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arXiv:2107.03849 · Physical Review A

Coherence-mediated squeezing of a cavity field coupled to a coherently driven single quantum dot

Parvendra Kumar, Agnikumar G. Vedeshwar

Published Mar 17, 2022• 0 citations
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Abstract

Coherence has been an important key for numerous applications of quantum physics ranging from quantum metrology to quantum information. We report here a theoretical paper demonstrating how maximally created coherence results in the squeezing of a cavity field coupled to a coherently driven single quantum dot. We employ a polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.

DOI
10.1103/physreva.105.033710

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Coherence has been an important key for numerous applications of quantum physics ranging from quantum metrology to quantum information. We report here a theoretical paper demonstrating how maximally created coherence results in the squeezing of a cavity field coupled to a coherently driven single quantum dot. We employ a polaron master equation theory for accurately incorporating the impact of exciton-phonon coupling on squeezing.
We theoretically demonstrate the enhanced and dephasing-immune squeezing in the resonance fluorescence of a single quantum dot (QD) confined to a pillar microcavity and driven by a continuous wave laser. We employ a formalism based on polaron master equation theory for incorporating the influence of exciton-phonon coupling quite accurately in the dot-cavity system. We show a significant enhancement of squeezing due to cavity coupling of the QD as compared to that of an ideal single two-level system in free space. Particularly, we show a fourfold enhancement in squeezing as compared to that of a single QD without cavity coupling. We further demonstrate the persistence of squeezing even when the pure dephasing becomes greater than the radiative decay rate. These features are attributed to the cavity-enhanced coherence causing partial reduction of the deteriorating effects of phonon-induced incoherent rates. We also show that the deteriorating effects of phonon-induced incoherent rates on squeezing can be partially circumvented by properly adjusting the detunings.
We theoretically propose a scheme for the quadrature squeezing of the cavity field via dissipative processes. The effects of the electron-phonon interaction (EPI) on the squeezing are investigated, where the cavity is off-resonantly coupled with a coherently driven quantum dot (QD) which is allowed to interact with an acoustic-phonon reservoir. Under certain conditions, the participation of the phonon induced by both the EPI and the off-resonant coupling of the cavity with the QD enables some dissipative processes to occur resonantly in the dressed-state basis of the QD. The cavity-mode photons emitted or absorbed during the phonon-mediated dissipative processes are correlated, thus leading to the squeezing of the cavity field. A squeezed vacuum reservoir for the cavity field is built up due to the EPI plus the off-resonant coupling between the cavity and the QD. The numerical results obtained with an effective polaron master equation derived using second-order perturbation theory indicate that, in low temperature limit, the degree of squeezing is maximal but the increasing temperature of the phonon reservoir could hinder the squeezing and degrade the degree of the squeezing of the cavity field. In addition, the presence of the photonic crystal could enhance the quadrature squeezing of the cavity field.
We demonstrate the generation of frequency-tunable squeezed single photons from a continuous wave laser-driven single-quantum-dot system using a rigorous theoretical formalism, the so-called polaron master equation theory for accurately incorporating the exciton–phonon coupling. We investigate the squeezing for both resonant and off-resonant excitations and show that even for an appropriate off-resonant excitation, the degree of quadrature squeezing can be equal to or even greater than the maximum value obtained for a resonant excitation due to the increased purity of the quantum dot system. We further demonstrate, without losing the degree of squeezing, the tunability of the central frequency of squeezed photons by adjusting the detuning. We show that the detrimental effects due to the exciton–phonon coupling remain negligible up to the phonon bath temperature of 20 K and become quite appreciable beyond this temperature, particularly at higher phonon cutoff frequencies.
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.
We introduce an intuitive and semianalytical polaron master equation approach to model pulse-driven population inversion and emitted single photons from a quantum dot exciton. The master equation theory allows one to identify important phonon-induced scattering rates analytically and fully includes the role of the time-dependent pump field. As an application of the theory, we first study a quantum dot driven by a time-varying laser pulse on and off resonance, showing the population inversion caused by acoustic phonon emission in direct agreement with recent experiments of Quilter et al. [Phys. Rev. Lett. 114, 137401 (2015)]. We then model quantum dots in weakly coupled cavities and show the difference in population response between exciton-driven and cavity-driven systems. Finally, we assess the nonresonant phonon-assisted loading scheme with a quantum dot resonantly coupled to a cavity as a deterministic single-photon source. We also compare and contrast the important single photon figures of merit with direct Rabi oscillation of the population using a resonant $\ensuremath{\pi}$ pulse, and show that the resonant scheme is much more efficient.
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.