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Journal of Applied Physics

Phonon-mediated squeezing of the cavity field off-resonantly coupled with a coherently driven quantum dot

Jia‐pei Zhu, Hui Sheng Huang, Gao‐xiang Li

Published Jan 15, 2014• 7 citations
Publisher

Abstract

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.

DOI
10.1063/1.4861739

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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.
The quadrature squeezing of a mechanical resonator (MR) coupled with two quantum dots (QDs) through the electromechanical coupling, where the QDs are driven by a strong and two weak laser fields is investigated. By tuning the gate voltage, the electron can be trapped in a quantum pure state. Under certain conditions, the discrepancies between the transition frequency and that of two weak fields are compensated by the phonons induced by the electromechanical coupling of the MR with QDs. In this case, some dissipative processes occur resonantly. The phonons created and (or) annihilated in these dissipative processes are correlated thus leading to the quadrature squeezing of the MR. A squeezed vacuum reservoir for the MR is built up. By tuning the gate voltage to control the energy structure of the QDs, the present squeezing scheme has strong resistance against the dephasing processes of the QDs in low temperature limit. The role of the temperature of the phonon reservoir is to damage squeezing of the MR.
We theoretically investigate the influence of the phonon bath on photon blockade in a simultaneously driven dot-cavity system. An optimal condition for avoiding two-photon excitation of a cavity field is put forward which can be achieved by modulating the phase difference and the strengths of the driving fields. The second-order correlation function and the mean photon number of the cavity field are discussed. In the absence of phonon effect, the strong photon blockade in a moderate quantum dot (QD)-cavity coupling regime occurs, which can be attributed to the destructive quantum interference arisen from different transition paths induced by simultaneously driving the dressed QD-cavity system. The participation of acoustic-phonon reservoir produces new transition channels for the QD-cavity system, which leads to the damage of destructive interference. As a result, the photon blockade effect is hindered when taking the electron-phonon interaction into account. It is also found that the temperature of the phonon reservoir is disadvantageous for the generation of photon blockade.
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 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.
Semiconductor quantum dots (QDs) in photonic nanocavities provide monolithic, robust platforms for both quantum information processing and cavity quantum electrodynamics (QED). An inherent feature of such solid-state cavity QED systems is the presence of electron-phonon interactions, which distinguishes these systems from conventional atomic cavity QED. Understanding the effects of electron-phonon interactions on these systems is indispensable for controlling and exploiting the rich physics that they exhibit. Here we investigate the effects of electron-phonon interactions on a QD-based cavity QED system. When the QD and the cavity are off-resonance, we observe phonon-assisted cavity mode emission that strongly depends on the temperature and cavity-detuning. When they are on-resonance, we observe an asymmetric vacuum Rabi doublet, the splitting of which narrows with increasing temperature. These experimental observations can be well reproduced using a cavity QED model that includes electron-acoustic-phonon interactions. Our work provides significant insight into the important but hitherto poorly understood mechanism of non-resonant QD-cavity coupling and into the physics of various cavity QED systems utilizing emitters coupled to phonons, such as nitrogen-vacancy centres in diamond and colloidal nanocrystals.