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Physical Review B

Chaotic Josephson oscillations of exciton-polaritons and their applications

Dmitry D. Solnyshkov, R. Johne, Ivan Andreevich Shelykh, G. Malpuech

Published Dec 2, 2009• 36 citations
Publisher

Abstract

We consider Josephson oscillations between two coupled, quasiresonantly pumped exciton-polariton (polariton) modes. We analyze the regions of stability and periodic oscillations of such a system and show that the spin degree of freedom allows a chaotic behavior. We show that two spatially separated polariton Josephson junctions can be synchronized and used for data encryption and transfer. Due to the strong nonlinearity of polariton-polariton interactions, chaos communication at rates up to 50 Gb/s is possible, which is at least ten times faster than the results obtained for other systems.

DOI
10.1103/physrevb.80.235303

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We consider Josephson oscillations between two coupled, quasiresonantly pumped exciton-polariton (polariton) modes. We analyze the regions of stability and periodic oscillations of such a system and show that the spin degree of freedom allows a chaotic behavior. We show that two spatially separated polariton Josephson junctions can be synchronized and used for data encryption and transfer. Due to the strong nonlinearity of polariton-polariton interactions, chaos communication at rates up to 50 Gb/s is possible, which is at least ten times faster than the results obtained for other systems.
We study the dynamics of exciton polaritons in a double-well configuration. The system consists of two weakly coupled Bose-Josephson junctions, each corresponding to a different circular polarization of the polaritons, forming a Josephson double dimer. We show that the Josephson oscillation between the wells is strongly coupled to the polarization rotation and that, consequently, Josephson excitation is periodically exchanged between the two polarizations. Linearized analysis agrees well with numerical simulations using typical experimental parameters.
We analyze theoretically the role of the exciton-phonon interactions in phenomena related to the Josephson effect between two spatially separated exciton and exciton-polariton condensates. We consider the role of the dephasing introduced by phonons in such phenomena as Josephson tunneling, self-trapping and spontaneous polarization separation. In the regime of cw pumping we find a remarkable bistability effect arising from exciton-exciton interactions as well as regimes of self-sustained regular and chaotic oscillations.
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 analyze theoretically the phenomena related to the Josephson effect for exciton and polariton condensates, taking into account their specific spin degrees of freedom. We distinguish between two types of Josephson effects: the extrinsic effect, related to the coherent tunneling of particles with the same spin between two spatially separated potential traps, and the intrinsic effect, related to the ``tunneling'' between different spinor components of the condensate within the same trap. We show that the Josephson effect in the nonlinear regime can lead to nontrivial polarization dynamics and produce spontaneous separation of the condensates with opposite polarization in real space.
Creating sufficiently strong entanglement between exciton-polaritons is a step of utmost importance towards the exploitation of these systems in quantum information processing with continuous variables. The generation of entanglement relies on the strength of the nonlinearity, which is weak for semiconductor microcavities. Recently, a way to essentially amplify the nonlinearity strength in these systems using two coherent laser fields was suggested, leading in theory to the creation of a fair amount of entanglement between exciton-polaritons in coupled cavities and networks in general. Throughout this process, the Josephson coupling and the enhanced nonlinearity in the two coupled cavities are held constant, with the former always larger. In this work we show that the entanglement generated with the above procedure can be substantially enhanced with the appropriate on-off switching of Josephson coupling between the cavities. Furthermore, we show that if we consider a time-dependent enhanced nonlinearity, through the modulation of the corresponding coherent laser fields, and allow it to attain larger values than the Josephson coupling, then we can generate larger values of entanglement using shortcuts to adiabaticity, a method developed to accelerate quantum adiabatic dynamics. The suggested methodologies are not restricted to exciton-polaritons but are expected to find applications in a wide spectrum of physical contexts, where nonlinear interacting bosons are encountered.
We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in the presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and exciton states in the polariton system without any oscillations of the phases of the two subcondensates, we demonstrate that any nonzero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the two condensates, and a crossover from Rabi-like to Josephson-like oscillations is predicted.