V. Gurarie
This paper examines the problem of molecule production in an atomic fermionic gas close to an s-wave Feshbach resonance by means of a magnetic field sweep through the resonance. The density of molecules at the end of the process is derived for narrow resonance and slow sweep.
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We study the stability of the paired fermionic p-wave superfluid made out of identical atoms all in the same hyperfine state close to a p-wave Feshbach resonance. First we reproduce known results concerning the lifetime of a 3D superfluid, in particular, we show that it decays at the same rate as its interaction energy, thus precluding its equilibration before it decays. Then we proceed to study its stability in case when the superfluid is confined to 2D by means of an optical harmonic potential. We find that the relative stability is somewhat improved in 2D in the BCS regime, such that the de…
Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and …
Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resona…
We investigate states of fermionic atoms across a broad Feshbach resonance in an optical superlattice which allows interaction only among a small number of lattice sites. The states are in general described by superpositions of atomic resonating valence bonds and dressed molecules. As one scans the magnetic field, level crossing is found between states with different symmetry properties, which may correspond to a quantum phase transition in the many-body case.
Fast sweep projection onto Feshbach molecules has been widely used as a probe of fermionic condensates. By determining the exact dynamics of a pair of atoms in time varying magnetic fields, we calculate the number of condensed and noncondensed molecules created after fast magnetic field sweeps from the BCS to the BEC side of the resonances in $^{40}$K and $^{6}$Li, for different sweep rates and a range of initial and final fields. We discuss the relation between the initial fermionic condensate fraction and the molecular condensate fraction measured after the sweep.
The relaxation processes in an ultra-cold degenerate atomic Fermi gas near a Feshbach resonance are considered. It is shown that the relaxation rate of the molecules being in a resonance with the atomic Fermi system is of the order of the part of the chemical potential determined by the interaction between resonance molecules. In this connection the lower part of the excitation spectrum in the system of resonance molecules is not well-defined.
We show that the high temperature behavior of atomic gases near Feshbach Resonance with non-zero orbital angular momentum $(\ell >0)$ belong to a universality class different from that of s-wave resonances. The universal interaction energy is $2(2\ell +1)$ times larger than that of the s-wave when approaching the resonance from the atomic side, but is essentially zero on the molecular side; contrary to s-wave resonances where interaction energies on both sides are the same except for a sign change. The measurement of these universality properties should be feasible in current experiments.
We present theoretical findings on the spin collective modes of a two-species Fermi liquid, prepared alternatively in a polarized equilibrium or a polarized non-equilibrium state. We explore the effects on these modes of a diverging s-wave scattering length, as occurs near a Feshbach resonance in a Fermionic atomic gas. We compare these atomic gas modes with those of the conventional Helium-3 system, and we find that they differ from the conventional systems, and that the gap and spin stiffness are tunable via the Feshbach resonance.
We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(μr_s) >> 1$. Here $(μ)^{-1}$ is the range of the two-body potential, and $r_s$ is defined thr…
We develop an effective low energy theory for multi-channel scattering of cold atomic alkali atoms with particular focus on Feshbach resonances. The scattering matrix is expressed in terms of observables only and the theory allows for the inclusion of many-body effects both in the open and in the closed channels. We then consider the frequency and damping of collective modes for Fermi gases and demonstrate how medium effects significantly increase the scattering rate determining the nature of the modes. Our results obtained with no fitting parameters are shown to compare well with experimental…
We theoretically examine a system of Fermi degenerate atoms coupled to bosonic molecules by a Feshbach resonance, focusing on the superfluid transition to a molecular Bose-Einstein condensate dressed by Cooper pairs of atoms. This problem raises an interest because it is unclear at present whether bimodal density distributions observed recently in 40-K and 6-Li are due to a condensate of bosonic molecules or fermionic atom pairs. As opposed to 40-K, we find that any measurable fraction of above-threshold bosonic molecules are necessarily absent for the 6-Li system in question, which strongly i…
We report on the observation of two Feshbach resonances in collisions between ultracold $^6$Li and $^{87}$Rb atoms in their respective hyperfine ground states $|F,m_F>=|1/2,1/2>$ and $|1,1>$. The resonances show up as trap losses for the $^6$Li cloud induced by inelastic Li-Rb-Rb three-body collisions. The magnetic field values where they occur represent important benchmarks for an accurate determination of the interspecies interaction potentials. A broad Feshbach resonance located at 1066.92 G opens interesting prospects for the creation of ultracold heteronuclear molecules. We furthermore ob…
We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for…
We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and therefore to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of |m|=1 (or m=0) can be inhibited. In two and three dimensions we observe the doublet structure of the p-wave Feshbach resonance. B…
Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as wel…
We study the properties of ultracold Fermi gases in a three-dimensional optical lattice when crossing a Feshbach resonance. By using a zero-temperature formalism, we show that three-body processes are enhanced in a lattice system in comparison to the continuum case. This poses one possible explanation for the short molecule lifetimes found when decreasing the magnetic field across a Feshbach resonance. Effects of finite temperatures on the molecule formation rates are also discussed by computing the fraction of double-occupied sites. Our results show that current experiments are performed at t…
We study the conversion efficiency of heteronuclear Feshbach molecules in population imbalanced atomic gases formed by ramping the magnetic field adiabatically. We extend the recent work [J. E. Williams et al., New J. Phys., 8, 150 (2006)] on the theory of Feshbach molecule formations to various combinations of quantum statistics of each atomic component. A simple calculation for a harmonically trapped ideal gas is in good agreement with the recent experiment [S. B. Papp and C. E. Wieman, Phys. Rev. Lett., 97, 180404 (2006)] without any fitting parameters. We also give the conversion efficienc…
We consider a mixture of single-component bosonic and fermionic atoms with an interspecies interaction that is varied using a Feshbach resonance. By performing a mean-field analysis of a two-channel model, which describes both narrow and broad Feshbach resonances, we find an unexpectedly rich phase diagram at zero temperature: Bose-condensed and non-Bose-condensed phases form a variety of phase-separated states that are accompanied by both critical and tricritical points. We discuss the implications of our results for the experimentally observed collapse of Bose-Fermi mixtures on the attractiv…
The capability to tune the strength of the elastic interparticle interaction is crucial for many experiments with ultracold gases. Magnetic Feshbach resonances are a tool widely used for this purpose, but future experiments would benefit from additional flexibility such as spatial modulation of the interaction strength on short length scales. Optical Feshbach resonances offer this possibility in principle, but suffer from fast particle loss due to light-induced inelastic collisions. Here we show that light near-resonant with a molecular bound-to-bound transition can be used to shift the magnet…
We investigate the dynamics of the system of multiple bright and dark quasisolitons generated in a one-component ultracold Fermi gas via the phase imprinting technique in terms of atomic orbitals approach. In particular, we analyze the collision between two bright quasisolitons and find that quasisolitons are subject to the superposition principle.
We derive pseudo-potentials that describe the scattering between two particles in two spatial dimensions for any partial wave m, whose scattering strength is parameterized in terms of the m-dependent phase shift. Using our m=0 pseudo-potential, we develop a coupled channel model with 2D zero-range interactions, which describes the two-body physics across a Feshbach resonance. Our model predicts the scattering length, the binding energy and the "closed channel molecular fraction" of two particles; these observables can be measured in experiments on ultracold quasi-2D atomic Bose and Fermi gases…
In this Chapter, we give an introduction into experiments with Feshbach molecules and their applications. In particular, we discuss the various creation and detection methods, and the internal-state manipulation of such molecules. We highlight two topics, namely Feshbach molecules in the halo regime and the application of Feshbach molecule to achieve ultracold gases of molecules in the rovibrational ground state. Our illustrative examples are mainly based on work performed at Innsbruck University.
We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for $^{85}$Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of $^…
We analyze molecular bound states of atomic quantum gases near a Feshbach resonance. A simple, renormalizable field theoretic model is shown to have exact solutions in the two-body sector, whose binding energy agrees well with observed experimental results in both Bosonic and Fermionic cases. These solutions, which interpolate between BEC and BCS theories, also provide a more general variational ansatz for resonant superfluidity and related problems.
We investigate the harmonically trapped 2D fermionic systems with a effective spin-orbit coupling and intrinsic s-wave superfluidity under the local density approximation, and find that there is a critical value for Zeeman field. When the Zeeman field larger than the critical value, the topological superfluid phases emerge and coexist with the normal superfluid phase, topological phase separation, in the trapped region. Otherwise, the superfluid phase is topologically trivial.
Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the lithium-6 system, we argue that its application to potassium-40, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of ``Pauli blocking'' are recorded in the internal structure of the condensate …
We perform extensive magnetic Feshbach spectroscopy of an ultracold mixture of fermionic 40K and bosonic 87Rb atoms. The magnetic-field locations of 14 interspecies resonances is used to construct a quantum collision model able to predict accurate collisional parameters for all K-Rb isotopic pairs. In particular we determine the interspecies s-wave singlet and triplet scattering lengths for the 40K-87Rb mixture as -111 +/- 5 Bohr and -215 +/- 10 Bohr respectively. We also predict accurate scattering lengths and position of Feshbach resonances for the other K-Rb isotopic pairs. We discuss the c…
We report on the observation of Feshbach resonances in an ultracold mixture of two fermionic species, 6Li and 40K. The experimental data are interpreted using a simple asymptotic bound state model and full coupled channels calculations. This unambiguously assigns the observed resonances in terms of various s- and p-wave molecular states and fully characterizes the ground-state scattering properties in any combination of spin states.
A universal characterization of interactions in few- and many-body quantum systems is often possible without detailed description of the interaction potential, and has become a defacto assumption for cold atom research. Universality in this context is defined as the validity to fully characterize the system in terms of two-body scattering length. We discuss universality in the following three contexts: closed-channel dominated Feshbach resonance, Efimov physics near Feshbach resonances, and corrections to the mean field energy of Bose-Einstein condensates with large scattering lengths. Novel e…
We investigate theoretically Fermionic superfluidity induced by Feshbach resonance in the orbital p-wave channel. We show that, 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 $k_z + i βk_y$ (up to a rotation about $\hat z$, here $β< 1$). A phase transition between these two states can occur under a change in the magnetic field or the density of the gas.
This thesis presents experiments probing physics in the crossover between Bose-Einstein condensation (BEC) and BCS superconductivity using an ultracold gas of atomic fermions. Scattering resonances in these ultracold gases (known as Feshbach resonances) provide the unique ability to tune the fermion-fermion interactions. The work presented here pioneered the use of fermionic Feshbach resonances as a highly controllable and tunable system ideal for studying the cusp of the BCS-BEC crossover problem. Here pairs of fermionic atoms have some properties of diatomic molecules and some properties of …
We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon tempe…
We discuss the possibility of a quantum phase transition in ultracold spin polarized fermionic gases which exhibit a p-wave Feshbach resonace. We show that when fermionic atoms form a condensate that can be externally tuned between the BCS and BEC limits, the zero temperature compressibility and the spin susceptibility of the fermionic gas are non-analytic functions of the two-body bound state energy. This non-analyticity is due to a massive rearrangement of the momentum distribution in the ground state of the system. Furthermore, we show that the low temperature superfluid density is also non…
We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length $a_F$. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: a single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As $1/a_F$ is increased from a negative v…
We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$…
One possibility for the creation of ultracold, high-phase-space-density quantum gases of molecules in the rovibrational ground state relies on first associating weakly-bound molecules from quantum-degenerate atomic gases on a Feshbach resonance and then transfering the molecules via several steps of coherent two-photon stimulated Raman adiabatic passage (STIRAP) into the rovibronic ground state. Here, in ultracold samples of Cs_2 Feshbach molecules produced out of ultracold samples of Cs atoms, we observe several optical transitions to deeply bound rovibrational levels of the excited 0_u^+ mol…
Two atoms in an optical lattice may be made to interact strongly at higher partial waves near a Feshbach resonance. These atoms, under appropriate constraints, could be bosonic or fermionic. The universal $l=2$ energy spectrum for such a system, with a caveat, is presented in this paper, and checked with the spectrum obtained by direct numerical integration of the Schrödinger equation. The results reported here extend those of Yip for p-wave resonance (Phys. Rev. A {\bf 78}, 013612 (2008)), while exploring the limitations of a universal expression for the spectrum for the higher partial waves.
We present a unified overview, from the mean-field to the unitarity regime, of the stability of a trapped Fermi gas with short range attractive interactions. Unlike in a system of bosons, a Fermi gas is always stable in these regimes, no matter how large the particle number. However, when the interparticle spacing becomes comparable to the range of the interatomic interactions, instability is not precluded.
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