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Universal Themes of Bose-Einstein Condensation
“Quantum Turbulence in Bose-Einstein Condensates”
Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. I shall motivate the use of atomic BECs for the study of quantum turbulence and distinguish three stages of turbulence - its generation, its steady state and its decay - and highlight some fundamental questions regarding our understanding in each of these regimes.
Focusing finally on the decay of the turbulence, I will discuss the use of vortex length to characterise this regime and show preliminary findings on the effect of finite temperature on this decay.
The system is modelled using the Zaremba-Nikuni-Griffin scheme , whereby the condensate is described by a dissipative Gross-Pitaevskii Equation, which is coupled to a quantum Boltzmann equation for the thermal cloud.
 E. Zaremba, T. Nikuni, and A. Griffin, JLTP 116, 277 (1999).
“Superfluidity of nucleons and quarks: from nuclei to neutron stars and color superconductors”
This talk will review superfluidity in nuclei and neutron stars, and proposed pairing states in color superconducting quark matter.
Neutron stars are expected to contain BCS superfluids of paired neutrons, as well as paired protons in the interior. High density quark matter, as should be present in the inner cores of neutron stars, can be paired in a variety of states. As will be discussed, such quark matter should exhibit strong analogies with the BEC-BCS crossover in ultracold gases of fermions.
“Finite temperature modelling in superfluid helium”
The vortex tangle dynamics and turbulence in superfluid helium exhibit a strong dependence on temperature. The Landau two fuid model is the most successful hydrodynamical theory of superfuid helium, but by the nature of scale separations can not give an adequate description of the processes involving vortex dynamics and interactions.
In my talk I suggest to use the classical field methods together with a generalised NLS models that incorporate the correct equation of
state and nonlocality of interactions. I will illustrate the idea
by applying the classical field method to study the behaviour of vortex rings during expansion and contraction following change in applied pressure.
“Lasers and BEC: two variants of the same phase transition?”
In this talk, I will try to give my personal view on the analogies and differences between textbook BEC of material particles, laser operation and those intermediate cases (in particular exciton-polariton BEC and photon BEC) that have attracted much interest in recent years. Attempts to develop a unitary theory of all these phenomena will be critically discussed and the most exciting open problems will be pointed out.
“Strongly interacting Bose gas and quantum dynamics with *ultracold atoms in reduced dimensions”
We prepare and study strongly interacting two-dimensional Bose gases with dimensionless gas parameter as high as g=2.8 by Feshbach tuning and by loading the sample into an optical lattice In the superfluid and BKT transition regimes, significant down-shifts from the mean-field and perturbation calculations are observed when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength. We also outline a prototypical approach to investigate quantum transport phenomena and quantum quenches. Starting with an almost pure bosonic superfluid, we quench the particle interactions and observe an oscillating density fluctuation in the time and momentum domains.These so called /Sakharov oscillations/, typically discussed in the context of early universe evolution, provide a common basis to understand the quantum quench dynamics of atomic superfluid and the anisotropy of the cosmic microwave background radiation.
“Optical Flux Lattices for Cold Atomic Gases”
One of the most important techniques in the ultracold atom toolbox is the optical lattice: a periodic scalar potential formed from standing waves of light. Optical lattices are central to the use of atomic gases to explore strong-correlation phenomena related to condensed
matter systems. I shall describe a novel form of optical lattice -- a
so-called ``optical flux lattice'' -- in which optically dressed atoms experience an effective magnetic field with high mean density. Optical flux lattices have narrow energy bands with nonzero Chern numbers, analogous to the Landau levels of a charged particle in a uniform magnetic field. These lattices will greatly facilitate the achievement of the quantum Hall regime for ultracold atomic gases.
“Nonequilibrium superfluidity and internal convection in finite temperature Bose gases”
Classical-field methods provide powerful tools for the non-perturbative simulation of weakly interacting Bose systems at finite temperatures, in both equilibrium and non-equilibrium regimes . Here we study a degenerate Bose gas coupled to two spatially separated heat reservoirs held at different temperatures, and simulate the onset of heat transport and superfluid internal convection . We consider the prospects for observing thermal-superfluid counterflow turbulence in this system. (Lukas Gilz, Tod M. Wright, James R. Anglin)
 P. B. Blakie, A. S. Bradley, M. J. Davis, R. J. Ballagh, and C. W.
Gardiner, Advances in Physics 57, 363 (2008); M. J. Davis, T. M. Wright, P. B. Blakie, A. S. Bradley, R. J. Ballagh, and C. W. Gardiner, arXiv:1206.5470.
 Lukas Gilz and James R. Anglin, Phys. Rev. Lett. 107, 090601 (2011).
Sergej O. Demokritov
“BEC of magnons at room temperature and spatio-temporal properties of magnon condensate”
Magnons are the quanta of magnetic excitations in a magnetically ordered media. In thermal equilibrium, they can be considered as a gas of quasiparticles obeying the Bose-Einstein statistics with zero chemical potential and a temperature dependent density. We will discuss the room-temperature kinetics and thermodynamics of the magnons gas in yttrium iron garnet films driven by a microwave pumping and investigated by means of the Brillouin light scattering spectroscopy. We show that the thermalization of the driven gas results in a quasi-equilibrium state described the Bose-Einstein statistics with a non-zero chemical potential, the latter being dependent on the pumping power. For high enough pumping powers Bose-Einstein condensation (BEC) of magnons can be experimentally achieved at room temperature. Spatio-temporal kinetics of the BEC-condensate will be discussed in detail. Among others interference of two condensates, vortices, and propagating waves of the condensate density will be addressed.
“Polariton condensates, how do they complement atom BECs “
Polariton condensates may be created both spontaneously through a “standard” phase transition towards a Bose Einstein condensate,or be resonantly driven with a well-defined
Initial phase, speed And spatial distribution. Thanks to the photonic component of polaritons, the properties of the quantum fluid may be accessed very directly, with in particular the possibility of detailed in terferometric studies. This allows for example to probe the long-range coherence properties of a quantum fluid with unprecedented ease.This also allows testing superfluid properties with great precision in space and time .Here, will describe the static and dynamics of vortices in polariton condensates, obtained with a picosecond time resolution,in different configurations, with in particular their phase configuration I will show in particular the dynamics of spontaneous creation of a vortex as well as the dissociation of a full vortex into two half vortices will also highlight some of the recent results obtainedthrough the shaping of the system ,either using nanotechnology processes or using all optical means or both of them his allows in particular the study superfluid hydrodynamics of polariton fluids. This work has been performed at EPFL by a dream team of Postdocs, PhDstudents and collaborators. Lagoudakis,
G. Nardin, T.Paraiso,G.Grosso,F.Manni, YLéger,S.Trebaol,M.Portella Oberli, F . Morier-Genoud and the help of our theorists friends V, Savona M. Wouters and T Liew. The CdTe sample that we have been using has been prepared by Regis André at the Universityof Grenoble,and we strongly benefited from the long time collaboration with the group of Le Si Dang.
“Magnon Bose-Einstein condensation via spin-current injection”
Spin-wave excitations (magnons) in magnetic insulators can undergo Bose-Einstein condensation provided magnetization relaxation is small and magnon-magnon interactions strong. In this talk I will discuss how a partially-condensed magnon gas in a magnetic insulator can absorb or emit spin current at an interface with a paramagnetic metal. In particular, I will discuss the dynamics of the magnon gas that results from coupling to the metal and show that it is in principle possible to reach magnon condensation by spin injection.
“Black holes as graviton BECs at the critical point”
We discuss a new quantum theory of a black hole according to which the black hole is a Bose-Einstein condensate of gravitons. This BEC slowly leaks due to quantum depletion and losses it's gravitons. The peculiarity of this condensate is that it is at the critical point of quantum phase transition, very similar to some cold atomic systems, but because of the special properties of gravitational interaction black hole BEC stays at the critical point all the time, even though the occupation number of gravitons slowly diminishes. This picture resolves all the known seeming puzzles of the black hole physics, such as the information paradox, or negative heat of Hawking radiation. It also naturally explains why the black hole entropy scales the way Bekenstein predicted. We shall review these ideas with a special emphasis on the physical analogies and possible experimental prospects in creating the black hole type systems in the lab.
“Bose-Einstein condensation in the quantum Hall bilayer”
Theory predicts that the ground state of an electron bilayer, in the quantum Hall regime with one electron per Landau orbital, is a Bose-Einstein condensate of interlayer excitons. I will introduce this concept and highlight some key experimental evidence for this state. I will point out that the measured current-voltage characteristics of the bilayer are those expected for a dissipative superfluid state with weakly pinned vortices, closely analogous to the mixed state of a type-II superconductor. Thus there is very good evidence for the presence of an equilibrium Bose-Einstein condensate of excitons. The bilayer condensate shows many of the universal themes of BEC, but there are new twists in the tale.
“Observation of a photonic Berezinskii-Kosterlitz-Thouless transition”
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a two-dimensional phase transition in which vortex creation competes with entropy production. Here, we experimentally demonstrate a photonic BKT transition by observing the 2+1D propagation of an optical beam in a nonlinear photorefractive crystal. A random-phase input beam sets up an effective thermodynamics, while interferometry at the output enables direct identification and counting of vortices. We show that both the number of vortices produced and the universal change in correlations agree with theoretical predictions, for both focusing and defocusing nonlinearity (attractive and repulsive interactions). We also give evidence for the unbinding of vortex pairs at transition. Non-equilibrium behavior is discussed, with an emphasis on the competition between condensation and BKT dynamics.
“Interfacing cold atoms and solids”
Hybrid quantum systems, which combine
ultra-cold atoms with solid state devices, have attracted considerable attention in the last few years. I report on our experimental efforts towards the realization of such systems based on ultra-cold atoms, superconductors and carbon nanowires.
In our experiments, atomic clouds are trapped by electromagnetic fields near nanostructured and functionalized surfaces.
This research field of “atom chips” delivered already important insights into fundamental interactions between atoms and surfaces and opens perspectives towards the coupling of atomic and solid state degrees of freedoms. In our experiments, we investigate the quantum interface between atomic clouds and superconducting devices and the interface between atoms and between mesoscopic electronic systems, represented by carbon nanowires.
“Bose-Einstein condensation and beyond in magnetic insulators”
Localized spin systems, and in particular dimer systems, provide a fantastic laboratory to study the interplay between quantum effects and the interaction between excitations. Magnetic field and temperature allow an excellent control on the density of excitations and various very efficient probes such as neutrons and NMR are available.
Magnetic insulators can thus be used as ``quantum simulators'' to tackle with great success questions that one would normally search in itinerant interacting quantum systems.
In particular they have provided excellent realizations of Bose-Einstein condensates [1,2]. They allowed to probe the properties of interacting bosons in a variety of dimensions, and the critical regimes of quantum phase transitions in such systems.
I will discuss this physics, and the extensions to other dimensions such as one dimensional systems, for which magnetic insulators allowed to quantitative probe for Tomonaga-Luttinger liquid physics (see e.g. [3,4]) or to investigate the effects of disorder and the physics of such phases as the Bose glass phase occuring for disordered bosons.
 T. Giamarchi and A. Tsvelik, Phys. Rev. B 59 11398 (1999).
 T. Giamarchi, C. R\"uegg and O. Tchernyshyov, Nat. Phys. 4 198 (2008).
 P. Bouillot et al., Phys. Rev. B 83, 054407 (2011).
 D. Schmidiger et al., Phys. Rev. Lett. 108, 167201
"The effects of confinement on coherence and superfluidity in atomic gases"
Under the broad umbrella of this title I will try to cover several topics that have been dear to me in recent years. First, I will introduce the basic physics of 2D atomic gases, where the interplay of harmonic confinement, interactions, and the finite sample size leads to an intricate interplay between the Berezinskii-Kosterlitz-Thouless (BKT) physics and Bose-Einstein condensation (BEC). Next, I will give an example of an important problem, the interaction shift of the BEC critical temperature, where even in 3D the harmonic confinement fundamentally changes the physics and the local density approximation fails. Motivated by these examples, I will then briefly introduce our new experiment in which we have achieved BEC in a homogeneous atomic gas. Finally, time permitting, I will also introduce some recent experiments performed in ring geometry, where the uniformity and periodicity of the trapping potential along one direction allow for studies of superfluidity in the most traditional transport sense.
“Superfluidity and coherence in non-equilibrium condensates”
The great experimental progress in realising and studying polariton condensates has made it possible to now study experimentally a number of fundemental questions about the relation between lasing, condensation, coherence and superfluidity. In my talk, I will discuss the consequences of finite particle lifetime on two particular examples of these. I will discuss how superfluid density can be calculated to remain finite despite particle loss, and discuss how it might be measured. I will also discuss quasi-long-range coherence in a non-equilibrium condensate as has been recently measured.
 J. Keeling, Phys. Rev. Lett. 107 080402 (2011)
 G. Roumpos et al, Proc. Natl. Acad. Sci, 109 6467 (2012)
“Superfluid Bose and Fermi gases”
The realization of Bose-Einstein condensation in dilute atomic gases has created a unique experimental platform to study superfluidity in Bose and Fermi gases. The control over the atoms and their interactions have allowed studies for weak and strong interactions. For fermions, the crossover from Bose-Einstein condensation of strongly bound fermion pairs to weakly bound Cooper pairs has been explored. These studies illustrate a new approach to condensed-matter physics where many-body phenomena are realized in dilute atomic gases.
Na Young Kim
“Multi-Orbital Condensates in Exciton-Polariton-Lattice Systems”
Microcavity exciton-polaritons are hybrid quantum quasi-particles as admixtures of cavity photons and quantum-well excitons. The inherent light-matter duality provides experimental advantages to form coherent condensates at high temperatures (e.g. 4-10 K in GaAs and room temperatures in GaN materials), offering immense opportunity to investigating hydrodynamic vortex properties, superfluidity, and low energy quantum state dynamics. Recently, we engineer exciton-polariton-lattice systems in various artificial periodic potential geometries: two-dimensional (2D) square, triangular, honeycomb and kagome lattices, where we explore exotic quantum phase order. We characterize our devices via micro-photoluminescence measurements in both real and momentum spaces, which enable us to construct band structures and access spatial ordering. We observe p- and d-orbital condensate states, vortex-antivortex phase order, Dirac dispersions, and flat bands in 2D square, honeycomb, triangular, and kagome lattices respectively. We envision that the polariton-lattice systems will be promising solid-state quantum emulators in the quest for better understanding strongly correlated materials.
“The BEC-BCS crossover:what (if anything) do we fundamentally not understand?”
I raise the question:are there any _conceptual_ questions concerning the BEC-BCS transition which are at present fundamentally not understood? and reach the conclusion:for the s-wave case,probably no,but for the p-wave case,at least arguably yes with respect to at least one fundamental issue,namely the changes (if any) of total angular momentun across the transition.
“Superfluid Transition and Transport Properties in Two-Dimensional, Disordered Bose Fluids”
The interplay of disorder and interactions in quantum fluids is attracting much attention at the frontier of condensed matter and ultracold atoms. For two-dimensional interacting bosons, the quantum phase diagram is largely debated and still at a conjectural stage.
In this contribution, we report the first ab-initio phase diagram of disordered and interacting ultra-cold atoms in two dimensions. We demonstrate that, although the disorder renormalizes the chemical potential in a non-local way, the critical properties at the superfluid to normal fluid transition are of the BKT type, even in the strong disorder regime, where the atomic density shows strong spatial modulations. In addition, we study the conducting properties of two-dimensional Bose fluid by means of a methodological improvement we hereby introduce. The resulting insulating phase at large disorder strength is shown to be well described by a thermally-activated behavior of the Arrhenius type, indicating the existence of a "bad metal" behavior.
“Superfluid 3He in the Zero-Temperature Limit: An Ideal Medium for Measuring the Energy Content of, and Visualizing in Real Time, Pure Quantum Turbulence”
We can cool superfluid 3He down to a temperature regime (~80 microK) where the condensate is essentially pure. Here only about 1 in 108 3He atoms remain unpaired and do not contribute to the condensate. Paradoxically, this vanishingly tenuous gas of unpaired atoms provides us with the tools for both measuring the energy content of the system and for imaging topological defects therein. This allows us access to many properties of the system. Here we concentrate on just two. First, we can measure the total energy contained in quantum turbulence by monitoring bolometrically the increase in temperature as the turbulence decays. (We believe this is the first measurement of the total energy in any turbulent system.) Secondly, we can use the unpaired ballistic quasiparticle excitations as a “light” source to illuminate turbulence which we can generate to order. By detecting the shadows thrown we can image the turbulent network (to surprisingly high accuracy) and are in the process of developing a “vortex video” to look at the spatial and temporal evolution of custom-generated turbulence in the condensate.
D. I. Bradley, S. N. Fisher, A. M. Guénault, R. P. Haley, G. R. Pickett and V. Tsepelin
“Probing Non-Equilibrium Dynamics in an isolated Quantum System”
Understanding non-equilibrium dynamics of many-body quantum systems is crucial for many fundamental and applied physics problems ranging from de-coherence and equilibration to the development of future quantum technologies such as quantum computers which are inherently non-equilibrium quantum systems. One of the biggest challenges is that there is no general approach to characterize the resulting quantum states. In the last years we developed techniques using the full distribution functions of a quantum observable, and the full phase correlation functions to study the relaxation dynamics in one-dimensional quantum systems and to characterize the underlying many body states.
Interfering two 1 dimensional quantum gases allows to study how the coherence created between the two many body systems by the splitting process  slowly dies by coupling to the many internal degrees of freedom available . The full distribution function of the shot to shot variations of the interference patterns [3,4], especially its higher moments, allows characterizing the underlying physical processes . Two distinct regimes are clearly visible: for short length scales the system is characterized by spin diffusion, for long length scales by spin decay . After a rapid evolution the distributions approach a steady state which can be characterized by thermal distribution functions. Interestingly, its (effective) temperature is over five times lower than the kinetic temperature of the initial system.
Our system, being a weakly-interacting Bosons in one dimension, is nearly integrable and the dynamics is constrained by constants of motion which leads to the establishment of a generalized Gibbs ensemble and pre-thermalization. We therefore interpret our observations as an illustration of the fast relaxation of a nearly integrable many-body system to a quasi-steady state through de-phasing. The observation of an effective temperature significant different from the expected kinetic temperature supports the observation of the generalized Gibbs state .
 T. Schumm et al. Nature Physics, 1, 57 (2005).
 S. Hofferberth et al. Nature 449, 324 (2007).
 A. Polkovnikov, et al. PNAS 103, 6125 (2006); V. Gritsev, et al., Nature Phys. 2, 705 (2006);
 S. Hofferberth et al. Nature Physics 4, 489 (2008);
 T. Kitagawa et al., Phys. Rev. Lett. 104, 255302 (2010); NJP, 13 073018 (2011)
 M. Gring et al., Science 337, 1318 (2012); M. Kuhnert et al. Phys. Rev. Lett 110, 090405 (2013)
D. Adu Smith et al. arXiv:1212.4645
“Bose-Einstein Condensation of Dark Matter Axions”
Axions are hypothetical particles whose existence would explain why the strong interactions are invariant under the discrete symmetries P and CP.
It has long been known that axions produced by vacuum realignment during the QCD phase transition in the early universe form a cold degenerate Bose gas and are a candidate for the dark matter. More recently it was found that dark matter axions thermalize through gravitational self-interactions and form a Bose-Einstein condensate (BEC). On time scales long compared to their rethermalization time scale, a large fraction of dark matter axions go to the lowest energy state available to them. In this behaviour they differ from all other dark matter candidates. Axions accreting onto a galactic halo fall in with net overall rotation because almost all go to the lowest energy available state for given angular momentum. In contrast, the other proposed forms of dark matter accrete onto galactic halos with an irrotational velocity field. The inner caustics are different in the two cases. I'll argue that the dark matter is axions because there is observational evidence for the type of inner caustic produced by, and only by, an axion BEC.
“Polariton high density states: vortices and solitons”
New physics observed in high density polariton systems in semiconductor microcavities will be described. Following a general overview, attention will be focussed on the ubiquitous effects of interactions in determining key properties of high density polariton states. These will include temporal coherence, vortices, where contrast with atom systems will be made, and bright solitons. The conditions for creation and stability of single solitons will be described, as will the observation of trains of solitons containing up to four phase correlated solitons, with size and separation determined by the healing length of the quantum fluid.
"Thermalization and Dissipationless Flow of Long Lifetime Microcavity Polaritons"
Many of the experiments on polaritons have used systems in which the lifetime of the polaritons is a few picoseconds while the thermalization time is just a bit shorter than this, perhaps by a factor of 4 or 5. This has led to interesting theory on the effects of nonequilibrium on BEC. We have recently developed new systems in which the lifetime of the polaritons is a few hundred picoseconds, while the thermalization time is about the same as before. This has allowed us to see new effects, such as dissipationless coherent flow over macroscopic distances, thermalization in a trap with well-defined temperature, and condensation in a ring trap (Mexican hat potential). I will present a survey of these recent results.
“Gauge fields with cold atoms”
Here I present our experimental work synthesizing static gauge fields for ultracold neutral atoms (bosonic and fermionic alkali atoms). I will discuss this gauge field in the language of spin-orbit coupling where it consists of an equal sum of Rashba and Dresselhaus couplings. In experiment, we couple two (or more) internal states of our alkali atoms with a pair of ``Raman'' lasers and load our degenerate quantum gas into the resulting adiabatic eigenstates which experience artificial gauge fields.
In this talk, I will explore how the atomic interaction is changed in the presence of this optical coupling, both for bosons and fermions.
“Superfluidity of ultracold atomic gases”
In this talk I will review some of the advances in our understanding of superfluid phenomena in ultracold atomic gases (both Bose and Fermi gases). Special emphasis will be given to the
implications of the hydrodynamic theory of superfluids at both zero and finite temperature, including the behavior of the collective oscillations in the presence of harmonic trapping and the recent observation of second sound and measurement of the temperature dependence of the superfluid density. The structure of quantized vortices, their effects on the dynamic properties of the gas, the quenching of the moment of inertia and the occurrence of Josephson-like oscillations will be also discussed.
Peter van der Straten
“Hydrodynamic excitations in a Bose-Einstein condensate”
Quantum hydrodynamics describes the interactions between a superfluid and a normal fluid, where the evolution of the system to equilibrium depends on their mutual response. Although quantum hydrodynamics has been studied extensively in liquid helium, ultra-cold atomic gases provide a new playground for its study, since the mutual interactions can be calculated ab initio. One of the drawbacks of ultra-cold gasses is the low densities, where the system is mostly collisionless. We have achieved large number condensates in sodium, which behave hydrodynamic even in the thermal cloud. We have studied hydrodynamic excitations above and below the critical temperature, like sound, heat conduction and out-of-phase dipole modes, and compared our results with theoretical models. The results show that the naive picture of frictionless flow of the superfluid has to be reexamined for trapped, ultra-cold gasses.
“Ultracold metastable helium atoms for quantum atom optics and metrology”
Helium atoms in the metastable triplet state (20 eV above the singlet ground state) offer unique possibilities for ultracold atom physics.
They can be detected with high efficiency allowing single-atom detection. This can be exploited in quantum atom optics experiment such as the Hanbury Brown Twiss effect, which we measured for both helium-3
(fermion: antibunching) and helium-4 (boson: bunching). The simple atomic structure of helium allows highly accurate calculation of molecular potentials as well as atomic energy levels. Ultracold helium atoms provide almost ideal experimental circumstances to measure transition frequencies and confront these with QED calculations. In this presentation I will discuss our recent measurement, in a BEC as well as a DFG, of the energy difference between the two metastable states of helium, allowing a stringent test of QED, and, by measuring the isotope shift between helium-4 and helium-3, a measurement of the nuclear charge radius difference between the alpha-particle and the helion (helium-3 nucleus). Further improvement of this measurement may contribute to the solution of the proton-size puzzle, i.e. the observation that the size of the proton, measured in different branches of physics, disagrees by 7 standard deviations.
“Bose-Einstein Condensation of Photons and Grandcanonical Condensate Fluctuations”
Bose-Einstein condensation, the macroscopic ground state accumulation of particles with integer spin (bosons) at low temperature and high density, has been observed in several physical systems, including cold atomic gases and solid state physics quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. The photon number is not conserved when the temperature of the photon gas is varied (vanishing chemical potential), and at low temperatures photons disappear in the cavity walls instead of occupying the cavity ground state. Here I will describe an experiment observing a Bose-Einstein condensation of photons in a dye-filled optical microcavity . Further, recent experiments investigating the second order coherence of the condensate will be reported. The results give evidence for Bose-Einstein condensation under grandcanonical ensemble conditions, as can be understood from effective particle exchange of condensate photons with dye electronic excitations.
 J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature 468, 545 (2010).
“Contrasting the classical-field method with the broken-symmetry description of Bose superfluidity”
Traditional descriptions of partially condensed Bose gases begin with the separation of the Bose field into condensed and non-condensed components. In such approaches, the condensed part is represented by a classical object -- the condensate order parameter -- that is in most cases associated with the concept of spontaneous symmetry breaking. An alternative computational approach to describing such systems exploits the fact that highly occupied (but not necessarily condensed) modes of a quantum Bose field can be accurately approximated by a classical field.
Quantities such as the condensate and the superfluid density are then determined a posteriori, from the correlations of multimode classical field trajectories. This talk will outline the classical-field method and review its advantages and limitations, before describing how characteristic features of the symmetry-breaking approach appear in classical-field calculations, and can be used to characterise the superfluid properties of the system. We will argue, however, that many of the most interesting regimes of nonequilibrium dynamics that can be described with classical-field methods are beyond the reach of methods based upon Bose symmetry breaking.
R. El-Ganainy, A. Eisfeld
“Two-site noninteracting Bose Hubbard Hamiltonian: state transfer, surface Bloch oscillations and supersymmetry” (slide)
Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany
We investigate the tunneling dynamics of bosonic particles between two quantum wells within the framework of the noninteracting Bose Hubbard Hamiltonian and we demonstrate a number of intriguing and overlooked features associated with these models. By projecting the system’s Hamiltonian on Hilbert subspaces spanning different numbers of boson excitations, we demonstrate that processes such as coherent transport, state localization and surface Bloch oscillations can take place in Fock space. Furthermore, we show that Hamiltonian representations of Fock space manifolds differing by one boson obey discrete supersymmetry relation.
“Vortices and the Berezinskii-Kosterlitz-Thouless, Transition in 2D Systems with Competing Order” (slide)
We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2 + M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/ ∆ and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/ ln(1/∆), where ∆ denotes the distance from the high- symmetry point.
Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.
“Quantum kinetic derivation of the non-Equilibrium Gross-Pitaevskii equation for micro-cavity poaritons” (slide)
The non-equilibrium Gross-Pitaevskii equation proposed by Wouters and Carossotto for non-resonantly excited polaritons is derived by means of contour time-ordered Green functions for bosons. The rate equation of the exciton reservoir is derived form the Kadanoff-Baym equation with slowly varying center coordinates and Fourier transformed relative coordinates for particle-particle and phonon-assisted scattering between the reservoir and the polariton condensate field.
“Nonthermal Fixed Points and Superfluid Turbulence in an Ultracold Bose Gas” (slide)
Authors: M. Karl*, B. Nowak and T. Gasenzer
Turbulence appears in situations in which, e.g., an energy flux goes from large to small scales where finally the energy is dissipated. As a result the distribution of occupation numbers of excitations follows a power law with a universal critical exponent. The situation can be described as a nonthermal fixed point of the dynamical equations.
Single-particle momentum spectra for a dynamically evolving Bose gas are analysed using semi-classical simulations and quantum-field theoretic methods based on effective-action techniques. These give information about possible universal scaling behaviour. The connection of this scaling with the appearance of topological excitations such as solitons and vortices in one-component gases and domain walls and spin textures in multi-component systems is discussed. In addition their relation to those found in a field-theory approach to strong wave turbulence is discussed. In particular for three dimensional systems, the concept of nonthermal fixed points and its connection to transport processes in a turbulent system shows new aspects of the condensation dynamics out of equilibrium. The results open a view on a possibility to study nonthermal fixed points and superfluid turbulence in experiment without the necessity of detecting solitons and vortices in situ.
“Conditions for nonmonotonic vortex interaction in two-band superconductors” (slide)
We describe a semianalytic and a fully numerical approach to the calculation of intervortex interaction in two-band Ginzburg-Landau theory and find conditions under which the vortices attract or repel in the short-range and in the long-range . This variability of behavior is the result of the presence of multiple length scales in the problem. Due to the similarity of the Ginzburg-Landau energy functional for superconductors to the Gross-Pitaevskii one for Bose-Einstein condensates it is likely that similar approach can be used to analyze the interaction between composite/fractional vortices in multicomponent Bose-Einstein condensates.
 A. Chaves, L. Komendova, M. V. Milosevic, J. S. Andrade Jr., G. A. Farias, and F. M. Peeters, Phys. Rev. B 83, 214523 (2011).
Peter Mason & Amandine Aftalion
“Rotation of a Spin-Orbit-Coupled Bose-Einstein Condensate” (slide)
Recent experiments  have engineered spin-obit (SO) coupling in a neutral atomic Bose-Einstein condensate through the dressing of two atomic spin states with a pair of lasers. This has led to an interest in the application of these systems, such as for spintronic devices. The addition of rotation to the system adds non-trivial topological defect effects. We consider a mean-field description of the rotating spin-1/2 Bose-Einstein condensate with spin-orbit interactions. Through a Thomas-Fermi approximation and working in the non-linear sigma model formalism, we are able to determine regimes of different topological defects and ground state profiles. We back these analytical results up with a series of numerical simulations on the full Gross-Pitaevskii equation. In particular, these simulations provide a series of phase diagrams according to the crucial parameters present in the system: the spin-coupling, the rotation frequency and the interaction strengths.
 Y.-J. Lin, K. Jimenez-Garcia & I. B. Spielman, Spin-orbit-coupled Bose-Einstein condensates, Nature 471, pp. 83-86 (2011).
“BCS-BEC crossover in a quasi-two-dimensional Fermi gas” (slide)
“Stochastic Modelling of Low-Dimensional Bose Gases” (slide)
Due to the prominent role of phase fluctuations, confined systems in low-dimensional geometries should best be modelled by a classical field method. We demonstrate that the stochastic Gross-Pitaevskii equation is an ideal model for describing low-dimensional ultracold atom experiments. In particular, we show that it can completely reproduce, in an entirely ab initio manner, a range of low dimensional experiments, including those discussing phase fluctuations, density profiles and density fluctuations in weakly-interacting 1d Bose gases and a study of the universal and scale invariant behaviour of 2d Bose gases. In all these cases, we propose suitable ways to deal with the cut-off problem of classical field theory, also implementing for the first time an approach that guarantees a very specific optimum cut-off choice (to the extent that a classical field theory with a specific cut-off can reproduce the full quantum behaviour of the system). While focusing here on the properties of the most relevant ‘classical’ low-energy part of the spectrum (condensate plus low-lying modes), the presented approach can in principle be generalized to also account for dynamics of the high-lying part of the spectrum (via a quantum Boltzmann equation) and is extendable to non-equilibrium polariton condensates.
“Coherence properties and influence of disorder in 2D Bose gases” (slide)
"The Onset of Phase Coherence in a Nonequilibrium Condensate"
Abstract: Recent experiments with BEC of non-interacting photons coupled to an incoherent phonon bath have raised questions about how to think about the onset of conference and superfluidity in BEC systems in general. It has been well established for some time that a Boltzmann equation which keeps no record of coherence can model the onset of a sharp peak in momentum space, known as a "quasicondensate". It is also well established that the Gross-Pitaveskii equation can be used to evolve an interacting system with "noisy coherence" (a single-valued wave function, but no long range correlation) to long-distance off-diagonal coherence. We have recently completed theory on the middle regime between these limits, namely, the onset of noisy coherence from a quasicondensate. This theory predicts, in agreement with experiments, that the non-interacting photon system should become a coherent BEC, but we expect it should have either no superfluidity, or very low critical velocity.
“Probing polaron physics with impurities in condensates” (slide)
Recently it was shown that the Hamiltonian describing impurity atoms immersed in a Bose-Einstein can be mapped onto the Fröhlich polaron Hamiltonian, provided the Bogoliubov approximation is valid. The polaron was introduced in condensed matter physics where it represents a quasiparticle that consists of an electron in a polar or ionic lattice, dressed by the lattice deformation. For the BEC-impurity polaron the role of the electron is played by the impurity and the phonons are replaced by the Bogoliubov excitations. We apply the Feynman all-coupling approach to describe the transition between the different coupling regimes and argue that the polaronic strong-coupling regime, which remains elusive for the solid state polaron, can be probed by using a Feshbach resonance . Then, we investigate the dynamic response properties of the BEC-impurity polaron for which we show that Bragg spectroscopy is an appropriate experimental probing technique . The resulting spectra exhibit the typically well-known polaronic features, and in particular the signature of the Relaxed Excited State (RES).
 J. Tempere, W. Casteels, M. K. Oberthaler, S. Knoop, E. Timmermans and J. T. Devreese, Phys. Rev. B 80, 184504 (2009).
 W. Casteels, J. Tempere and J. T. Devreese, Phys. Rev. A 83, 033631 (2011).
Hugo Terças, D. D. Solnyshkov and G. Malpuech
“Topological Wigner crystal of half-solitons in a spinor Bose-Einstein condensate" (slide)
We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves towards a Wigner crystal.
“Measures of turbulence in Bose-Einstein condensates” (slide)
We present methods to create and characterize turbulent tangles of vortices in Bose-Einstein condensates. Motivated by work in classical fluids, we investigate if techniques that are known to efficiently mix classical fluids, classified as pseudo-Anosov stirring protocols, also efficiently mix vortices in trapped atomic condensates. In order to characterise turbulence, we develop some measures that are experimentally accessible, based on the density and distributin of vortices in trapped atomic condensates. At scales larger than the vortex core size, we describe how the momentum spectrum of vortices scales with vortex number.