Ultracold Dipolar Gas of Fermionic 23^{23}Na40^{40}K Molecules in their Absolute Ground State

We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1\Sigma^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 Debye. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of $^{23}$Na$^{40}$K molecules is in experimental reach.Comment: 5 pages, 5 figure

Two-Photon Pathway to Ultracold Ground State Molecules of 23^{23}Na40^{40}K

We report on high-resolution spectroscopy of ultracold fermionic \nak~Feshbach molecules, and identify a two-photon pathway to the rovibrational singlet ground state via a resonantly mixed \Bcres intermediate state. Photoassociation in a $^{23}$Na-$^{40}$K atomic mixture and one-photon spectroscopy on \nak~Feshbach molecules reveal about 20 vibrational levels of the electronically excited \ctrip state. Two of these levels are found to be strongly perturbed by nearby \Bsing states via spin-orbit coupling, resulting in additional lines of dominant singlet character in the perturbed complex {${\rm B}^1\Pi |v{=}4\rangle {\sim} {\rm c}^3\Sigma^+ | v{=}25\rangle$}, or of resonantly mixed character in {${\rm B}^1\Pi | v{=}12 \rangle {\sim}{\rm c}^3\Sigma^+ | v{=}35 \rangle$}. The dominantly singlet level is used to locate the absolute rovibrational singlet ground state ${\rm X}^1\Sigma^+ | v{=}0, J{=}0 \rangle$ via Autler-Townes spectroscopy. We demonstrate coherent two-photon coupling via dark state spectroscopy between the predominantly triplet Feshbach molecular state and the singlet ground state. Its binding energy is measured to be 5212.0447(1) \cm, a thousand-fold improvement in accuracy compared to previous determinations. In their absolute singlet ground state, \nak~molecules are chemically stable under binary collisions and possess a large electric dipole moment of $2.72$ Debye. Our work thus paves the way towards the creation of strongly dipolar Fermi gases of NaK molecules.Comment: 23 pages, 8 figure

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

We have observed the superfluid phase transition in a strongly interacting Fermi gas via high-precision measurements of the local compressibility, density and pressure down to near-zero entropy. Our data completely determine the universal thermodynamics of strongly interacting fermions without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity. In particular, the heat capacity displays a characteristic lambda-like feature at the critical temperature of $T_c/T_F = 0.167(13)$. This is the first clear thermodynamic signature of the superfluid transition in a spin-balanced atomic Fermi gas. Our measurements provide a benchmark for many-body theories on strongly interacting fermions, relevant for problems ranging from high-temperature superconductivity to the equation of state of neutron stars.Comment: 11 pages, 8 figure

Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State

Whether it occurs in superconductors, helium-3 or inside a neutron star, fermionic superfluidity requires pairing of fermions, particles with half-integer spin. For an equal mixture of two states of fermions ("spin up" and "spin down"), pairing can be complete and the entire system will become superfluid. When the two populations of fermions are unequal, not every particle can find a partner. Will the system nevertheless stay superfluid? Here we study this intriguing question in an unequal mixture of strongly interacting ultracold fermionic atoms. The superfluid region vs population imbalance is mapped out by employing two complementary indicators: The presence or absence of vortices in a rotating mixture, as well as the fraction of condensed fermion pairs in the gas. Due to the strong interactions near a Feshbach resonance, the superfluid state is remarkably stable in response to population imbalance. The final breakdown of superfluidity marks a new quantum phase transition, the Pauli limit of superfluidity.Comment: 15 pages, 5 figure

Direct Observation of the Superfluid Phase Transition in Ultracold Fermi Gases

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)%.Comment: 16 pages (incl. Supplemental Material), 5 figure

Particle correlations in a fermi superfluid

We discuss correlations between particles of different momentum in a superfluid fermi gas, accessible through noise measurements of absorption images of the expanded gas. We include two elements missing from the simplest treatment, based on the BCS wavefunction: the explicit use of a conserving approximation satisfying particle number conservation, and the inclusion of the contribution from Cooper pairs at finite momentum. We expect the latter to be a significant issue in the strongly correlated state emerging in the BCS-BEC crossover.Comment: Published versio

Pairing without Superfluidity: The Ground State of an Imbalanced Fermi Mixture

Radio-frequency spectroscopy is used 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 is observed. This demonstrates that 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

Superfluidity in a Three-flavor Fermi Gas with SU(3) Symmetry

We investigate the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with SU(3) global symmetry. The s-wave pairing occurs in flavor anti-triplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the SU(3) symmetry to a SU(2) symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law and the mass gap have significant effect on the low temperature thermodynamics of the matter.Comment: 9 pages, 2 figures, published versio

Coherent Microwave Control of Ultracold 23^{23}Na40^{40}K Molecules

We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable $^{23}$Na$^{40}$K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, $J{=}1$, we observe collisional lifetimes of more than $3\, \rm s$, comparable to those in the rovibrational ground state, $J{=}0$. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements and quantum information processing.Comment: 5 pages, 4 figure

Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems

When cold atoms are trapped in a square or cubic optical lattice, it should be possible to pump the atoms into excited $p-$level orbitals within each well. Following earlier work, we explore the metastable equilibrium that can be established before the atoms decay into the $s-$wave orbital ground state. We will discuss the situation with integer number of bosons on every site, and consider the strong correlation "insulating" regime. By employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". The gapless nature of this phase is stabilized due to the emergence of symmetries which lead to a quasi-one dimensional behavior. Within the algebraic liquid phase, both bond operators and particle flavor occupation number operators have correlations which decay algebraically in space and time. Upon varying parameters, the algebraic bond liquid can be unstable to either a Mott insulator phase which spontaneously breaks lattice symmetries, or a $\mathbb{Z}_2$ phase. The possibility of detecting the algebraic liquid phase in cold atom experiments is addressed. Although the momentum distribution function is insufficient to distinguish the algebraic bond liquid from other phases, the density correlation function can in principle be used to detect this new phase of matter.Comment: 15 pages, 10 figure