We have studied the characteristic feature of coherent photon transport in a semiconductor waveguide. We have presented a semiconductor master equation formalism that accurately simulated coherent input or output coupling of semiconductor cavity quantum electrodynamics systems such as planar photonic crystals and micropillar cavities. The role of quantized multiphoton effects pointed out the possible failure of weak excitation approximation, which was found to fail even for low input powers and small mean cavity photon numbers. For increasing field strengths, possible failure of the semiclassical approach was taken into account. In the weak coupling regime, higher order quantum correlation effects, were shown to be significant. We have introduced the general theoretical technique to simulate coherent photon transport outside both the weak excitation approximation and the semi classical approximation. Electron-phonon interactions at a microscopic level were derived using polaron transformation. We have demonstrated that substantial deviations from the weak excitation approximation resulted for very small mean photon numbers. We have modified the master equation approach to include the mechanism of electron-acoustic scattering and studied the impact of electron-phonon interaction on incoherent scattering and coherent renormalization of the exciton cavity coupling rate, qualitative differences from simple Lorentzian decay model containing quantum dot were found. We have also studied the transmission of light in the strong coupling regime and simulated a phase gate. We have found that coupling to an acoustic phonon bath caused considerable qualitative changes in light propagation characteristics modeled by a simple pure dephasing process. We have used the model to simulate a conditional phasegate. The obtained results were found in good agreement with previously obtained results.
We have studied the characteristic feature of coherent photon transport in a semiconductor waveguide. We have presented a semiconductor master equation formalism that accurately simulated coherent input or output coupling of semiconductor cavity quantum electrodynamics systems such as planar photonic crystals and micropillar cavities. The role of quantized multiphoton effects pointed out the possible failure of weak excitation approximation, which was found to fail even for low input powers and small mean cavity photon numbers. For increasing field strengths, possible failure of the semiclassical approach was taken into account. In the weak coupling regime, higher order quantum correlation effects, were shown to be significant. We have introduced the general theoretical technique to simulate coherent photon transport outside both the weak excitation approximation and the semi classical approximation. Electron-phonon interactions at a microscopic level were derived using polaron transformation. We have demonstrated that substantial deviations from the weak excitation approximation resulted for very small mean photon numbers. We have modified the master equation approach to include the mechanism of electron-acoustic scattering and studied the impact of electron-phonon interaction on incoherent scattering and coherent renormalization of the exciton cavity coupling rate, qualitative differences from simple Lorentzian decay model containing quantum dot were found. We have also studied the transmission of light in the strong coupling regime and simulated a phase gate. We have found that coupling to an acoustic phonon bath caused considerable qualitative changes in light propagation characteristics modeled by a simple pure dephasing process. We have used the model to simulate a conditional phasegate. The obtained results were found in good agreement with previously obtained results.
We present a semiconductor master equation technique to study the input/output characteristics of coherent photon transport in a semiconductor waveguide-cavity system containing a single quantum dot. We use this approach to investigate the effects of photon propagation and anharmonic cavity-QED for various dot-cavity interaction strengths, including weakly-coupled, intermediately-coupled, and strongly-coupled regimes. We demonstrate that for mean photon numbers much less than 0.1, the commonly adopted weak excitation (single quantum) approximation breaks down, even in the weak coupling regime. As a measure of the multiphoton correlations, we compute the Fano factor and the correlation error associated with making a semiclassical approximation. We also explore the role of electron--acoustic-phonon scattering and find that phonon-mediated scattering plays a qualitatively important role on the light propagation characteristics. As an application of the theory, we simulate a conditional phase gate at a phonon bath temperature of 20 K in the strong coupling regime.
We present a semiconductor quantum optics formalism to study the dynamics of a coherently-driven semiconductor quantum dot interacting with an acoustic phonon bath and a high Q microcavity. A quantum master equation is derived in the polaron frame, where multiphoton and multiphoton effects are included to all orders. As applications of the theory, we study the Mollow triplet of a driven quantum dot in the regime of semiconductor cavity-QED. Pronounced signatures of electron-phonon-photon scattering are observed through excitation-induced dephasing and off-resonant cavity coupling. We also present an effective phonon master in Lindblad form and show example quantum trajectory simulations that help one to understand the features in the Mollow triplet spectra.
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-Q limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.
The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.
We study a cavity-photon-switched coherent electron transport in a symmetric double quantum waveguide. The waveguide system is weakly connected to two electron reservoirs, but strongly coupled to a single quantized photon cavity mode. A coupling window is placed between the waveguides to allow electron interference or inter-waveguide transport. The transient electron transport in the system is investigated using a quantum master equation. We present a cavity-photon tunable semiconductor quantum waveguide implementation of an inverter quantum gate, in which the output of the waveguide system may be selected via the selection of an appropriate photon number or “photon frequency” of the cavity. In addition, the importance of the photon polarization in the cavity, that is, either parallel or perpendicular to the direction of electron propagation in the waveguide system is demonstrated.
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.