Chapter 14. Bose Condensation: Effective Potentials

Arie‐Willem de Leeuw

In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.

Pierre C. Hohenberg

G. Benfatto, Giovanni Gallavotti

Jasur A. Abdullaev

This thesis includes theoretical studies regarding stability and manipulation of Bose-Einstein condensates (BECs) of ultra-cold atoms in 2D trapping geometry, as well as formation of steady states of exciton-polariton Bose-Einstein condensates created in solid states. We analyze and numerically model the dynamics and localization of the condensates using mean-field model. Chapter 1 contains an introduction to the physics of ultra-cold atom BEC and excitonpolariton BEC which provides a framework for the work presented in later chapters. In Chapter 2, we consider a method for achieving dynamically controllable transport of highly mobile matter-wave solitons in an ultra-cold atom BEC with attractive interparticle interaction loaded into a driven two-dimensional optical lattice. Our numerical analysis based on the mean-field model and the theory based on the effective particle approach demonstrate that fast, time-periodic rocking of the two-dimensional optical lattice enables efficient stabilization and manipulation of spatially localized matter wave packets via induced reconfigurable mobility channels. Chapter 3 consists of an investigation of the instability - collapse of a BEC with attractive interactions. In this chapter we explore the influence of an orbital angular momentum on the collapse of vortex-free elliptic clouds of Bose-Einstein condensates trapped in a radially symmetric harmonic potential or a rotating elliptic potential. The results of our analysis show that the number of trapped ultracold atoms corresponding to the collapse threshold can be radically increased for such rotating nonlinear matter waves in a radially harmonic trap. The results corresponding to a BEC cloud confined in a rotating elliptic trap show that the elongated stationary states can be parallel or perpendicular to the long axis of the trap and display bistable nature. In Chapter 4, we examine spatial localization and dynamical stability of Bose-Einstein condensates of exciton-polaritons in microcavities under the condition of off-resonant spatially inhomogeneous optical pumping both with and without a harmonic trapping potential. We employ the open-dissipative Gross-Pitaevskii model for describing an incoherently pumped polariton condensate coupled to an exciton reservoir. We reveal that spatial localization of the steady-state condensate occurs due to effective self-trapping created by the polariton flows, regardless of the presence of the external potential. A ground state of the polariton condensate with repulsive interactions between the quasiparticles represents a dynamically stable bright dissipative soliton. We also investigate the conditions for sustaining spatially localized structures, with nonzero angular momentum, in the form of single-charge vortices. Chapter 5 consider the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic inplane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We show that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultra-cold alkali atoms.

Richard A. Dunlap

This chapter discusses the way in which the cooling and trapping methods presented in the previous chapter can be used to create a Bose–Einstein condensate. This discussion begins with an overview of the basic properties of this condensate and the necessary requirements for its formation. The means by which it can be unequivocally identified are presented. Finally, some potential applications of the Bose–Einstein condensate are considered.

Adelchi Fabrocini