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

Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.

Fractional quantum Hall states of atoms in optical lattices

We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. In a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type, and we show how these states can be reached by melting a Mott-insulator state in a superlattice potential. Finally, we discuss techniques to observe these strongly correlated states.

Probing the excitation spectrum of a fermi gas in the BCS-BEC crossover regime

We measure excitation spectra of an ultracold gas of fermionic (40)K atoms in the BCS-Bose-Einstein-condensation (BEC) crossover regime. The measurements are performed with a novel spectroscopy that employs a small modulation of the B field close to a Feshbach resonance to give rise to a modulation of the interaction strength. With this method we observe both a collective excitation as well as the dissociation of fermionic atom pairs in the strongly interacting regime. The excitation spectra reveal the binding energy or excitation gap for pairs in the crossover region.

Heat Capacity of a Strongly Interacting Fermi Gas

We have measured the heat capacity of an optically trapped, strongly interacting Fermi gas of atoms. A precise addition of energy to the gas is followed by single-parameter thermometry, which determines the empirical temperature parameter of the gas cloud. Our measurements reveal a clear transition in the heat capacity. The energy and the spatial profile of the gas are computed using a theory of the crossover from Fermi to Bose superfluids at finite temperatures. The theory calibrates the empirical temperature parameter, yields excellent agreement with the data, and predicts the onset of superfluidity at the observed transition point.

Density profiles of strongly interacting trapped fermi gases

We study density profiles in trapped fermionic gases, near Feshbach resonances, at all T< or =Tc and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.

BCS-BEC crossover in a gas of Fermi atoms with a p-wave feshbach resonance

We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasimolecules with finite orbital angular momenta Lz=+/-1,0, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper pairs and molecules which are not Bose condensed.

Quantum mechanical investigation of rovibrational relaxation of H2 and D2 by collisions with Ar atoms

We report quantum mechanical calculations of cross sections and rate coefficients for rovibrational relaxation of H2 and D2 by collisions with Ar atoms over a wide range of temperatures including the ultracold limit. Limiting values of the rate coefficients for vibrational and rotational quenching at zero temperature were computed and sensitivity of the results to the choice of the interaction potential is investigated. We also demonstrate dramatic change in the behavior of the rate coefficients at low temperatures when the van der Waals potential supports a quasibound level very close to the dissociation threshold.

Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.

Collective modes and ballistic expansion of a fermi gas in the BCS-BEC crossover

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm nonmonotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast et al. [Phys. Rev. Lett. 92, 150402 (2004)]] and of the axial breathing mode by Bartenstein et al. [Phys. Rev. Lett. 92, 203201 (2004)]].

Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.

Molecular matter-wave amplifier

We describe a matter-wave amplifier for vibrational ground-state molecules which uses a Feshbach resonance to first form quasibound molecules starting from an atomic Bose-Einstein condensate. The quasibound molecules are then driven into their stable vibrational ground state via a two-photon Raman transition inside an optical cavity. The transition from the quasibound state to the electronically excited state is driven by a classical field. Amplification of ground state molecules is then achieved by using a strongly damped cavity mode for the transition from the electronically excited molecules to the molecular ground state.

Observation of Feshbach resonances between two different atomic species

We have observed three Feshbach resonances in collisions between 6Li and 23Na atoms. The resonances were identified as narrow loss features when the magnetic field was varied. The molecular states causing these resonances have been identified, and additional 6Li-23Na resonances are predicted. These resonances will allow the study of degenerate Bose-Fermi mixtures with adjustable interactions and could be used to generate ultracold heteronuclear molecules.

On the role of van der Waals interaction in chemical reactions at low temperatures

It is shown that van der Waals interaction potential plays a crucial role in chemical reactions at low temperatures. By taking the Cl+HD reaction as an illustrative example, we demonstrate that quasibound states of the van der Waals potential preferentially undergo chemical reaction rather than vibrational predissociation. Prereaction occurs even when the wave functions of the quasibound states peak far out into the entrance channel, outside the region of the van der Waals well. It is found that chemical reaction dominates over nonreactive vibrational quenching in collisions of vibrationally excited HD molecules with ground state chlorine atoms at ultracold temperatures.

Bose-Einstein condensation of particle-hole pairs in ultracold fermionic atoms trapped within optical lattices

We investigate the Bose-Einstein condensation (BEC, superfluidity) of particle-hole pairs in ultracold fermionic atoms with repulsive interactions and arbitrary polarization, which are trapped within optical lattices. In the strongly repulsive limit, the dynamics of particle-hole pairs can be described by a hard-core Bose-Hubbard model. The insulator-superfluid and charge-density-wave- (CDW) superfluid phase transitions can be induced by decreasing and increasing the potential depths with controlling the trapping laser intensity, respectively. The parameter and polarization dependence of the critical temperatures for the ordered states (BEC and/or CDW) are discussed simultaneously.

Pairing fluctuations in trapped fermi gases

We examine the contribution of pairing fluctuations to the superfluid order parameter for harmonically trapped atomic Fermi gases in the BCS regime. In the limit of small systems we consider, both analytically and numerically, their space and temperature dependence. We predict a parity effect, i.e., that pairing fluctuations show a maximum or a minimum at the center of the trap, depending on the value of the last occupied shell being even or odd. We propose to detect pairing fluctuations by measuring the density-density correlation function after a ballistic expansion of the gas.

Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover

Theoretical predictions for the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of 6Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean-field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.

Weakly bound dimers of fermionic atoms

We discuss the behavior of weakly bound bosonic dimers formed in a two-component cold Fermi gas at a large positive scattering length a for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing a. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.

Dilute Fermi gas in quasi-one-dimensional traps: from weakly interacting fermions via hard core bosons to a weakly interacting Bose gas

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size l(perpendicular). In the dilute limit (nl(perpendicular)<<1, where n is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF. When l(perpendicular)/aF goes from -infinity to +infinity, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at aF approximately +/-nl2(perpendicular). In conclusion, we discuss experimental implications of these results.

Pairing Gap and In-Gap Excitations in Trapped Fermionic Superfluids

We consider trapped atomic Fermi gases with Feshbach-resonance enhanced interactions in pseudogap and superfluid temperatures. We calculate the spectrum of radio-frequency (or laser) excitations for transitions that transfer atoms out of the superfluid state. The spectrum displays the pairing gap and also the contribution of unpaired atoms, that is, in-gap excitations. The results support the conclusion that a superfluid, in which pairing is a manybody effect, was observed in recent experiments on radio-frequency spectroscopy of the pairing gap.

Observation of the Pairing Gap in a Strongly Interacting Fermi Gas

We studied fermionic pairing in an ultracold two-component gas of 6Li atoms by observing an energy gap in the radio-frequency excitation spectra. With control of the two-body interactions through a Feshbach resonance, we demonstrated the dependence of the pairing gap on coupling strength, temperature, and Fermi energy. The appearance of an energy gap with moderate evaporative cooling suggests that our full evaporation brought the strongly interacting system deep into a superfluid state.

Experimental study of the BEC-BCS crossover region in lithium 6

We report Bose-Einstein condensation of weakly bound 6Li2 molecules in a crossed optical trap near a Feshbach resonance. We measure a molecule-molecule scattering length of 170(+100)(-60) nm at 770 G, in good agreement with theory. We study the 2D expansion of the cloud and show deviation from hydrodynamic behavior in the BEC-BCS crossover region.

Superfluidity of trapped dipolar fermi gases

We derive the phase diagram for ultracold trapped dipolar Fermi gases. Below the critical value of the dipole-dipole interaction energy, the BCS transition into a superfluid phase ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter exhibits a novel nonmonotonic behavior at the criticality.

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.

Collective excitations of a degenerate gas at the BEC-BCS crossover

We study collective excitation modes of a fermionic gas of (6)Li atoms in the BEC-BCS crossover regime. While measurements of the axial compression mode in the cigar-shaped trap close to a Feshbach resonance confirm theoretical expectations, the radial compression mode shows surprising features. In the strongly interacting molecular BEC regime, we observe a negative frequency shift with increasing coupling strength. In the regime of a strongly interacting Fermi gas, an abrupt change in the collective excitation frequency occurs, which may be a signature for a transition from a superfluid to a collisionless phase.

Condensation of pairs of fermionic atoms near a Feshbach resonance

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.