We theoretically study the dynamics of a strongly coupled quantum dot–bimodal microcavity system under an external magnetic field, where the nondegenerate excitonic spin states caused by the Zeeman effect are coupled to both orthogonal cavity modes. We develop an effective cavity quantum electrodynamics model, demonstrate the polarization-related nonlinear response under a linearly polarized pulse excitation by calculating the time-resolved intracavity photon number, and investigate the dependence of system parameters on the nonlinearity. In addition, we show that, when driven by two pulses with perpendicular polarization and a relative time delay, the coupled system suppresses the delayed one, which can be applied to polarized optical switching at a single-photon level.
We theoretically study the dynamics of a strongly coupled quantum dot–bimodal microcavity system under an external magnetic field, where the nondegenerate excitonic spin states caused by the Zeeman effect are coupled to both orthogonal cavity modes. We develop an effective cavity quantum electrodynamics model, demonstrate the polarization-related nonlinear response under a linearly polarized pulse excitation by calculating the time-resolved intracavity photon number, and investigate the dependence of system parameters on the nonlinearity. In addition, we show that, when driven by two pulses with perpendicular polarization and a relative time delay, the coupled system suppresses the delayed one, which can be applied to polarized optical switching at a single-photon level.
We theoretically investigate the optical response of a quantum dot, embedded in a microcavity and incoherently excited by pulsed pumping. The exciton and biexciton transition are off-resonantly coupled with the left- and right-polarized mode of the cavity, while the two-photon resonance condition is fulfilled. Rich behaviours are shown to occur in the time dependence of the second-order correlation functions which refer to counter-polarized photons. The corresponding time-averaged quantities, which are accessible to experiments, confirm that such a dot-cavity system behaves as a good emitter of single, polarization-correlated photon pairs.
We theoretically study cross-polarized pump-probe spectra of a quantum dot (QD) embedded in a microcavity in the cavity quantum electrodynamics treatment. Recently, observations of a vacuum Rabi splitting for a QD in microcavity have been reported. The vacuum Rabi splitting is the level separation of one-excitation dressed states (1e states). However, two-excitation dressed states (2e states) have not been observed in this system. We discuss the possibility to observe pump-probe signal coming from the cross-polarized 2e states, in which the energy levels of a QD are modeled by a four-level system consisting of the ground state, right- and left-polarized excitons, and a biexciton. The signal peaks due to the cross-polarized 2e states are found when the quality factor of the cavity is extremely large. The spectral intensity is dramatically enhanced due to the cavity effect. The enhancement rate is independent of the coupling constants between the exciton (biexciton) and a cavity photon when a well-defined vacuum Rabi splitting is formed. However, a strong suppression of the signal occurs at a condition where the energy of the 1e state coincides with the energy difference between 1e and cross-polarized 2e states.
We study the coherent time-resolved response of a semiconductor microcavity excited by an ultrashort light pulse. The cavity contains embedded quantum wells and quantum well excitons are strongly coupled to cavity photons. Two experimental situations are examined. We describe a linear regime when the exciting light pulse is weak. Further, a low-temperature pump-and-probe experiment in a nonlinear regime is analyzed, with a cw pump beam circularly polarized opposite to a weak ultrashort probe pulse in conditions yielding a bipolariton-mediated optical Stark effect. In both cases we examine the response of a single quantum well and contrast it with that of several quantum wells. In the latter case light is coupled only to a symmetric linear combination (bright exciton) of excitonic states in individual quantum wells. We find distinctive fingerprints of other linear combinations of exciton states (dark excitons). In the linear regime, in addition to a pattern of Rabi oscillations between the two polariton states, additional beating frequencies appear, related to dark states. In the nonlinear case, the bipolariton formalism outlined by Ivanov et al. [Phys. Rev. B 52, 11 017 (1995)] allows one to deduce a similar additional beating frequency and a splitting of bipolariton frequencies related to their dark or bright state character. This work identifies the effect of the microcavity parameters on its coherent response and determines the experimental conditions in which the influence of dark states may be observed.
Achieving strong optical nonlinearity in a low excitation power level is crucial in micro- and nanophotonics, central to many applications. Here, we explore optical linear and nonlinear responses in a single quantum dot (QD) embedded into a single-mode cavity under the effect of an external magnetic field and a continuous-wave laser excitation in the weak-coupling regime. Using experimentally realistic parameters, we find that the magnetic field introduced in such a coupled cavity-QD system can drastically modify the properties of photons and thus can be employed as a flexible control parameter. Especially, the enhanced optical Kerr nonlinearity can be achieved by tuning the applied magnetic field appropriately, which can reach over 11-fold improvement as compared to the case without the magnetic field. Physically, this is the consequence of the magnetic-field-induced resonance shifts and the cavity-field-mediated interferences. As an example of its applications, in the basis of this attainable strong Kerr nonlinearity, we show a feasible way of generating an optical high-order sideband efficiently, with small sideband spacing, as small as a few tens of megahertz, and low input excitation power, as low as a few nanowatts. Moreover, the manipulation of the high-order sideband is also discussed by changing the magnetic field from 0 to 3 T, where the variation of the sideband power is in good agreement with that of the Kerr nonlinearity. Considering realistic experimental conditions we elaborate the possible implementation of our proposal. In addition to being of fundamental interest, the results of our paper hold potential in optical frequency combs, nonlinear optics, and high precision measurement.
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 develop an exact analytical approach to four-wave mixing and higher-order optical nonlinearities of a quantum dot-microcavity system. This approach allows us \nto analyse the non-linear response in terms of coherent transitions between rungs \nof the Jaynes-Cummings ladder, finding their complex amplitudes and frequencies. \nIncreasing the pulse area of the excitation field, a transition from quantum strong \ncoupling to coherent classical regime is observed, which manifests itself in a formation of the famous Mollow triplet, with the observation in the three-level model \nof a quantum dot, including a biexciton, to predict two new effects: One is the \nexistence of a Mollow-like quintuplet, the other is a complete elimination of the \nfour-wave-mixing optical non-linearity under certain parameter constraints. We further develop a simple and accurate approximation in the low-damping limit of the \nJaynes-Cummings model of the quantum dot-microcavity system, for nonlinear response of any order in a closed analytic form, predicting the positions and widths \nof the spectral lines. For higher damping, we demonstrate a strong relaxation down \nthe ladder, shown by both numerical and analytic calculation.