We measure the effect of a magnetic Feshbach resonance (FR) on the rate and light-induced frequency shift of a photoassociation resonance in ultracold $^7$Li. The photoassociation-induced loss rate coefficient, $K_p$, depends strongly on magnetic field, varying by more than a factor of 10$^4$ for fields near the FR. At sufficiently high laser intensities, $K_p$ for a thermal gas decreases with increasing intensity, while saturation is observed for the first time in a Bose-Einstein condensate. The frequency shift is also strongly field-dependent and exhibits an anomalous blue-shift for fields just below the FR.
A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudo-potential treatment of atom-atom interactions. It is shown by explicit comparison to an exactly-solvable finite-range model that replacing the molecular bound-state wavefunction with a regularized delta-function can reproduce the exact scattering amplitude in the long-wavelength limit. Using this approach we find an analytical solution to the two-channel Feshbach resonance problem for two atoms in a spherical harmonic trap.
In this paper we formulate the time-dependent many-body theory of photoassociation in an atomic Bose-Einstein condensate with realistic interatomic interactions, using and comparing two approximations: the first-order cumulant approximation, originally developed by Kohler and Burnett [Phys. Rev. A 65, 033601 (2002)], and the reduced pair wave approximation, based on a previous paper [Phys. Rev. A 68 033612 (2003)] generalizing to two channels the Cherny-Shanenko approach [Phys. Rev. E 62, 1046 (2000)]. The two approximations differ only by the way a pair of condensate atoms is influenced by th…
We investigate theoretically the molecular yield in photoassociation of Bose-Einstein condensed sodium atoms for light intensities of the order of and above those applied in a recent experiment. Our results show that the rate at which ground state molecules may be formed saturates at high light intensities whereas the loss rate of condensate atoms does not. This is caused by the opposing roles of the short and long range pair correlations present near resonance under the influence of the laser and is crucial for the development of efficient photoassociation procedures in a condensate.
We study the photo-association of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a new dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between a…
We study supersymmetric (SUSY) responses to a photoassociation process in a mixture of Bose molecules $b$ and Fermi atoms $f$ which turn to mutual superpartners for a set of proper parameters. We consider the molecule $b$ to be a bound state of the atom $f$ and another Fermi atom $F$ with different species. The $b$-$f$ mixture and a free $F$ atom gas are loaded in an optical lattice. The SUSY nature of the mixture can be signaled in the response to a photon induced atom-molecule transition: While two new types of fermionic excitations, an individual $b$ particle-$f$ hole pair continuum and the…
A dynamical many body theory of single color photoassociation in a Bose-Einstein condensate is presented. The theory describes the time evolution of a condensed atomic ensemble under the influence of an arbitrarily varying near resonant laser pulse, which strongly modifies the binary scattering properties. In particular, when considering situations with rapid variations and high light intensities the approach described in this article leads, in a consistent way, beyond standard mean field techniques. This allows to address the question of limits to the photoassociation rate due to many body ef…
Gross-Pitaevskii equation with gain is used to model Bose Einstein condensation (BEC) fed by the surrounding thermal cloud. It is shown that the number of atoms continuously injected into BEC from the reservoir can be controlled by applying the external magnetic field via Feshbach resonance.
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…
We have created a dark quantum superposition state of a Rb Bose-Einstein condensate (BEC) and a degenerate gas of Rb$_2$ ground state molecules in a specific ro-vibrational state using two-color photoassociation. As a signature for the decoupling of this coherent atom-molecule gas from the light field we observe a striking suppression of photoassociation loss. In our experiment the maximal molecule population in the dark state is limited to about 100 Rb$_2$ molecules due to laser induced decay. The experimental findings can be well described by a simple three mode model.
We consider the dissociation of a molecular Bose-Einstein condensate during a magnetic-field sweep through a Feshbach resonance that starts on the molecular side of the resonance and ends on the atomic side. In particular, we determine the energy distribution of the atoms produced after the sweep. We find that the shape of the energy distribution strongly depends on the rate of the magnetic-field sweep, in a manner that is in good agreement with recent experiments.
We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach (Phys. Rev. E 62, 1646-59 (2000) ) where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and non-condensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the …
We discuss the atom-atom scattering problem across a Feshbach resonance in a two-dimensional dilute Bose gas at zero temperature, in the limit where the s-wave scattering length exceeds the width of the vertical confinement. We determine a tunable coupling-strength parameter and by controlling it we evaluate how the condensate wave function spreads out with increasing atom-atom repulsions. We also discuss the stability of the condensate in the magnetic-field regime where the coupling has become attractive.
The production of pairs of fast atoms leads to a pronounced loss of atoms during upward ramps of Feshbach resonance levels in dilute Bose-Einstein condensates. We provide comparative studies on the formation of these bursts of atoms containing the physical predictions of several theoretical approaches at different levels of approximation. We show that despite their very different description of the microscopic binary physics during the passage of a Feshbach resonance, all approaches lead to virtually the same prediction on the total loss of condensate atoms, provided that the ramp of the magne…
We present how to control interactions between solitons, either bright or dark, in Bose-Einstein condensates by synchronizing Feshbach resonance and harmonic trap. Our results show that as long as the scattering length is to be modulated in time via a changing magnetic field near the Feshbach resonance, and the harmonic trapping frequencies are also modulated in time, exact solutions of the one-dimensional nonlinear Schrödinger equation can be found in a general closed form, and interactions between two solitons are modulated in detail in currently experimental conditions. We also propose expe…
Complex, localized stable solitons, characterized by a power law behaviour, are found for a quasi-one-dimensional Bose-Einstein condensate near Feshbach resonance. Both dark and bright solitons can be excited in the experimentally allowed parameter domain, when two and three-body interactions are respectively repulsive and attractive. These solutions are obtained for non-zero chemical potential, unlike their unstable real counterparts which exist in the limit of vanishing $μ$. The dark solitons travel with constant speed, which is quite different from the Lieb mode, where profiles with differe…
In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the break-up of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on $^{23}$Na in a wide range of magnetic fields.
We put forward a scheme for controlling Josephson-like tunneling in two-component Bose-Einstein condensates coupled with microwave field via Feshbach resonance and tuning aspect ratio of trapping potential. We prove how to realize a perfect periodic oscillation from a fast damped and irregular oscillation on relative number of atoms in future experiment. In particular, intensity of Josephson-like tunneling can be successfully controlled through controlling speed of recovering the initial value of intra-atomic interaction and aspect ratio of trapping potential. Interestingly, we find that relat…
We predict the resonance enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}$Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.
We give an overview of recent experiments on an ultracold Fermi-Bose quantum gas where the interspecies interaction can be tuned via magnetic Feshbach resonances. We first describe the various steps that have led to the observation of Feshbach resonances in the K-Rb system we investigate, and their accurate characterization. We then describe experiments in which Feshbach resonances are exploited to study interaction effects and to associate weakly bound KRb dimers.
It has recently been demonstrated that quantum degenerate gases of very weakly bound molecules can be produced by atomic gases with Feshbach resonances. More strongly bound molecules can be produced with Raman photoassociation of a quantum gas, although this process has not yet been shown to produce a quantum degenerate molecular gas. In principle, Feshbach resonance and Raman photoassociation can be quantum-mechanically reversible, and lead to collective coherent phenomena such as Rabi cycling between an atomic and a molecular gas. However, such atom-molecular coherence has only partly been r…
We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibrium is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular en…
In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to ``engineer'' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tract…
We study the steady state of a zero-temperature Bose gas near a Feshbach or photoassociation resonance using a two-channel mean-field model that incorporates atomic and molecular condensates, as well as correlated atom pairs originating from dissociation of molecules into pairs of atoms. We start from a many-body Hamiltonian for atom-molecule conversion, and derive the time dependent version of the mean-field theory. The stationary solution of the time dependent model is rendered unique with an approximation that entails that all noncondensate atoms are correlated, as if emerging from dissocia…
We study the conversion of $^{40}$K and $^{87}$Rb atoms into stable molecules through the stimulated Raman adiabatic passage (STIRAP) in photoassociation assisted with Feshbach resonance. Starting with the mean-field Langrange density, we show that the atom-to-molecule conversion efficiency by STIRAP aided by Feshbach resonance is much larger than that by bare Feshbach resonance. We also study the influence of the population imbalance on the atom-to-molecule conversion.
In many experiments involving conversion of quantum degenerate atomic gases into molecular dimers via a Feshbach resonance, an external magnetic field is linearly swept from above the resonance to below resonance. In the adiabatic limit, the fraction of atoms converted into molecules is independent of the functional form of the sweep and is predicted to be 100%. However, for non-adiabatic sweeps through resonance, Landau-Zener theory predicts that a linear sweep will result in a negligible production of molecules. Here we employ a genetic algorithm to determine the functional time dependence o…
We consider a mixture of two-species atomic Bose-Einstein codensates coupled to a bound molecular state at zero temperature via interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collision…
We test a non equilibrium approach to study the behavior of a Bose-Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations of motion for, the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe …
We use a Feshbach resonance to tune the scattering length a of a Bose-Einstein condensate of 7Li in the |F = 1, m_F = 1> state. Using the spatial extent of the trapped condensate we extract a over a range spanning 7 decades from small attractive interactions to extremely strong repulsive interactions. The shallow zero-crossing in the wing of the Feshbach resonance enables the determination of a as small as 0.01 Bohr radii. In this regime, evidence of the weak anisotropic magnetic dipole interaction is obtained by comparison with different trap geometries.
We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of 41K and 87Rb, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to thermal distribution of the atoms, and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantita…
We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schroedinger equation (NPSE) for BEC trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.
We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length and con ned only by a one dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment. For moderate con nement we discover a new island of stability in the 3D case, not present in the quasi 2D treatment. Stable solutions from this region have nontrivial dynamics in the lattice direction, hence they describe fully 3D breather …
We demonstrate a reversible conversion of a Li2 molecular Bose-Einstein condensate to a degenerate Fermi gas of atoms by adiabatically crossing a Feshbach resonance. By optical in situ imaging, we observe a smooth change of the cloud size in the crossover regime. On the Feshbach resonance, the ensemble is strongly interacting and the measured cloud size is 75(7)% of the one of a non-interacting zero-temperature Fermi gas. The high condensate fraction of more than 90% and the adiabatic crossover suggest our Fermi gas to be cold enough to form a superfluid.
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 study the bosonic atoms with a wide Feshbach resonance at zero temperature in terms of the renormalization group. We indicate that this system will always collapse in the dilute limit. On the side with a positive scattering length, the atomic superfluid is an unstable local minimum in the dilute limit and it determines the thermodynamics of this system within its lifetime. We calculate the equilibrium properties at zero temperature in the unitary regime. They exhibit universal scaling forms in the dilute limit due to the presence of a nontrivial zero temperature, zero density fixed point. M…
We present a theoretical model for Bragg scattering from a Bose-Einstein condensate (BEC) in the vicinity of a magnetic Feshbach resonance, using a two c-field formalism, one c-field for the atom and the other for a molecule formed of two atoms. We use this model to numerically simulate a recent experiment [S. B. Papp et al., Phys. Rev. Lett., 101(13):135301, Sep 2008] investigating the effects of strong interactions on the Bragg spectrum from a 85Rb BEC. Results from these simulations are in very good quantitative agreement with the experimental results, confirming the importance of the reson…
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky (GP) equation with a periodic potential, we employ an envelope wave approximation to derive coupled-mode equations describing the slow BEC dynamics in the first spectral gap of the optical lattice. We construct exact analytical formulas describing gap soliton solutions and examine their spectral stability using the Chebyshev interpolation method. We show that these gap solitons are unstable far from the threshold of loc…
In this paper, we study the phase diagram of a homogeneous Bose gas with a repulsive interaction near a wide Feshbach resonance at zero temperature. The Bose-Einstein-condensation (BEC) state of atoms is a metastable state. When the scattering length $a$ exceeds a critical value depending on the atom density $n$, $na^3>0.035$, the molecular excitation energy is imaginary and the atomic BEC state is dynamically unstable against molecule formation. The BEC state of diatomic molecules has lower energy, where the atomic excitation is gapped and the molecular excitation is gapless. However when the…
Mean-field approach has recently been used to model coupled atom-molecular Bose-Einstein condensates (BEC) and coupled Fermi-Bose condensates near Feshbach resonance. Sweeping of magnetic field across the resonance gives a new (nonlinear) version of Landau-Zener problem. We investigate the structure of the corresponding classical phase space and calculate change in the action which corresponds to finite-rate efficiency of the sweep. We consider the case of non-zero initial action, which corresponds to some finite initial molecular fraction.
A model of two 1D ideal Bose gases A and B with strong AB attractions induced by a p-wave AB Feshbach resonance is studied. The model is solved exactly by a Bose-Bose duality mapping, and it is shown that there is no A-component or B-component Bose-Einstein condensation and no AB-pair off-diagonal long-range order (ODLRO), but both AA-pair and BB-pair ODLRO. After generalization by adding even-wave AA and BB repulsion and reducing the strength of the odd-wave AB attraction by Feshbach resonance detuning, a quantum phase transition occurs between a phase with AB contact nodes and one with no su…
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 quasi-molecules with finite orbital angular momenta $L_z=\pm1,0$, 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 mol…
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…
