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Journal of Physics A Mathematical and Theoretical

Bipartite non-local correlations in a double-quantum-dot excitonic system

A-B A Mohamed, Amitabh Joshi, Saad S. M. Hassan

Published Aug 4, 2014• 36 citations
Publisher

Abstract

Quantum correlations, such as quantum entanglement (QE), measurement-induced non-locality (MIN) and Bell non-locality, are investigated in a system of two coupled quantum dots (QDs) entangled through their interaction with a cavity mode, including F?rster and exciton?phonon interactions. When the two QDs are situated very close to and symmetrically about the antinode of the sustained longitudinal mode, the violation of Bell?s inequality only occurs with strong MIN and QE. If one of the QDs is located very near to the node while the other one is located slightly far away from the node, the violation does not occur even with strong MIN and QE. When both QDs are located in the cavity in such a way that they see different cavity field amplitudes, the violation occurs with weak or strong MIN and QE. The generalized Rabi frequency acts as a control for the occurrence of these different types of the quantum correlation in the system, with MIN more general than the conventionally mentioned quantum non-locality related to the QE or violation of Bell?s inequalities.

DOI
10.1088/1751-8113/47/33/335301

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Quantum correlations, such as quantum entanglement (QE), measurement-induced non-locality (MIN) and Bell non-locality, are investigated in a system of two coupled quantum dots (QDs) entangled through their interaction with a cavity mode, including F?rster and exciton?phonon interactions. When the two QDs are situated very close to and symmetrically about the antinode of the sustained longitudinal mode, the violation of Bell?s inequality only occurs with strong MIN and QE. If one of the QDs is located very near to the node while the other one is located slightly far away from the node, the violation does not occur even with strong MIN and QE. When both QDs are located in the cavity in such a way that they see different cavity field amplitudes, the violation occurs with weak or strong MIN and QE. The generalized Rabi frequency acts as a control for the occurrence of these different types of the quantum correlation in the system, with MIN more general than the conventionally mentioned quantum non-locality related to the QE or violation of Bell?s inequalities.
In this article, we investigate the dynamics of a bipartite system under the action of a local non-Hermitian system. We study the quantum correlation of the bipartite system quantified by the entanglement, measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm, trace distance, and Bell inequality. We find that the quantum correlations of the system depend on the initial conditions and system parameters. We observe that the states with nonzero quantum correlation obey the Bell inequality even in the absence of entanglement. Moreover, the Bell inequality completely fails to manifest the nonlocality for the mixed quantum state. However, we have identified the nonlocal attributes of the mixed quantum state in terms of MIN and trace distance MIN. Our results show that the trace distance-based correlation is more robust against the nonunitary evolution compared to the other quantifiers.
No instrument is able to measure directly the quantum entanglement of a system. However, both theory and experiment, following the well-known Bell inequality, reveal the existence of the entanglement phenomenon in quantum mechanics. To examine the characterization of quantum entanglement, here we present a two-site cavity system, in which each cavity contains a Λ-type three-level atom and the two sites are identical and coupled with each other. We investigate and calculate the bipartite entanglement entropy of the system for the ground states. For photons of different types, corresponding to the two ground states of the atom, we investigate the correlations and violation of the Bell inequality.
We investigate the preservation and dynamics of entanglement and Bell nonlocality in a two-photon system subject to local dephasing, particularly emphasizing environments exhibiting non-Markovian memory effects. By analyzing the interplay between entanglement, as measured by concurrence, and Bell inequality violation, we identify time regions where Bell inequality is not violated, even when concurrence remains high. This indicates that strongly entangled states do not always exhibit nonclassical correlations with certainty. Our study further explores the effects of refractive index variations, spectral width, and interaction symmetry, demonstrating how structured environments and controlled environmental interactions can mitigate decoherence and enhance the resilience of quantum correlations. We propose that these theoretical predictions can be tested using modifications of recent experimental optical setups. These findings provide valuable insights into the conditions under which quantum correlations remain irreproducible by classical local hidden-variable models, with direct implications for quantum communication, quantum information processing, and foundational studies in quantum mechanics. Furthermore, our findings highlight the crucial importance of quantum coherence in maintaining entanglement and nonlocality over extended time evolution. These results show remarkable alignment with the experimental observations, demonstrating high accuracy and consistency within the expected parameter range.
Using a polaron master equation approach, we investigate the cooperative two-photon resonance behavior between two modes of a field inside a semiconductor microcavity containing two quantum dots. The cooperative two-mode two-photon resonance occurs when two off-resonant quantum dots, initially prepared in exciton states, emit one photon in each cavity mode and deexcite simultaneously. Using this two-photon two-mode interaction, we demonstrate how to generate an entangled state of two qutrits (tripartite unit of quantum information). The bases for the qutrits are formed by the states of the cavity modes containing zero, one, and two photons. We also study the effect of exciton-phonon coupling on the entanglement and the probability of generating two-qutrit states, and explore the role of the phonon bath temperature.
The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.