Nir Navon

Exploring the thermodynamics of a universal Fermi gas

One of the greatest challenges in modern physics is to understand the behaviour of an ensemble of strongly interacting particles. A class of quantum many-body systems (such as neutron star matter and cold Fermi gases) share the same universal thermodynamic properties when interactions reach the maximum effective value allowed by quantum mechanics, the so-called unitary limit. This makes it possible in principle to simulate some astrophysical phenomena inside the highly controlled environment of an atomic physics laboratory. Previous work on the thermodynamics of a two-component Fermi gas led to thermodynamic quantities averaged over the trap, making comparisons with many-body theories developed for uniform gases difficult. Here we develop a general experimental method that yields the equation of state of a uniform gas, as well as enabling a detailed comparison with existing theories. The precision of our equation of state leads to new physical insights into the unitary gas. For the unpolarized gas, we show that the low-temperature thermodynamics of the strongly interacting normal phase is well described by Fermi liquid theory, and we localize the superfluid transition. For a spin-polarized system, our equation of state at zero temperature has a 2 per cent accuracy and extends work on the phase diagram to a new regime of precision. We show in particular that, despite strong interactions, the normal phase behaves as a mixture of two ideal gases: a Fermi gas of bare majority atoms and a non-interacting gas of dressed quasi-particles, the fermionic polarons.

The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions

Determining the Crossover Point The equation of state of an equilibrated system at zero temperature relates its pressure to other macroscopic parameters (such as the chemical potential) and can be used to deduce all relevant thermodynamic properties. For a quantum interacting gas, both the measurement and the theoretical derivation of the equation of state have been challenging. Now, Navon et al. (p. 729, published online 15 April) have used a two-component ultracold Fermi gas of lithium atoms with tunable interactions to quantify the corrections to the mean-field predictions for the equation of state in the crossover between Bose-Einstein condensation and Bardeen-Cooper-Schrieffer limits at near-zero temperature. The polaron mass in the spin-imbalanced gas was also measured. The results agree with known beyond-the-mean-field corrections and present a challenge to future theoretical efforts. A Fermi gas is characterized along the crossover regime between its weak and strongly interacting limits. Interacting fermions are ubiquitous in nature, and understanding their thermodynamics is an important problem. We measured the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin-imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.

Collective Oscillations of an Imbalanced Fermi Gas: Axial Compression Modes and Polaron Effective Mass

We investigate the low-lying compression modes of a unitary Fermi gas with imbalanced spin populations. For low polarization, the strong coupling between the two spin components leads to a hydrodynamic behavior of the cloud. For large population imbalance we observe a decoupling of the oscillations of the two spin components, giving access to the effective mass of the Fermi polaron, a quasiparticle composed of an impurity dressed by particle-hole pair excitations in a surrounding Fermi sea. We find m*/m = 1.17(10), in agreement with the most recent theoretical predictions.

Lifetime of the Bose gas with resonant interactions.

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient L(3). Our data follow a L(3)=λ(3)/T(2) law with λ(3)=2.5(3)(stat)(6)(syst)×10(-20) (μK)(2) cm(6) s(-1) and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length a at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where |a| is smaller than the thermal wavelength. We find that L(3) is continuous across the resonance, and over the whole a<0 range our data quantitatively agree with our calculation.

Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose Gas

Breaking the symmetry in an atomic gas Cooling a physical system through a phase transition typically makes it less symmetrical. If the cooling is done very slowly, this symmetry change is uniform throughout the system. For a faster cooling process, the system breaks up into domains: The faster the cooling, the smaller the domains. Navon et al. studied this process in an ultracold gas of Rb atoms near its transition to a condensed state (see the Perspective by Ferrari). The authors found that the size of the domains froze in time in the vicinity of the transition and that it depended on the cooling speed, as predicted by theory. Science, this issue p. 167; see also p. 127 Interferometry is used to confirm the predictions of the Kibble-Zurek theory in a quenched gas of rubidium atoms. [Also see Perspective by Ferrari] 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.

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 in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. 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 ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.

Measurement of the magnetic interaction between two bound electrons of two separate ions

Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin)1. The magnetic interaction between two electrons can therefore impose a change in their spin orientation. Similar dipolar magnetic interactions exists between other spin systems and were studied experimentally. Examples include the interaction between an electron and its nucleus or between several multi-electron spin complexes2–8. The process for two electrons, however, was never observed in experiment. The challenge is two-fold. At the atomic scale, where the coupling is relatively large, the magnetic interaction is often overshadowed by the much larger coulomb exchange counterpart2. In typical situations where exchange is negligible, magnetic interactions are also very weak and well below ambient magnetic noise. Here we report on the first measurement of the magnetic interaction between two electronic spins. To this end, we used the ground state valence electrons of two Sr ions, co-trapped in an electric Paul trap and separated by more than two micrometers. We measured the weak, millihertz scale (alternatively 10−18 eV or 10−14 K), magnetic interaction between their electronic spins. This, in the presence of magnetic noise that was six ∗Current address: Physical Measurement Laboratory, National Institute of Science and Technology, Boulder CO, 80305, USA. †Current address: Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB30HE, United Kingdom.

Fermi-Liquid Behavior of the Normal Phase of a Strongly Interacting Gas of Cold Atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

Stability of a unitary Bose gas.

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

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.