We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.

We observe a long-lived solitary wave in a superfluid Fermi gas of 6 Li atoms after phase imprinting. Tomographic imaging reveals the excitation to be a solitonic vortex, oriented transverse to the long axis of the cigar-shaped atom cloud. The precessional motion of the vortex is directly observed, and its period is measured as a function of the chemical potential in the BEC-BCS crossover. The long period and the correspondingly large ratio of the inertial to the bare mass of the vortex are in good agreement with estimates based on superfluid hydrodynamics that we derive here using the known equation of state in the BEC-BCS crossover. DOI: 10.1103/PhysRevLett.113.065301 PACS numbers: 67.85.-d, 03.75.Kk, 03.75.Lm, 03.75.Ss Solitary waves that do not spread as they propagate are ubiquitous in nonlinear systems, from classical fluids and fiber optics to superfluids and superconductors. These waves are localized objects with defined energy and mass, and as such they can be described as an effective single particle emerging from a many-body environment. This distinguishes them from larger-scale collective excitations such as shape oscillations of a superfluid, or from perturbative linear excitations such as phonons. Paradigmatic examples of solitary waves in superfluids are planar solitons that separate regions of differing phase, as well as vortex rings or single vortex lines [see Fig. 1(a)]. The direct creation of such localized and highly nonlinear objects "on demand" in ultracold quantum gases allows for an excellent dynamical probe of novel superfluids, such as strongly interacting Fermi gases [1] or spin-orbit coupled Bose-Einstein condensates [2,3].In a recent experiment on fermionic superfluids at MIT [1], long-lived solitary waves were produced that featured a large ratio of inertial to bare (missing) mass of over 200, evidenced by an oscillation period over 15 times longer than the period for a single atom. The observed absorption images suggested the interpretation of the waves as planar solitons, but the longevity as well as the large effective mass ratio were unexpected for this type of defect [4][5][6][7]. Indeed, the nodal plane of a soliton is energetically more costly than the nodal line of a vortex, and planar solitons can decay into lower energy excitations via the snake instability, the undulation of the soliton plane [4]. Several recent works therefore suggested that these solitary waves are vortex rings [8][9][10]. For weakly interacting BoseEinstein condensates, solitons have been created [11,12] and observed to decay into vortex rings [13,14]. The latter further decay into a vortex-antivortex pair that eventually breaks up, leaving behind a single remnant vortex [15][16][17]. The exact process was recently elucidated in a discussion of apparent soliton oscillations observed in weakly interacting BECs [18,19]. In the case of strongly interacting fermionic superfluids, the understanding of such nontrivial dynamics presents a challenging nonequilibrium many-body problem [8,20].In this Letter,...

We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T . In this regime, we observe a characteristic T 2 dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T , the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝ T −1/2 . In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.Landau's Fermi liquid theory provides a quasiparticle description of the low-temperature behavior for a large class of unordered fermionic states of matter, including most normal metals, atomic nuclei, and liquid helium-3 [1]. Strongly interacting Fermi gases with highly imbalanced spin populations have been identified as belonging to the same class [2][3][4][5][6][7][8][9][10][11][12][13][14]. The quasiparticles in spin-imbalanced Fermi gases are Fermi polarons: spin impurities dressed by an excess cloud of majority fermions. The stability of quasiparticles in a Fermi liquid is a consequence of the restricted phase space for collisions due to Pauli blocking. With increasing temperature T , the accessible phase space increases, and the lifetime of quasiparticles shortens, leading to the breakdown of Fermi liquid theory. In this intermediate temperature regime the gas is neither a Fermi liquid nor a classical Boltzmann gas. For strong interactions, this regime is void of well-defined quasiparticles and controlled by the quantum critical point of the unitary, spin-balanced gas at zero chemical potential and temperature [15][16][17].Ultracold Fermi gases offer a unique opportunity to study the crossover from a low-temperature Fermi liquid to a classical Boltzmann gas, due to the large accessible temperature range. In spin-imbalanced Fermi gases, the two inequivalent Fermi surfaces provide additional richness. As the temperature is lowered from the classical regime, the Fermi surface of the majority forms first, giving minority spins the quasiparticle character of polarons. At even lower temperatures, the polarons themselves become quantum degenerate and form a Fermi surface.In this work, we access the entire crossover from degenerate polarons to the classical Boltzmann gas through the quantum critical region. The internal properties of the polaronic quasiparticles are measured via radio-frequency (rf) spectroscopy [10,[18][19][20] on a homogeneous Fermi gas [21,22]. At low temperatures, the...

We follow the time evolution of a superfluid Fermi gas of resonantly interacting 6 Li atoms after a phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, its subsequent snaking, and its decay into a vortex ring, which, in turn, breaks to finally leave behind a single solitonic vortex. In intermediate stages, we find evidence for an exotic structure resembling the Φ soliton, a combination of a vortex ring and a vortex line. Direct imaging of the nodal surface reveals its undulation dynamics and its decay via the puncture of the initial soliton plane. The observed evolution of the nodal surface represents dynamics beyond superfluid hydrodynamics, calling for a microscopic description of unitary fermionic superfluids out of equilibrium.

We measure radio frequency (rf) spectra of the homogeneous unitary Fermi gas at temperatures ranging from the Boltzmann regime through quantum degeneracy and across the superfluid transition. For all temperatures, a single spectral peak is observed. Its position smoothly evolves from the bare atomic resonance in the Boltzmann regime to a frequency corresponding to nearly one Fermi energy at the lowest temperatures. At high temperatures, the peak width reflects the scattering rate of the atoms, while at low temperatures, the width is set by the size of fermion pairs. Above the superfluid transition, and approaching the quantum critical regime, the width increases linearly with temperature, indicating non-Fermi-liquid behavior. From the wings of the rf spectra, we obtain the contact, quantifying the strength of short-range pair correlations. We find that the contact rapidly increases as the gas is cooled below the superfluid transition.PACS numbers: 03.75. Ss, 05.30.Fk, 51.30.+i, 71.18.+y Understanding fermion pairing and pair correlations is of central relevance to strongly interacting Fermi systems such as nuclei [1,2], ultracold gases [3-6], liquid 3 He [7], high temperature superconductors [8], and neutron stars [9]. Strong interactions on the order of the Fermi energy challenge theoretical approaches, especially methods that predict dynamic properties such as transport or the spectral response at finite temperature [10]. Atomic Fermi gases at Feshbach resonances realize a paradigmatic system where the gas becomes as strongly interacting as allowed by unitarity [3][4][5][6]11]. Here, the system becomes universal, requiring only two energy scales: the Fermi energy E F and thermal energy k B T , where k B is the Boltzmann constant and T is the temperature. The corresponding length scales are the interparticle spacing λ F = n −1/3 and the thermal de Broglie wavelength λ T = h/ √ 2πmk B T , where m and n are the mass and number density of the atoms respectively. When the two energy scales are comparable, the system enters a quantum critical regime separating the high temperature Boltzmann gas from the fermionic superfluid [12]. Quantum criticality is often associated with the absence of quasiparticles [10,12,13], spurring a debate on the applicability of Fermi liquid theory to the degenerate normal fluid below the Fermi temperature [14][15][16]. It has been conjectured that preformed pairs exist above T c , up to a pairing temperature T * [3,5,11,[17][18][19][20][21].Radio frequency (rf) spectroscopy measures the momentum integrated, occupied spectral function, providing a powerful tool for studying interactions and correlations in Fermi gases [22][23][24][25][26][27]. Here, a particle is ejected from the interacting many-body state and transferred into a weakly interacting final state. Shifts in rf spectra indicate attractive or repulsive interactions in the gas. At high temperatures, the width of the rf spectrum reflects the scattering rate in the gas, while at low temperatures, the width has been used to infe...

Laser cooling to sub-Doppler temperatures by optical molasses is thought to be inhibited in atoms with unresolved, near-degenerate hyperfine structure in the excited state. We demonstrate that such cooling is possible in one to three dimensions, not only near the standard D2 line for laser cooling, but over a wide range extending to the D1 line. Via a combination of Sisyphus cooling followed by adiabatic expansion, we reach temperatures as low as 40 µK, which corresponds to atomic velocities a factor of 2.6 above the limit imposed by a single photon recoil. Our method requires modest laser power at a frequency within reach of standard frequency locking methods. It is largely insensitive to laser power, polarization and detuning, magnetic fields, and initial hyperfine populations. Our results suggest that optical molasses should be possible with all alkali species.Sisyphus cooling of neutral atoms is vital for reaching the ultracold temperatures needed in experiments ranging from metrology [1] to quantum information [2]. It is simple to apply for species with resolved hyperfine structure, e.g. sodium [3], cesium [4], and rubidium [5], which have thus become workhorses in atomic physics. A new generation of experiments, however, requires atoms offering lighter mass or bosonic and fermionic isotopes. Achieving sub-Doppler temperatures with these atoms has relied upon sympathetic and/or evaporative cooling -methods that are intrinsically lossy, require timescales of seconds, and favorable collisional properties -or optical lattices that require high laser intensities [6] or detunings of several hundred gigahertz [7]. Sisyphus cooling has been demonstrated with potassium [8,9], which has partially resolved hyperfine structure, but the same method does not apply to lithium, which has inverted and unresolved hyperfine structure [9]. Standard Sisyphus cooling of lithium, which has not been demonstrated [10][11][12][13][14][15], would open the door to simpler, faster, and more efficient experiments in ultracold chemistry, quantum gas microscopy, quantum simulation, and tests of the equivalence principle [16][17][18][19][20][21][22][23][24]. Recently, a sub-Doppler cooling scheme for lithium has been demonstrated using a bichromatic lattice and enhancement from a Λ-type level structure [25]. Here, we demonstrate simple, efficient (up to ∼ 45% cooled fraction), Sisyphus cooling of lithium to temperatures as low as 40 µK in one dimension to 100 µK in three dimensions using polarization-gradient cooling beams with a detuning of 1-9 GHz. These detunings can be produced using a standard offset laser lock. The cooling process operates on a timescale of milliseconds and requires only modest laser power. It can thus be integrated easily into experiments using existing diode lasers.Historically, when lithium was first laser cooled, sub-

Transport of strongly interacting fermions is crucial for the properties of modern materials, nuclear fission, the merging of neutron stars, and the expansion of the early Universe. Here, we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting atomic Fermi gas by studying sound propagation and its attenuation through the coupled transport of momentum and heat. In the normal state, the sound diffusivity D monotonically decreases upon lowering the temperature, in contrast to the diverging behavior of weakly interacting Fermi liquids. Below the superfluid transition temperature, D attains a universal value set by the ratio of Planck’s constant and the particle mass. Our findings inform theories of fermion transport, with relevance for hydrodynamic flow of electrons, neutrons, and quarks.

The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits’ centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.