We study ultracold three-body collisions of bosons and fermions when the interatomic interaction is tuned near a narrow Feshbach resonance. We show that the width of the resonance has a substantial impact on the collisional properties of ultracold gases in the strongly interacting regime. We obtain numerical and analytical results that allow us to identify universal features related to the resonance width. For narrow resonances, we have found a suppression of all inelastic processes in boson systems leading to deeply bound states and an enhancement for fermion systems.
Ultracold molecules offer a broad variety of applications, ranging from metrology to quantum computing. However, forming "real" ultracold molecules, {\it i.e.} in deeply bound levels, is a very difficult proposition. Here, we show how photoassociation in the vicinity of a Feshbach resonance enhance 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 rates, and discuss future applications of the Feshbach Opti…
Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of "broad" and "narrow" resonances of arbitrary $l$ and their different scattering characteristics, and (c) the…
We propose a new type of Feshbach resonance occurring when two different ultracold atoms in their ground state undergo an s-wave collision in the presence of a continuous-wave laser light. The atoms collide in the dissociation continuum of the molecular electronic ground state which is coupled by the light to a rovibrational level of the same electronic ground state: we name this a Laser-Assisted Self-Induced Feshbach Resonance (LASIFR). This mechanism, valid for all polar molecules, is analyzed on the example of ultracold 87Rb and 84Sr atoms, for which the laser frequency falls in the THz ran…
We measure chemical reactions between a single trapped $^{174}$Yb$^+$ ion immersed in an ultracold bath of $^6$Li atoms containing trace amounts of Li$_2$ dimers. This produces LiYb$^+$ molecular ions that we detect via mass spectrometry. We explain the reaction rates by modelling the dimer density as a function of the magnetic field and obtain excellent agreement when we assume the reaction to follow the Langevin rate. Our results present a novel approach towards the creation of cold molecular ions and point to the exploration of ultracold chemistry in ion molecule collisions. What is more, w…
We investigate the presence of Feshbach resonances in ultracold alkali-dialkali reactive collisions. Quantum scattering calculations are performed on a new Na_3 quartet potential energy surface. An analysis of scattering features is performed through a systematic variation of the nonadditive three-body interaction potential. Our results should provide useful information for interpreting future atom-molecule collision experiments.
We have studied magnetic Feshbach resonances in an ultracold sample of Na prepared in the absolute hyperfine ground state. We report on the observation of three s-, eight d-, and three g-wave Feshbach resonances, including a more precise determination of two known s-wave resonances, and one s-wave resonance at a magnetic field exceeding 200mT. Using a coupled-channels calculation we have improved the sodium ground-state potentials by taking into account these new experimental data, and derived values for the scattering lengths. In addition, a description of the molecular states leading to the …
Controlling physical systems and their dynamics on the level of individual quanta propels both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral and charged, are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing and quantum metrology. Studying the long-range interactions between these systems when combined in a hybrid atom-ion trap has lead to landmark results. Reaching the ultracold regime, however, where quantum mechanics dominates the interaction, e.g., g…
We have observed 26 interspecies Feshbach resonances at fields up to 2050 G in ultracold $^6$Li+$^{23}$Na mixtures for different spin-state combinations. Applying the asymptotic bound-state model to assign the resonances, we have found that most resonances have d-wave character. This analysis serves as guidance for a coupled-channel calculation, which uses modified interaction potentials to describe the positions of the Feshbach resonances well within the experimental uncertainty and to calculate their widths. The scattering length derived from the improved interaction potentials is experiment…
Two-color photoassociation of ground state $^6$Li$^{87}$Rb molecules via the $\mathrm{B}^1Π$ electronic state using short pulses near a magnetic Feshbach resonance is studied theoretically. A near-resonant magnetic field is applied to mix the hyperfine singlet and triplet components of the initial wave function and enhance the photoassociation rate, before the population is transferred to the ground state by a second pulse. We show that an increase of up to three orders of magnitude in the absolute number of molecules produced is attainable for deeply bound vibrational levels. This technique c…
We report the observation of resonance-like loss in the trap population of ultracold dysprosium as a function of magnetic field, which we attribute to anisotropy-induced Fano-Feshbach resonances arising from Dy's large magnetic dipole moment and nonzero electronic orbital angular momentum. We recorded these resonances for four different isotopes, three bosonic and one fermionic, over a field range of 0-6 G and show that the number of resonances changes significantly as a function of temperature, even in the nK regime. Most of the observed resonances are of very narrow width. The fermionic isot…
We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more…
We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of non-degenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states ex…
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 investigate the prospects of controlling charge-exchange in ultracold collisions of heteroisotopic combinations of atoms and ions of the same element. The treatment, readily applicable to alkali or alkanine-earth metals, is illustrated in the process $^9$Be$^{+}$ + $^{10}$Be $\leftrightarrow$ $^{9}$Be + $^{10}$Be$^{+}$, which exhibits favorable electronic, nuclear, and hyperfine structure. Feshbach resonances are obtained from quantum scattering calculations in a standard coupled-channel formalism with non-BO terms originating from the nuclear kinetic operator. Near a narrow resonance predi…
Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions and collisions between Feshbach molecules which are very weakly bound. Whether such resonances exist for ultracold ground state molecules has been debated due to the possibly high density of states and/or rapid decay of the resonant complex. Here we report a v…
We have studied interspecies scattering in an ultracold mixture of $^{87}$Rb and $^{133}$Cs atoms, both in their lowest-energy spin states. The three-body loss signatures of 30 incoming s- and p-wave magnetic Feshbach resonances over the range 0 to 667 G have been catalogued. Magnetic field modulation spectroscopy was used to observe molecular states bound by up to 2.5 MHz$\times h$. Magnetic moment spectroscopy along the magneto-association pathway from 197 to 182 G gives results consistent with the observed and calculated dependence of the binding energy on magnetic field strength. We have c…
Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of $^{87}$Rb, between the $|\rm{F} = 1, \rm{m_F}=1 \rangle$ and $|\rm{F} = 2, \rm{m_F}=0 \rangle$ states. Despite the loss features being $\lesssim0.1$ G wide, we require only 21 experimental runs to explore a magnetic field range >18 G, where $1~\rm{G}=10^{-4}$ T. The resonances cons…
We develop a complete theoretical description of photoassociative Stimulated Raman Adiabatic Passage (STIRAP) near a Feshbach resonance in a thermal atomic gas. We show that it is possible to use low intensity laser pulses to directly excite the continuum at a Feshbach resonance and transfer nearly the entire atomic population to the lowest rovibrational level in the molecular ground state. In case of a broad resonance, commonly found in several diatomic alkali molecules, our model predicts a transfer efficiency $η$ up to 97% for a given atom pair, and up to 70% when averaged over an atomic en…
We investigate magnetically tunable Feshbach resonances between ultracold europium atoms and between europium and alkali-metal atoms using multichannel quantum scattering calculations. For ultracold gases of europium atoms both homonuclear $^{153}$Eu+$^{153}$Eu and heteronuclear $^{151}$Eu+$^{153}$Eu systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of $^{153}$Eu+$^{87}$Rb and $^{153}$Eu+$^7$Li. We analyze the prospects for the control of scattering properties, observation of quantum chaotic behavior, and magnetoassociation …
Most of the current theories on the p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low energy p-wave scattering amplitude $f_1(k)$ is given by $% f_1(k)=-1/[ik+1/(\mathcal{V}k^2)+1/\mathcal{R}]$, where $k$ is the incident momentum, and $\mathcal{V}$ and $\mathcal{R}$ are the $k$-independent scattering volume and effective-range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the p-wave scattering amplitude of the two atoms is not described by the e…
Recently a new type of Feshbach resonance, i.e., orbital Feshbach resonance (OFR) was proposed for the ultracold alkali-earth (like) atoms, and experimentally observed in the ultracold gases of $^{\rm 173}$Yb atoms. Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when the OFR of $^{\rm 173}$Yb atoms appears, the energy gap between the thresholds of the open channel (OC) and the closed channel (CC) is much smaller than the characteristic energy of the inter-atomic interaction, i.e., the van der Waals energy. In this paper we study the OFR in the systems with small CC-…
Decay of bound states due to coupling with free particle states is a general phenomenon occurring at energy scales from MeV in nuclear physics to peV in ultracold atomic gases. Such a coupling gives rise to Fano-Feshbach resonances (FFR) that have become key to understanding and controlling interactions - in ultracold atomic gases, but also between quasiparticles such as microcavity polaritons. The energy positions of FFR were shown to follow quantum chaotic statistics. In contrast, lifetimes which are the fundamental property of a decaying state, have so far escaped a similarly comprehensive …
We consider a fully polarized ultracold Fermi gas interacting through a p-wave Feshbach resonance. Using a two-channel model, we find the effective potential at the point where the p-wave scattering length goes to zero. Here the effective interaction provides attraction and one can therefore ask about the stability of the system. We calculate the energy density of the system in the Thomas-Fermi approximation, determine the profile of the gas, and the critical number of particle in the system as function of the relevant interaction parameters. The instability can be deduced from a simple breath…
We employ a quantum defect theory framework to provide a detailed analysis of the interplay between a magnetic Feshbach resonance and a shape resonance in cold collisions of ultracold $\rm ^{87}Rb$ atoms as captured in recent experiments using a laser-based collider [Phys. Rev. Research 3, 033209 (2021)]. By exerting control over a parameter space spanned by both collision energy and magnetic field, the width of a Feshbach resonance can be tuned over several orders of magnitude. We apply a quantum defect theory specialized for ultracold atomic collisions to fully describe of the experimental o…
In the vicinity of a narrow Feshbach resonances Efimov features are expected to be characterized by the resonance's properties rather than the van der Waals length of the interatomic potential. Although this theoretical prediction is well-established by now, it still lacks experimental confirmation. Here, we apply our recently developed three-channel model [Yudkin and Khaykovich, Phys. Rev. A 103, 063303 (2021)] to the experimental result obtained in a mass-imbalanced $^6$Li-$^{133}$Cs mixture in the vicinity of the narrowest resonance explored to date [Johansen at. al. Nat. Phys. 13, 731 (201…
We have analyzed our recently-measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet 4He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides new evidence for a universal 3BP, the first outside the group of alkali-metal elements.…
We report on the detection of extremely narrow Feshbach resonances by employing a Mott-insulating state for cesium atoms in a three-dimensional optical lattice. The Mott insulator protects the atomic ensemble from high background three-body losses in a magnetic field region where a broad Efimov resonance otherwise dominates the atom loss in bulk samples. Our technique reveals three ultra-narrow and previously unobserved Feshbach resonances in this region with widths below $\approx 10\,μ$G, measured via Landau-Zener-type molecule formation and confirmed by theoretical predictions. For comparati…
We perform one- and two-photon high resolution spectroscopy on ultracold samples of RbCs Feshbach molecules with the aim to identify a suitable route for efficient ground-state transfer in the quantum-gas regime to produce quantum gases of dipolar RbCs ground-state molecules. One-photon loss spectroscopy allows us to probe deeply bound rovibrational levels of the mixed excited (A1Σ+ - b3Π0) 0+ molecular states. Two-photon dark state spectroscopy connects the initial Feshbach state to the rovibronic ground state. We determine the binding energy of the lowest rovibrational level |v"=0,J"=0> of t…
We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for $^{87}$Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.
Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known r…
The many-boson problem in presence of an asymptotically narrow Feshbach resonance is considered. The low energy properties are investigated using a two-channel Hamiltonian. The energy spectrum of this model is shown to be bounded from below in the limit of zero range interaction. This implies the promising possibility of achieving a strongly interacting bosonic phase in a dilute regime where the details of the actual interatomic forces are irrelevant. The integral relation between the energy and the one-body momentum distribution is derived.
The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground state ener…
In this paper we explore the spin-orbit-induced bound state and molecular signature of the degenerate Fermi gas in a narrow Feshbach resonance based on a generalized two-channel model. Without the atom-atom interactions, only one bound state can be found even if spin-orbit coupling exists. Moreover, the corresponding bound-state energy depends strongly on the strength of spin-orbit coupling, but is influenced slightly by its type. In addition, we find that when increasing the strength of spin-orbit coupling, the critical point at which the molecular fraction vanishes shifts from zero to the ne…
