Polariton linewidth and the reservoir temperature dynamics in a semiconductor microcavity

Microcavity polaritons are hybrid quasiparticles emerging from the strong coupling between quantum well excitons and light in the resonator. Their unique half-light half-matter nature brings in specific properties like low effective mass, nonlinearity due to the repulsive interactions, and ability to directly access the polaritonic wavefunction through optical means. Due to their specific features, polaritons can form macroscopic quantum states and even undergo Bose-Einstein condensation, which makes them very interesting system for studying the quantum phenomena occurring on a macroscopic scale. This thesis is devoted to the investigation of dynamics of the second-order coherence of the microcavity polaritons. The evolution of the coherence of the polariton system occurs on a timescale of few picoseconds only, which required assembly of a new ultrafast photon correlation setup based on the streak-camera. The operation of this setup and requirements for high-quality measurements are discussed in details. After this, the experiments under both nonresonant and resonant excitation of polaritons are reported. Under nonresonant excitation, the formation of the polariton Bose-Einstein condensate is observed, and the change of the polariton coherence during this phase transition is measured. This indicates the time which is required to formthe condensate, and also allows to estimate its propagation velocity. The latter is compared with the measurements of the first-order spatial correlation function. Finally, polaritons confined in two coupled potential traps are studied. The traps are fabricated using the wet etching of the microcavity. In the resulting Josephson junction, polaritons are excited resonantly and demonstrate clear Josephson oscillations between the two traps. At the same time, the correlation measurements demonstrate strong perturbations of the light statistics in phase with the oscillations. This behavior is well represented with the quantum simulations, which also indicate presence of a significant quadrature squeezing in the system. The origin of the squeezing, the perspective for generating the nonclassical light, and other features of this phenomenon are discussed.

Bose-Einstein condensation (BEC) is a thermodynamic phase transition of an interacting Bose gas. Its key signatures are remarkable quantum effects like superfluidity and a phonon-like Bogoliubov excitation spectrum, which have been verified for atomic BECs. In the solid state, BEC of exciton-polaritons has been reported. Polaritons are strongly coupled light-matter quasiparticles in semiconductor microcavities and composite bosons. However, they are subject to dephasing and decay and need external pumping to reach a steady state. Accordingly the polariton BEC is a nonequilibrium process of a degenerate polariton gas in self-equilibrium, but out of equilibrium with the baths it is coupled to and therefore deviates from the thermodynamic phase transition seen in atomic BECs. Here we show that key signatures of BEC can even be observed without fulfilling the self-equilibrium condition in a highly photonic quantum degenerate nonequilibrium system.

Topologically nontrivial systems can be protected by band topology in momentum space, as seen in topological insulators and semimetals, or real-space topology, such as in lattice deformations known as topological disclinations (TDs). TDs, with inherent chiral symmetry, can support localized states pinned spectrally to the middle of the topological gap, preventing hybridization with bulk bands, and making them promising for topological lasers. Here, we experimentally realize a C4v symmetric TD laser based on perovskite exciton-polariton lattices at room temperature. Protected by the chiral and point group symmetries of the lattice, the TD state emerges in the middle of the gap and at the core of the perovskite lattice. Under a non-resonant pulsed excitation, coherent polariton lasing occurs precisely at the TD state with a low threshold of 9.5 μJ/cm2, as confirmed by momentum space and real space spectra measurements. This study not only introduces a class of symmetry-protected topological lasers, but also expands the landscape for exploring exciton-polariton light-matter interactions with novel topological structures.

We describe recent continuous wave studies of stimulated polariton scattering in semiconductor microcavities, with emphasis on the variety of new physics which has been observed in the last few years. The ability to manipulate both exciton and photon properties, and how they interact together to form strongly coupled exciton–photon coupled modes, exciton polaritons, leads to a number of novel phenomena, previously unreported in bulk semiconductors or quantum wells. The unusual dispersion of the lower polariton branch, which allows energy and momentum conserving polariton–polariton parametric scattering under resonant excitation, is shown to be a key factor enabling much of the new physics. A classical theoretical treatment of the phenomena which draws parallels between the equivalent pictures of stimulated polariton scattering and those of a triply resonant optical parametric oscillator is discussed. Higher order parametric phenomena and the factors which control the threshold for stimulation are also described. The results obtained under resonant excitation are contrasted with phenomena which occur under conditions of non-resonant excitation. Prospects to achieve ‘polariton lasing’ under non-resonant excitation are discussed.

Polaritonic coupling and spin dynamics in GaAs microcavities

Real- and momentum-space spectrally resolved images of microcavity polariton emission in the regime of condensation are investigated under nonresonant excitation using a laser source with reduced intensity fluctuations on the time scale of the exciton lifetime. We observe that the polariton emission consists of many macroscopically occupied modes. Lower-energy modes are strongly localized by the spatial polaritonic potential disorder on a scale of a few microns. Higher-energy modes have finite k vectors and are delocalized over 10– 15 m. All the modes exhibit long-range spatial coherence comparable to their size. We provide a theoretical model describing the behavior of the system with the results of the simulations in good agreement with the experimental observations. We show that the multimode emission of the polariton condensate is a result of its nonequilibrium character, the interaction with the local polaritonic potential, and the reduced intensity fluctuations of the excitation laser.

Anisotropic polariton scattering and spin dynamics of cavity polaritons

We have used stress to create a harmonic potential for polaritons in GaAs microcavities and have previously reported that the polaritons undergo spontaneous coherence in the trap. In this paper we present results for both trapped conditions and resonant, nontrapped conditions in the same sample. We find that the results are qualitatively different with two distinct types of transitions. At low density in the trap, the polaritons remain in the strong coupling regime while going through the threshold for onset of coherence; at higher density, there is a different threshold behavior, which occurs with weak coupling and can be identified with lasing; this transition occurs both with and without a trap. The transition at lower density can therefore be identified as a type of nonequilibrium Bose–Einstein condensation.

The present work is devoted to the study of the dynamics of multi-photon processes in semiconductor heterostructures. A time-dependent description is important for understanding in detail the transient response of semiconductors excited by ultrashort optical pulses. In the first part of this thesis, we set up a phenomenological model based on rate equations, in order to investigate the possibility of measuring degenerate two-photon gain in a semiconductor microcavity. The amplification predicted by the model is fairly low ( 2%) and mainly limited by the intra-band relaxation of the carriers, which leads to rapid saturation. In the second part, we develop a general theory for the dynamics of multi-photon processes in semiconductors. It will give insight into complex effects related to the coherence between the bands, which are not included in usual absorption coefficients or susceptibilities. For this purpose, we derive effective multi-band Bloch equations that include resonant multi-photon processes induced by two linearly polarized electromagnetic pulses of frequency close to the band gap and close to the half of the band gap respectively. The benefit of the proposed approach is two-fold. First, the description of the dynamics is restricted to a reduced number of bands. However, the discarded bands are not neglected, but consistently taken into account in the higher order processes. Second, all quantities appearing in the effective multi-band Bloch equations vary on the same time scale, which makes the numerical integration much more efficient. The time-dependent polarization current, as well as some susceptibilities, are derived on a consistent level of approximation, and are discussed in detail. The propagation of the electromagnetic fields is neglected. Such a model is appropriate for the description of low-dimensional quantum confined systems (e.g. quantum wells or quantum wires) excited by two colinearly propagating pulses. It accounts for various linear and nonlinear optical processes, such as one- and two-photon absorption, second-harmonic generation, difference-frequency mixing, or coherent control of photocurrent. In this thesis, the general theory is applied to the study of three specific physical situations. First, we investigate the charge and spin current in a symmetric AlGaAs/GaAs quantum well, injected by interference between one- and two-photon inter-band transitions. We identify new coherent terms in the expression of the current, which contribute significantly to the terahertz emission. The effects of the Stark shifts and the inter-valence band two-photon transitions are also calculated and discussed. Second, we calculate the anisotropic two-photon absorption spectra of an AlGaAs/GaAs V-shaped quantum wire with realistic band structure. The Coulomb interaction is taken into account within the Hartree-Fock approximation. The various excitonic peaks are identified with respect to the involved subbands and to the symmetry properties. We also show that excitons that are dark for one-photon excitation may become bright for two-photon spectroscopy, when the light is polarized perpendicularly to the growth direction, but not along a symmetry axis of the wire. Finally, the last application focuses on the optical injection of current in the presence of excitonic effects. Concentrating on the same AlGaAs/GaAs V-shaped quantum wire, we show that the Coulomb interaction within the Hartree-Fock approximation induces terahertz oscillations in the injected charge current. The oscillation frequency corresponds to the energy spacing between the two lowest excitonic resonances, slightly below the band gap, excited respectively by the laser pulse with frequency close to the band gap, and the one with frequency close to the half of the band gap.

Investigation of light–matter interactions in two-dimensional (2D) semiconductors is essential to understand many-body effects and explore their applications in photonics. 2D semiconductor microcavities can be formed by the integration of 2D semiconductor active media with planar Fabry–Perot resonant cavities. The emerging exciton–photon interactions between the strongly bound excitons in 2D semiconductors and the cavity photons allow exploring on the wealthy photonic and polaritonic physics of bosonic quasiparticles in the 2D limit. This Perspective focuses on recent advances in exciton–photon interactions of 2D semiconductor microcavities and their inspiring applications. First, we picture the research scope of 2D semiconductor microcavities, sort out the historical development from conventional semiconductor microcavities to the emerged 2D semiconductor microcavities, and illustrate mostly employed device structures. Second, we classify exciton–photon interactions in 2D semiconductor microcavities according to their coupling strengths. In the weak coupling regime, control of spontaneous emission and photon lasing are discussed together with the Purcell effect. In the strong coupling regime, we summarize experimental observations and theoretical predictions on Rabi splitting, Bose–Einstein condensation, polariton lasing, superfluidity, and superconductivity. Third, four types of leading-edge applications are outlined, including on-chip coherent light sources, microcavity-enhanced single-photon sources, topological photonics, and other nonlinear optics. Finally, we highlight the remaining challenges and future opportunities for fundamental physics of 2D semiconductor microcavities and their technological applications.

Light-matter interactions associated with excitons and exciton related complexes are explored in bulk GaAs and semiconductor microcavities using multidimensional coherent spectroscopy (MDCS). This approach provides rich spectra determining quantum excitation pathways, structural influences on the excitons, and coherence times.;Polarization, excitation density, and temperature-dependent MDCS is performed on excitons in strained bulk GaAs layers, probing the coherent response for differing amounts of strain. Biaxial tensile strain lifts the degeneracy of heavy-hole and light-hole valence states, leading to an observed splitting of the associated excitons at low temperature. Increasing the strain increases the magnitude of the heavy-/light- hole exciton peak splitting, induces an asymmetry in the off-diagonal interaction coherences, increases the difference in the heavy- and light- hole exciton homogenous linewidths, and increases the inhomogeneous broadening of both exciton species. All results arise from strain-induced variations in the local electronic environment, which is not uniform along the growth direction of the thin layers. For cross-linear polarized excitation, wherein excitonic signals give way to biexcitonic signals, the high-strain sample shows evidence of bound light-, heavy- and mixed- hole biexcitons.;2DCS maps the anticrossing associated with normal mode splitting in a semiconductor microcavity. For a detuning range near zero, it is observed that there are two diagonal features related to the intra-action of exciton-polariton branches and two off-diagonal features related to coherent interaction between the polaritons. At negative detuning, the line shape properties of the diagonal intra-action features are distinguishable and can be associated with cavity-like and exciton-like modes. A biexcitonic companion feature is observed, shifted from the exciton feature by the biexciton binding energy. Closer to zero detuning, all features are enhanced and the diagonal intra-action features become nearly equal in amplitude and linewidth. At positive detuning the exciton-like and cavity-like characteristics return to the diagonal intra-action features. Off-diagonal interaction features exhibit asymmetry in their amplitudes throughout the detuning range. The amplitudes are strongly modulated as the lower polariton branch crosses the bound biexciton energy determined from negatively detuned spectra.

Motional narrowing in a microcavity: contribution to the lower polariton linewidth

The effect of a classical electron gas on the cavity polariton linewidths is studied experimentally in a GaAs/AlAs microcavity with an embedded quantum well that contains photogenerated electrons (at $T=80 \mathrm{K}).$ The linewidth dependence on the electron density and on the cavity mode energy is explained by a theoretical model based on calculating the asymmetric bare exciton line shape, due to electron-exciton scattering. For a given electron density, the exciton line shape is inserted into the linear dispersion theory of the coupled excitons and cavity mode, yielding the reflection spectra that are formed of the three polariton branches. This model reproduces the reduced lower-polariton linewidth and the complex dependence of the middle- and upper-polariton linewidths on the cavity mode energy.

We demonstrate that high-dimensionality coherent spectroscopy yields "super-resolved" spectra whereby peaks may be localized far below their homogeneous line width by resolving them across multiple, coherently coupled dimensions. We implement this technique using a fifth-order photon-echo spectroscopy called Gradient-Assisted Multidimensional Electronic-Raman Spectroscopy (GAMERS) that combines resonant and nonresonant excitation to disperse the optical response across three spectral dimensions: two involving excitonic transitions and one that encodes phonon energies. In analogy to super-resolution localization microscopies, which separate spatially overlapping signals in time, GAMERS isolates signals spectrally using combined electronic and nuclear resolution. Optical phonon lines in a colloidal solution of CdSe quantum dots at room temperature separated by less than 150 μeV are resolved despite the homogeneous line width of these transitions being nearly an order of magnitude broader. The frequency difference between these phonon modes is attributed to softening of the longitudinal phonon mode upon excitation to the lowest exciton state. Further, such phonon mode selectivity yields spectra with electronic line widths that approach the single particle limit. Through this enhanced spectral resolution, the GAMERS method yields insights into the nature of coupling between longitudinal optical and acoustic phonons and specific excitonic transitions that were previously hidden.

Picosecond pump–probe experiments at room temperature on a bulk GaAs microcavity are presented. The microcavity device is designed to adjust the cavity mode energy 15 meV below the band gap energy of the intracavity bulk GaAs material. For low pump-energy densities (∼μJ/cm2), ultrafast modulation of the reflectivity is demonstrated due to the purely coherent refractive index change. A 5:1 contrast ratio is achieved and shows the potential of the semiconductor microcavities for implementation in ultrafast all optical switching.