Chapter of the book: "Cold Molecules: Theory, Experiment, Applications" edited by R. V. Krems, B. Friedrich and W. C. Stwalley (publication expected in March 2009)
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.
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 …
We report on the observation of interspecies Feshbach resonances in an ultracold, optically trapped mixture of Rb and Cs atoms. In a magnetic field range up to 300 G we find 23 interspecies Feshbach resonances in the lowest spin channel and 2 resonances in a higher channel of the mixture. The extraordinarily rich Feshbach spectrum suggests the importance of different partial waves in both the open and closed channels of the scattering problem along with higher-order coupling mechanisms. Our results provide, on one hand, fundamental experimental input to characterize the Rb-Cs scattering proper…
Quantum lattice solitons in a system of two ultracold bosons near Feshbach resonance are investigated. It is shown that their binding energy, effective mass, and spatial width, can be manipulated varying the detuning from the Feshbach resonance. In the case of attractive atomic interactions, the molecule creation stabilizes the solitons. In the case of repulsive interactions, the molecule creation leads to the possibility of existence of bright solitons in some interval of detunings. Due to quantum fluctuations the soliton width is a random quantity. Its standard deviation is larger than the m…
We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level crossing which allows us to transfer the molecules into another state. In the new state, two Feshbach-like collision resonances show up as strong inelastic loss features. We interpret these resonances as being induced by Cs4 bound states near the molecular scattering continuum. The tunability of the interactions between molecules opens up novel applications such a…
We have observed Feshbach resonances in elastic collisions between ultracold ${}^{52}$Cr atoms. This is the first observation of collisional Feshbach resonances in an atomic species with more than one valence electron. The zero nuclear spin of ${}^{52}$Cr and thus the absence of a Fermi-contact interaction leads to regularly-spaced resonance sequences. By comparing resonance positions with multi-channel scattering calculations we determine the s-wave scattering length of the lowest $^{2S+1}Σ_{g}^{+}$ potentials to be $\unit[112(14)]{a_0}$, $\unit[58(6)]{a_0}$ and $-\unit[7(20)]{a_0}$ for S=6, …
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 report on the observation of five Feshbach resonances in collisions between ultracold $^7$Li and $^{87}$Rb atoms in the absolute ground state mixture where both species are in their $|f,m_f>=|1,1>$ hyperfine states. The resonances appear as trap losses for the $^7$Li cloud induced by inelastic heteronuclear three-body collisions. The magnetic field values where they occur are important quantities for an accurate determination of the interspecies interaction potentials. Results of coupled channels calculations based on the observed resonances are presented and refined potential parameters ar…
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.
We investigate magnetic Feshbach resonances in two different ultracold K-Rb mixtures. Information on the K(39)-Rb(87) isotopic pair is combined with novel and pre-existing observations of resonance patterns for K(40)-Rb(87). Interisotope resonance spectroscopy improves significantly our near-threshold model for scattering and bound-state calculations. Our analysis determines the number of bound states in singlet/triplet potentials and establishes precisely near threshold parameters for all K-Rb pairs of interest for experiments with both atoms and molecules. In addition, the model verifies the…
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 study collisions in an optically trapped, pure sample of ultracold Cs$_2$ molecules in various internal states. The molecular gas is created by Feshbach association from a near-degenerate atomic gas, with adjustable temperatures in the nanokelvin range. We identify several narrow loss resonances, which point to the coupling to more complex molecular states and may be interpreted as Feshbach resonances in dimer-dimer interactions. Moreover, in some molecular states we observe a surprising temperature dependence in collisional loss. This shows that the situation cannot be understood in terms …
We present an analysis of experimentally accessible magnetic Feshbach resonances in ultra-cold hetero-nuclear 85Rb-87Rb and 6Li-87Rb mixtures. Using recent experimental measurements of the triplet scattering lengths for 6Li-87Rb and 7Li-87Rb mixtures and Feshbach resonances for one combination of atomic states, we create model potential curves and fine tune them to reproduce the measured resonances and to predict the location of several experimentally relevant resonances in Li-Rb collisions. To model 85Rb-87Rb collisions, we use accurate Rb_2 potentials obtained previously from the analysis of…
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…
The effects of combined external electric and magnetic fields on elastic collisions in ultracold Li--Rb mixtures is studied using recently obtained, experimentally verified potentials. Our analysis provides both quantitative predictions for and a detailed physical interpretation of the phenomena arising from electric-field-induced interactions. It is shown that the electric field shifts the positions of intrinsic magnetic Feshbach resonances, generates copies of resonances previously restricted to a particular partial-wave collision to other partial wave channels, and splits Feshbach resonance…
We explore the rich internal structure of Cs_2 Feshbach molecules. Pure ultracold molecular samples are prepared in a CO_2-laser trap, and a multitude of weakly bound states is populated by elaborate magnetic-field ramping techniques. Our methods use different Feshbach resonances as input ports and various internal level crossings for controlled state transfer. We populate higher partial-wave states of up to eight units of rotational angular momentum (l-wave states). We investigate the molecular structure by measurements of the magnetic moments for various states. Avoided level crossings betwe…
Scattering length, which can be measured in Bose-Einstein condensate and Feshbach molecule experiments, is extremely sensitive to the variation of fundamental constants, in particular, the electron-to-proton mass ratio (m_e/m_p or m_e/Lambda_{QCD}, where Lambda_{QCD} is the QCD scale). Based on single- and two-channel scattering model, we show how the variation of the mass ratio propagates to the scattering length. Our results suggest that variation of m_e/m_p on the level of 10^{-11}~10^{-14} can be detected near a narrow magnetic or an optical Feshbach resonance by monitoring the scattering …
We present a detailed analysis of the production efficiency of weakly bound heteronuclear KRb-Feshbach molecules using radio frequency association in a harmonic trap. The efficiency was measured in a wide range of temperatures, binding energies and radio frequencies. A comprehensive analytical model is presented, explaining the observed asymmetric spectra and achieving good quantitative agreement with the measured production rates. This model provides a deep understanding of the molecule association process and paves the way for future experiments which rely on Feshbach molecules e.g. for the …
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 determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in the harmonic trap by using the local density approximation. The adiabatic phase diagram shows the fermionic condensate fraction composed of condensed molecules and Cooper pair atoms. The key idea of our work is conservation of entropy through the adiabatic process, extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123 (2004)] for an ideal gas mixture to include the resonant interaction in a mean-field theory. We also calculate the molecular conversion eff…
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 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 experimental evidence of universality in ultracold 7Li atoms' three-body recombination loss in the vicinity of a Feshbach resonance. We observe a recombination minimum and an Efimov resonance in regions of positive and negative scattering lengths, respectively, which are connected through the pole of the Feshbach resonance. Both observed features lie deeply within the range of validity of the universal theory and we find that the relations between their properties, i.e. widths and locations, are in an excellent agreement with the theoretical predictions.
We present a two-channel model to describe the quantum state of two atoms with finite-range interaction near a Feshbach resonance. This model provides a simple picture to analytically derive the wave function and the binding energy of the molecular bound state. The results agree excellently with the measurements and multichannel calculations. For small binding energies, the system enters a threshold regime in which the Feshbach molecules are identical to long range atom pairs in single channel. According to their threshold behavior, we find Feshbach resonances can be classified into two types.
We detected the formation of p-wave Feshbach molecules for all three combinations of the two lowest atomic spin states of 6Li. By creating a pure molecular sample in an optical trap, we measured the inelastic collision rates of p-wave molecules. The elastic collision rate was measured from the thermalization rate of a breathing mode excited spontaneously upon molecular formation.
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.
We discuss the prospects for observing the characteristic features of the Efimov effect in a two-component ultracold atomic gas near an interspecies Feshbach resonance. In the ultracold regime, the Efimov effect is expected to be manifested in the three-body collision rates through the appearance of series of minima or maxima as a function of the two-body s-wave scattering length $a$. Here, we propose the observation of this Efimov physics through measurements of the inelastic three-body rate constants near a Feshbach resonance. Our analysis suggests that boson-fermion mixtures, where the boso…
We consider the binding energy and the wave function of Feshbach molecules confined in a one-dimensional matter waveguide. We compare the binding energy with the experiment of Moritz et al. and find excellent agreement for the full magnetic field range explored experimentally.
A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a DC magnetic field near the 155G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the initial phase space density of the sample. This technique offers high conversion efficienci…
We report on the observation of ultracold heteronuclear Feshbach molecules. Starting with a $^{87}$Rb BEC and a cold atomic gas of $^{85}$Rb, we utilize previously unobserved interspecies Feshbach resonances to create up to 25,000 molecules. Even though the $^{85}$Rb gas is non-degenerate we observe a large molecular conversion efficiency due to the presence of a quantum degenerate $^{87}$Rb gas; this represents a key feature of our system. We compare the molecule creation at two different Feshbach resonances with different magnetic-field widths. The two Feshbach resonances are located at $265…
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 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 m_l = +/- 1 and m_l = 0 angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasi-bound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier.
The spontaneous dissociation of 85Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance which was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by three 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 close to resonance.
Using the technique of stimulated Raman adiabatic passage (STIRAP) we have coherently transferred ultracold 87Rb2 Feshbach molecules into a more deeply bound vibrational quantum level. Our measurements indicate a high transfer efficiency of up to 87%. As the molecules are held in an optical lattice with not more than a single molecule per lattice site, inelastic collisions between the molecules are suppressed and we observe long molecular lifetimes of about 1 s. Using STIRAP we have created quantum superpositions of the two molecular states and tested their coherence interferometrically. These…
We investigate three-body recombination loss across a Feshbach resonance in a gas of ultracold 7Li atoms prepared in the absolute ground state and perform a comparison with previously reported results of a different nuclear-spin state [N. Gross et.al., Phys. Rev. Lett. 103 163202, (2009)]. We extend the previously reported universality in three-body recombination loss across a Feshbach resonance to the absolute ground state. We show that the positions and widths of recombination minima and Efimov resonances are identical for both states which indicates that the short-range physics is nuclear-s…
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 have created and trapped a pure sample of 87Rb2 Feshbach molecules in a three-dimensional optical lattice. Compared to previous experiments without a lattice we find dramatic improvements such as long lifetimes of up to 700 ms and a near unit efficiency for converting tightly confined atom pairs into molecules. The lattice shields the trapped molecules from collisions and thus overcomes the problem of inelastic decay by vibrational quenching. Furthermore, we have developed a novel purification scheme that removes residual atoms, resulting in a lattice in which individual sites are either em…
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.
We experimentally demonstrate Cs2 Feshbach molecules well above the dissociation threshold, which are stable against spontaneous decay on the timescale of one second. An optically trapped sample of ultracold dimers is prepared in an l-wave state and magnetically tuned into a region with negative binding energy. The metastable character of these molecules arises from the large centrifugal barrier in combination with negligible coupling to states with low rotational angular momentum. A sharp onset of dissociation with increasing magnetic field is mediated by a crossing with a g-wave dimer state …
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 …
