Condensation Energy of a Spin-1/2 Strongly Interacting Fermi Gas

We report a measurement of the condensation energy of a two-component Fermi gas with tunable interactions. From the equation of state of the gas, we infer the properties of the normal phase in the zero-temperature limit. By comparing the pressure of the normal phase at T=0 to that of the low-temperature superfluid phase, we deduce the condensation energy, i.e. the energy gain of the system in being in the superfluid rather than normal state. We compare our measurements to a ladder approximation description of the normal phase, and to a fixed node Monte-Carlo approach, finding excellent agreement. We discuss the relationship between condensation energy and pairing gap in the BEC-BCS crossover.Comment: 4 figure

Emergent isotropy of a wave-turbulent cascade in the Gross-Pitaevskii model

The restoration of symmetries is one of the most fascinating properties of turbulence. We report a study of the emergence of isotropy in the Gross-Pitaevskii model with anisotropic forcing. Inspired by recent experiments, we study the dynamics of a Bose-Einstein condensate in a cylindrical box driven along the symmetry axis of the trap by a spatially uniform force. We introduce a measure of anisotropy $A(k,t)$ defined on the momentum distributions $n(\boldsymbol{k},t)$, and study the evolution of $A(k,t)$ and $n(\boldsymbol{k},t)$ as turbulence proceeds. As the system reaches a steady state, the anisotropy, large at low momenta because of the large-scale forcing, is greatly reduced at high momenta. While $n(\boldsymbol{k},t)$ exhibits a self-similar cascade front propagation, $A(k,t)$ decreases without such self-similar dynamics. Finally, our numerical calculations show that the isotropy of the steady state is robust with respect to the amplitude of the drive.Comment: 7 pages, 5 figure

Emergence of a turbulent cascade in a quantum gas.

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.This work was supported by AFOSR, ARO, DARPA OLE, EPSRC (Grant No. EP/N011759/1) and ERC (QBox). The GeForce GTX TITAN X used for the numerical simulations was donated by the NVIDIA Corporation. N.N. and A.L.G. acknowledge support from Trinity College, Cambridge; R.P.S. acknowledges support from the Royal Society.This is the author accepted manuscript. The final version is available from Nature Publishing Group via https://doi.org/10.1038/nature2011

Quantum gases. Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas.

Kibble-Zurek theory models the dynamics of spontaneous symmetry breaking, which plays an important role in a wide variety of physical contexts, ranging from cosmology to superconductors. We explored these dynamics 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 verified 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 confirmed its underlying hypothesis, the freezing of the correlation length near the transition. Our measurements agree with a beyond-mean-field theory and support the expectation that the dynamical critical exponent for this universality class is z = 3/2.We thank M. Robert-de-Saint-Vincent for experimental assistance; R. Fletcher for comments on the manuscript; and N. Cooper, J. Dalibard, G. Ferrari, B. Phillips, and W. Zwerger for insightful discussions. This work was supported by AFOSR, ARO, DARPA OLE, and EPSRC (grant no. EP/K003615/1). N.N. acknowledges support from Trinity College, Cambridge, and R.P.S. from the Royal Society.This is the accepted manuscript of a paper published in Science, 9 January 2015, Vol. 347, no. 6218 pp. 167-170 DOI: 10.1126/science.125867

Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of $^7$Li atoms by analyzing the \emph{in-situ} density distributions of trapped samples. For increasing repulsive interactions our data shows a clear departure from mean-field theory and provides a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang and Yang. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant $\xi>0.44(8)$ that would characterize the universal Bose gas at the unitary limit