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arXiv:2411.11744 · Physical review. B./Physical review. B

Correlated emission lasing in a single quantum dot embedded inside a bimodal photonic crystal cavity

Lavakumar Addepalli, Pradyumna K. Pathak

Published Mar 28, 2025• 0 citations
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Abstract

We investigate the phenomenon of correlated emission lasing in a coherently driven single quantum dot coupled to a bimodal photonic crystal cavity, utilizing a master equation to describe the system dynamics. To account for exciton-phonon interactions, we incorporate a nonperturbative approach through a polaron transformed master equation. By analyzing fluctuations in the Hermitian operators associated with relative and average phase, we derive a Fokker-Planck equation to assess phase drift and diffusion coefficients, demonstrating that correlated emission suppresses quantum noise in the presence of exciton-phonon interaction at low temperature. Additionally, we calculate the single- and two-photon excess emission rates (difference between emission and absorption rates) into the cavity modes and explore the generation of continuous-variable entanglement between these modes.

DOI
10.1103/physrevb.111.125422

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We propose cooperative two-photon lasing in two quantum dots coupled to a single-mode photonic crystal cavity. We consider both quantum dots are driven either incoherently or coherently using an external pump. We incorporate exciton-phonon coupling using polaron transformed master equation. Using quantum laser theory, single- and multiphoton excess emission rates (difference between emission and absorption) into cavity mode are investigated. The single- and two-photon excess emission rates contribute to cavity photons, predominantly. Varying the pump strength can lead to single-photon excess emission rate change from negative to positive, and thus, by appropriately selecting pump strength, single-photon excess emission rate can be made negligible.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication. This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.
Abstract We propose methods for the realization of a continuous two-photon source using a coherently driven quantum dot embedded inside a photonic crystal cavity. We analyze the steady state population in quantum dot energy levels and field inside the cavity mode. We find conditions for population inversion in coherently driven and incoherently driven quantum dots. We discuss the effect of phonon coupling using the recently developed polaron transformed master equation at low temperatures. We show that on increasing temperature, two-photon gain decreases and single photon gain increases, due to phonon-assisted cavity mode feeding. We also propose a scheme for generating a squeezed state of field using four wave mixing.
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.
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.