Observation of a Space-Time Crystal in a Superfluid Quantum Gas.

Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we show the observation of a space-time crystal using ultracold atoms, where the periodic structure in both space and time is directly visible in the experimental images. The underlying physics in our superfluid can be described ab initio and allows for a clear identification of the mechanism that causes the spontaneous symmetry breaking. Our results pave the way for the usage of space-time crystals for the discovery of novel nonequilibrium phases of matter.

Interaction effects on number fluctuations in a Bose-Einstein condensate of light.

We investigate the effect of interactions on condensate-number fluctuations in Bose-Einstein condensates. For a contact interaction we variationally obtain the equilibrium probability distribution for the number of particles in the condensate. To facilitate comparison with experiment, we also calculate the zero-time delay autocorrelation function g((2))(0) for different strengths of the interaction. Finally, we focus on the case of a condensate of photons and find good agreement with recent experiments.

Momentum-dependent scaling exponents of nodal self-energies measured in strange metal cuprates and modelled using semi-holography.

The anomalous strange metal phase found in high-Tc cuprates does not follow the conventional condensed-matter principles enshrined in the Fermi liquid and presents a great challenge for theory. Highly precise experimental determination of the electronic self-energy can provide a test bed for theoretical models of strange metals, and angle-resolved photoemission can provide this as a function of frequency, momentum, temperature and doping. Here we show that constant energy cuts through the nodal spectral function in (Pb,Bi)2Sr2-xLaxCuO6+δ have a non-Lorentzian lineshape, consistent with a self-energy that is k dependent. This provides a new test for aspiring theories. Here we show that the experimental data are captured remarkably well by a power law with a k-dependent scaling exponent smoothly evolving with doping, a description that emerges naturally from anti-de Sitter/conformal-field-theory based semi-holography. This puts a spotlight on holographic methods for the quantitative modelling of strongly interacting quantum materials like the cuprate strange metals.

Magnetization relaxation and geometric forces in a Bose ferromagnet.

We construct the hydrodynamic theory for spin-1/2 Bose gases at arbitrary temperatures. This theory describes the coupling between the magnetization and the normal and superfluid components of the gas. In particular, our theory contains the geometric forces on the particles that arise from their spin's adiabatic following of the magnetization texture. The phenomenological parameters of the hydrodynamic theory are calculated in the Bogoliubov approximation and using the Boltzmann equation in the relaxation-time approximation. We consider the topological Hall effect due to the presence of a Skyrmion, and show that this effect manifests itself in the collective modes of the system. The dissipative coupling between the magnetization and the normal component is shown to give rise to magnetization relaxation that is fourth order in spatial gradients of the magnetization direction.

Quantum rotor model for a Bose-Einstein condensate of dipolar molecules.

We show that a Bose-Einstein condensate of heteronuclear molecules in the regime of small and static electric fields is described by a quantum rotor model for the macroscopic electric dipole moment of the molecular gas cloud. We solve this model exactly and find the symmetric, i.e., rotationally invariant, and dipolar phases expected from the single-molecule problem, but also an axial and planar nematic phase due to many-body effects. Investigation of the wave function of the macroscopic dipole moment also reveals squeezing of the probability distribution for the angular momentum of the molecules.

Probing the topological exciton condensate via Coulomb drag.

The onset of exciton condensation in a topological insulator thin film was recently predicted. We calculate the critical temperature for this transition, taking into account screening effects. Furthermore, we show that the proximity to this transition can be probed by measuring the Coulomb drag resistivity between the surfaces of the thin film as a function of temperature. This resistivity shows an upturn upon approaching the exciton-condensed state.

Spin caloritronics in noncondensed Bose gases.

We consider coupled spin and heat transport in a two-component atomic Bose gas in the noncondensed state. We find that the transport coefficients show a temperature dependence reflecting the bosonic enhancement of scattering and discuss experimental signatures of the spin-heat coupling in spin accumulation, spin separation, and total dissipation. Close to the critical temperature for Bose-Einstein condensation, we find that the spin-heat coupling is strongly reduced, which is also reflected in the spin caloritronics figure of merit that determines the thermodynamic efficiency of spin-heat conversion.

Spin drag in an ultracold fermi gas on the verge of ferromagnetic instability.

Recent experiments [Jo, Science 325, 1521 (2009)] have presented evidence of ferromagnetic correlations in a two-component ultracold Fermi gas with strong repulsive interactions. Motivated by these experiments we consider spin drag, i.e., frictional drag due to scattering of particles with opposite spin, in such systems. We show that when the ferromagnetic state is approached from the normal side, the spin drag relaxation rate is strongly enhanced near the critical point. We also determine the temperature dependence of the spin diffusion constant. In a trapped gas the spin drag relaxation rate determines the damping of the spin dipole mode, which therefore provides a precursor signal of the ferromagnetic phase transition that may be used to experimentally determine the proximity to the ferromagnetic phase.

Spin-drag Hall effect in a rotating Bose mixture.

We show that in a rotating two-component Bose mixture, the spin drag between the two different spin species shows a Hall effect. This spin-drag Hall effect can be observed experimentally by studying the out-of-phase dipole mode of the mixture. We determine the damping of this mode due to spin drag as a function of temperature. We find that due to Bose stimulation there is a strong enhancement of the damping for temperatures close to the critical temperature for Bose-Einstein condensation.

Spin drag in noncondensed Bose gases.

We show how time-dependent magnetic fields lead to spin motive forces and spin drag in a spinor Bose gas. We propose to observe these effects in a toroidal trap and analyze this particular proposal in some detail. In the linear-response regime we define a transport coefficient that is analogous to the usual drag resistivity in electron bilayer systems. Because of Bose enhancement of atom-atom scattering, this coefficient strongly increases as temperature is lowered. We also investigate the effects of heating.

Lifshitz point in the phase diagram of resonantly interacting 6Li-40K mixtures.

We consider a strongly interacting 6Li-40K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This point is characterized by the effective mass of the Cooper pairs becoming negative, which signals an instability towards a supersolid phase.

Damping of superfluid flow by a thermal cloud.

One of the principal signatures of superfluidity is the frictionless flow of a superfluid through another substance. Here, we study the flow of a Bose-Einstein condensate through a thermal cloud and study its damping for different harmonic confinements and temperatures. The damping rates close to the collisionless regime are found to be in good agreement with Landau damping and become smaller for more homogeneous systems. In the hydrodynamic regime, we observe additional damping due to collisions, and we discuss the implications of these findings for superfluidity in this system.

Nash Equilibria in the Response Strategy of Correlated Games.

In nature and society, problems that arise when different interests are difficult to reconcile are modeled in game theory. While most applications assume that the players make decisions based only on the payoff matrix, a more detailed modeling is necessary if we also want to consider the influence of correlations on the decisions of the players. We therefore extend here the existing framework of correlated strategies by giving the players the freedom to respond to the instructions of the correlation device by probabilistically following or not following its suggestions. This creates a new type of games that we call "correlated games". The associated response strategies that can solve these games turn out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and pure or mixed-strategy solutions and also gives better payoffs in certain cases. We here determine these Nash equilibria for all possible correlated Snowdrift games and we find these solutions to be describable by Ising models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.

Theory of Interacting Quantum Gases.

We present a unified picture of the interaction effects in dilute atomic quantum gases. We consider fermionic as well as bosonic gases and, in particular, discuss for both forms of statistics the fundamental differences between a gas with effectively repulsive and a gas with effectively attractive inter atomic interactions, i.e., between a gas with either a positive or a negative scattering length.

Renormalization group theory for the imbalanced Fermi gas.

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)10.1038/nature06473].

Trapped fermionic clouds distorted from the trap shape due to many-body effects.

We present a general approach for describing trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in a trapped imbalanced Fermi mixture. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.

Theory for p-wave Feshbach molecules.

We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.

Vortex-lattice melting in a one-dimensional optical lattice.

We investigate quantum fluctuations of a vortex lattice in a one-dimensional optical lattice for realistic numbers of particles and vortices. Our method gives full access to all the modes of the vortex lattice and we discuss in particular the Bloch bands of the Tkachenko modes. Because of the small number of particles in the pancake Bose-Einstein condensates at every site of the optical lattice, finite-size effects become very important. Therefore, the fluctuations in the vortex positions are inhomogeneous and the melting of the lattice occurs from the outside inwards. By looking into correlations between neighboring vortices, we identify new solid and liquid phases. Tunneling between neighboring pancakes substantially reduces the inhomogeneity as well as the size of the fluctuations.

Sarma phase in trapped unbalanced fermi gases.

We consider a trapped unbalanced Fermi gas at nonzero temperatures where the superfluid Sarma phase is stable. We determine, in particular, the phase boundaries between the superfluid, normal, and phase-separated regions of the trapped unbalanced Fermi mixture. We show that the physics of the Sarma phase is sufficient to understand the recent observations of Zwierlein et al. [Science 311, 492 (2006); Nature (London) 442, 54 (2006)] and indicate how the apparent contradictions between this experiment and the experiment of Partridge et al. [Science 311, 503 (2006)] may be resolved.

Deformation of a trapped Fermi gas with unequal spin populations.

The real-space densities of a polarized strongly interacting two-component Fermi gas of 6Li atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.