Bose-Einstein Condensation of Molecules

Majorana fermions in equilibrium and in driven cold-atom quantum wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.

Crossover from 2D to 3D in a weakly interacting Fermi gas

We have studied the transition from two to three dimensions in a low temperature weakly interacting 6Li Fermi gas. Below a critical atom number N(2D) only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above N(2D) the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

Note: A helical velocity selector for continuous molecular beams

We report on a modern realization of the classic helical velocity selector for gas phase particle beams. The device operates stably under high vacuum conditions at rotational frequencies limited only by commercial dc motor capabilities. Tuning the rotational frequency allows selective scanning over a broad velocity band. The width of the selected velocity distributions at full-width-half-maximum is as narrow as a few percent of the selected mean velocity and independent of the rotational speed of the selector. The selector generates low vibrational noise amplitudes comparable to mechanically damped state-of-the-art turbo-molecular pumps and is therefore compatible with vibration sensitive experiments like molecule interferometry.

s-Wave interaction in a two-species Fermi-Fermi mixture at a narrow Feshbach resonance

We investigate s-wave interactions in a two-species Fermi-Fermi mixture of 6Li and 40K. We develop for this case the method of cross-dimensional relaxation and find from a kinetic model, Monte Carlo simulations, and measurements that the individual relaxation rates differ due to the mass difference. The method is applied to measure the elastic cross section at the Feshbach resonance that we previously used for the production of heteronuclear molecules. Location (B0=155.09(5)  G) and width are determined for this resonance. This reveals that molecules are being produced on the atomic side of the resonance within a range related to the Fermi energies, therefore establishing the first observation of a many body effect in the crossover regime of a narrow Feshbach resonance.

Universal behavior of pair correlations in a strongly interacting Fermi gas

We show that short-range pair correlations in a strongly interacting Fermi gas follow a simple universal law described by Tan's relations. This is achieved through measurements of the static structure factor which displays a universal scaling proportional to the ratio of Tan's contact to the momentum C/q. Bragg spectroscopy of ultracold 6Li atoms from a periodic optical potential is used to measure the structure factor for a wide range of momenta and interaction strengths, providing broad confirmation of this universal law. We calibrate our Bragg spectra using the f-sum rule, which is found to improve the accuracy of the structure factor measurement.

Local observation of antibunching in a trapped Fermi gas

Local density fluctuations and density profiles of a Fermi gas are measured in situ and analyzed. In the quantum degenerate regime, the weakly interacting 6Li gas shows a suppression of the density fluctuations compared to the nondegenerate case, where atomic shot noise is observed. This manifestation of antibunching is a direct result of the Pauli principle and constitutes a local probe of quantum degeneracy. We analyze our data using the predictions of the fluctuation-dissipation theorem and the local density approximation, demonstrating a fluctuation-based temperature measurement.

Observation of a two-dimensional fermi gas of atoms

We have prepared a degenerate gas of fermionic atoms which move in two dimensions while the motion in the third dimension is "frozen" by tight confinement and low temperature. In situ imaging provides direct measurement of the density profile and temperature. The gas is confined in a defect-free optical potential, and the interactions are widely tunable by means of a Fano-Feshbach resonance. This system can be a starting point for exploration of 2D Fermi physics and critical phenomena in a pure, controllable environment.

Decay of polarons and molecules in a strongly polarized Fermi gas

The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.

A pump-probe study of the photoassociation of cold rubidium molecules

The dynamics of the excited state during the photoassociation of cold molecules from cold rubidium atoms is studied in a series of pump-probe experiments. Dipole transitions similar to those of the atoms are observed in the molecular signal. While such behaviour is characteristic of the long-range molecules, the photoassociation of bound molecules is confirmed in additional experiments. The pump-probe signal observed on a 250 ps time scale did not, however, reveal wavepacket oscillations predicted by theory. This result is discussed using numerical simulations of photoassociation and a modification to the current experiments that could lead to the detection of wavepacket dynamics is suggested.

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.

Induced interactions and the superfluid transition temperature in a three-component Fermi gas

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6Li mixture which can deviate strongly from the one in a weakly interacting two-component system.

Collisional stability of 40K immersed in a strongly interacting Fermi gas of 6Li

We investigate the collisional stability of a sample of 40K atoms immersed in a tunable spin mixture of 6Li atoms. In this three-component Fermi-Fermi mixture, we find very low loss rates in a wide range of interactions as long as molecule formation of 6Li is avoided. The stable fermionic mixture with two resonantly interacting spin states of one species together with another species is a promising system for a broad variety of phenomena in few- and many-body quantum physics.

Lifshitz point in the phase diagram of resonantly interacting 6Li-40K mixtures

We consider a strongly interacting 6Li-40K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This point is characterized by the effective mass of the Cooper pairs becoming negative, which signals an instability towards a supersolid phase.

Manipulating higher partial-wave atom-atom interactions by strong photoassociative coupling

We show that it is possible to change not only s-wave but also higher partial-wave atom-atom interactions in a cold collision in the presence of relatively intense laser fields tuned near a photoassociative transition.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Fermi condensates for dynamic imaging of electromagnetic fields

Ultracold gases provide micrometer size samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors in atom chips. Here we propose that condensates of fermions can be used for noninvasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations by the field create collective excitations and quasiparticles. The latter requires the frequency of the perturbation to exceed the gap. The frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable, e.g., by rf spectroscopy. We analyze the method by calculating the density-density susceptibility and discuss its sensitivity and spatial resolution.

New light on the intriguing history of superfluidity in liquid (4)He

Surprisingly, it was 30 years after the first liquefaction of (4)He in 1908 that the discovery that liquid (4)He is not just a 'cold' liquid was made. Below T = 2.18 K, it is a 'quantum' liquid which exhibits spectacular macroscopic quantum behaviour that can be seen with the naked eye. Since the observation of superfluidity in liquid (4)He is one of the greatest discoveries in modern physics, we present a day-to-day chronology of the tangled events which preceded the seminal discovery of zero viscosity in 1938 by Kapitza in Moscow and by Allen and Misener in Cambridge. On the theory side, London argued in 1938 that the microscopic basis for this new superfluid phase was the forgotten phenomenon of Bose-Einstein condensation (BEC) first suggested by Einstein in 1925. In 1941, Landau developed a very successful theory of superfluid (4)He, but it was not anchored in a microscopic theory of interacting atoms. It took another 20 years for theorists to unify the two seemingly different theories of Landau and London. Experiments on trapped superfluid atomic gases since 1995 have shone new light on superfluid (4)He. In the mid-1930s, London had emphasized that superconductivity in metals and superfluidity in liquid (4)He were similar. Experiments on trapped two-component Fermi gases in the last five years have shown that a Bose condensate is indeed the basis of both of these superfluid phases. This confirms the now famous Bardeen-Cooper-Schrieffer-BEC crossover scenario developed for superfluidity by Leggett and Nozières in the early 1980s but largely ignored until a few years ago. The study of superfluid (4)He will increasingly overlap with strongly interacting dilute quantum gases, perhaps opening up a new era of research on this most amazing liquid.

Efimov trimer formation via ultracold four-body recombination

We discuss the collisional formation of Efimov trimers via ultracold four-body recombination. In particular, we consider the reaction A+A+A+B-->A_{3}+B with A and B ultracold atoms. We obtain expressions for the four-body recombination rate up to an overall constant and show that it reflects the three-body Efimov physics either as a function of collision energy or as a function of the two-body s-wave scattering length between A atoms. In addition, we briefly discuss issues important for experimentally observing this interesting and unexplored process.

Cold fermionic atoms in two-dimensional traps: pairing versus Hund's rule

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

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.

Bell test for the free motion of material particles

We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.

Bragg spectroscopy of a strongly interacting Fermi gas

We present a comprehensive study of the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover in fermionic 6Li using Bragg spectroscopy. A smooth transition from molecular to atomic spectra is observed with a clear signature of pairing at and above unitarity. These spectra probe the dynamic and static structure factors of the gas and provide a direct link to two-body correlations. We have characterized these correlations and measured their density dependence across the broad Feshbach resonance at 834 G.

Polarized superfluidity in the attractive hubbard model with population imbalance

We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling, we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast with the unpolarized Bose-Einstein condensate which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.

Collisional stability of a three-component degenerate fermi gas

We report on the creation of a degenerate Fermi gas consisting of a balanced mixture of atoms in three different hyperfine states of 6Li. This new system consists of three distinguishable fermions with different and tunable interparticle scattering lengths a_{12}, a_{13}, and a_{23}. We are able to prepare samples containing 5x10;{4} atoms in each state at a temperature of about 215 nK, which corresponds to T/T_{F} approximately 0.37. We investigated the collisional stability of the gas for magnetic fields between 0 and 600 G and found a prominent loss feature at 130 G. From lifetime measurements, we determined three-body loss coefficients, which vary over nearly 3 orders of magnitude.

Ultracold triplet molecules in the rovibrational ground state

We report here on the production of an ultracold gas of tightly bound Rb2 triplet molecules in the rovibrational ground state, close to quantum degeneracy. This is achieved by optically transferring weakly bound Rb2 molecules to the absolute lowest level of the ground triplet potential with a transfer efficiency of about 90%. The transfer takes place in a 3D optical lattice which traps a sizeable fraction of the tightly bound molecules with a lifetime exceeding 200 ms.

Giant formation rates of ultracold molecules via Feshbach-optimized photoassociation

Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, i.e., in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhances molecular formation rates by several orders of magnitude. We illustrate this effect in heteronuclear systems, and find giant rate coefficients even in deeply bound levels. We also give a simple analytical expression for the photoassociation rate and discuss future applications of the Feshbach-optimized photoassociation technique.

Coherent transients in the femtosecond photoassociation of ultracold molecules

We demonstrate the photoassociation of ultracold rubidium dimers using coherent femtosecond pulses. Starting from a cloud of ultracold rubidium atoms, electronically excited rubidium molecules are formed with shaped photoassociation pump pulses. The excited state molecules are projected with a time-delayed probe pulse onto molecular ion states which are detected in a mass spectrometer. Coherent transient oscillations of the excited state population are observed in the wings of the pump pulse, in agreement with the time-dependent solution of the Schrödinger equation of the excitation process.

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.

Simple empirical order parameter for a first-order quantum phase transition in atomic nuclei

A simple, empirical, easy-to-measure effective order parameter of a first-order phase transition in atomic nuclei is presented, namely, the ratio of the energies of the first excited 6+ and 0+ states, distinguishing between first- and second-order transitions, and taking on a special value in the critical region, as data in Nd-Dy show. In the large NB limit of the interacting boson approximation model, a repeating degeneracy between alternate yrast and successive 0+ states is found in the critical region around the line of a first-order phase transition, pointing to a possible underlying symmetry.

Quantitative determination of the hubbard model phase diagram from optical lattice experiments by two-parameter scaling

We propose an experiment to obtain the phase diagram of the fermionic Hubbard model, for any dimensionality, using cold atoms in optical lattices. It is based on measuring the total energy for a sequence of trap profiles. It combines finite-size scaling with an additional "finite-curvature scaling" necessary to reach the homogeneous limit. We illustrate its viability in the 1D case, simulating experimental data in the Bethe-ansatz local-density approximation. Including experimental errors, the filling corresponding to the Mott transition can be determined with better than 3% accuracy.

Superfluid equation of state of dilute composite bosons

We present an exact theory of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime, which treats explicitly dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n(3/2), the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a(M), the composite nature of the dimers appearing only in the next order term proportional to n(2).

Bose-Einstein condensation in semiconductors: the key role of dark excitons

Bose-Einstein condensation in semiconductors is controlled by the nonelementary-boson nature of excitons. Pauli exclusion between the fermionic components of composite excitons produces dramatic exchange couplings between bright and dark states. In microcavities, where bright excitons and photons form polaritons, they force the condensate to be linearly polarized, as observed. In bulk, they also force linear polarization, but of dark states, due to interband Coulomb scatterings. To evidence this dark condensate, indirect processes are thus needed.

Finite-temperature collective dynamics of a Fermi gas in the BEC-BCS crossover

We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of the quantum gas in terms of hydrodynamic or near-collisionless behavior. We obtain a crossover phase diagram for collisional properties, showing a large region where a nonsuperfluid strongly interacting gas shows hydrodynamic behavior. In a narrow interaction regime on the BCS side of the crossover, we find a novel temperature-dependent damping peak, suggesting a relation to the superfluid phase transition.