Atomic Fermi Gas Research Articles

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as $ S_\mathrm{t}^{(D)} = N(a D - b \ln N) $ , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.

Metastability in Spin-Polarized Fermi Gases

We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2s.

Fermi polaron in two dimensions: Importance of the two-body bound state

We investigate a single impurity interacting with a free two-dimensional atomic Fermi gas. The interaction between the impurity and the gas is characterized by an arbitrary attractive short-range potential, which, in two dimensions, always admits a two-particle bound state. We provide analytical expressions for the energy and the effective mass of the dressed impurity by including the two-body bound state, which is crucial for strong interactions, in the integral equation for the effective interaction. Using the same method we give also the results for the polaron parameters in one and three dimensions finding a pretty good agreement with previous known results. Thus our relations can be used as a simple way to estimate the polaron parameters once the two-body bound state of the interaction potential is known.

Atomic Fermi gas in the unitary limit by quantum Monte Carlo methods: Effects of the interaction range

We calculate the ground-state properties of an unpolarized two-component Fermi gas with the aid of the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find $E/{E}_{\mathrm{free}}$ in the unitary limit to be 0.212(2), 0.407(2), 0.409(3), and 0.398(3) for 4, 14, 38, and 66 atoms, respectively. Our calculations indicate that the dependence of the total energy on the effective range of the interaction ${R}_{\mathrm{eff}}$ is sizable and the extrapolation to ${R}_{\mathrm{eff}}=0$ is therefore important for reaching the true unitary limit. To test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation, we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations, which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66-atom system converges to 0.56(1) after the extrapolation to the zero interaction range.

Fluctuations and phase transitions in Larkin-Ovchinnikov liquid-crystal states of a population-imbalanced resonant Fermi gas

Motivated by a realization of imbalanced Feshbach-resonant atomic Fermi gases, we formulate a low-energy theory of the Fulde-Ferrell and the Larkin-Ovchinnikov (LO) states and use it to analyze fluctuations, stability, and phase transitions in these enigmatic finite momentum-paired superfluids. Focusing on the unidirectional LO pair-density wave state, that spontaneously breaks the continuous rotational and translational symmetries, we show that it is characterized by two Goldstone modes, corresponding to a superfluid phase and a smectic phonon. Because of the liquid-crystalline "softness" of the latter, at finite temperature the 3d state is characterized by a vanishing LO order parameter, quasi-Bragg peaks in the structure and momentum distribution functions, and a "charge"-4, paired Cooper-pairs, off-diagonal-long-range order, with a superfluid-stiffness anisotropy that diverges near a transition into a nonsuperfluid state. In addition to conventional integer vortices and dislocations the LO superfluid smectic exhibits composite half-integer vortex-dislocation defects. A proliferation of defects leads to a rich variety of descendant states, such as the "charge"-4 superfluid and Fermi-liquid nematics and topologically ordered nonsuperfluid states, that generically intervene between the LO state and the conventional superfluid and the polarized Fermi-liquid at low and high imbalance, respectively. The fermionic sector of the LO gapless superconductor is also quite unique, exhibiting a Fermi surface of Bogoliubov quasiparticles associated with the Andreev band of states, localized on the array of the LO domain-walls.

Probing the homogeneous spectral function of a strongly interacting superfluid atomic Fermi gas in a trap using phase separation and momentum-resolved radio-frequency spectroscopy

It is of central importance to probe the \emph{local} spectral function $A(\mathbf{k},\omega)$ of a strongly interacting Fermi gas in a trap. Momentum resolved rf spectroscopy has been demonstrated to be able to probe the trap averaged $A(\mathbf{k},\omega)$. However, the usefulness of this technique was limited by the trap inhomogeneity. Independent of a specific theory, here we propose that by studying the momentum resolved rf spectra of the minority fermions of a phase separated, population imbalanced Fermi gas at low temperature, one can effectively extract $A(\mathbf{k},\omega)$ of a homogeneous superfluid Fermi gas (at the trap center). In support, we present calculated spectral functions and spectral intensity maps for various cases from BCS through BEC regimes using different theories.

Quantum criticality and universal scaling of strongly attractive spin-imbalanced Fermi gases in a one-dimensional harmonic trap

We investigate thermodynamics and quantum criticality of strongly attractive Fermi gases confined in a one-dimensional (1D) harmonic trap. Finite temperature density profiles, entropy, compressibility and susceptibility of the trapped gas are studied using analytic results for the thermodynamics within the local density approximation. We demonstrate that current experiments are capable of measuring universal Tomonaga-Luttinger liquid physics and quantum criticality of 1D strongly interacting Fermi gases. The results provide insights on recent measurements of key features of the phase diagram of a spin-imbalanced atomic Fermi gas [Liao et al., Nature 467, 567 (2010)] and point to further study of quantum critical phenomena in ultracold atomic Fermi gases.

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

We review the functional renormalization group (RG) approach to the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

Anomalous dimers in quantum mixtures near broad resonances: Pauli blocking, Fermi surface dynamics, and implications

We study the energetics and dispersion of anomalous dimers that are induced by the Pauli blocking effect in a quantum Fermi gas of majority atoms near interspecies resonances. Unlike in vacuum, we find that both the sign and magnitude of the dimer masses are tunable via Feshbach resonances. We also investigate the effects of particle-hole fluctuations on the dispersion of dimers and demonstrate that the particle-hole fluctuations near a Fermi surface (with Fermi momentum $\ensuremath{\hbar}{k}_{F}$) generally reduce the effective two-body interactions and the binding energy of dimers. Furthermore, in the limit of light minority atoms the particle-hole fluctuations disfavor the formation of dimers with a total momentum $\ensuremath{\hbar}{k}_{F}$, because near $\ensuremath{\hbar}{k}_{F}$ the modes where the dominating particle-hole fluctuations appear are the softest. Our calculation suggests that near broad interspecies resonances when the minority-majority mass ratio ${m}_{B}/{m}_{F}$ is smaller than a critical value (estimated to be $0.136$), dimers in a finite-momentum channel are energetically favored over dimers in the zero-momentum channel. We apply our theory to quantum gases of $^{6}\mathrm{Li}$$^{40}\mathrm{K}$, $^{6}\mathrm{Li}$$^{87}\mathrm{Rb}$, $^{40}\mathrm{K}$$^{87}\mathrm{Rb}$, and $^{6}\mathrm{Li}$$^{23}\mathrm{Na}$ near broad interspecies resonances, and discuss the limitations of our calculations and implications.

Searching for perfect fluids: quantum viscosity in a universal Fermi gas

We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.

Realizing analogues of color superconductivity with ultracold alkali atoms

A degenerate three-component Fermi gas of atoms with identical attractive interactions is expected to exhibit superfluidity and magnetic order at low temperature and, for sufficiently strong pairwise interactions, become a Fermi liquid of weakly interacting trimers. The phase diagram of this system is analogous to that of quark matter at low temperature, motivating strong interest in its investigation. We describe how a three-component gas below the superfluid critical temperature can be prepared in an optical lattice. To realize an SU(3)-symmetric system, we show how pairwise interactions in the three-component atomic system can be made equal by applying radiofrequency and microwave radiation. Finally, motivated by the aim to make more accurate models of quark matter, which have color, flavor and spin degrees of freedom, we discuss how an atomic system with SU(2)⊗SU(3) symmetry can be achieved by confining a three-component Fermi gas in the p-orbital band of an optical lattice potential.

Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.

Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.

The atomic quantum ring

We investigate the dynamics of neutral fermions trapped in a one-dimensional ring. Weconstruct an effective magnetic field in the ring using the adiabatic motion of dark statescreated by light beams carrying an orbital angular momentum. We illustrate the effectof the orbital angular momentum by looking at the induced mass current andshow how the Aharonov–Bohm effect manifests itself in an atomic Fermi gas as aperiodic mass current as a function of the optically induced artificial magnetic flux.

Trimers, Molecules, and Polarons in Mass-Imbalanced Atomic Fermi Gases

We consider the ground state of a single "spin-down" impurity atom interacting attractively with a "spin-up" atomic Fermi gas. By constructing variational wave functions for polarons, molecules, and trimers, we perform a detailed study of the transitions between these dressed bound states as a function of mass ratio r=m↑/m↓ and interaction strength. Crucially, we find that the presence of a Fermi sea enhances the stability of the p-wave trimer, which can be viewed as a Fulde-Ferrell-Larkin-Ovchinnikov molecule that has bound an additional majority atom. For sufficiently large r, we find that the transitions lie outside the region of phase separation of the imbalanced Fermi gas and should thus be observable in experiment, unlike the well-studied equal-mass case.

Effect of three-body loss on itinerant ferromagnetism in an atomic Fermi gas

A recent experiment has provided tentative evidence for itinerant ferromagnetism in an ultracold atomic gas. However, the interpretation of the results is complicated by significant atom losses. We argue that during the loss process the system gradually heats up but remains in local equilibrium.To quantify the consequences of atom loss on the putative ferromagnetic transition we adopt an extended Hertz-Millis theory. The losses damp quantum fluctuations, thus increasing the critical interaction strength needed to induce ferromagnetism and revert the transition from being first order to second order. This effect may resolve a discrepancy between the experiment and previous theoretical predictions. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.

Observation of Shock Waves in a Strongly Interacting Fermi Gas

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-dependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.

High-resolution imaging of ultracold fermions in microscopically tailored optical potentials

We report on the local probing and preparation of an ultracold Fermi gas on the length scale of one micrometer, i.e. of the order of the Fermi wavelength. The essential tool of our experimental setup is a pair of identical, high-resolution microscope objectives. One of the microscope objectives allows local imaging of the trapped Fermi gas of 6Li atoms with a maximum resolution of 660 nm, while the other enables the generation of arbitrary optical dipole potentials on the same length scale. Employing a two-dimensional (2D) acousto-optical deflector, we demonstrate the formation of several trapping geometries, including a tightly focused single optical dipole trap, a 4×4 site 2D optical lattice and an 8 site ring lattice configuration. Furthermore, we show the ability to load and detect a small number of atoms in these trapping potentials. A site separation down to one micrometer in combination with the low mass of 6Li results in tunneling rates that are sufficiently large for the implementation of Hubbard models with the designed geometries.

Universal spin transport in a strongly interacting Fermi gas

Transport of fermions, particles with half-integer spin, is central to many fields of physics. Electron transport runs modern technology, defining states of matter such as superconductors and insulators, and electron spin is being explored as a new carrier of information. Neutrino transport energizes supernova explosions following the collapse of a dying star, and hydrodynamic transport of the quark-gluon plasma governed the expansion of the early Universe. However, our understanding of non-equilibrium dynamics in such strongly interacting fermionic matter is still limited. Ultracold gases of fermionic atoms realize a pristine model for such systems and can be studied in real time with the precision of atomic physics. Even above the superfluid transition, such gases flow as an almost perfect fluid with very low viscosity when interactions are tuned to a scattering resonance. In this hydrodynamic regime, collective density excitations are weakly damped. Here we experimentally investigate spin excitations in a Fermi gas of (6)Li atoms, finding that, in contrast, they are maximally damped. A spin current is induced by spatially separating two spin components and observing their evolution in an external trapping potential. We demonstrate that interactions can be strong enough to reverse spin currents, with components of opposite spin reflecting off each other. Near equilibrium, we obtain the spin drag coefficient, the spin diffusivity and the spin susceptibility as a function of temperature on resonance and show that they obey universal laws at high temperatures. In the degenerate regime, the spin diffusivity approaches a value set by [planck]/m, the quantum limit of diffusion, where [planck]/m is Planck's constant divided by 2π and m the atomic mass. For repulsive interactions, our measurements seem to exclude a metastable ferromagnetic state.

Spin drag in a perfect fluid

Beautiful experiments in an ultracold, strongly interacting atomic Fermi gas reveal that, unexpectedly, unpaired atomic spins flow in the system with the maximum resistance permitted by the laws of quantum mechanics. See Letter p.201 Strongly interacting Fermi gases are ubiquitous in nature, from electrons in high-temperature superconductors, to nuclear matter. Their transport properties, such as the speed of diffusion, are poorly understood. Sommer et al. use controlled collisions of ultracold atomic clouds to investigate spin transport in a strongly interacting Fermi gas. They find that the spin excitations are maximally damped (leading to high spin drag), and that interactions are strong enough to reverse spin currents so that opposite spin components reflect off each other. The speed of diffusion is set by a fundamental quantum limit. The results have implications for any area involving fermion transport, from spintronics to studies of the early Universe.