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Acta Physica Sinica

Stationary structures of spin-orbit coupled polariton condensates in Bessel lattices

Haijun Chen, Yuan Ren, Hua Wang

Published Jan 1, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.7498/aps.71.20211949

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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.
Abstract We propose a superposed Bessel optical lattice formed by multiple Bessel optical lattices. The static and rotational structures are formed in the presence of a spin-orbit coupling (SOC) interaction in the atomic in Bose–Einstein condensates are investigated, it is shown that the two structures can be manipulated by adjusting the parameters of the superposed Bessel optical lattices. The results show that the SOC interaction has an important effect on the two structures in the superposed Bessel optical lattices, and the SOC interaction can enhance the robustness of the structures. The Gaussian, toroidal and vortex superposition structures in the superposition lattice are presented, the interference processes in the steady state structures are analyzed, and the effects of SOC interactions on the Gaussian vortex and toroidal vortex structures are investigated, and the angular momentum of the vortex states can be increased by SOC interactions.
Applying a variational approach and numerical analysis to the system of Gross-Pitaevskii equations, we find three-dimensional (3D) stable solitons in binary atomic Bose-Einstein condensates with spin-orbit coupling (SOC) and out-of-phase linear and nonlinear Bessel optical lattices. We discuss the stability of 3D solitons by utilizing their norm and energy. The introduction of Bessel potentials makes the evolution and collisions of solitons more stable and improves their resistance to collapse. Depending on the strength of the intra- and intercomponent spatial modulation of the nonlinearity and SOC, we find stable solitons of the semivortex and mixed-mode structures. Furthermore, we show that the solitons are stable against small perturbations in propagation and collisions.
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 investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radially periodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.
We consider a model of the exciton-polariton condensate based on a system of two Gross–Pitaevskii equations coupled by the second-order differential operator, which represents the spin–orbit coupling in the system. Also included are the linear gain, effective diffusion, nonlinear loss, and the standard harmonic-oscillator trapping potential, as well as the Zeeman splitting. By means of combined analytical and numerical methods, we identify stable two-dimensional modes supported by the nonlinear system. In the absence of the Zeeman splitting, these are mixed modes, which combine zero and nonzero vorticities in each of the two spinor components, and vortex–antivortex complexes. We have also found a range of parameters where the mixed-mode and vortex–antivortex states coexist and are stable. Sufficiently strong Zeeman splitting creates stable semi-vortex states, with vorticities 0 in one component and 2 in the other.
Abstract Employing the variational principle and the two-mode approximation, we have carried out a study on the nonlinear energy spectrum and current density of spin-1 spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in a one-dimensional shallow optical lattice. The energy spectrum structure diagrams in the momentum space are given. When certain conditions for the system parameters are satisfied, we find that the loop structure appears at the boundary of the Brillouin zone. Furthermore, we analyze the influence of the parameters in the system on the critical condition and width of the loop structure. It is revealed that the optical lattice and Raman coupling can suppress the emergence of the loop. On the contrary, the quadratic Zeeman strength, spin-orbit-coupling and atomic interactions are favorable for the generation of the loop, which leads to the complication of the energy band structure. Intriguingly, the change of the band structure is closely related to the current density distribution of the condensates. The spin-orbit-coupling leads to a strong asymmetry in the current density distribution of different spin states in the momentum space, so as to cause a separation phenomenon. However, the optical lattice and Raman coupling weaken this asymmetry and promote the current density distribution of different spin states to re-coincidence. Our results provide a theoretical basis for further understanding the nonlinear energy spectrum characteristics of this system.