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arXiv:2003.03974 · Physical review. B./Physical review. B

Transiently changing shape of the photon number distribution in a quantum-dot–cavity system driven by chirped laser pulses

M. Cosacchi, Tim Seidelmann, F. Ungar, Moritz Cygorek, Alexei Vagov, V. M. Axt

Published May 13, 2020• 5 citations
arXivHTMLPDF

Abstract

We have simulated the time evolution of the photon number distribution in a semiconductor quantum-dot--microcavity system driven by chirped laser pulses and compare with unchirped results. When phonon interactions with the dot are disregarded---thus corresponding to the limit of atomic cavity systems---chirped pulses generate photon number distributions that change their shape drastically in the course of time. Phonons have a strong and qualitative impact on the photon statistics. The asymmetry between phonon absorption and emission destroys the symmetry of the photon distributions obtained for positive and negative chirps. While for negative chirps transient distributions resembling thermal ones are observed, for positive chirps the photon number distribution still resembles its phonon-free counterpart but with overall smoother shapes. In sharp contrast, using unchirped pulses of the same pulse area and duration wave packets are found that move up and down the Jaynes-Cummings ladder with a bell shape that changes little in time. For shorter pulses and lower driving strength Rabi-like oscillations occur between low photon number states. For all considered excitation conditions transitions between sub- and super-Poissonian statistics are found at certain times. For resonant driving with low intensity the Mandel parameter oscillates and is mostly negative, which indicates a nonclassical state in the cavity field. Finally, we show that it is possible that the Mandel parameter dynamically approaches zero and still the photon distribution exhibits two maxima and thus is far from being a Poissonian.

DOI
10.1103/physrevb.101.205304

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We have simulated the time evolution of the photon number distribution in a semiconductor quantum-dot--microcavity system driven by chirped laser pulses and compare with unchirped results. When phonon interactions with the dot are disregarded---thus corresponding to the limit of atomic cavity systems---chirped pulses generate photon number distributions that change their shape drastically in the course of time. Phonons have a strong and qualitative impact on the photon statistics. The asymmetry between phonon absorption and emission destroys the symmetry of the photon distributions obtained for positive and negative chirps. While for negative chirps transient distributions resembling thermal ones are observed, for positive chirps the photon number distribution still resembles its phonon-free counterpart but with overall smoother shapes. In sharp contrast, using unchirped pulses of the same pulse area and duration wave packets are found that move up and down the Jaynes-Cummings ladder with a bell shape that changes little in time. For shorter pulses and lower driving strength Rabi-like oscillations occur between low photon number states. For all considered excitation conditions transitions between sub- and super-Poissonian statistics are found at certain times. For resonant driving with low intensity the Mandel parameter oscillates and is mostly negative, which indicates a nonclassical state in the cavity field. Finally, we show that it is possible that the Mandel parameter dynamically approaches zero and still the photon distribution exhibits two maxima and thus is far from being a Poissonian.
The generation of photons in a microcavity coupled to a laser-driven quantum dot interacting with longitudinal acoustic (LA) phonons is studied in the regime of simultaneously strong driving and strong dot-cavity coupling. The stationary cavity photon number is found to depend in a nontrivial way on the detuning between the laser and the exciton transition in the dot. In particular, the maximal efficiency of the cavity feeding is obtained for detunings corresponding to transition energies between cavity-dressed states with excitation numbers larger than one. Phonons significantly enhance the cavity feeding at large detunings. In the strong-driving, strong-coupling limit, the photon statistics is highly non-Poissonian. While without phonons a double-peaked structure in the photon distribution is predicted, phonons make the photon statistics thermal-like with very high effective temperatures $\ensuremath{\sim}{10}^{5}$ K, even for low phonon temperatures $\ensuremath{\sim}4$ K. These results were obtained by numerical calculations where the driving, the dot-cavity coupling, and the dot-phonon interactions are taken into account without approximations. This is achieved by a reformulation of an exact iterative path-integral scheme which is applicable to a large class of quantum-dissipative systems and which in our case reduces the numerical demands by 15 orders of magnitude.
Entangled photon pairs are essential for many applications in quantum technologies. Recent theoretical studies demonstrated that different types of entangled Bell states can be created in a constantly driven four-level quantum emitter-cavity system. Unlike other candidates for the realization of the four-level emitter, semiconductor quantum dots unavoidably interact with their environment, resulting in carrier-phonon interactions. Surprisingly, phonons change the entanglement of emitted photon pairs in a qualitative way, already at low temperatures on the order of 4 K. While one type of Bell state can still be generated using small driving strengths, the other type is suppressed due to phonon interactions in strongly confined quantum dots. The degree of entanglement decreases with rising temperature and driving strength until it vanishes at a certain parameter value. Because it remains zero afterward, we encounter a phonon-induced transition between entangled and nonentangled photon emission that resembles a phase transition. The transition occurs at temperatures below 30 K and, independent of the driving strength, the concurrence as a function of the reduced temperature is found to obey a power law with exponent one near the transition point.
We theoretically investigate the dynamic interaction of a quantum dot in a nanocavity with time-symmetric single-photon pulses. The simulations, based on a wave-function approach, reveal that almost perfect single-photon absorption occurs for quantum-dot--cavity systems operating on the edge between strong- and weak-coupling regimes. The computed maximum absorption probability is close to unity for pulses with a typical length comparable to half of the Rabi period. Furthermore, the dynamic control of the quantum-dot energy via electric fields allows the freezing of the light-matter interaction, leaving the quantum dot in its excited state. Shaping of single-photon wave packets by the electric field control is limited by the occurrence of chirping of the single-photon pulse. This understanding of the interaction of single-photon pulses with the quantum-dot--cavity system provides the basis for the development of advanced protocols for quantum-information processing in the solid state.
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.
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 theoretically analyze the steady state emission spectrum and transient temporal dynamics in a coupled biexciton quantum dot (QD)—cavity system. For steady state, a phonon-assisted biexciton—exciton cascade model under continuous wave (CW) excitation is presented to explain the asymmetric QD—cavity emission spectrum intensities (intensities of cavity, exciton, and biexciton emission peak) in off-resonance condition. Results demonstrate that the electron—phonon process is crucial to the asymmetry of emission spectrum intensity. Moreover the transient characteristics of the biexciton—exciton cascade system under pulse excitation show abundant nonlinear temporal dynamic behaviors, including complicated oscillations which are caused by the four-level structure of QD model. We also reveal that under off-resonance condition the cavity outputs are slightly reduced due to the electron—phonon interaction.