We present numerical analysis of steady states in a two-component (spinor) driven-dissipative quantum fluid formed by condensed exciton polaritons in an annular optically induced trap. We demonstrate that an incoherent ring-shaped optical pump creating the exciton-polariton confinement supports the existence of stationary and rotating azimuthon steady states with azimuthally modulated density associated with Josephson vortices. Such states can be imprinted by coherent light pulses with a defined orbital angular momentum, as well as generated spontaneously in the presence of thermal noise.
We present numerical analysis of steady states in a two-component (spinor) driven-dissipative quantum fluid formed by condensed exciton polaritons in an annular optically induced trap. We demonstrate that an incoherent ring-shaped optical pump creating the exciton-polariton confinement supports the existence of stationary and rotating azimuthon steady states with azimuthally modulated density associated with Josephson vortices. Such states can be imprinted by coherent light pulses with a defined orbital angular momentum, as well as generated spontaneously in the presence of thermal noise.
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.
We predict the spontaneous symmetry breaking in a spinor Bose-Einstein condensate of exciton-polaritons (polaritons) caused by the coupling of its spin and orbital degrees of freedom. We study a polariton condensate trapped in a ring-shaped effective potential with a broken rotational symmetry. We propose a realistic scheme of generating controllable spinor azimuthal persistent currents of polaritons in the trap under the continuous wave optical pump. We propose a new type of half-quantum circulating states in a spinor system characterized by azimuthal currents in both circular polarizations and a vortex in only one of the polarizations. The spontaneous symmetry breaking in the spinor polariton condensate that consists in the switching from co-winding to opposite-winding currents in opposite spin states is revealed. It is characterized by the change of the average orbital angular momentum of the condensate from zero to non-zero values. The radial displacement of the pump spot and the polarization of the pump act as the control parameters. The considered system exhibits a fundamental similarity to a superconducting flux qubit, which makes it highly promising for applications in quantum computing.
We consider two concentric rings formed by bosonic condensates of exciton-polaritons. A circular superfluid flow of polaritons in one of the rings can be manipulated by acting upon the second annular polariton condensate. The complex coupling between the rings with different topological charges triggers nucleation of stable Josephson vortices (JVs) which are revealed as topological defects of the angular dependence of the relative phase between rings. Being dependent on the coupling strength, the structure of the JV governs the difference of the mean angular momenta of the inner and the outer rings. At the vanishing coupling the condensates rotate independently demonstrating no correlations of their winding numbers. At the moderate coupling, the interaction between two condensates tends to equalize their mean angular momenta despite the mismatch of the winding numbers demonstrating the phenomenology of a drag effect. Above the critical coupling strength the synchronous rotation is established via the phase slip events.
Abstract We report on the experimental realization and characterization of an exciton-polariton qubit prototype. In our system, a Bose-Einstein condensate of semiconductor exciton-polaritons is confined by a spatially-patterned pump laser in an annular trap that supports energy-degenerate circulating currents of the polariton superfluid. Using non-invasive temporal interference measurements, we observe coherent oscillations between a pair of counter-circulating superfluid vortex states of the polaritons coupled by elastic scattering off the laser-imprinted potential. The qubit basis states correspond to the symmetric and antisymmetric superpositions of the two vortex states forming orthogonal double-lobe spatial wavefunctions. By engineering the potential, we tune the coupling and coherent oscillations between the two circulating current states, control the energies of the qubit basis states and thereby initialize the qubit in the desired state. The dynamics of the system is accurately reproduced by our theoretical two-state model, and we discuss potential avenues to achieve complete control over our polaritonic qubit and implement controllable interactions and quantum gates between such qubits.
Microcavity-polaritons are quasi-particles formed when light and matter excitations couple strongly in cavities that have confinement lengths similar to the wavelength of light. Polariton’s light e↵ective mass, due to the photonic component, in conjunction with their composite boson nature, allows a transition into a macroscopically occupied quantum degenerate state (polariton condensate) for temperatures ranging from 4K up to room temperature. Due to the exciton reservoirs produced under non-resonant excitation and polariton’s strong interparticle interactions (originating from their matter component) potential landscapes for the polaritons can be sculpted with the non-resonant laser beam(s) pumping the system. The work presented in this thesis is specifically concerned with inorganic polariton condensates in optically imprinted potential landscapes. With annular excitation geometries it is possible to form optically trapped polariton condensates, where the condensate is spatially delocalised from the exciton reservoir. Implementing this optical trap geometry, the first all-optical polariton bistability under non-resonant excitation is demonstrated in the spinor of the condensate. Furthermore, the separation from the exciton reservoir results in significant enhancement of the coherence properties. First order coherence times exceeding 1.5ns are demonstrated for the optical trap excitation geometry; whilst excitation regimes where the condensate overlaps the reservoir demonstrate sub 100ps coherence times. For narrow Gaussian excitation geometries, the spatial overlap of the condensate and the reservoir results in polaritons ballistically propagating away from pump with a well defined in-plane wavevector. Utilising this inherent in-plane propagation, two freely expanding polariton condensates (a polariton dyad) are shown to remain coupled, even for separation distances exceeding 100μm. Through an in-depth experimental and theoretical investigation of the polariton dyad, it is determined that it is critically important to account for the finite propagation time of polaritons from one condensate centre to the other (i.e. the coupling is time-delayed). The experimental work in this thesis is then concluded by introducing all-optical polariton band structure engineering. Utilising optically imprinted polariton condensates and their exciton reservoirs to both create and image the band structures. In addition to the experimental results, experimental procedures and analysis techniques, that have been developed and implemented to facilitate the research, are presented.
This thesis includes theoretical studies regarding stability and manipulation of Bose-Einstein condensates (BECs) of ultra-cold atoms in 2D trapping geometry, as well as formation of steady states of exciton-polariton Bose-Einstein condensates created in solid states. We analyze and numerically model the dynamics and localization of the condensates using mean-field model. Chapter 1 contains an introduction to the physics of ultra-cold atom BEC and excitonpolariton BEC which provides a framework for the work presented in later chapters. In Chapter 2, we consider a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in an ultra-cold atom BEC with attractive interparticle interaction loaded into a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the effective particle approach demonstrate that fast, time-periodic rocking of the two-dimensional optical lattice enables efficient stabilization and manipulation of spatially localized matter wave packets via induced reconfigurable mobility channels. Chapter 3 consists of an investigation of the instability - collapse of a BEC with attractive interactions. In this chapter we explore the influence of an orbital angular momentum on the collapse of vortex-free elliptic clouds of Bose-Einstein condensates trapped in a radially symmetric harmonic potential or a rotating elliptic potential. The results of our analysis show that the number of trapped ultracold atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves in a radially harmonic trap. The results corresponding to a BEC cloud confined in a rotating elliptic trap show that the elongated stationary states can be parallel or perpendicular to the long axis of the trap and display bistable nature. In Chapter 4, we examine spatial localization and dynamical stability of Bose-Einstein condensates of exciton-polaritons in microcavities under the condition of off-resonant spatially inhomogeneous optical pumping both with and without a harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii model for describing an incoherently pumped polariton condensate coupled to an exciton reservoir. We reveal that spatial localization of the steady-state condensate occurs due to effective self-trapping created by the polariton flows, regardless of the presence of the external potential. A ground state of the polariton condensate with repulsive interactions between the quasiparticles represents a dynamically stable bright dissipative soliton. We also investigate the conditions for sustaining spatially localized structures, with nonzero angular momentum, in the form of single-charge vortices. Chapter 5 consider the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic inplane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We show that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultra-cold alkali atoms.