Lifetime of molecule-atom mixtures near a Feshbach resonance in 40K

A generalized molecule approach capturing the Feshbach-induced pairing physics in the BEC-BCS crossover

By including the effect of a trap with characteristic energy given by the Fermi temperatureT_Fin a two-body two-channel model for Feshbach resonances, we reproduce the measured binding energy of ultracold molecules in a⁴⁰K atomic Fermi gas. We also reproduce the experimental closed-channel fractionZacross the BEC-BCS crossover and into the BCS regime of a⁶Li atomic Fermi gas. We obtain the expected behaviorZ∝TFat unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of theZdependency onT_Fon the BCS side, where a significant quantitative discrepancy between experimental data and theory's predictions has been repeatedly reported. In order to contrast with future experiments we report the proportionality constant at unitarity betweenZandTFpredicted by our model for a⁴⁰K atomic Fermi gas.

Resonantly Interacting Fermi-Fermi Mixture of ^{161}Dy and ^{40}K

We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of ^{161}Dy and ^{40}K, we identify a broad Feshbach resonance centered at a magnetic field of 217 G. Hydrodynamic expansion profiles in the resonant interaction regime reveal a bimodal behavior resulting from mass imbalance. Lifetime studies on resonance show a suppression of inelastic few-body processes by orders of magnitude, which we interpret as a consequence of the fermionic nature of our system. The resonant mixture opens up intriguing perspectives for studies on novel states of strongly correlated fermions with mass imbalance.

Thermalization and Sub-Poissonian Density Fluctuations in a Degenerate Molecular Fermi Gas

We observe thermalization in the production of a degenerate Fermi gas of polar ^{40}K^{87}Rb molecules. By measuring the atom-dimer elastic scattering cross section near the Feshbach resonance, we show that Feshbach molecules rapidly reach thermal equilibrium with both parent atomic species. Equilibrium is essentially maintained through coherent transfer to the ground state. Sub-Poissonian density fluctuations in Feshbach and ground-state molecules are measured, giving an independent characterization of degeneracy and directly probing the molecular Fermi-Dirac distribution.

Cluster Formation in Two-Component Fermi Gases

Two-component fermions are known to behave like a gas of molecules in the limit of Bose-Einstein condensation of diatomic pairs tightly bound with zero-range interactions. We discover that the formation of cluster states occurs when the effective range of two-body interaction exceeds roughly 0.46 times the scattering length, regardless of the details of the short-range interaction. Using an explicitly correlated Gaussian basis set expansion approach, we calculate the binding energy of cluster states in trapped few-body systems and show the difference of structural properties between cluster states and gaslike states. We identify the condition for cluster formation and discuss the potential observation of cluster states in experiments.

Realization of a Strongly Interacting Fermi Gas of Dipolar Atoms

We realize a two-component dipolar Fermi gas with tunable interactions, using erbium atoms. Employing a lattice-protection technique, we selectively prepare deeply degenerate mixtures of the two lowest spin states and perform high-resolution Feshbach spectroscopy in an optical dipole trap. We identify a comparatively broad Feshbach resonance and map the interspin scattering length in its vicinity. The Fermi mixture shows a remarkable collisional stability in the strongly interacting regime, providing a first step towards studies of superfluid pairing, crossing from Cooper pairs to bound molecules, in presence of dipole-dipole interactions.

Realizing Fulde-Ferrell Superfluids via a Dark-State Control of Feshbach Resonances

We propose that the long-sought Fulde-Ferrell superfluidity with nonzero momentum pairing can be realized in ultracold two-component Fermi gases of ^{40}K or ^{6}Li atoms by optically tuning their magnetic Feshbach resonances via the creation of a closed-channel dark state with a Doppler-shifted Stark effect. In this scheme, two counterpropagating optical fields are applied to couple two molecular states in the closed channel to an excited molecular state, leading to a significant violation of Galilean invariance in the dark-state regime and hence to the possibility of Fulde-Ferrell superfluidity. We develop a field theoretical formulation for both two-body and many-body problems and predict that the Fulde-Ferrell state has remarkable properties, such as anisotropic single-particle dispersion relation, suppressed superfluid density at zero temperature, anisotropic sound velocity, and rotonic collective mode. The latter two features can be experimentally probed using Bragg spectroscopy, providing a smoking-gun proof of Fulde-Ferrell superfluidity.

Inelastic collisions of ultracold triplet Rb2 molecules in the rovibrational ground state

Exploring and controlling inelastic and reactive collisions on the quantum level is a main goal of the developing field of ultracold chemistry. For this, the preparation of precisely defined initial atomic and molecular states in tailored environments is necessary. Here we present experimental studies of inelastic collisions of metastable ultracold Rb₂ molecules in an array of quasi-1D potential tubes. In particular, we investigate collisions of molecules in the absolute lowest triplet energy level where any inelastic process requires a change of the electronic state. Remarkably, we find similar decay rates as for collisions between rotationally or vibrationally excited triplet molecules where other decay paths are also available. The decay rates are close to the ones for universal reactions but vary considerably when confinement and collision energy are changed. This might be exploited to control the collisional properties of molecules.

Investigating the collisional behaviour of molecules on the quantum level is the key in understanding and controlling chemical reactions. Here the authors measure inelastic collision rates for ultracold Rb₂ dimers in precisely defined quantum states and show that the rates can be tuned via external parameters.

Observation of an Orbital Interaction-Induced Feshbach Resonance in (173)Yb

We report on the experimental observation of a novel interorbital Feshbach resonance in ultracold (173)Yb atoms. This opens up the possibility of tuning the interactions between the (1)S(0) and (3)P(0) metastable state, both possessing zero total electronic angular momentum. The resonance is observed at experimentally accessible magnetic field strengths and occurs universally for all hyperfine state combinations. We characterize the resonance in the bulk via interorbital cross thermalization as well as in a three-dimensional lattice using high-resolution clock-line spectroscopy. Our measurements are well described by a generalized two-channel model of the orbital-exchange interactions.

Critical Velocity and Dissipation of an Ultracold Bose-Fermi Counterflow

We study the dynamics of counterflowing bosonic and fermionic lithium atoms. First, by tuning the interaction strength we measure the critical velocity v(c) of the system in the BEC-BCS crossover in the low temperature regime and we compare it to the recent prediction of Castin et al., C. R. Phys. 16, 241 (2015). Second, raising the temperature of the mixture slightly above the superfluid transitions reveals an unexpected phase locking of the oscillations of the clouds induced by dissipation.

Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems

We demonstrate that dynamical probes provide direct means of detecting the topological phase transition (TPT) between conventional and topological phases, which would otherwise be difficult to access because of loss or heating processes. We propose to avoid such heating by rapidly quenching in and out of the short-lived topological phase across the transition that supports gapless excitations. Following the quench, the distribution of excitations in the final conventional phase carries signatures of the TPT. We apply this strategy to study the TPT into a Majorana-carrying topological phase predicted in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. The resulting spin-resolved momentum distribution, computed by self-consistently solving the time-dependent Bogoliubov-de Gennes equations, exhibits Kibble-Zurek scaling and Stückelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.

Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions--the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.

Deviation from universality in collisions of ultracold 6Li2 molecules

Collisions of 6Li2 molecules with free 6Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li2 closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance and decay via two-body collisions with Li2, Li, and Na. For Li2 + Li2 and Li2 + Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li2 + Li is exceptionally small, with an upper bound 10 times smaller than the universal prediction. This can be explained by the low density of available decay states in systems of light atoms [G. Quéméner, J.-M. Launay, and P. Honvault, Phys. Rev. A 75, 050701 (2007)], for which such collisions have not been studied before.

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

Verification of universal relations in a strongly interacting Fermi gas

Many-body fermion systems are important in many branches of physics, including condensed matter, nuclear, and now cold atom physics. In many cases, the interactions between fermions can be approximated by a contact interaction. A recent theoretical advance in the study of these systems is the derivation of a number of exact universal relations that are predicted to be valid for all interaction strengths, temperatures, and spin compositions. These equations, referred to as the Tan relations, relate a microscopic quantity, namely, the amplitude of the high-momentum tail of the fermion momentum distribution, to the thermodynamics of the many-body system. In this work, we provide experimental verification of the Tan relations in a strongly interacting gas of fermionic atoms by measuring both the microscopic and macroscopic quantities in the same system.

Broad Feshbach resonance in the 6Li-40K mixture

We study the widths of interspecies Feshbach resonances in a mixture of the fermionic quantum gases 6Li and 40K. We develop a model to calculate the width and position of all available Feshbach resonances for a system. Using the model, we select the optimal resonance to study the {6}Li/{40}K mixture. Experimentally, we obtain the asymmetric Fano line shape of the interspecies elastic cross section by measuring the distillation rate of 6Li atoms from a potassium-rich 6Li/{40}K mixture as a function of magnetic field. This provides us with the first experimental determination of the width of a resonance in this mixture, DeltaB=1.5(5) G. Our results offer good perspectives for the observation of universal crossover physics using this mass-imbalanced fermionic mixture.

Independent control of scattering lengths in multicomponent quantum gases

We develop a method of simultaneous and independent control of different scattering lengths in ultracold atomic gases, such as ;{40}K or a ;{40}K-;{6}Li mixture. Our method can be used to engineer multicomponent quantum phases and Efimov trimer states.

Inelastic collisions of a Fermi gas in the BEC-BCS crossover

We measure inelastic three-body and two-body collisional decay rates for a two-component Fermi gas of 6Li, which are highly suppressed by the Pauli exclusion principle. Our measurements are made in the BEC-BCS crossover regime, near the two-body collisional (Feshbach) resonance. At high temperature (energy) the data show a dominant three-body decay process, which is studied as a function of bias magnetic field. At low energy, the data show a coexistence of two-body and three-body decay processes near and below the Feshbach resonance. Below resonance, the observed two-body inelastic decay can arise from molecule-atom and molecule-molecule collisions. We suggest that at and above resonance, an effective two-body decay rate arises from collisions between atoms and correlated (Cooper) pairs that can exist at sufficiently low temperature.

Ultracold heteronuclear fermi-fermi molecules

We report on the first creation of ultracold bosonic heteronuclear molecules of two fermionic species, 6Li and 40K, by a magnetic field sweep across an interspecies s-wave Feshbach resonance. This allows us to associate up to 4x10(4) molecules with high efficiencies of up to 50%. Using direct imaging of the molecules, we measure increased lifetimes of the molecules close to resonance of more than 100 ms in the molecule-atom mixture stored in a harmonic trap.

Suppression of molecular decay in ultracold gases without Fermi statistics

We study inelastic processes for ultracold three-body systems in which only one interaction is resonant. We show that at ultracold temperatures three-body recombination in such systems leads mainly to the formation of weakly bound molecules. In addition, and perhaps more importantly, we have found that the decay rates for weakly bound molecules due to collisions with other atoms can be suppressed not only without fermionic statistics but also when bosonic statistics applies. These results indicate that recombination in three-component atomic gases can be used as an efficient mechanism for molecular formation, allowing the achievement of high molecular densities.

Quantum degenerate two-species fermi-fermi mixture coexisting with a bose-einstein condensate

We report on the generation of a quantum degenerate Fermi-Fermi mixture of two different atomic species. The quantum degenerate mixture is realized employing sympathetic cooling of fermionic 6Li and 40K gases by an evaporatively cooled bosonic 87Rb gas. We describe the combination of trapping and cooling methods that proved crucial to successfully cool the mixture. In particular, we study the last part of the cooling process and show that the efficiency of sympathetic cooling of the 6Li gas by 87Rb is increased by the presence of 40K through catalytic cooling. Because of the differing physical properties of the two components, the quantum degenerate 6Li-40K Fermi-Fermi mixture is an excellent candidate for a stable, heteronuclear system allowing the study of several so far unexplored types of quantum matter.

Interactions and dynamics in Li+Li2 ultracold collisions

A potential energy surface for the lowest quartet electronic state ((4)A(')) of lithium trimer is developed and used to study spin-polarized Li+Li(2) collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li(2). Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.

p-Wave Feshbach molecules

We have produced and detected molecules using a p-wave Feshbach resonance between 40K atoms. We have measured the binding energy and lifetime for these molecules and we find that the binding energy scales approximately linearly with the magnetic field near the resonance. The lifetime of bound p-wave molecules is measured to be 1.0+/-0.1 ms and 2.3+/-0.2 ms for the ml=+/-1 and ml=0 angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasibound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier.

Three-fermion problems in optical lattices

We present exact results for the spectra of three fermionic atoms in a single well of an optical lattice. For the three lowest hyperfine states of 6Li atoms, we find a Borromean state across the region of the distinct pairwise Feshbach resonances. For 40K atoms, nearby Feshbach resonances are known for two of the pairs, and a bound three-body state develops towards the positive scattering-length side. In addition, we study the sensitivity of our results to atomic details. The predicted few-body phenomena can be realized in optical lattices in the limit of low tunneling.

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.

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.

Molecules of fermionic atoms in an optical lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.

Atom-molecule collisions in an optically trapped gas

Cold inelastic collisions between confined cesium (Cs) atoms and Cs2 molecules are investigated inside a CO2 laser dipole trap. Inelastic atom-molecule collisions can be observed and measured with a rate coefficient of approximately 2.6 x 10(-11) cm3 s(-1), mainly independent of the molecular rovibrational state populated. Lifetimes of purely atomic and molecular samples are essentially limited by rest gas collisions. The pure molecular trap lifetime ranges 0.3-1 s, 4 times smaller than the atomic one, as is also observed in a pure magnetic trap. We give an estimation of the inelastic molecule-molecule collision rate to be approximately 10(-11) cm3 s(-1).

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.

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.

Confinement induced molecules in a 1D Fermi gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.

Production efficiency of ultracold feshbach molecules in bosonic and fermionic systems

We investigate the production efficiency of ultracold molecules in bosonic 85Rb and fermionic 40K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the 85Rb molecule conversion efficiency follow a Landau-Zener model.

Ultracold Li + Li2 collisions: bosonic and fermionic cases

We have carried out quantum dynamical calculations of vibrational quenching in Li + Li(2) collisions for both bosonic (7)Li and fermionic (6)Li. These are the first ever such calculations involving fermionic atoms. We find that for the low initial vibrational states considered here (v < or = 3), the quenching rates are not suppressed for fermionic atoms. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.

Spontaneous dissociation of 85Rb Feshbach molecules

The spontaneous dissociation of 85Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance that was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by 3 orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation. Molecule lifetimes of tens of milliseconds can be achieved within approximately a 1 G wide region directly above the Feshbach resonance.

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.

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.

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.

Emergence of a molecular Bose–Einstein condensate from a Fermi gas

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen-Cooper-Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose-Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose-Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS-BEC continuum.