Exciton polariton condensates are the most well-studied case of Bose-Einstein condensation (BEC) of quasiparticles. Together with their prominent fundamental importance, the exciton-polariton condensates have a wide spectrum of engineering applications covering interferometry and metrology, different types of SQUIDs and accelerometers, and forming a universal gate set for quantum computing via the control with external laser pulses. The efficient experimental manipulation with the polariton BEC can be realized via the bosonic final-state stimulation, matter-wave amplification, or by lasing of polaritons, but a satisfactory theoretical model for such control has not been developed yet. Here we study the polariton matter-wave amplifier based on the stimulated scattering of massive particles. The amplification of the injected quasiparticles is achieved through an elastic scattering of so-called lower polaritons (LPs). Such an amplifier has many advantages compared with a standard lasing or using a photon amplifier: it can provide a sufficient gain coefficient. To develop an efficient control algorithm for the polariton amplifier we use here the dynamical model for the LP population proposed by Ciuti, Savona, et al. in 1998. The phenomenological model for the gain coefficient is based on the experiments with cold collisions of polaritons performed by Deng, Haug, and Yamamoto in 2010 and later. We use different feedback algorithms (speed gradient vs target attractor) to track efficiently the polariton population in the amplifier. We compare the pros and cons of our alternative approaches and discuss their possible engineering applications.
Exciton polariton condensates are the most well-studied case of Bose-Einstein condensation (BEC) of quasiparticles. Together with their prominent fundamental importance, the exciton-polariton condensates have a wide spectrum of engineering applications covering interferometry and metrology, different types of SQUIDs and accelerometers, and forming a universal gate set for quantum computing via the control with external laser pulses. The efficient experimental manipulation with the polariton BEC can be realized via the bosonic final-state stimulation, matter-wave amplification, or by lasing of polaritons, but a satisfactory theoretical model for such control has not been developed yet. Here we study the polariton matter-wave amplifier based on the stimulated scattering of massive particles. The amplification of the injected quasiparticles is achieved through an elastic scattering of so-called lower polaritons (LPs). Such an amplifier has many advantages compared with a standard lasing or using a photon amplifier: it can provide a sufficient gain coefficient. To develop an efficient control algorithm for the polariton amplifier we use here the dynamical model for the LP population proposed by Ciuti, Savona, et al. in 1998. The phenomenological model for the gain coefficient is based on the experiments with cold collisions of polaritons performed by Deng, Haug, and Yamamoto in 2010 and later. We use different feedback algorithms (speed gradient vs target attractor) to track efficiently the polariton population in the amplifier. We compare the pros and cons of our alternative approaches and discuss their possible engineering applications.
Summary form only given. Final state stimulation is the origin of amplification in optical lasers and atom lasers. Matter-wave amplification based on an incoherent gain medium has yet to be demonstrated, but is very attractive, particularly for the excitonic system, because electrically injected incoherent excitons can amplify probe excitons without requiring a coherent pump laser. In previous work, we have shown final state stimulation using the exciton-exciton scattering of polaritons in a GaAs based microcavity quantum well; the gain was negligibly small due to the small exciton-exciton scattering rate. However, the rate of exciton-exciton scattering at the exciton saturation density is 9 times larger in CdTe microcavity exciton-polaritons compared to those in GaAs.
Exciton-polariton Bose-Einstein condensates (BECs) are newly emerged quantum systems that are capable of showing macroscopic quantum phenomena with intrinsic open-dissipative nature. The spatial distribution of the polariton density, without any external potential, can be controlled by the geometric shape of the pumping laser, enabling the investigation of polariton dynamics with topologically non-trivial configurations. Meanwhile, exciton-polaritons have spin degrees of freedom inherited from excitons and photons, making it a candidate for the realization of quantum logic gates. In this thesis, we will investigate theoretically the nonlinear dynamics of exciton-polariton BECs involving both polaritons' spatial degrees of freedom and spin degrees of freedom, and interactions between them. This thesis is organised as follows: In Chapter 1, we will present an overall review of exiton-polariton systems and important properties of polariton BECs and then introduce the dynamical equations with various interactions that will serve as the main theoretical tool for subsequent chapters. Several polariton pumping and trapping techniques appearing in later chapters will also be introduced. In Chapter 2, we will investigate the superfluidity properties of a single-component polariton condensate under an incoherent annular pumping configuration. By studying the stability properties of polariton persistent currents, we find that the persistent currents can exhibit dynamical instability and energetic-like instability according to different parameter region. A stability phase diagram will be given and its relation with the Landau's criterion will be discussed. In Chapter 3, we will investigate the spin dynamics of a two-component polariton condensate under a homogeneous pumping configuration. Owing to the Josephson coupling, there exist multiple steady state solutions that allow of controlled spin state switching. A desynchronized region where there exists no stable steady solution is found. In the desynchronized region, a desynchronized state beating periodically over time can exist, which will serve as a building block of spin waves presented in the next chapter. In Chapter 4, by combining results from the previous two chapters we will investigate generally the nonlinear dynamics of polariton condensates under an annular pumping configuration. The spin-orbit interaction provided by the Josephson coupling supports azimuthon states that have simultaneous modulations in both amplitude and phase. The azimuthon states, when viewed in a different polarization basis, form rotating spin waves that can be referred to as the optical ferris wheel. In Chapter 5, results from previous chapters will be extended to micocavities that support the anisotropic TE-TM splitting interaction. Rotating singularities (small-scale vortices) are found as a result. Their properties and experimental observation techniques will be discussed. Chapter 2-5 provide a theoretical framework for the nonlinear dynamics of polariton condensates. They rely mostly on optical trapping techniques and are ready to be tested in experiments. In Chapter 6, polaritons trapped by an engineered periodic mesa potential will be discussed. We will investigate the band structure of polaritons under the influence of the periodic potential together with discussions on the phase-modulated interference pattern which corresponds to the polariton Talbot patterns observed in experiments.
This reference book explains the fundamentals of Bose Einstein Condensation (BEC) in excitons and polaritons. It presents five chapters exploring fundamental concepts and recent developments on the subject. Starting with a historical overview of BEC, the book progresses into the origins and behaviors of excitons and polaritons. Chapters also cover the unique thermalization and relaxation kinetics of excitons, and the distinctive features of polaritons, such as lasing, superfluidity, and quantized vortices. The chapters dedicated to BEC in excitons and polaritons detail experimental techniques, theoretical modeling, recent advancements, and practical applications in a simplified way for beginners. This book serves as a resource for researchers, physicists, and students interested in the phenomena of BEC, providing insights into both the theoretical foundations and the practical implications of excitons and polaritons.
The wavefunction of a collection of identical quantum particles of integer spin (bosons) is even under exchange of the coordinates of any two of them. This symmetrization rule of quantum mechanics leads to stimulation of the scattering rate into final states whose population is larger than one. For massless photons, it is routinely observed in the laser. For massive bosons, most previous efforts concentrated in realizing the largely populated equilibrium Bose-Einstein condensate, and observing stimulated emission into it. Here we show that we do not need to produce such a condensate to observe final state stimulation. Instead, we take advantage of the highly non-equilibrium exciton reservoir and of the large polariton populations produced by external laser action on a semiconductor microcavity, and measure final state stimulation of the scattering rate of these excitons into the polaritons.
Introduction. Polaritons and Semiconductor Microcavities As we have mentioned previously, BEC of excitons or biexcitons and lasing can be seen as two limits of the same theory. Lasing occurs in the case of strong electron-photon coupling (recombination rate fast compared with interparticle-scattering rate) while excitonic BEC occurs in the case of weak electron-photon coupling (recombination rate slow compared with the interparticle-scattering rate.) A laser can be seen as a Bose condensate in which the long-range phase coherence exists in the photon states [1], while in the exciton condensate the coherence exists in the electronic states. This is one of the reasons for some of the confusing debates in the early history of excitonic Bose condensation – in many systems there is not a sharp distinction between an excitonic condensate and supperradiance, i.e., luminescence with enhanced intensity due to stimulated emission [2-4]. In the previous chapters, we have so far considered a laser light source only as a source of excitons by means of quantum transitions. In Chapter 6, the laser radiation was taken into account as a given external factor. This chapter is dedicated to phenomena related to a strong and noticeable exciton-photon interaction, when the light significantly influences the energy spectrum of the high-density excitons [5-9]. As we will see, this leads to many fascinating effects related to instabilities. A strong exciton-photon interaction implies a strong polariton effect, in which photon and exciton states are mixed (as in Fig. 1.3). When this mixing is strong, it is not obvious how to define the ground state of the system.
We analyze elementary properties of exciton and polariton lasers --- devices that generate coherent optical and matter waves using final-state stimulation of exciton-phonon scattering. First we discuss the relation between the conditions for the onset of equilibrium and nonequilibrium excitonic condensates. Provided that the thermal de Broglie wavelength ${\ensuremath{\lambda}}_{\mathit{T}}$ exceeds the exciton Bohr radius aB, an exciton laser operates without electronic population inversion. In contrast to previous proposals, this is a different type of laser without inversion which utilizes many-body coherences. When the excitonic character of the polariton branch vanishes, a polariton laser becomes indistinguishable from a photon laser. \textcopyright{} 1996 The American Physical Society.