons, which are treated as atomic-like qubits. Entangled states of multiple qubits are useful in quantum error correction codes. We have monitored the time evolution of the concurrence, three-πππ, mutual information, and especially the negativity. We have demonstrated that coherent pumping can create lasting entanglement between the excitons. However, the entanglement only persists when the rate at which photons are pumped is smaller than the decay rate of the cavity. Our results show that the degree in entanglement between the excitons is increased with the intensity of the strain-induced pseudomagnetic field in the graphene sheet. Additionally, we have shown that a maximum amount of entanglement occurs at a finite number of excitons in the system which depends on the parameters describing the structure.
The quantum entanglement between two excitons in two-dimensional materials, embedded in an optical microcavity, was investigated. The energy eigenstates of a Jaynes-Cummings like Hamiltonian for two qubits coupled to a single cavity mode have been calculated. The quantum entanglement between such states was estimated by calculating the concurrence between two qubits in each of these eigenstates. According to the results of our calculations, if the system is allowed to decay only through the emission of cavity photons at low temperatures, then there is a maximally entangled eigenstate, protected from decay. We demonstrated that the existence of such a state results in the counterintuitive conclusion that, for some initial states of the system, the fact that the cavity is leaky can actually lead to an increase in the average concurrence on the timescales of the average photonic lifetime. By briefly analyzing the three-qubit model, we have demonstrated that the probability for the entanglement to be preserved is enhanced when the number of qubits is increased. In addition, we calculated the time evolution of the concurrence between a pair of excitons in a strained graphene monolayer.
Creating sufficiently strong entanglement between exciton-polaritons is a step of utmost importance towards the exploitation of these systems in quantum information processing with continuous variables. The generation of entanglement relies on the strength of the nonlinearity, which is weak for semiconductor microcavities. Recently, a way to essentially amplify the nonlinearity strength in these systems using two coherent laser fields was suggested, leading in theory to the creation of a fair amount of entanglement between exciton-polaritons in coupled cavities and networks in general. Throughout this process, the Josephson coupling and the enhanced nonlinearity in the two coupled cavities are held constant, with the former always larger. In this work we show that the entanglement generated with the above procedure can be substantially enhanced with the appropriate on-off switching of Josephson coupling between the cavities. Furthermore, we show that if we consider a time-dependent enhanced nonlinearity, through the modulation of the corresponding coherent laser fields, and allow it to attain larger values than the Josephson coupling, then we can generate larger values of entanglement using shortcuts to adiabaticity, a method developed to accelerate quantum adiabatic dynamics. The suggested methodologies are not restricted to exciton-polaritons but are expected to find applications in a wide spectrum of physical contexts, where nonlinear interacting bosons are encountered.
We investigate the generation of multipartite entangled state in a system of N quantum dots embedded in a microcavity and examine the emergence of genuine multipartite entanglement by three different characterizations of entanglement. At certain times of dynamical evolution one can generate multipartite entangled coherent exciton states or multiqubit W states by initially preparing the cavity field in a superposition of coherent states or the Fock state with one photon, respectively. Finally, we study environmental effects on multipartite entanglement generation and find that the decay rate for the entanglement is proportional to the number of excitons.
In this work, we theoretically analyze the population and entanglement dynamics for two identical qubits interacting with a graphene nanodisk. We consider qubits with various free-space decay rates in order to study how the coupling strength influences the dynamics of our composite system, as well as their entanglement evolution as quantified by concurrence. We find that for relatively large free-space decay rates, the population dynamics of each qubit features Rabi oscillations, while for smaller decay rates it exhibits a complex behavior, which nevertheless can be understood by semianalytical expressions using the sub- and superradiant states of the system. Additionally, we observe phenomena, such as population and entanglement trapping, induced by the strong interaction of the qubits with the graphene nanodisk, with trapping values depending solely on the initial conditions of the two qubits. Lastly, we compare our results with those obtained in the case of the two qubits interacting independently with a graphene nanodisk.
Recent proposals and advances in quantum simulations, quantum cryptography, and quantum communications substantially rely on quantum entanglement formation. Contrary to the conventional wisdom that dissipation destroys quantum coherence, coupling with a dissipative environment can also generate entanglement. We consider a system composed of two quantum-dot qubits coupled with a common, damped surface plasmon mode; each quantum dot is also coupled to a separate photonic cavity mode. Cavity quantum electrodynamics calculations show that upon optical excitation by a femtosecond laser pulse, entanglement of the quantum-dot excitons occurs, and the time evolution of the g(2){g}^{(2)}g(2) pair correlation function of the cavity photons is an indicator of the entanglement. We also show that the degree of entanglement is conserved during the time evolution of the system. Furthermore, if coupling of the photonic cavity and quantum-dot modes is large enough, the quantum-dot entanglement can be transferred to the cavity modes to increase the overall entanglement lifetime. This latter phenomenon can be viewed as a signature of entangled, long-lived quantum-dot exciton-polariton formation. The preservation of total entanglement in the strong-coupling limit of the cavity--quantum-dot interactions suggests a novel means of entanglement storage and manipulation in high-quality optical cavities.