We have observed the Bose-Einstein condensation of an atomic gas in the (quasi)uniform three-dimensional potential of an optical box trap. Condensation is seen in the bimodal momentum distribution and the anisotropic time-of-flight expansion of the condensate. The critical temperature agrees with the theoretical prediction for a uniform Bose gas. The momentum distribution of a noncondensed quantum-degenerate gas is also clearly distinct from the conventional case of a harmonically trapped sample and close to the expected distribution in a uniform system. We confirm the coherence of our condensate in a matter-wave interference experiment. Our experiments open many new possibilities for fundamental studies of many-body physics.

In this letter we report the discovery of superconductivity in the isostructural graphite intercalation compounds C 6 Yb and C 6 Ca, with transition temperatures of 6.5K and 11.5K respectively. A structural characterisation of these compounds shows them to be hexagonal layered systems in the same class as other graphite intercalates. If we assume that all the outer s-electrons are transferred from the intercalant to the graphite sheets, then the charge transfer in these compounds is comparable to other superconducting graphite intercalants such as C 8 K 1,2 . However, the superconducting transition temperatures of C 6 Yb and C 6 Ca are up to two orders of magnitude greater. Interestingly, superconducting upper critical field studies and resistivity measurements suggest that these compounds are significantly more isotropic than pure graphite. This is unexpected as the effect of

Materials tuned to the neighbourhood of a zero temperature phase transition often show the emergence of novel quantum phenomena. Much of the effort to study these new effects, like the breakdown of the conventional Fermi-liquid theory of metals has been focused in narrow band electronic systems. Ferroelectric crystals provide a very different type of quantum criticality that arises purely from the crystalline lattice. In many cases the ferroelectric phase can be tuned to absolute zero using hydrostatic pressure or chemical or isotopic substitution. Close to such a zero temperature phase transition, the dielectric constant and other quantities change into radically unconventional forms due to the quantum fluctuations of the electrical polarization. The simplest ferroelectrics may form a text-book paradigm of quantum criticality in the solid-state as the difficulties found in metals due to a high density of gapless excitations on the Fermi surface are avoided. We present low temperature high precision data demonstrating these effects in pure single crystals of SrTiO 3 and KTaO 3 . We outline a model for describing the physics of ferroelectrics close to quantum criticality and highlight the expected 1/T 2 dependence of the dielectric constant measured over a wide temperature range at low temperatures. In the neighbourhood of the quantum critical point we report the emergence of a small frequency independent peak in the dielectric constant at approximately 2 K in SrTiO 3 and 3 K in KTaO 3 believed to arise from coupling to acoustic phonons. Looking ahead, we suggest that ferroelectrics could be used as systems in which to controllably build in extra complexity around the quantum critical point. For example, in ferroelectric or antiferroelectric materials supporting mobile charge carriers, quantum paraelectric fluctuations may mediate new effective electron-electron interactions giving rise to a number of possible states such as superconductivity.The study of quantum matter at low temperatures has given rise to a fascinating and often surprising catalogue of phenomena important to our understanding of nature 1 and to technological development 2 . In particular, the study of materials close to a continuous low temperature phase transition or so called quantum critical point forms an important branch of research within condensed matter physics. A chief reason for this is that close to such a transition, materials become highly degenerate and new states of matter are frequently found to emerge. In fact, it turns out that many materials end up being close to or within the quantum critical regime. This is because quantum critical phenomena can affect materials over a wide range of temperatures, pressures and other variables. In electrically conducting materials, the standard model of the metallic state, Landau's Fermi liquid theory is seen to breakdown close to the low temperature boundary between a magnetic and paramagnetic phase and is replaced with other forms of novel quantum liquid. For example, in some weakly magnet...

We explore the dynamics of spontaneous symmetry breaking in a homogeneous system by thermally quenching an atomic gas with short-range interactions through the Bose-Einstein phase transition. Using homodyne matter-wave interferometry to measure first-order correlation functions, we verify the central quantitative prediction of the Kibble-Zurek theory, namely the homogeneous-system power-law scaling of the coherence length with the quench rate. Moreover, we directly confirm its underlying hypothesis, the freezing of the correlation length near the transition due to critical slowing down. Our measurements agree with beyond mean-field theory, and support the previously unverified expectation that the dynamical critical exponent for this universality class, which includes the λ-transition of liquid 4 He, is z = 3/2.Continuous symmetry-breaking phase transitions are ubiquitous, from the cooling of the early universe to the λ-transition of superfluid helium. Near a second-order transition, critical long-range fluctuations are characterized by a diverging correlation length ξ and details of the short-range physics are largely unimportant. Consequently, all systems can be classified into a small number of universality classes, according to their generic features such as symmetries, dimensionality and range of interactions (1). Close to the critical point, many physical quantities exhibit power-law behavior governed 1 arXiv:1410.8487v1 [cond-mat.quant-gas]

We study the metastability and decay of multiply-charged superflow in a ring-shaped atomic Bose-Einstein condensate. Supercurrent corresponding to a giant vortex with topological charge up to q = 10 is phaseimprinted optically and detected both interferometrically and kinematically. We observe q = 3 superflow persisting for up to a minute and clearly resolve a cascade of quantised steps in its decay. These stochastic decay events, associated with vortex-induced 2π phase slips, correspond to collective jumps of atoms between discrete q values. We demonstrate the ability to detect quantised rotational states with > 99 % fidelity, which allows a detailed quantitative study of time-resolved phase-slip dynamics. We find that the supercurrent decays rapidly if the superflow speed exceeds a critical velocity in good agreement with numerical simulations, and we also observe rare stochastic phase slips for superflow speeds below the critical velocity.

A central concept in the modern understanding of turbulence is the existence of cascades of excitations from large to small length scales, or vice versa. This concept was introduced in 1941 by Kolmogorov and Obukhov, and such cascades have since been observed in various systems, including interplanetary plasmas, supernovae, ocean waves and financial markets. Despite much progress, a quantitative understanding of turbulence remains a challenge, owing to the interplay between many length scales that makes theoretical simulations of realistic experimental conditions difficult. Here we observe the emergence of a turbulent cascade in a weakly interacting homogeneous Bose gas-a quantum fluid that can be theoretically described on all relevant length scales. We prepare a Bose-Einstein condensate in an optical box, drive it out of equilibrium with an oscillating force that pumps energy into the system at the largest length scale, study its nonlinear response to the periodic drive, and observe a gradual development of a cascade characterized by an isotropic power-law distribution in momentum space. We numerically model our experiments using the Gross-Pitaevskii equation and find excellent agreement with the measurements. Our experiments establish the uniform Bose gas as a promising new medium for investigating many aspects of turbulence, including the interplay between vortex and wave turbulence, and the relative importance of quantum and classical effects.

No abstract

In many-body systems governed by pairwise contact interactions, a wide range of observables is linked by a single parameter, the two-body contact, which quantifies two-particle correlations. This profound insight has transformed our understanding of strongly interacting Fermi gases. Here, using Ramsey interferometry, we study coherent evolution of the resonantly interacting Bose gas, and show that it cannot be explained by only pairwise correlations. Our experiments reveal the crucial role of three-body correlations arising from Efimov physics, and provide a direct measurement of the associated three-body contact.A fundamental challenge in many-body quantum physics is to connect the macroscopic behaviour of a system to the microscopic interactions between its constituents. In ultracold atomic gases the strength of interactions is most commonly characterised by the s-wave scattering length a, which can be tuned via Feshbach resonances [1]. On resonance a diverges and one reaches the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases [2][3][4], while the unitary Bose gas represents a new experimental frontier [5][6][7][8][9][10].In these systems, universal properties of the short-range particle correlations imply universal thermodynamic relations between macroscopic observables such as the momentum distribution, energy, and the spectroscopic response [11][12][13][14][15][16][17][18][19]. In the case of (mass-balanced) two-component Fermi gases, at the heart of these relations is a single fundamental thermodynamic parameter, the two-body contact density C 2 , which measures the strength of two-particle correlations. However, the case of the Bose gas is more subtle. In this system Efimov physics gives rise to three-body bound states [20][21][22][23][24][25][26], and more generally introduces three-particle correlations that cannot be deduced from the knowledge of pairwise ones [17][18][19]27]. The implication for many-body physics is that complete understanding of the macroscopic coherent phenomena requires knowledge of both C 2 and its three-body analogue C 3 [17][18][19].The relative importance of three-particle correlations generally grows with the strength of interactions. At moderate interaction strengths C 2 was measured spectroscopically, but C 3 was not observed [24]. However, the momentum distribution of the unitary Bose gas [7] suggested deviations from two-body physics [19,28].Here we interferometrically measure both C 2 and C 3 in a resonantly interacting thermal Bose gas, and find excellent agreement with theoretical predictions. The idea of our experiment is illustrated in Fig. 1. We perform radio-frequency (RF) Ramsey interferometry on a gas of atoms with two internal (spin) states, ↑ and ↓, and use a magnetic Feshbach resonance to enhance ↑↑ interactions, while both ↑↓ and ↓↓ interactions are negligible. For a measurement at a given magneticRamsey interferometry of a many-body system. The first π/2 pulse pu...