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.
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.
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 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 review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
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.
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.
We experimentally observe harmonic oscillations in a bosonic condensate of exciton-polaritons confined within an elliptical trap. These oscillations arise from quantum beats between two size-quantized states of the condensate, split in energy due to the trap’s ellipticity. By precisely targeting specific spots inside the trap with nonresonant laser pulses, we control frequency, amplitude, and phase of these quantum beats. The condensate wave function dynamics is visualized on a streak camera and mapped to the Bloch sphere, demonstrating Hadamard and Pauli-Z operations. We conclude that a qubit based on a superposition of these two polariton states would exhibit a coherence time exceeding the lifetime of an individual exciton-polariton by at least two orders of magnitude.