Time-Resolved Observation of Competing Attractive and Repulsive Short-Range Correlations in Strongly Interacting Fermi Gases.

We exploit a time-resolved pump-probe spectroscopic technique to study the out-of-equilibrium dynamics of an ultracold two-component Fermi gas, selectively quenched to strong repulsion along the upper branch of a broad Feshbach resonance. For critical interactions, we find the rapid growth of short-range anticorrelations between repulsive fermions to initially overcome concurrent pairing processes. At longer evolution times, these two competing mechanisms appear to macroscopically coexist in a short-range correlated state of fermions and pairs, unforeseen thus far. Our work provides fundamental insights into the fate of a repulsive Fermi gas, and offers new perspectives towards the exploration of complex dynamical regimes of fermionic matter.

Superfluidity in a gas of strongly interacting fermions.

After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by rf spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.

Critical velocity for superfluid flow across the BEC-BCS crossover.

Critical velocities have been observed in an ultracold superfluid Fermi gas throughout the BEC-BCS crossover. A pronounced peak of the critical velocity at unitarity demonstrates that superfluidity is most robust for resonant atomic interactions. Critical velocities were determined from the abrupt onset of dissipation when the velocity of a moving one-dimensional optical lattice was varied. The dependence of the critical velocity on lattice depth and on the inhomogeneous density profile was studied.

Tomographic rf spectroscopy of a trapped Fermi gas at unitarity.

We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at 0.48(4)epsilonF with respect to the free atomic line, where epsilonF is the local Fermi energy.

Pairing without superfluidity: the ground state of an imbalanced Fermi mixture.

We used radio-frequency spectroscopy to study pairing in the normal and superfluid phases of a strongly interacting Fermi gas with imbalanced spin populations. At high spin imbalances, the system does not become superfluid even at zero temperature. In this normal phase, full pairing of the minority atoms was observed. Hence, mismatched Fermi surfaces do not prevent pairing but can quench the superfluid state, thus realizing a system of fermion pairs that do not condense even at the lowest temperature.

Phase-sensitive recombination of two bose-einstein condensates on an atom chip.

The recombination of two split Bose-Einstein condensates on an atom chip is shown to result in heating which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms between 10% and 40% and provides a robust way to read out the phase of an atom interferometer without the need for ballistic expansion. The heating may be caused by the dissipation of dark solitons created during the merging of the condensates.

Long phase coherence time and number squeezing of two Bose-Einstein condensates on an atom chip.

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to approximately 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

Superfluid expansion of a rotating Fermi gas.

We study the expansion of a rotating, superfluid Fermi gas. The presence and absence of vortices in the rotating gas are used to distinguish the superfluid and normal parts of the expanding cloud. We find that the superfluid pairs survive during the expansion until the density decreases below a critical value. Our observation of superfluid flow in the expanding gas at 1/kFa=0 extends the range where fermionic superfluidity has been studied to densities of 1.2x10(11) cm(-3), about an order of magnitude lower than any previous study.

Spin-exchange collisions of submerged shell atoms below 1 Kelvin.

Angular momentum changing collisions can be suppressed in atoms whose valence electrons are submerged beneath filled shells of higher principle quantum number. To determine whether spin-exchange collisions are suppressed in these "submerged shell" atoms, we measured collisional rates for six hyperfine states of Mn at T < 1 K. Although the 3d valence electrons in Mn are submerged beneath a filled 4s orbital, we find spin-exchange rate coefficients similar to Na and H (both nonsubmerged shell atoms).

Matter-wave interferometry with phase fluctuating Bose-Einstein condensates.

Elongated Bose-Einstein condensates (BECs) exhibit strong spatial phase fluctuations even well below the BEC transition temperature. We demonstrate that atom interferometers using such condensates are robust against phase fluctuations; i.e., the relative phase of the split condensate is reproducible despite axial phase fluctuations. However, larger phase fluctuations limit the coherence time, especially in the presence of some asymmetries in the two wells of the interferometer.

Evidence for superfluidity of ultracold fermions in an optical lattice.

The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. By using cold atomic gases, various models of condensed matter can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the copper oxides. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in bulk atomic gases include the observation of fermion-pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported but have not yet addressed superfluid behaviour. Here we report the observation of distinct interference peaks when a condensate of fermionic atom pairs is released from an optical lattice, implying long-range order (a property of a superfluid). Conceptually, this means that s-wave pairing and coherence of fermion pairs have now been established in a lattice potential, in which the transport of atoms occurs by quantum mechanical tunnelling and not by simple propagation. These observations were made for interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly as a result of a transition from superfluid to insulator. Such strongly interacting fermions in an optical lattice can be used to study a new class of hamiltonians with interband and atom-molecule couplings.

Low velocity quantum reflection of Bose-Einstein condensates.

We study how interactions affect the quantum reflection of Bose-Einstein condensates. A patterned silicon surface with a square array of pillars resulted in high reflection probabilities. For incident velocities greater than 2.5 mm/s, our observations agreed with single-particle theory. At velocities below 2.5 mm/s, the measured reflection probability saturated near 60% rather than increasing towards unity as predicted by the accepted theoretical model. We extend the theory of quantum reflection to account for the mean-field interactions of a condensate which suppresses quantum reflection at low velocity. The reflected condensates show collective excitations as recently predicted.

Observation of phase separation in a strongly interacting imbalanced fermi gas.

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using phase-contrast imaging and 3D image reconstruction. A shell structure is clearly identified where the superfluid region of equal densities is surrounded by a normal gas of unequal densities. The phase transition induces a dramatic change in the density profiles as excess fermions are expelled from the superfluid.

Observation of strong quantum depletion in a gaseous Bose-Einstein condensate.

We studied quantum depletion in a gaseous Bose-Einstein condensate. An optical lattice enhanced the atomic interactions and modified the dispersion relation resulting in strong quantum depletion. The depleted fraction was directly observed as a diffuse background in the time-of-flight images. Bogoliubov theory provides a semiquantitative description for our observations of depleted fractions in excess of 50%.

Optical weak link between two spatially separated Bose-Einstein condensates.

Two spatially separate Bose-Einstein condensates were prepared in an optical double-well potential. A bidirectional coupling between the two condensates was established by two pairs of Bragg beams which continuously outcoupled atoms in opposite directions. The atomic currents induced by the optical coupling depend on the relative phase of the two condensates and on an additional controllable coupling phase. This was observed through symmetric and antisymmetric correlations between the two outcoupled atom fluxes. A Josephson optical coupling of two condensates in a ring geometry is proposed. The continuous outcoupling method was used to monitor slow relative motions of two elongated condensates and characterize the trapping potential.

Vortices and superfluidity in a strongly interacting Fermi gas.

Quantum degenerate Fermi gases provide a remarkable opportunity to study strongly interacting fermions. In contrast to other Fermi systems, such as superconductors, neutron stars or the quark-gluon plasma of the early Universe, these gases have low densities and their interactions can be precisely controlled over an enormous range. Previous experiments with Fermi gases have revealed condensation of fermion pairs. Although these and other studies were consistent with predictions assuming superfluidity, proof of superfluid behaviour has been elusive. Here we report observations of vortex lattices in a strongly interacting, rotating Fermi gas that provide definitive evidence for superfluidity. The interaction and therefore the pairing strength between two 6Li fermions near a Feshbach resonance can be controlled by an external magnetic field. This allows us to explore the crossover from a Bose-Einstein condensate of molecules to a Bardeen-Cooper-Schrieffer superfluid of loosely bound pairs. The crossover is associated with a new form of superfluidity that may provide insights into high-transition-temperature superconductors.

Formation dynamics of a fermion pair condensate.

The dynamics of pair condensate formation in a strongly interacting Fermi gas close to a Feshbach resonance was studied. We employed a phase-shift method in which the delayed response of the many-body system to a modulation of the interaction strength was recorded. The observable was the fraction of condensed molecules in the cloud after a rapid magnetic field ramp across the Feshbach resonance. The measured response time was slow compared to the rapid ramp, which provides final proof that the molecular condensates reflect the presence of fermion pair condensates before the ramp.

Coherent molecular optics using ultracold sodium dimers.

Coherent molecular optics is performed using two-photon Bragg scattering. Molecules were produced by sweeping an atomic Bose-Einstein condensate through a Feshbach resonance. The spectral width of the molecular Bragg resonance corresponded to an instantaneous temperature of 20 nK, indicating that atomic coherence was transferred directly to the molecules. An autocorrelating interference technique was used to observe the quadratic spatial dependence of the phase of an expanding molecular cloud. Finally, atoms initially prepared in two momentum states were observed to cross pair with one another, forming molecules in a third momentum state. This process is analogous to sum-frequency generation in optics.

Light scattering to determine the relative phase of two Bose-Einstein condensates.

We demonstrated an experimental technique based on stimulated light scattering to continuously sample the relative phase of two spatially separated Bose-Einstein condensates of atoms. The phase measurement process created a relative phase between two condensates with no initial phase relation, read out the phase, and monitored the phase evolution. This technique was used to realize interferometry between two trapped Bose-Einstein condensates without need for splitting or recombining the atom cloud.

Quantum reflection from a solid surface at normal incidence.

We observed quantum reflection of ultracold atoms from the attractive potential of a solid surface. Extremely dilute Bose-Einstein condensates of 23Na, with peak density 10(11)-10(12) atoms/cm(3), confined in a weak gravitomagnetic trap were normally incident on a silicon surface. Reflection probabilities of up to 20% were observed for incident velocities of 1-8 mm/s. The velocity dependence agrees qualitatively with the prediction for quantum reflection from the attractive Casimir-Polder potential. Atoms confined in a harmonic trap divided in half by a solid surface exhibited extended lifetime due to quantum reflection from the surface, implying a reflection probability above 50%.