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Physical Review A

Influence of the phonon-mediated coupling on the properties of a single quantum-dot laser

Jia‐pei Zhu, Hui Huang, Gao‐xiang Li

Published Aug 19, 2013• 3 citations
Publisher

Abstract

We theoretically investigate the influence of the phonon-mediated coupling on the properties of the laser generated by a single red-detuned quantum dot (QD), where the QD is coherently driven and coupled to a microscopic cavity which can be engineered in a photonic band-gap (PBG) material. In the low-temperature limit, the phonon-mediated coupling is deleterious to the emission of photon into cavity field and the threshold behavior of the laser persists after the inclusion of the phonon-mediated processes. Without being engineered in the PBG material, if the damping rate $\ensuremath{\kappa}$ of the cavity is close to but smaller than the phonon-mediated spontaneous emission rate $\ensuremath{\gamma}$ of the dot, the photon statistics of the cavity field change from super-Poissonian to sub-Poissonian. The nonclassical effect can be achieved due to the phonon-mediated processes induced by the electron-phonon interaction and the off-resonant dot-cavity coupling. The nonclassical effect can be enhanced by the PBG material. When the effect of the thermal phonon is taken into account, the cavity field exhibits the super-Poissonian property. If $\ensuremath{\kappa}$ is much smaller than $\ensuremath{\gamma}$, the phonon-mediated processes can lead to the increase (decrease) of the photons provided that the incoherent pumping rate is lower (higher) than the effective phonon-mediated threshold. But, if $\ensuremath{\kappa}$ is close to or larger than $\ensuremath{\gamma}$, the emission of the photon may dominate the absorption process, strengthening the intensity of the cavity field.

DOI
10.1103/physreva.88.023835

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We theoretically investigate the influence of the phonon-mediated coupling on the properties of the laser generated by a single red-detuned quantum dot (QD), where the QD is coherently driven and coupled to a microscopic cavity which can be engineered in a photonic band-gap (PBG) material. In the low-temperature limit, the phonon-mediated coupling is deleterious to the emission of photon into cavity field and the threshold behavior of the laser persists after the inclusion of the phonon-mediated processes. Without being engineered in the PBG material, if the damping rate \ensuremathκ\ensuremath{\kappa}\ensuremathκ of the cavity is close to but smaller than the phonon-mediated spontaneous emission rate \ensuremathγ\ensuremath{\gamma}\ensuremathγ of the dot, the photon statistics of the cavity field change from super-Poissonian to sub-Poissonian. The nonclassical effect can be achieved due to the phonon-mediated processes induced by the electron-phonon interaction and the off-resonant dot-cavity coupling. The nonclassical effect can be enhanced by the PBG material. When the effect of the thermal phonon is taken into account, the cavity field exhibits the super-Poissonian property. If \ensuremathκ\ensuremath{\kappa}\ensuremathκ is much smaller than \ensuremathγ\ensuremath{\gamma}\ensuremathγ, the phonon-mediated processes can lead to the increase (decrease) of the photons provided that the incoherent pumping rate is lower (higher) than the effective phonon-mediated threshold. But, if \ensuremathκ\ensuremath{\kappa}\ensuremathκ is close to or larger than \ensuremathγ\ensuremath{\gamma}\ensuremathγ, the emission of the photon may dominate the absorption process, strengthening the intensity of the cavity field.
We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored'' electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
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.
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.
We study the role of electron-phonon scattering for a pulse-triggered quantum dot single-photon source which utilizes a modified version of stimulated Raman adiabatic passage and cavity coupling. This on-demand source is coherently pumped with an optical pulse in the presence of a continuous-wave laser drive, allowing for efficient generation of indistinguishable single photons with polarizations orthogonal to the applied fields. In contrast to previous studies, we explore the role of electron-phonon scattering on this semiconductor system by using a polaron master equation approach to model the biexciton-exciton cascade and cavity mode coupling. In addition to background zero-phonon-line decoherence processes, microscopic electron--acoustic-phonon coupling, which usually degrades the indistinguishability and efficiency of semiconductor photon sources, is rigorously taken into account. We study how different system parameters (including cavity and laser detunings, cavity spectral width, temperature) affect the device performance and contrast the relative influence of intrinsic phonon coupling with other dephasing mechanisms. We describe how this biexciton-exciton cascade scheme allows for true single photons to be generated with over 90% quantum indistinguishability and efficiency simultaneously using realistic experimental parameters. We also show how the double-field dressing can be probed through the cavity-emitted spectrum.
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
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