Session O4: Degenerate Fermi Gases

Spin-Imbalance in a 1-Dimensional Trapped Fermi-Gas

Spin-polarized trapped Fermi gases have been observed to phase separate into normal and superfluid phases\footnote{G. B. Partridge et al., Science 311, 503-505 (2006); C.H. Schunck et al., Science 316, 867-870 (2007)}. The elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, predicted more than 40 years ago has, however, not yet been found in the 3-dimensional gas. Theory predicts that the FFLO phase occupies only a small part of the phase diagram in 3D\footnote{D.E. Sheehy, L. Radzihovsky, Ann. Phys. 332(8), 1790 (2006)}, whereas in a 1D gas it is expected to be more prominent and is further expected to exhibit an interesting dimensional crossover\footnote{G. Orso, Phys. Rev. Lett. 98, 070402 (2007); H. Hu et. al, Phys. Rev. Lett. 98, 070403 (2007)}. We have implemented a 2D optical lattice to create an array of 1D tubes in order to explore the phase diagram of the 1D polarized Fermi gas. Our progress will be reported.   

Radiofrequency Spectroscopy of Imbalanced Fermi Gases

We studied the radiofrequency spectrum of the majority component of a number imbalanced ultracold Fermi gas of Lithium-6 in the BEC-BCS crossover. Using 3D density reconstruction we extracted the local excitation spectrum in the different parts of the atomic cloud ranging from the superfluid central core with equal densities of the two spin components to the spin-polarized part in the outer wings of the trapped atomic sample.   

The Effect of Trap Geometry on Phase Separation in a Polarized Fermi Gas

We have observed phase separation in a polarized $^6$Li atomic Fermi gas in an elongated (aspect ratio of 30) single-beam optical trap.\footnote{G. B. Partridge {\it et al.}, {\it Science} {\bf 311}, 503 (2006); {\it PRL} {\bf 97}, 190407 (2006).} The phase-separated phase consists of a paired superfluid core surrounded on each end of the trap by a completely polarized normal gas. The observed density distributions represent a violation of the local density approximation, and have been explained by surface tension. In addition, we find that the superfluid core survives until the system is nearly completely polarized, with $P\geq 0.95$. These results contrast with a similar experiment, done at MIT, that observes the superfluid core to survive up to $P\sim 0.74$, in agreement with the Clogston limit. In this case, no surface tension is observed.\footnote{C. H. Schunck {\it et al.}, {\it Science} {\bf 316}, 867 (2007).} Though the the explanation of these discrepancies is not yet clear, one major difference is trap geometry, since the MIT trap has an aspect ratio 6 times smaller than ours. We have implemented a crossed beam trap with an aspect ratio $\sim$3 in order to study the effects of trap geometry. Our latest experimental results will be presented.   

Phase diagram of a two-component Fermi gas with resonant interactions

The pairing of fermions is at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state. In this talk, the phase diagram of a two-component Fermi gas at unitarity, i.e. when the fermions interact resonantly, will be presented. The phase diagram has experimentally obtained by mapping out the superfluid phases versus temperature and density imbalance. At low temperature, the superfluid-to-phase transition occurs with a jump in the spin polarization, the signature of a first-order phase transition. At high temperature, the phase transition is smooth and therefore of second-order. We have identified a tricritical point where the nature of the phase transition changes from first-order to second-order. In our experiment, absolute temperatures were obtained using in situ thermometry applied to the non-interacting Fermi gas in the outer part of the trapped samples. Furthermore, the quantitative analysis of the density profiles of the sample at our lowest temperature shows that at zero temperature, there is a quantum phase transition from a fully-paired superfluid to a partially-polarized normal gas. (Y. Shin et al., arXiv:0709.3027)   

Radio Frequency spectroscopy of a strongly interacting Fermi gas

Experiments using ultra-cold atoms have allowed researchers to study the BCS-BEC crossover. We report on studies of the crossover using an ultracold gas of potassium-40 atoms and radio-frequency (RF) spectroscopy. Atoms from one of the two strongly interacting spin states are transfered into a third spin state, which can then be selectively imaged. Our experiments differ from previous measurements using lithium-6 atoms in that we output couple the atoms to a weakly interacting state.   

Universal behavior of the critical temperature and condensate fraction of a strongly interacting molecular condensate

We have observed the universal behavior of the critical temperature and condensate fraction of strongly interacting molecules of fermionic $^6$Li atoms on the BEC side of the Feshbach resonance [1]. The Bragg diffraction is applied to probe the momentum distribution of strongly interacting molecules to deduce the temperature and condensate fraction. The Bragg technique is instrumental in clearly identifying the onset of Bose-Einstein condensation, allowing us to determine the critical temperature precisely. As we approach the Feshbach resonance from the BEC side, the critical temperature decreases and eventually levels off and the temperature dependence of the condensate fraction approaches a universal curve. [1] Y. Inada, et al., cond-mat /0712.1445.   

Determination of the equation of state of a two-component Fermi gas at unitarity

We report on the measurement of the equation of state of a two-component Fermi gas of 6Li atoms with resonant interactions. By analyzing the in situ density distributions of a population-imbalanced Fermi mixture confined in a harmonic trap, we determine the energy density of a resonantly interacting Fermi gas as a function of the densities of the two components. The presence of the non-interacting ideal Fermi gas in the outer region of the trapped sample allows measuring the equation of state directly from the shape of the cloud without any absolute calibration of particle density. From the density profiles obtained at our lowest temperature, we estimate the zero-temperature equation of state. (Y. Shin, arXiv:0801.1523)   

Determination of the Fermion Pair Size in a Strongly Interacting Superfluid

Fermionic superfluidity requires the formation of pairs. The pair size relative to the interparticle spacing has a strong impact on the properties of the superfluid. This can be explored in ultracold atomic gases where a resonantly interacting superfluid in the crossover from a Bardeen-Cooper-Schrieffer type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensates of tightly bound molecules has been realized. We probe the microscopic properties of the fermion pairs in the crossover regime with radio-frequency (rf) spectroscopy. Previous measurements of rf spectra were difficult to interpret due to strong final state interactions. Here we present, using a new superfluid spin mixture where such interactions have a negligible influence, fermion-pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine the fermion pair size in the resonantly interacting gas to be 1.4(2)/kF smaller than the interparticle spacing and the smallest pairs observed in fermionic superfluids (kF is the Fermi wave number). This finding highlights the importance of small fermion pairs for superfluidity at high critical temperatures.   

Matter wave probe for detecting Fermi superfluidity in trapped ultra-cold atom experiments

We propose a robust matter wave probe for detecting Bardeen-Cooper-Schrieffer (BCS) superfluidity in a trapped two-component Fermi gas.In hear the matter wave corresponds to a Bose condensed state (BEC) of some third species of atoms- `probe-atoms'. This detection scheme is based on the extreme control of atom-atom interactions that is made available by techniques based on scattering resonances such as a magnetic/optical Feshbach. We show that when the experimental parameters are fine tuned within a certain region of parameter space, the density of the bosonic atoms give a direct measure of the BCS gap associated with the fermions.   

Dynamics of a rotating, strongly interacting Fermi gas

We report on experimental studies on the dynamics of a rotating, strongly interacting Fermi gas of $^6$Li atoms confined in a harmonic trap. To detect the angular momentum of the gas we exploit the fact that the behavior of a collective quadrupole excitation depends on the rotation frequency of the gas. We measure the lifetime of the angular momentum for different temperatures and trap anisotropies. The measurements show the expected decrease of the lifetime with increasing trap anisotropy and are in very good agreement with recent theory.   

Diagrammatic Monte Carlo

Diagrammatic Monte Carlo (DiagMC) is a technique that allows one to simulate quantities specified in terms of diagrammatic expansions, the latter being a standard tool of many-body quantum statistics. The sign problem that is typically fatal to Monte Carlo approaches, appears to be manageable with DiagMC. We introduce a general DiagMC scheme, and present results for strongly interacting fermions (Hubbard model). This is the first example of a full-scale many-body problem being solved by diagrammatic Monte Carlo.   

Ferromagnetic coherence in ultracold fermions

The interactions between electrons in a metal give rise to itinerant ferromagnetism when the kinetic energy required to promote electrons from one spin state to the other is less than potential energy saved by putting electrons into the same, and thus non-interacting, state. An analogous phenomenon in a system of ultracold neutral fermions has been proposed [1], where the coherence of a superposition of two internal states is maintained against the effects of decoherence for strong repulsive interactions between the constituent states. Ultracold $^{40}$K atoms near a Feshbach resonance can be used to study this state. To perform this experiment, atoms are cooled sympathetically by $^{87}$Rb in a microchip trap, transferred to an optical dipole trap provided by a Nd:YAG laser at 1064 nm, and exposed to a magnetic field near ($201 \pm 6$) G. We have demonstrated state manipulation of $^{40}$K atoms with both radio- and microwaves and have seen the Feshbach resonance in collisional losses from the trap. We are working on a high stability magnetic field to allow for precise control of the interaction strength near the Feshbach resonance. [1] R.A. Duine and A.H. MacDonald, Phys. Rev. Lett. 95, 230403.