Recently, there are several experiments demonstrating the possibility to tune the interaction constants using biexcitonic Feshbach resonance in resonantly created polariton condensate and single quantum well. Motivated by these experiments, we theoretically study the stationary state of a polariton condensate whose interatomic scattering length is periodically modulated with optical Feshbach resonance, which represents a novel kind of non-equilibrium superfluidity. In more detail, the spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations are investigated based on driven-dissipative Gross–Pitaevskii equations coupled to the rate equation of a reservoir.
Recently, there are several experiments demonstrating the possibility to tune the interaction constants using biexcitonic Feshbach resonance in resonantly created polariton condensate and single quantum well. Motivated by these experiments, we theoretically study the stationary state of a polariton condensate whose interatomic scattering length is periodically modulated with optical Feshbach resonance, which represents a novel kind of non-equilibrium superfluidity. In more detail, the spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations are investigated based on driven-dissipative Gross–Pitaevskii equations coupled to the rate equation of a reservoir.
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 theoretically the superfluidity and stability of a Bose-Einstein condensate (BEC) whose interatomic scattering length is periodically modulated with optical Feshbach resonance. Our numerical study finds that the properties of this periodic BEC are strongly influenced by the modulation strength. When the modulation strength is small, only the Bloch waves close to the Brillouin zone edge suffer both Landau and dynamical instabilities. When the modulation strength is strong enough, all Bloch waves become dynamically unstable. In other words, the periodic BEC loses its superfluidity completely.
Magnetic soliton is an intriguing nonlinear topological excitation that carries magnetic charges while featuring a constant total density. So far, it has only been studied in the ultracold atomic gases with the framework of the equilibrium physics, where its stable existence crucially relies on a nearly spin-isotropic, antiferromagnetic, interaction. Here, we demonstrate that magnetic soliton can appear as the exact solutions of dissipative Gross–Pitaevskii equations in a linearly polarized spinor polariton condensate with the framework of the non-equilibrium physics, even though polariton interactions are strongly spin anisotropic. This is possibly due to a dissipation-enabled mechanism, where spin excitation decouples from other excitation channels as a result of gain-and-loss balance. Such unconventional magnetic soliton transcends constraints of equilibrium counterpart and provides a novel kind of spin-polarized polariton soliton for potential application in opto-spintronics.
A mechanism leading to spontaneous breaking of the space symmetry, and to the appearance of spatial patterns in the most recently created state of matter, the Bose-Einstein condensate (BEC), is proposed. The pattern formation are due to a periodic modulation in time of the scattering length of the condensed atoms. Experimentally this can be achieved via the Feshbach resonance, or, for low dimensional (1D or 2D) condensates, also by modulation of the trapping potential along a spatial coordinate normal to the "working" space. The parametric excitation of patterns in condensates by considering the mean-field Gross-Pitaevskii equation, and its dissipative generalization are investigated.
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.
Superfluids under specific conditions can exhibit spontaneous breaking of continuous translation symmetries and form exotic spatially ordered states of matter known as supersolids. Despite its early theoretical prediction, it took over half-a-centrury to experimentally demonstrate the supersolid phase in ultracold atomic Bose-Einstein condensates, forming due to long-range interatomic interactions. Here we propose as a promising new platform for supersolidity exciton-polariton superfluids, confined in annular optically induced traps. The supersolid phase emerges due to effective attractive interactions, mediated by the normal excitonic component of the system. Experimental demonstration of spontaneously formed spatially ordered phase is in agreement with detailed mean-field theoretical analysis and numerical simulation. The spontaneous character of the observed supersolid transition is further evidenced by the formation of specific zero-energy Nambu-Goldstone modes in the collective excitation spectrum.