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arXiv:1606.03999 · Physical Review A

Origins and optimization of entanglement in plasmonically coupled quantum dots

Matthew Otten, Jeffrey M. Larson, Misun Min, Stefan M. Wild, Matthew A. Pelton, Stephen K. Gray

Published Aug 11, 2016• 34 citations
arXivHTMLPDF

Abstract

A system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimization for the two- and three-dot cases are used to develop guidelines for maximizing the bipartite entanglements. For any number of quantum dots, we show that through simple starting states and parameter guidelines, one quantum dot can be made to share a strong amount of bipartite entanglement with all other quantum dots in the system, while entangling all other pairs to a lesser degree.

DOI
10.1103/physreva.94.022312

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A system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimization for the two- and three-dot cases are used to develop guidelines for maximizing the bipartite entanglements. For any number of quantum dots, we show that through simple starting states and parameter guidelines, one quantum dot can be made to share a strong amount of bipartite entanglement with all other quantum dots in the system, while entangling all other pairs to a lesser degree.
Although the enhanced near fields produced by plasmon resonances in metal nanoparticles can enable strong local light-matter interactions, the strong dissipation of plasmon resonances would seem to be incompatible with quantum-mechanical phenomena such as entanglement. Counter to this intuition, the dissipation can in fact lead to the production of transient entanglement between the occupation states of dots coupled to a common plasmonic system. Building on previous results that showed entanglement between pairs of dots, we scale to larger systems of two, three, and more closely spaced dots. Moreover, we show that tuning the degree of coupling between each dot and the common plasmonic nanostructure enables entanglement to be created in the case where the entire system begins in its ground state and is excited by a single laser pulse. Entanglement is achieved without the need for the dots to be individually addressable, and without the need for controlled quantum gates, postselective measurements, or engineering of the dissipative environment. Through analytical solutions and numerical simulation of a model Hamiltonian based on a cavity-quantum-electrodynamics approach, we determine system configurations that maximize pairwise entanglement among the quantum dots, illustrating in principle the potential for true “quantum plasmonics.
Can quantum light reliably generate entanglement in systems with dissipation? Our cavity quantum electrodynamics calculations demonstrate that a single-mode squeezed light source can robustly generate steady-state entanglement between a plasmonically coupled pair of quantum dots. The strong coupling of plasmons to the light source and the pairwise nature of squeezed photon generation enable entanglement between quantum dots. This entanglement, measured as concurrence, can be improved by replacing an entangled photon-pair pulsed source of light with continuous pumping of squeezed photons. Unlike previously introduced schemes, the concurrence is robust against variations in the system parameters. Specifically, the generation of entanglement does not rely on fine-tuning of the plasmon-quantum dot coupling. These results provide a new perspective for robust entangled-state preparation in open quantum systems.
We study the systems of two and three quantum dots positioned near a metallic nanoring having a surface plasmon in a particular mode. Interaction of surface plasmon with quantum dots generates entanglement between quantum dots as well as among the incident and reflected modes of the surface plasmons. We show that the maximum amount of entanglement is generated among two initially unentangled quantum dots separated by distance and with interaction parameter , while entanglement among two counter-propagating modes of the surface plasmons can be generated with interdot distance and interaction parameter , where k and μ are the propagation vector and coupling constant, respectively. In case of three quantum dots, the maximum entanglement among the quantum dots is obtained at kd = mπ /3 and Finally, the scheme is straightforwardly generalized to generate quantum entanglement among N quantum dots as well as among two counter-propagating modes of the surface plasmon due to their interactions with quantum dots.
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.
We theoretically investigate a general scheme for determining quantum entanglement of two detuned quantum dots (QDs) mediated by plasmon nanoparticle for weakly driven dissipative systems. By adiabatically eliminating the field operators, an effective model is proposed to find the underlying mechanism for this determination. Two specific hybrid systems composed of two QDs and a metallic nanoparticle (MNP) are considered. In the QD-MNP-QD system, the concurrence maxima generated by the detunings are several times larger than those in the resonance condition because of the robust superposition between the two separated entangled states. However, in the MNP-QD-QD system, the detunings generally reduce entanglement because the dipole-dipole interaction strongly suppresses the superposition of the entangled states. Moreover, the plateau of large concurrence exists for a broad range of parameters in both cases. The scheme is robust to dissipative systems and paves the way to improve entanglement in quantum information devices at the nanoscale.
Cavity quantum electrodynamics of multipartite systems are studied in depth, which consists of an arbitrary number of emitters in interaction with an arbitrary number of cavity modes. The governing model is obtained by taking the full field-dipole and dipole-dipole interactions into account, and is solved in the Schrödinger picture with assumption of vanishing field and dipole interactions at high energies. An extensive code is developed that is able to solve the system and track its evolution in time, while maintaining sufficient degrees of arbitrariness in setting up the initial conditions and interacting partitions. Using this code, we have been able to numerically evaluate various parameters such as probabilities, expectation values (of field and atomic operators), and the concurrence as the most rigorously defined measure of entanglement of quantum systems. We present and discuss several examples including a seven-partition system consisting of six quantum dots interacting with one cavity mode. We observe for the first time that the behavior of quantum systems under ultrastrong coupling is significantly different than the weakly and strongly coupled systems, marked by onset of chaos and abrupt phase changes. We also discuss how to implement spin into the theoretical picture and thus, successfully simulate a recently reported spin-entanglement experiment.