The physics of Feshbach resonance is analyzed using an analytic expression for the $s$-wave scattering phase-shift and the scattering length $a$ which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that for strong inter-channel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultra-cold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of $a$ on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift $\varepsilon-\varepsilon_B$, where $\varepsilon$ is the scattering energy and $\varepsilon_B$ is the bound state energy in the closed channel (when there is one).
We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectroscopy in a range where one broad and two narrow Feshbach resonances overlap. From the data we accurately determine the Cs atomic scattering length and the positions and widths of two particular resonances…
Using a two-channel model, we investigate theoretically the binding energy of confinement-induced Feshbach molecules in two- and one-dimensional ultracold atomic systems, near a Feshbach resonance. We show that the two-channel prediction will evidently deviate from the simple single-channel theory as the width of Feshbach resonances decreases. For one-dimensional system, we perform a full two-channel calculation, with the inclusion of bare interatomic interactions in the open channel. Away from the resonance, we find a sizable correction to the binding energy, if we neglect incorrectly the bar…
In the ultracold gases of alkali-earth (like) atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}$Yb atoms. When the OFR of the $^{173}$Yb atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitudes than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multi-channel quantum defect theory (MQDT), which is based on the exact solution of the Schr$\ddot{\rm o}$dinger equation wit…
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.
The line shape of radio frequency spectra of tightly bound Feshbach molecules in strong transverse confinement can be described by a simple analytic formula that includes final state interactions. By direct comparison to experimental data, we clarify the role of effective range corrections to two-body bound-state energies in lower dimensions.
We have measured the binding energy of $^7$Li Feshbach molecules deep into the non-universal regime by associating free atoms in a Bose-Einstein condensate by modulating the magnetic field. We extract the scattering length from these measurements, correcting for non-universal short-range effects using several different methods. We find that field-dependent effective range corrections agree well with the data. With this more precise determination of the scattering length vs. field we reanalyze our previous data on the location of atom loss features produced by the Efimov effect \cite{PollackSci…
Feshbach resonances are among the essential control tools used in ultracold atom experiments. However, for complex atomic species the theoretical characterization of resonances becomes challenging. For closely spaced resonances, the measurement of three-body losses does not provide sufficient resolution to discriminate them. For this reason, resonance spectroscopy of trapped isolated atoms is becoming the state of the art. Here we show that trapping the atoms in a double well potential such as an optical lattice or a pair of optical tweezers enables precise characterization of not only the res…
We compare and contrast the wide Fehbach resonances and the corresponding weakly bound states in the lowest scattering channels of ultracold $^6$Li and $^7$Li. We use high-precision measurements of binding energies and scattering properties to determine new interaction potentials, incorporating non-Born-Oppenheimer terms to account for the failure of mass scaling between $^6$Li and $^7$Li. Correction terms are needed for both the singlet and the triplet potential curves. The universal formula relating binding energy to scattering length is not accurate for either system. The $^6$Li resonance i…
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value due to many-body effect. When the scattering length $a_s$ of atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most reg…
The ultracold mixture of \Na and \Rb atoms has become an important system for investigating physics in Bose-Bose atomic mixtures and for forming ultracold ground-state polar molecules. In this work, we provide an improved characterization of the most commonly used Feshbach resonance near 347.64 G between \Na and \Rb in their absolute ground states. We form Feshbach molecules using this resonance and measure their binding energies by dissociating them via magnetic field modulation. We use the binding energies to refine the singlet and triplet potential energy curves, using coupled-channel bound…
We reveal the existence of high-density Feshbach resonances in the collision between the ground and metastable states of $^{171}$Yb and coherently produce the associated Feshbach molecules by photoassociation. The extremely small transition rate is overcome by the enhanced Franck-Condon factor of the weakly bound Feshbach molecule, allowing us to observe Rabi oscillations with long decay time between an atom pair and a molecule in an optical lattice. We also perform the precision measurement of the binding energies, which characterizes the observed resonances. The ultra-narrow photoassociation…
The orbital Feshbach resonance (OFR) is a novel scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block, or frustrate, the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional $^{173}$Yb system. We find that by adding a closed-…
We study the interspecies scattering properties of ultracold Li-Cs mixtures in their two energetically lowest spin channels in the magnetic field range between 800 G and 1000 G. Close to two broad Feshbach resonances we create weakly bound LiCs dimers by radio-frequency association and measure the dependence of the binding energy on the external magnetic field strength. Based on the binding energies and complementary atom loss spectroscopy of three other Li-Cs s-wave Feshbach resonances we construct precise molecular singlet and triplet electronic ground state potentials using a coupled-channe…
We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wavefunction, binding energy and effective mass, are determined from the two-particle solution of two-interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Ferm…
We studied the thermodynamic behaviors of non-interacting bosons and fermions trapped by a scale-invariant branching structure of adjustable degree of heterogeneity. The full energy spectrum in tight-binding approximation was analytically solved . We found that the log-periodic oscillation of the specific heat for Fermi gas depended on the heterogeneity of hopping. Also, low dimensional Bose-Einstein condensation occurred only for non-homogeneous setup.
We report the creation of ultracold bosonic $^{23}$Na$^{87}$Rb Feshbach molecules via magneto-association. By ramping the magnetic field across an interspecies Feshbach resonance, at least 4000 molecules can be produced out of the near degenerate ultracold mixture. Fast loss due to inelastic atom-molecule collisions is observed, which limits the pure molecule number, after residual atoms removal, to 1700. The pure molecule sample can live for 21.8(8) ms in the optical trap, long enough for future molecular spectroscopy studies toward coherently transferring to the singlet ro-vibrational ground…
Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshb…
We report on the observation of Feshbach resonances at low magnetic field strength (below 10 G) in the Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for applications, we consider a resonance near 7.29 G, which combines accurate magnetic tunability and access to the universal regime of interactions with experimental simplicity. We show that lifetimes of a few 100 ms can be achieved for the optically trapped, resonantly interacting mixture. We al…
We produce Bose-Einstein condensates of $^{162}$Dy atoms employing an innovative technique based on a resonator-enhanced optical trap that allows efficient loading from the magneto-optical trap and fast evaporation. We characterize the scattering properties of the ultracold atoms for magnetic fields between 6 and 30 G. In addition to the typical chaotic distribution of narrow Feshbach resonances in Lanthanides, we discover two rather isolated broad features at around 22 G and 27 G. A characterization using the complementary measurements of losses, thermalization, anisotropic expansion and mole…
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…
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 have performed radio-frequency dissociation spectroscopy of weakly bound ^6Li_2 Feshbach molecules using low-density samples of about 30 molecules in an optical dipole trap. Combined with a high magnetic field stability this allows us to resolve the discrete trap levels in the RF dissociation spectra. This novel technique allows the binding energy of Feshbach molecules to be determined with unprecedented precision. We use these measurements as an input for a fit to the ^6Li scattering potential using coupled-channel calculations. From this new potential, we determine the pole positions of t…
We study the use of an optical Feshbach resonance to modify the p-wave interaction between ultracold polarized Yb-171 spin-1/2 fermions. A laser exciting two colliding atoms to the 1S_0 + 3P_1 channel can be detuned near a purely-long-range excited molecular bound state. Such an exotic molecule has an inner turning point far from the chemical binding region and thus three-body-recombination in the Feshbach resonance will be highly suppressed in contrast to that typically seen in a ground state p-wave magnetic Feshbach resonance. We calculate the excited molecular bound-state spectrum using a m…
We explore the scattering properties of ultracold ground-state Cs atoms at magnetic fields between 450 G (45 mT) and 1000 G. We identify 17 new Feshbach resonances, including two very broad ones near 549 G and 787 G. We measure the binding energies of several different dimer states by magnetic field modulation spectroscopy. We use least-squares fitting to these experimental results, together with previous measurements at lower field, to determine a new 6-parameter model of the long-range interaction potential, designated M2012. Coupled-channels calculations using M2012 provide an accurate mapp…
We consider the stability of an ultracold trapped Bose-Einstein condensate near a Feshbach resonance. Using a modified Gross-Pitaevskii equation that includes higher-order terms and a multi-channel model of Feshbach resonances, we find regions where stability can be enhanced or suppressed around experimentally measured resonances. We suggest a number of ways to probe the stability diagram. Using scattering length zero-crossings huge deviations are founds for the critical particle number. Effects are enhanced for narrow resonances or tighter traps. Macroscopic tunneling of the condensate is ano…
We discuss how to construct tight-binding models for ultra cold atoms in honeycomb potentials, by means of the maximally localized Wannier functions (MLWFs) for composite bands introduced by Marzari and Vanderbilt [1]. In particular, we work out the model with up to third-nearest neighbors, and provide explicit calculations of the MLWFs and of the tunneling coefficients for the graphene-lyke potential with two degenerate minima per unit cell. Finally, we discuss the degree of accuracy in reproducing the exact Bloch spectrum of different tight-binding approximations, in a range of typical exper…
We consider finite-range effects when the scattering length goes to zero near a magnetically controlled Feshbach resonance. The traditional effective-range expansion is badly behaved at this point and we therefore introduce an effective potential that reproduces the full T-matrix. To lowest order the effective potential goes as momentum squared times a factor that is well-defined as the scattering length goes to zero. The potential turns out to be proportional to the background scattering length squared times the background effective range for the resonance. We proceed to estimate the applicab…
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy $\varepsilon_0$ and the resonance is triggered by the microscopic interchannel coupling $U_{12}$. The binding energy $\varepsilon_0$ …
We study ideal Bose gas upon two scale-free structures with identical degree distribution. Energy spectra belonging to tight-binding Hamiltonian are exactly solved and the related spectral dimensions of $G_1$ and $ G_2$ are obtained as $d_{s_1} = 2$ and $d_{s_2} = 2 \ln 4/ \ln 3$. We show Bose-Einstein condensation will only take place upon $G_2$ instead of $G_1$. The topology and thermodynamical property of the two structures are proven to be totally different.
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…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. Béri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).
We present an accurate ab initio tight-binding model, capable of describing the dynamics of Dirac points in tunable honeycomb optical lattices following a recent experimental realization [L. Tarruell et al., Nature 483, 302 (2012)]. Our scheme is based on first-principle maximally localized Wannier functions for composite bands. The tunneling coefficients are calculated for different lattice configurations, and the spectrum properties are well reproduced with high accuracy. In particular, we show which tight binding description is needed in order to accurately reproduce the position of Dirac p…
Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals require unphysical conditions such as realizing purely non-Hermitian systems. Here we present a way for the realization of free Fock parafermions in the tight-binding model with controlled dissipation of a very simple form. Introducing dissipation transforms an originally non-integrable quantum model to an exactly solvable classical one.
