Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas

Theory for p-wave Feshbach molecules

We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.

Superfluidity and magnetism in multicomponent ultracold fermions

We study the interplay between superfluidity and magnetism in a multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain possible mean-field states describing order parameters for both pairing and magnetization. The structure of global phase diagrams arises from competition among these states as functions of anisotropies in chemical potential, density, or interactions. They exhibit first and second order phase transition as well as multicritical points, metastability regions, and phase separation. We comment on experimental signatures in ultracold atoms.

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.

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.

Trapped fermionic clouds distorted from the trap shape due to many-body effects

We present a general approach for describing trapped Fermi gases, when the cloud shape is distorted with respect to the trap shape. Our approach provides a consistent way to explore physics beyond the local density approximation, if this is necessary due to the distortion. We illustrate this by analyzing in detail experimentally observed distortions in a trapped imbalanced Fermi mixture. In particular, we demonstrate in that case dramatic deviations from ellipsoidal cloud shapes arising from the competition between surface and bulk energies.

Color superfluidity and "baryon" formation in ultracold fermions

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.

Precision measurements of collective oscillations in the BEC-BCS crossover

We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of (6)Li atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting Bose-Einstein condensation (BEC) regime.

Degenerate Fermi gases of ytterbium

Evaporative cooling was performed to cool fermionic 173Yb atoms in a crossed optical dipole trap. The large elastic collision rate leads to efficient evaporation and we have successfully cooled the atoms to 0.37+/-0.06 of the Fermi temperature, that is to say, to a quantum degenerate regime. In this regime, a plunge of evaporation efficiency was observed as a result of Fermi degeneracy.

Vanishing bulk viscosities and conformal invariance of the unitary fermi gas

By requiring general-coordinate and conformal invariance of the hydrodynamic equations, we show that the unitary Fermi gas has zero bulk viscosity, zeta=0, in the normal phase. In the superfluid phase, two of the bulk viscosities have to vanish, zeta1=zeta2=0, while the third one zeta3 is allowed to be nonzero.

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half filling, a quantum critical point between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the quantum critical point at half filling. For a range of densities around half filling, the "underlying Fermi surface" of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which changes nonmonotonically with interaction. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. Finally, we consider possible implications for ultracold atoms in optical lattices and the high temperature SCs.

Potential energy of a 40K Fermi gas in the BCS-BEC crossover

We present a measurement of the potential energy of an ultracold trapped gas of 40K atoms in the BCS-BEC crossover and investigate the temperature dependence of this energy at a wide Feshbach resonance, where the gas is in the unitarity limit. In particular, we study the ratio of the potential energy in the region of the unitarity limit to that of a noninteracting gas, and in the T=0 limit we extract the universal many-body parameter beta. We find beta=-0.54_{-0.12};{+0.05}; this value is consistent with previous measurements using 6Li atoms and also with recent theory and Monte Carlo calculations. This result demonstrates the universality of ultracold Fermi gases in the strongly interacting regime.

Unitary quantum three-body problem in a harmonic trap

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short-range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.

Tuning of heteronuclear interactions in a degenerate Fermi-Bose mixture

We demonstrate tuning of interactions between fermionic 40K and bosonic 87Rb atoms by Feshbach resonances and access the complete phase diagram of the harmonically trapped mixture from phase separation to collapse. On the attractive side of the resonance, we observe a strongly enhanced mean-field energy of the condensate due to the mutual mean-field confinement, predicted by a Thomas-Fermi model. As we increase heteronuclear interactions beyond a threshold, we observe an induced collapse of the mixture. On the repulsive side of the resonance, we observe vertical phase separation of the mixture in the presence of the gravitational force, thus entering a completely unexplored part of the phase diagram of the mixture. In addition, we identify the 515 G resonance as p wave by its characteristic doublet structure.

Two-species fermion mixtures with population imbalance

We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space regions of zero quasiparticle energies. Lastly, near the critical temperature, we derive the Ginzburg-Landau equation and show that it describes a dilute mixture of composite bosons and unpaired fermions in the BEC limit.

E expansion for a Fermi gas at infinite scattering length

We show that there exists a systematic expansion around four spatial dimensions for Fermi gas in the unitarity regime. We perform the calculations to leading and next-to-leading orders in the expansion over E = 4-d, where d is the dimensionality of space. We find the ratio of chemical potential and Fermi energy to be mu/epsilon(F) =1/2 (E 3/2) + 1/16 (E 5/2) lnE -0.0246E (5/2) + ... and the ratio of the gap in the fermion quasiparticle spectrum and the chemical potential to be Delta/mu =2E(-1) - 0.691 + ... . The minimum of the fermion dispersion curve is located at |p|=(2mepsilon(0))(1/2), where epsilon_(0)/mu=2+O(E). Extrapolation to d=3 gives results consistent with Monte Carlo simulations.

Direct observation of the superfluid phase transition in ultracold Fermi gases

Phase transitions are dramatic phenomena: water freezes into ice, atomic spins spontaneously align in a magnet, and liquid helium becomes superfluid. Sometimes, such a drastic change in behaviour is accompanied by a visible change in appearance. The hallmark of Bose-Einstein condensation and superfluidity in trapped, weakly interacting Bose gases is the sudden formation of a dense central core inside a thermal cloud. However, in strongly interacting gases--such as the recently observed fermionic superfluids--there is no longer a clear separation between the superfluid and the normal parts of the cloud. The detection of fermion pair condensates has required magnetic field sweeps into the weakly interacting regime, and the quantitative description of these sweeps presents a major theoretical challenge. Here we report the direct observation of the superfluid phase transition in a strongly interacting gas of 6Li fermions, through 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 distribution of non-interacting excess atoms serves 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 that drive the normal-to-superfluid transition at the critical population imbalance of 70 +/- 5 per cent (ref. 12).

Localization of bosonic atoms by fermionic impurities in a three-dimensional optical lattice

We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular, we study the dependence of this transition on the fermionic (40)K impurity concentration by a comparison to the corresponding superfluid to Mott-insulator transition in a pure bosonic (87)Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a simple mean-field argument, which indicates that disorder-related effects play a significant role.

Critical temperature and thermodynamics of attractive fermions at unitarity

The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of two-component lattice fermions with an on-site attractive interaction. We perform a systematic-error-free finite-temperature simulation of this system by diagrammatic determinant Monte Carlo method. The critical temperature in units of Fermi energy is found to be T(C)/epsilonF=0.152(7). We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.

Bose-Einstein condensation with an entangled order parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation, which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single-particle orbital wave function. Experimental feasibility and several methods of probe are discussed. We urge the study of multichannel scattering between different species of atoms.

Density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations

We present a theoretical study of the density profile of a trapped strongly interacting Fermi gas with unbalanced spin populations. Making the assumption of the existence of a first order phase transition between an unpolarized superfluid phase and a fully polarized normal phase, we show good agreement with a recent experiment presented by Partridge et al.

Spin 1/2 fermions in the unitary regime: a superfluid of a new type

We study, in a fully nonperturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction are calculated and we also determine the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid.

Vortex-antivortex lattice in ultracold fermionic gases

We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.

Pairing and Phase Separation in a Polarized Fermi Gas

We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.

Dressed Feshbach molecules in the BEC-BCS crossover

We present the random phase approximation (RPA) theory of the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge et al. [95, 020404 (2005)10.1103/PhysRevLett.95.020404] with , who have measured the same quantity.

Momentum distribution of a Fermi gas of atoms in the BCS-BEC crossover

We observe dramatic changes in the atomic momentum distribution of a Fermi gas in the crossover region between the BCS theory superconductivity and Bose-Einstein condensation (BEC) of molecules. We study the shape of the momentum distribution and the kinetic energy as a function of interaction strength. The momentum distributions are compared to a mean-field crossover theory, and the kinetic energy is compared to theories for the two weakly interacting limits. This measurement provides a unique probe of pairing in a strongly interacting Fermi gas.

Momentum distribution and condensate fraction of a fermion gas in the BCS-BEC crossover

By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

Ab initio calculation of the NH(Σ−3)−NH(Σ−3) interaction potentials in the quintet, triplet, and singlet states

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.

Ultracold molecule production via a resonant oscillating magnetic field

A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases

We report on the observation of sympathetic cooling of a cloud of fermionic 6Li atoms which are thermally coupled to evaporatively cooled bosonic 87Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud is colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |amx|=20(+9)(-6)aB. We found that the presence of residual rubidium atoms in the |2, 1> and the |1, -1> Zeeman substates gives rise to important losses due to inelastic collisions.

Resonant fermi gases with a large effective range

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.002 fm(-3) < rho < 0.02 fm(-3), for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.

Reactivity enhancement of ultracold O(P3)+H2 collisions by van der Waals interactions

The role of van der Waals forces in O((3)P)+H(2)(upsilon=1,j=0) collisions is investigated theoretically at low and ultralow temperatures. Quantum scattering calculations have been performed for zero total angular momentum using the lowest London-Eyring-Polanyi-Sato double-polynomial (3)A(") potential-energy surface reported by [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)] and its recent BMS1 and BMS2 extensions developed by [Brandao et al., J. Chem. Phys. 121, 8861 (2004)] which provide a more accurate treatment of the van der Waals interaction. Our calculations show that van der Waals forces strongly influence chemical reactivity at ultracold translational energies. The presence of a zero-energy resonance for the BMS1 surface is found to enhance reactivity in the ultracold regime and shift the Wigner threshold to lower temperatures.

Specific heat of a fermionic atomic cloud in the unitary regime

In the unitary regime, when the scattering amplitude greatly exceeds in magnitude the average interparticle separation, and below the critical temperature thermal properties of an atomic fermionic cloud are governed by the collective modes, specifically the Bogoliubov-Anderson sound modes. The specific heat of an atomic cloud in an elongated trap, in particular, has a rather complex temperature dependence, which changes from an exponential behavior at very low temperatures (T << h omega(parallel)), to proportional T for h omega(parallel) << T << h omega(perpendicular) and then continuously to proportional T4 at temperatures just below the critical temperature, when the surface modes play a dominant role. Only the low (h omega(parallel) << T << h omega(perpendicular)) and high (h omega(perpendicular) << T << T(c)) temperature power laws are well defined. For the intermediate temperatures one can introduce at most a gradually increasing with temperature exponent.

Virial theorem and universality in a unitary fermi gas

Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.

Ultracold two-component fermionic gases with a magnetic field gradient near a feshbach resonance

We study theoretically the ultracold two-component fermionic gases when a gradient magnetic field is used to tune the scattering length between atoms. For 6Li at the narrow resonance B0=543.25 G, it is shown that the gases would be in a coexistence of the regimes of BCS, Bose-Einstein condensation (BEC), and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC, and unitarity limit.

Dynamic projection on feshbach molecules: a probe of pairing and phase fluctuations

We describe and justify a simple model for the dynamics associated with rapid sweeps across a Feshbach resonance, from the atomic to the molecular side, in an ultracold Fermi system. The model allows us to relate the observed molecule momentum distribution to equilibrium properties of the initial state. In particular, the dependence of the total molecule number on the sweep rate is found to be a sensitive probe of pairing in the initial state, whether condensed or not. This can be used to establish the presence of a phase fluctuation induced "pseudogap" phase in these systems.

Density and spin response functions in ultracold fermionic atom gases

We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin-response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the normal-ordered part of the density response function signals the transition between a BEC and a BCS regime, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC-to-BCS crossover. Spin rotational symmetry breaking due to the magnetic field, if observed, can be used to validate the one-channel model.

Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length a(aa) displays a confinement-induced resonance. We compute the dimer-dimer scattering length a(dd) and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.

Anisotropic Fermi superfluid via p-wave Feshbach resonance

We investigate theoretically fermionic superfluidity induced by Feshbach resonance in the orbital p-wave channel and determine the general phase diagram. In contrast with superfluid (3)He, due to the dipole interaction, the pairing is extremely anisotropic. When this dipole interaction is relatively strong, the pairing has symmetry k(z). When it is relatively weak, it is of symmetry k(z) + ibetak(y) (up to a rotation about z;, here beta < 1). A phase transition between these two states can occur under a change in the magnetic field or the density of the gas.

Asymmetric two-component Fermion systems in strong coupling

We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.

Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover

We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean-field BCS theory and of recent Monte Carlo calculations, are discussed in detail.

Molecular probe of pairing in the BEC-BCS crossover

We have used optical molecular spectroscopy to probe the many-body state of paired 6Li atoms near a broad Feshbach resonance. The optical probe projects pairs of atoms onto a vibrational level of an excited molecule. The rate of excitation enables a precise measurement of the closed-channel contribution to the paired state. This contribution is found to be quite small, supporting the concept of universality for the description of broad Feshbach resonances. The dynamics of the excitation provide clear evidence for pairing across the BEC-BCS crossover and into the weakly interacting BCS regime.

Quantum phase transitions across a p-wave Feshbach resonance

We study a single-species polarized Fermi gas tuned across a narrow p-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a px-wave to a px+ipy-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological px+ipy to px+ipy transition at zero chemical potential mu. In two dimensions, for mu > 0 it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

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.

Calculation of accurate permanent dipole moments of the lowest Σ+1,3 states of heteronuclear alkali dimers using extended basis sets

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction.

Quantum dynamics of the Li+HF→H+LiF reaction at ultralow temperatures

Quantum-mechanical calculations are reported for the Li+HF(v=0,1,j=0)-->H+LiF(v',j') bimolecular scattering process at low and ultralow temperatures. Calculations have been performed for zero total angular momentum using a recent high-accuracy potential-energy surface for the X2A' electronic ground state. For Li+HF(v=0,j=0), the reaction is dominated by resonances due to the decay of metastable states of the Li cdots,...F-H van der Waals complex. Assignment of these resonances has been carried out by calculating the eigenenergies of the quasibound states. We also find that while chemical reactivity is greatly enhanced by vibrational excitation, the resonances get mostly washed out in the reaction of vibrationally excited HF with Li atoms. In addition, we find that at low energies, the reaction is significantly suppressed due to the less-efficient tunneling of the relatively heavy fluorine atom.

Observation of Feshbach-like resonances in collisions between ultracold molecules

We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level crossing which allows us to transfer the molecules into another state. In the new state, two Feshbach-like collision resonances show up as strong inelastic loss features. We interpret these resonances as being induced by Cs4 bound states near the molecular scattering continuum. The tunability of the interactions between molecules opens up novel applications such as controlled chemical reactions and synthesis of ultracold complex molecules.

Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules

We employ radio-frequency spectroscopy on weakly bound (6)Li(2) molecules to precisely determine the molecular binding energies and the energy splittings between molecular states for different magnetic fields. These measurements allow us to extract the interaction parameters of ultracold (6)Li atoms based on a multichannel quantum scattering model. We determine the singlet and triplet scattering lengths to be a(s) = 45.167(8)a(0) and a(t) = -2140(18)a(0) (1a(0) = 0.052 917 7 nm), and the positions of the broad Feshbach resonances in the energetically lowest three s-wave scattering channels to be 83.41(15), 69.04(5), and 81.12(10) mT.

Number statistics of molecules formed from ultracold atoms

We calculate the number statistics of a single-mode molecular field excited by photo-association or via a Feshbach resonance from an atomic Bose-Einstein condensate (BEC), a normal atomic Fermi gas, and a Fermi system with pair correlations (BCS state). We find that the molecule formation from a BEC leads for short times to a coherent molecular state in the quantum optical sense. Atoms in a normal Fermi gas, on the other hand, result for short times in a molecular field analog of a classical chaotic light source. The BCS situation is intermediate between the two and goes from producing an incoherent to a coherent molecular field with an increasing gap parameter. This distinct signature of the initial atomic state in the resulting molecular field makes single molecule counting into a powerful diagnostic tool.