We review the problem of description of the dynamics of driven-disspipative spinor polariton condensates, focusing on the terms corresponding to the coupling between a macroscopic wavefunction of the condensdate and incoherent excitonic reservoir created by a non-resonant pump. We demonstrate that the existing version of the theory breaks down in case, when reservoir has non-zero components of the Stokes vector corresponding to in-plane linear polarization. The polarization invariant theory of reservoir to condensate coupling is formulated with use of the spin density matrix formalism.
We review the problem of description of the dynamics of driven-disspipative spinor polariton condensates, focusing on the terms corresponding to the coupling between a macroscopic wavefunction of the condensdate and incoherent excitonic reservoir created by a non-resonant pump. We demonstrate that the existing version of the theory breaks down in case, when reservoir has non-zero components of the Stokes vector corresponding to in-plane linear polarization. The polarization invariant theory of reservoir to condensate coupling is formulated with use of the spin density matrix formalism.
We theoretically investigate a spinor polariton condensate under nonresonant pumping, based on driven-dissipative Gross-Pitaevskii equations coupled to the rate equation of a spin-unpolarized reservoir. We find the homogeneous polariton condensate can transit from the spin-unpolarized phase, where it is linearly polarized, to the spin-polarized phase, where it is elliptically polarized, depending on the cross-spin versus same-spin interactions and the linear polarization splitting. In both phases, we study elementary excitations using Bogoliubov approach, in a regime where the decay rate of total exciton density in reservoir crosses over from the slow to the fast limit. Depending on reservoir parameters, the global-phase mode can be either diffusive or gapped. By contrast, the relative-phase mode always possesses a gapped energy, undamped in the spin-unpolarized phase but weakly damped in the spin-polarized phase. In the spin-unpolarized phase, both modes are linearly polarized despite pumping and decay. However, in the spin-polarized phase, the mode polarization can be significantly affected by the reservoir and depends strongly on the circular polarization degree of the condensate. Interestingly, we demonstrate that the ``ghost'' branch of the Bogoliubov spectrum of the relative-phase mode can be visualized in the photoluminescence emission, distinguishable from that of the global-phase mode and thus allowing for experimental observation, when the spinor polariton condensate is elliptically polarized.
We study the relation between the models commonly used to describe the dynamics of nonresonantly pumped exciton-polariton condensates, namely the ones described by the complex Ginzburg-Landau equation, and by the open-dissipative Gross-Pitaevskii equation including a separate equation for the reservoir density. In particular, we focus on the validity of the adiabatic approximation and small density fluctuations approximation that allow one to reduce the coupled condensate-reservoir dynamics to a single partial differential equation. We find that the adiabatic approximation consists of three independent analytical conditions that have to be fulfilled simultaneously. By investigating stochastic versions of the two corresponding models, we verify that the breakdown of these approximations can lead to discrepancies in correlation lengths and distributions of fluctuations. Additionally, we consider the phase diffusion and number fluctuations of a condensate in a box, and show that self-consistent description requires treatment beyond the typical Bogoliubov approximation.
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.
It is shown that a condensate of microcavity exciton-polaritons exhibits bistability between its two orthogonal linearly polarized components for varying nonresonant excitation power.A non-Hermitian splitting of these components results in two parity-symmetric fixed-point solutions of opposite polarization, making up the hysteresis branches.These solutions correspond to the lowest threshold linearly polarized mode, which dominates at low pump powers, and a cross-polarized mode, which appears due to nonlinear pinning at higher excitation powers.The spin symmetry of the solutions extends the nonresonant bistable operation of polariton condensates to the entire equatorial plane of the Poincaré sphere.The results pave the way towards development of tailored bistable, linearly polarized, coherent sources of light.
We implement full polarization tomography on photon correlations in a spinor exciton-polariton condensate. Our measurements reveal condensate pseudospin mean-field dynamics spanning from stochastic switching between linear polarization components, limit cycles, and stable fixed points, and their intrinsic relation to the condensate photon statistics. We optically harness the cavity birefringence, polariton interactions, and the optical orientation of an incoherent exciton reservoir to engineer photon statistics with precise control. Our results demonstrate a smooth transition from a highly coherent to a super-thermal state of the condensate polarization components.
We develop a theory for the dynamics of the density matrix describing a multimode polariton condensate. In such a condensate several single-particle orbitals become highly occupied, due to stimulated scattering from reservoirs of high-energy excitons. A generic few-parameter model for the system leads to a Lindblad equation which includes saturable pumping, decay, and condensate interactions. We show how this theory can be used to obtain the population distributions, and the time-dependent first- and second-order coherence functions, in such a multimode condensate. As a specific application, we consider a polaritonic Josephson junction, formed from a double-well potential. We obtain the population distributions, emission line shapes, and widths (first-order coherence functions), and predict the dephasing time of the Josephson oscillations.