We predict the limit cycle solution for a ring-shape bosonic condensate of exciton-polaritons confined in an optically induced rotating trap. The limit cycle manifests itself with polarization oscillations on a characteristic timescale of tens of picoseconds. The effect arises due to the interplay between orbital motion and the polarization degree of freedom. It is specific to spinor bosonic condensates and would be absent in a scalar case, where a bistability of stationary solutions would be observed instead. This work offers a tool of initialization and control of qubits based on superpositions of polariton condensates characterized by different topologic charges. Published by the American Physical Society 2024
We predict the limit cycle solution for a ring-shape bosonic condensate of exciton-polaritons confined in an optically induced rotating trap. The limit cycle manifests itself with polarization oscillations on a characteristic timescale of tens of picoseconds. The effect arises due to the interplay between orbital motion and the polarization degree of freedom. It is specific to spinor bosonic condensates and would be absent in a scalar case, where a bistability of stationary solutions would be observed instead. This work offers a tool of initialization and control of qubits based on superpositions of polariton condensates characterized by different topologic charges. Published by the American Physical Society 2024
Recently, split-ring bosonic condensates of exciton polaritons have been proposed for realisation of qubits. We formulate an analytical model of a polariton condensate in a one-dimensional ring split by a delta-function potential. The persistent current is stopped by the potential defect embedded in a scalar condensate of non-interacting particles, however, it reappears in the presence of an up-critical non-linearity. The nonlinear supercurrents are characterised by fractional orbital momenta while their eigenfunctions may feature grey or dark solitons. The coupling between the spin and the orbital angular momentum of a spinor condensate affects persistent currents crucially. We show that the spin-orbit interaction (SOI) induces the net superfluid current in the condensate with a spatially uniform spin polarisation. We also find solutions where the SOI-induced currents of two spin components of the condensate propagate in opposite directions. The corresponding states of spinor condensates obey a combined mirror reflection and the spin-flip symmetry.
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.
Bosonic condensates of spinless noninteracting particles confined on a ring cannot propagate circular periodic currents once rotation symmetry of the system is broken. However, a persistent current may appear due to interparticle interactions exceeding some critical strength. In this up-critical regime breaking of the symmetry between the clockwise and anticlockwise rotations takes place. We consider this symmetry-breaking scenario in the case of a spinor condensate of exciton polaritons trapped on a ring split by a potential barrier. Due to the intrinsic symmetry of the effective spin-orbit interaction, which stems from the linear splitting between transverse-electric and transverse-magnetic microcavity modes, the potential barrier blocks the circulating current and imposes linear polarization patterns. On the other hand, circularly polarized polaritons form circular currents propagating in opposite directions with equal absolute values of angular momentum. In the presence of interparticle interactions, the symmetry of clockwise and anticlockwise currents can be broken spontaneously. We describe several symmetry-breaking scenarios, which imply either restoration of the global condensate rotation or the onset of the circular polarization in the symmetry-broken state.
We investigate the indistinguishability of polaritons in optically trapped Bose-Einstein condensates by implementing Hong-Ou-Mandel (HOM) interferometry and test the limitations of two-polariton interference in the coherent, limit-cycle, and thermal statistical regimes. We observe that the HOM dynamics of a circularly polarized condensate follows the condensate coherence time with the characteristic HOM dip approaching the classical limit. Linearly polarized condensates exhibit a combined effect of polariton bunching and two-polariton interference. Under elliptically polarized excitation, the temporal evolution of the spinor condensate results in the revival of the HOM dip at the spinor Larmor precession frequency.
Bessel optical lattice yields a non-spatially periodic column-symmetric optical lattice potential field, which has the characteristics of both infinite deep potential well and the ring-shaped potential well. A deep potential is formed in the center of the 0-order Bessel optical lattice. In the non-zero-order Beseel optical lattice, a ring-shaped shallow potential well with a central barrier can be formed. Exciton-polariton is a semi-light and semi-matter quasi-particle, which can achieve the Bose-Einstein condensate phase transition even at room temperature to form a polariton condensate. In addition, the polariton condensate is likely to realize sufficiently strong spin-orbit coupling due to the cavity-induced TE-TM splitting of the polariton energy levels. The polariton condensate can be realized at room temperature, and there can be spin-orbit coupling in it, which provides a new platform for the studying of quantum physics. In this paper, the Bessel optical lattice is introduced into a polariton condensate. The stationary state structure of spinor two-component polariton condensate with spin-orbit coupling is investigated. By solving the Gross-Pitaevskii equation, we first give a stationary state structures of the polariton condensate both in the laboratory coordinate frame and in the rotating coordinate frame. Owing to the introduction of the Bessel optical lattice, the stationary state structures of polariton condensate are diverse. We dispaly the stationary state structures of the basic Gaussian solitons and multipole solitons in the central deep potential well in the laboratory coordinate frame, and the ring solitons and multipole solitons in the central shallow potential well. We also dispaly the vortex ring soliton that exists in the rotating coordinate frame, and the stationary state structure of the component separation caused by the spin-orbit interaction. We analyze not only the influences of the spin-orbit coupling on the stationary state structures in the two coordinate frames, but also the stability of the multipole solitons in the rotating coordinate frame. It is found that the multipole solitons formed in the ring-shaped shallow potential well have better stability than in the central deep potential well, and they can maintain the relative structure and spatial distribution for a long time in the rotation process. In the rotating coordinate frame, even if the two-component separation conditions are not satisfied, the introduction of spin-orbit coupling can cause the two components to separate.