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.
| The temperature-imbalance diagram shows where the rf spectra presented in this work were taken. All spectra were obtained on resonance at 833 G. The arrows indicate the order in which the spectra are displayed in the figures. The shaded region indicates the superfluid phase.
Except for the data close to zero imbalance, for which the interacting temperature T´ is given, temperatures have been determined from the noninteracting wings of the majority cloud.
| Radio-frequency spectra of the minority component obtained while crossing the phase transition by reducing imbalance (A to C) and temperature (D to F). The rf spectra do not reveal the phase transition.
The onset of superfluidity is indirectly observed by fermion pair condensation. The onset of superfluidity as a function of temperature occurs between (D) and (F). The insets in (A) to (F) show the column density profile (red) of the minority cloud after a rapid magnetic field ramp to the BEC side and further expansion. The additional insets in (D) to (F) show phase-contrast images for a trapped cloud, obtained at imbalances of the opposite sign.
We have studied the expansion of a rotating, superfluid Fermi gas. The presence and absence of vortices in the rotating gas were used to distinguish the superfluid and normal parts of the expanding cloud. We found 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 1.2 x 1011 cm-3, about an order of magnitude lower than any previous study.
| Shown are absorption images for different expansion times on the BCS side of the Feshbach resonance at 910 G (0.0, 1.0, 2.0, 3.0, 3.5, 4.0, and 4.5 ms) and 960 G (0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3 ms), before the magnetic field was ramped to the BEC side for further expansion.
The vortices served as markers for the superfluid parts of the cloud. Superfluidity survived the expansion for several milliseconds and was gradually lost from the low density edges of the cloud towards its center. Compared to 910 G (a=7200 a0), superfluidity decayed faster at 960 G (a=5000 a0) due to the reduced interaction strength.
| Starting at a peak kFa in the optical trap (triangles) vortices survived up to a critical peak kFa of -0.8 ± 0.1 (squares), almost independent of the magnetic field (scattering length).
Solid circles correspond to partially superfluid, open circles to normal clouds. The observed number of vortices is color coded. The critical kFa was obtained for each magnetic field separately by taking the average of the peak kF of the last partially superfluid and the first completely normal cloud.
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 supefluid 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.
| (a) The probe beam is tuned to the red for the |1> to |e> transition and to te blue for the |2> to |e> transition. the resulting optical signal in the phase contrast image is proportional to the density difference of the atoms in the two atomic states.
(b) Phase contrast images of trapped atomic clouds in state |1> (left) and state |2> (right) and of and equal mixture of the two states (center).
| As a sample with imbalanced population in the two spin states is cooled down, the formation of a region with equal densities in the two spin states can be observed.
The temperature of the cloud was controlled by varying the final value of the trap depth Uf in the evaporation process. The whole evaporation process was performed in the unitary regime at a magnetic field of 834G.
Water freezes into ice, atomic spins spontaneously align in a magnet, liquid helium becomes superfluid: Phase transitions are dramatic phenomena. However, despite the drastic change in the system's behaviour, observing the transition can sometimes be subtle. The hallmark of Bose-Einstein condensation (BEC) and superfluidity in trapped, weakly interacting Bose gases is the sudden appearance of a dense central core inside a thermal cloud. In strongly interacting gases, such as the recently observed fermionic superfluids, this clear separation between the superfluid and the normal parts of the cloud is no longer given. Condensates of fermion pairs could be detected only using magnetic field sweeps into the weakly interacting regime. The quantitative description of these sweeps presents a major theoretical challenge. Here we demonstrate that the superfluid phase transition can be directly observed by sudden changes in the shape of the clouds, in complete analogy to the case of weakly interacting Bose gases. By preparing unequal mixtures of the two spin components involved in the pairing, we greatly enhance the contrast between the superfluid core and the normal component. Furthermore, the non-interacting wings of excess atoms serve as a direct and reliable thermometer. Even in the normal state, strong interactions significantly deform the density profile of the majority spin component. We show that it is these interactions which drive the normal-to-superfluid transition at the critical population imbalance of 70(5)%
|Top a-c and bottom d-f rows show the normal and the superfluid state, respectively. The appearance of a dense central feature in the smaller component marks the onset of condensation. The condensate causes a clear depletion in the difference profiles (bottom of each panel). Both in the normal and in the superfluid state, interactions between the two spin states are manifest in the strong deformation of the larger component. The dashed lines show Thomas-Fermi fits to the wings of the column density.|
|The curvature of the observed column density is encoded in shades of gray with white (black) corresponding to positive (negative) curvature. The outer radii of the two components and the condensate radius are shown as an overlay in the lower panel. As a direct consequence of strong interactions, the minority component causes a pronounced bulge in the majority density that is reflected in the rapid variation of the profile's curvature. The condensate is clearly visible in the minority component (± > 0), but also leaves a faint trace in the minority component (± < 0).|
We established superfluidity in a two-state mixture of ultracold fermionic atoms with imbalanced state populations. This study relates to the long-standing debate about the nature of the superfluid state in Fermi systems. Indicators for superfluidity were condensates of fermion pairs and vortices in rotating clouds. For strong interactions, near a Feshbach resonance, superfluidity was observed for a broad range of population imbalances. We mapped out the superfluid regime as a function of interaction strength and population imbalance and characterized the quantum phase transition to the normal state, known as the Pauli limit of superfluidity.
|Vortices as a tool of Metrology: When is the cloud superfluid? Preparation of several spin-mixtures at 853G and 812G, respectively. Before evaporation and stirring, the population transfer from spin state |1> to spin state |2> is varied from 0% to 100% by the Landau-Zener ramp speed.|
|Radial density profiles of the two components of a strongly interacting Fermi gas mixture with unequal populations. The profiles are azimuthal averages of the axially integrated density. A) and B): Profiles of the component in state |1> and |2>, respectively, originating from 883 G (1/kFa =-0.27). The population imbalance was δ=0% (red), δ=46% (blue), and δ=86% (green). (C) Difference between the distributions in state |1> and |2> . The clear dip in the blue curve caused by the pair condensate indicates phase separation of the superfluid from the normal gas. (D) Color-coded profiles of clouds prepared at three different interaction strengths. The condensate is clearly visible as the dense central part surrounded by unpaired fermions or uncondensed molecules.|
|Transition from the Superfluid to the Normal State. Critical difference in Fermi energies δEF between the two spin states for which the superfluid to normal transition is observed. δEF for each interaction strength and temperature is obtained from the critical population imbalance determined in the figure above. Representative density profiles illustrate the quantum phase transition for fixed interaction and for fixed population imbalance along the dashed lines.|
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. In the June 23 issue of Nature, we report our observation 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.
|The pictures show vortex lattices on the BEC-side of the Feshbach resonance (left), in the unitary regime on resonance (middle) and on the BCS-side of the resonance (right).|
|A condensate of Fermion pairs (red) is trapped in the waist of a focussed Laser beam (pink). Two additional Laser beams (green) rotate around the edges to stir the condensate. Current-carrying coils (blue) generate the magnetic field used for axial confinement and to tune the interaction strength by means of a Feshbach resonance. After releasing the atomic cloud from the electromagnetic trap, the cloud expands ballistically and inverts its aspect ratio. Resonant absorption imaging yields a density profile of the atomic cloud containing vortices.|
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 manybody 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.
|Imaging of molecular condensates. The rapid ramp to zero field after release from the trap created a cloud containing both molecules and unpaired atoms. A Stern-Gerlach field gradient separated atoms (magnetic moment ±1/3µB for states |1> and |2>, respectively) from molecules, which are purely singlet at zero field. At the end of 5 ms of ballistic expansion, the molecules were dissociated in a fast ramp (in 3 ms to 1200 G) across the Feshbach resonance. After another 2 ms expansion again at zero field, an absorption image of the separated clouds was taken. Condensate fractions were determined from the molecular cloud, and the numbers in each component were recorded. An absorption image is shown on the bottom, the field of view is 3 mm x 1 mm.|
|Shown is the delayed response of the observed condensate fraction (data points and thick line to guide the eye) to a 250 Hz magnetic field modulation (thin line) on the BCS side of the Feshbach resonance at 834 G. The vertical lines indicate the points of maximum condensate fraction, which are delayed with respect to the times at which the magnetic field is closest to resonance. For our trap parameters, the response was delayed by 500µs. This time is far longer than the time spent within the resonance region during the conversion of fermion pairs into molecules. This provides final proof that the observed molecular condensates originated from condensates of pairs of fermions above the resonance.|
|Condensation of Fermion Pairs Near a Feshbach Resonance||Observation of Bose-Einstein Condensation of Molecules|
|Feshbach Resonances in Fermionic 6Li||Observation of Feshbach Resonances between Two Different Atomic Species|
|Spectroscopic Insensitivity to Cold Collisions in a Two-State Mixture of Fermions||Fiftyfold Improvement in the Number of Quantum Degenerate Fermionic Atoms|
|Radio-Frequency Spectroscopy of Ultracold Fermions||Two-Species Mixture of Quantum Degenerate Bose and Fermi Gases|
|Decay of Ultracold Fermionic Lithium Gas Near a Feshbach Resonance||Collisions in zero temperature Fermi gases|