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Physical Review A

Phonon-induced interactions and entanglement formation between two microcavity modes mediated by two semiconductor quantum dots

Jitendra K. Verma, Harmanpreet Singh, Pradyumna K. Pathak, Stephen Hughes

Published Dec 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.102.063701

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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.
We show unusual cooperative two-photon resonance between two-modes of field inside a photonic crystal cavity. The two-photon resonance occurs when two off resonant quantum dots emit one photon in each cavity mode and de-excite simultaneously. In the presence of phonon coupling the conditions for two-photon resonance change significantly. Using such two-photon two-mode interaction we propose to generate entangled state of two qutrits. The basis of a qutrit are formed by the state of the cavity mode containing 000, 111 and 222 photons. We also discuss effect of phonon coupling on negativity of the generated entangled state.
We predict dominating cooperative two-photon emission from two quantum dots coupled with a single-mode photonic crystal cavity. The cooperative two-photon emission occurs when excitons in two off-resonantly coupled quantum dots decay simultaneously. The interaction with a common cavity field leads to cavity-induced two-photon emission which is strongly inhibited by electron-phonon coupling. The interaction with a common phonon bath produces phonon-induced two-photon emission which increases on increasing temperature. For identical quantum dots, cavity-induced two-photon emission is negligible, but phonon-induced two-photon emission could be large.
A microscopic theory to study the combined dynamics of a quantum dot exciton coupled to a single cavity mode as well as acoustic phonons is presented. By considering the phonon subsystem in the coherent state representation, the phonon’s impact on the emitted photons is investigated. The single photon emission probability and phonon effects on this quantity are studied. On the other hand, we illustrate that while a quantum dot interacts with a single cavity mode, the collapse and revival phenomenon will occur. It is demonstrated that acoustic phonons have a pronounced impact on the collapse and revival of the quantum dot exciton. Our finding reveals that at elevated temperatures the phonon interaction decreases the Rabi frequency. Moreover, the cavity mode possesses non-classical features such as sub-Poissonian statistics.
The dynamics of the entanglement for coherent excitonic states in the system of two, coupled, large semiconductor quantum dots ${(R/a}_{B}\ensuremath{\gg}1)$ mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is present in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of the excitons.
We discuss the generation of two types of entangled state of two photons-- noon state which is entangled in number and polarization, and polarization entangled state which is entangled in polarization and frequency. We consider a single quantum dot coupled with a bimodal cavity in strong coupling regime. We analyze the effect of exciton-phonon coupling on the concurrence of the generated entangled states. We find that for both states concurrence is maximum in the absence of the anisotropic energy gap between exciton states and remains unchanged in the presence of exciton-phonon coupling. However, for finite anisotropic energy gap concurrence decreases on the increasing temperature of phonon bath.