The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay.
The dynamics of coupled condensates is a wide-encompassing problem with relevance to superconductors, BECs in traps, superfluids, etc. Here, we provide a unified picture of this fundamental problem that includes i) detuning of the free energies, ii) different self-interaction strengths and iii) finite lifetime of the modes. At such, this is particularly relevant for the dynamics of polaritons, both for their internal dynamics between their light and matter constituents, as well as for the more conventional dynamics of two spatially separated condensates. Polaritons are short-lived, interact only through their material fraction and are easily detuned. At such, they bring several variations to their atomic counterpart. We show that the combination of these parameters results in important twists to the phenomenology of the Josephson effect, such as the behaviour of the relative phase (running or oscillating) or the occurence of self-trapping. We undertake a comprehensive stability analysis of the fixed points on a normalized Bloch sphere, that allows us to provide a generalized criterion to identify the Rabi and Josephson regimes in presence of detuning and decay.
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.
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.
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 dynamics of two-component Bose–Einstein condensates, composed of atoms in two distinct hyperfine states, which are linearly coupled by two-photon Raman transitions. The condensate is loaded into a double-well potential. A variety of dynamical behaviour, ranging from regular Josephson oscillations to mixed Rabi–Josephson oscillations and to regimes featuring increasing complexity are described in terms of a reduced Hamiltonian system with four degrees of freedoms, which are the numbers of atoms in each component in the left and right potential wells, whose canonically conjugate variables are phases of the corresponding wavefunctions. Using the system with four degrees of freedom, we study the dynamics of fractional imbalances of the two bosonic components and compare the results to direct simulations of the Gross–Pitaevskii equations describing the bosonic mixture. We perform this analysis when the fractional imbalance oscillates around a zero-time averaged value and in the self-trapping regime as well.
We review recent results on the coherence and superfluidity of driven dissipative condensates, i.e., systems of weakly interacting nonconserved bosons, such as polariton condensates. The presence of driving and dissipation has dramatically different effects depending on dimensionality and anisotropy. In three dimensions, equilibrium behaviour is recovered at large scales for static correlations, while the dynamical behaviour is altered by the microscopic driving. In two dimensions, for an isotropic system, drive and dissipation destroy the algebraic order that would otherwise exist; however, a sufficiently anisotropic system can still show algebraic phase correlations. We discuss the consequences of this behaviour for recent experiments measuring phase coherence and outline potential measurements that might directly probe superfluidity. Introduction This chapter is dedicated to superfluidity and its relation to Bose-Einstein condensation (BEC), a topic with a long history. Many reviews of the concepts of condensation and superfluidity in thermal equilibrium can be found; see for example Refs. [1, 2, 3, 4]. The focus of this chapter is on how these concepts apply (or fail to apply) to driven dissipative condensates – systems of bosons with a finite lifetime, in which loss is balanced by continuous pumping. We focus entirely on the steady state of such systems, neglecting transient, time-dependent behaviour. Experimentally, the most studied example of a driven dissipative condensate has been microcavity polaritons, an overview of which is given in Ref. [5] and Chapter 4. However, similar issues can arise in many other systems, most obviously photon condensates [6] (see also Chapter 19), magnon condensates [7] (see also Chapters 25–26), and potentially exciton condensates (although typical exciton lifetimes are much longer than for polaritons). Even experiments on cold atoms (see, e.g., Chapter 3) could be driven into a regime in which such physics occurs, when considering continuous loading of atoms balancing threebody losses [8] or atom laser setups [9, 10, 11]. Experiments on polaritons are two-dimensional, and in two dimensions it is particularly important to clearly distinguish three concepts often erroneously treated as equivalent: superfluidity, condensation, and phase coherence. This is because no true Bose-Einstein condensate exists in a homogeneous two-dimensional system.
I present an overview of the physics of the Josephson effect between Bose condensed systems, with emphasis on the recently achieved BEC's in trapped alkali gases. I focus mostly on those physical phenomena that are likely to be observed only (or more easily) in these novel systems. Thus I omit the discussion of problems which may be viewed as straightforward applications of well known Josephson physics. In particular, I review the external and the internal Josephson effects, and discuss how in the latter case it may be possible to explore the crossover between collective Josephson behavior and independent boson Rabi dynamics. I also describe novel macroscopic quantum phenomena such as self-trapping and interference between separate Bose condensates.