Subcritical bifurcation and on-off bistability in ballistic polariton condensates
Oleg I. Utesov, Soohong Choi, Pavel Kozhevin, Min Park, Daegwang Choi, Hyungdo Lee, Alexey N. Osipov, Alexey V. Yulin, Se Kwon Kim, Yong‐Hoon Cho, Igor S. Aranson, Hyoungsoon Choi, Anton V. Nalitov, S. V. Koniakhin
Dynamics of exciton-polariton condensates under continuous-wave incoherent Gaussian optical pumping is considered. It is shown that the conventional supercritical Stuart-Landau picture is invalid in a certain domain of the parameter space. For strong polariton repulsion from the reservoir and relatively small pump spots, the dynamics is adequately described by the quintic Stuart-Landau equation. The corresponding subcritical pitchfork bifurcation leads to condensate formation, accompanied by bistability between the trivial and nontrivial states over a finite pump-power range and a one-bit memory. Further increase of the repulsion parameter or decrease of the spot size breaks down the perturbative approach and leads to a peculiar self-trapping regime with complex dynamics. Experimental evidence of the emergence of the proposed behavior is provided. Our findings can be used to design polaritonic setups that exploit the predicted memory effect.
Dynamics of exciton-polariton condensates under continuous-wave incoherent Gaussian optical pumping is considered. It is shown that the conventional supercritical Stuart-Landau picture is invalid in a certain domain of the parameter space. For strong polariton repulsion from the reservoir and relatively small pump spots, the dynamics is adequately described by the quintic Stuart-Landau equation. The corresponding subcritical pitchfork bifurcation leads to condensate formation, accompanied by bistability between the trivial and nontrivial states over a finite pump-power range and a one-bit memory. Further increase of the repulsion parameter or decrease of the spot size breaks down the perturbative approach and leads to a peculiar self-trapping regime with complex dynamics. Experimental evidence of the emergence of the proposed behavior is provided. Our findings can be used to design polaritonic setups that exploit the predicted memory effect.
By imaging single-shot realizations of an organic polariton quantum fluid, we observe the long-sought dynamical instability of nonequilibrium condensates. We find an excellent agreement between the experimental data and a numerical simulation of the open-dissipative Gross-Pitaevskii equation, without performing any parameter fitting, which allows us to draw several important conclusions about the physics of the system. We find that the reservoir dynamics are in the strongly nonadiabatic regime, which renders the complex Ginzburg–Landau description invalid. The observed transition from stable to unstable fluid can only be explained by taking into account the specific form of reservoir-mediated instability as well as particle currents induced by the finite extent of the pump spot.
Dynamics of exciton-polaritonic condensate under incoherent pumping is studied using the non-Markovian stochastic Gross-Pitaevskii equation with the pseudo-differential dispersion term. This term corresponds to the lower energy branch of polaritons. It is shown that an increasing of the pumping spot area leads to the appearance of various spatial structures whose properties depend on the duration of the dynamical memory. In the regime of short memory time, condensate can form an extended state that spans outside the pumping area. We conclude that onset of such extended states is related to the specific form of the dispersion term causing the ``traffic jam'' effect. The case of long memory time corresponds to enhanced condensate formation, when increasing of the pumping area leads to appearance of angular condensate structures which partially suppress emission of matter waves from the pumping area.
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 realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10 μs, 1 s], offering a promising route to spin switches and spin memory elements.
Exciton–polariton condensates (EPCs) have emerged as a paradigmatic platform for investigating nonequilibrium quantum many-body phenomena, particularly due to their intrinsic open-dissipative nature and strong nonlinear interactions governed by the interplay between stimulated scattering and reservoir-mediated damping. Recent advances in Feshbach resonance engineering now enable precise tuning of interaction strengths, opening new avenues to explore exotic nonlinear excitations in these driven-dissipative systems. In this work, we systematically investigate the quench dynamics and stability of dark solitons in repulsive one-dimensional EPCs under sudden parameter variations in both nonlinear interaction strength g and pump intensity P. Through a Hamiltonian variational approach that incorporates reservoir damping effects, we derive reduced equations of motion for soliton velocity evolution that exhibit remarkable qualitative agreement with direct numerical simulations of the underlying open-dissipative Gross–Pitaevskii equation. Our results reveal three distinct dynamical regimes: (i) stable soliton propagation at intermediate pump powers, (ii) velocity-dependent soliton breakup above critical pumping thresholds, and (iii) parametric excitation of soliton trains under simultaneous interaction quenches. These findings establish a quantitative framework for understanding soliton dynamics in nonresonantly pumped EPCs, with implications for quantum fluid dynamics and nonequilibrium Bose–Einstein condensates.
Considered as a fundamental step for the development of the atomic laser and quantum computing, as well as the theoretical explanation of super fluidity, the Bose- Einstein condensate (BEC) has emerged as one of the most important topics in modern physics. This project is devoted to the analysis of a condensate based on exciton-polaritons. This BEC is characterized by a high critical temperature of condensation (about 20 K) and non-equilibrium dynamics. A mathematical model called complex Gross- Pitaevskii equation (cGPE) is used to describe its behavior. The steady state solutions of the cGPE are studied and a numerical method based on a collocation method is proposed in order to find these solutions. Once the steady state solutions are found, a linear stability analysis is performed, demonstrating that the steady state solutions become unstable as the pumping spot radius increases. Finally, the manifestations of these instabilities are analyzed by direct simulation of the cGPE, using a second order time-splitting spectral method. As a result, it is possible to see the formation of quantum vortices, which increase in number as the pumping spot radius increases.