Magnetic Feshbach Resonances Research Articles

Effects of magnetic dipole-dipole interactions in atomic Bose-Einstein condensates with tunables-wave interactions

The s-wave interaction is usually the dominant form of interactions in atomic Bose-Einstein condensates (BECs). Recently, Feshbach resonances have been employed to reduce the strength of the s-wave interaction in many atomic speicies. This opens the possibilities to study magnetic dipole-dipole interactions (MDDI) in BECs, where the novel physics resulting from long-range and anisotropic dipolar interactions can be explored. Using a variational method, we study the effect of MDDI on the statics and dynamics of atomic BECs with tunable s-wave interactions. We benchmark our calculation against previously observed MDDI effects in $^{52}$Cr with excellent agreement, and predict new effects that should be promising to observe experimentally. A parameter of magnetic Feshbach resonances, $\epsilon_{dd,\text{max}}$, is used to quantitatively indicate the feasibility of experimentally observing MDDI effects in different atomic species. We find that strong MDDI effects should be observable in both in-trap and time-of-flight behaviors for the alkali BECs of $^{7}$Li, $^{39}$K, and $^{133}$Cs. Our results provide a helpful guide for experimentalists to realize and study atomic dipolar quantum gases.

Causality, universality, and effective field theory for van der Waals interactions

We analyze low-energy scattering for arbitrary short-range interactions plus an attractive 1/r^6 tail. We derive the constraints of causality and unitarity and find that the van der Waals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1/r^6 tail. We argue that a similar universality class exists for any attractive potential 1/r^{alpha} for alpha >= 2. We also discuss the extension to multi-channel systems near a magnetic Feshbach resonance. We discuss the implications for effective field theory with attractive singular power law tails.

Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances

We report on a proposal to reduce the group velocity of a small ``laser'' Bose-Einstein condensate upon passing through a larger ``medium'' condensate of the same isotopic species in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaevskii equation is used to derive an expression for the group velocity in a homogeneous medium as well as for the spatial delay $\ensuremath{\delta}$, through a finite-sized medium BEC with a Thomas-Fermi density distribution. We predict a maximum reduction of the group velocity by a half, which physically corresponds to freely propagating Feshbach molecules. For typical narrow Feshbach resonances and a medium with number density ${10}^{15}$ cm${}^{\ensuremath{-}3}$, up to $85%$ of the lower bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal.

Many Bosons in a Narrow Magnetic Feshbach Resonance

The many-boson problem in the 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 a 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.

Control of Resonant Interaction between Electronic Ground and Excited States

We observe magnetic Feshbach resonances in a collision between the ground and metastable states of two-electron atoms of ytterbium (Yb). We measure the on-site interaction of doubly occupied sites of an atomic Mott-insulator state in a three-dimensional optical lattice as a collisional frequency shift in a high-resolution laser spectroscopy. The observed spectra are well fitted by a simple theoretical formula, in which two particles with an s-wave contact interaction are confined in a harmonic trap. This analysis reveals a wide variation of the interaction with a resonance behavior around a magnetic field of about 1.1 G for the energetically lowest magnetic sublevel of 170Yb, as well as around 360 mG for the energetically highest magnetic sublevel of 174Yb. The observed Feshbach resonance can only be induced by an anisotropic interatomic interaction. This scheme will open the door to a variety of studies using two-electron atoms with tunable interaction.

Dynamic effects of a Feshbach resonance on Bragg scattering from a Bose-Einstein condensate

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 an experiment [Papp et al., Phys. Rev. Lett. 101, 135301 (2008)] investigating the effects of strong interactions on the Bragg spectrum from a ${}^{85}$Rb BEC. Results from these simulations and from our previous calculations using an atom-molecule Bogoliubov approach are in very good quantitative agreement with the experimental results, confirming the importance of the resonance bound state in the dynamics of the condensate for fast experiments like Bragg scattering.

Fermion pairing across a dipolar interaction induced resonance.

It is known from the solution of the two-body problem that an anisotropic dipolar interaction can give rise to s-wave scattering resonances, which are named dipolar interaction induced resonances (DIIR). In this Letter, we study the zero-temperature many-body physics of a two-component Fermi gas across a DIIR. In the low-density regime, it is very striking that the resulting pairing order parameter is a nearly isotropic singlet pairing and the physics can be well described by an s-wave resonant interaction potential with finite range conditions, despite the anisotropic nature of the dipolar interaction. The pairing energy is as strong as a unitary Fermi gas near a magnetic Feshbach resonance. In the high-density regime, the anisotropic effect plays an important role. We find phase transitions from singlet pairing to a state with mixed singlet and triplet pairing and then from mixed pairing to pure triplet pairing. The state with mixed pairing spontaneously breaks the time-reversal symmetry.

Shifts and widths of Feshbach resonances in atomic waveguides

We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of $s$-, $d$-, and $g$-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of $s$-wave resonant scattering.

Resonant manipulation ofd-wave interaction of cold atoms with two lasers and a magnetic field

We present a theory for manipulation of $d$-wave interaction of cold atoms with two lasers strongly driving two photoassociative transitions. The theory predicts the occurrence of a coherence between two excited ro-vibrational bound states due to the photoassociative dipole couplings of ground-state $d$-wave scattering state to the bound states. We show that this excited-state coherence significantly influences atom-atom interaction. In particular, this leads to the enhancement of $d$-wave elastic scattering and to the suppression of inelastic scattering. In the presence of an $s$-wave magnetic Feshbach resonance, the two lasers can couple the $s$-wave resonance with the $d$-wave scattering state, leading to the further enhancement in $d$-wave scattering at relatively low energy. Our numerical calculations based on realistic parameters show that $d$-wave manipulation would be most effective in case of atoms having excited diatomic states with narrow natural linewidth. We estimate that at an energy of 100 $\ensuremath{\mu}$K the inelastic scattering rate in Yb can be reduced to 20 s${}^{\ensuremath{-}1}$ while the elastic scattering rate can be two orders of magnitude larger.

Direct evaporative cooling of39K atoms to Bose-Einstein condensation

We report the realization of a Bose-Einstein condensate of ${}^{39}$K atoms without the aid of an additional atomic coolant. Our route to Bose-Einstein condensation comprises sub-Doppler laser cooling of large atomic clouds with more than ${10}^{10}$ atoms and evaporative cooling in an optical dipole trap where the collisional cross section can be increased using magnetic Feshbach resonances. Large condensates with almost ${10}^{6}$ atoms can be produced in less than 15 s. Our achievements eliminate the need for sympathetic cooling with Rb atoms, which was the usual route implemented until now due to the unfavorable collisional property of ${}^{39}$K. Our findings simplify the experimental setup for producing Bose-Einstein condensates of ${}^{39}$K atoms with tunable interactions, which have a wide variety of promising applications, including atom interferometry to studies on the interplay of disorder and interactions in quantum gases.

Preparation and Spectroscopy of a Metastable Mott-Insulator State with Attractive Interactions

We prepare and study a metastable attractive Mott-insulator state formed with bosonic atoms in a three-dimensional optical lattice. Starting from a Mott insulator with Cs atoms at weak repulsive interactions, we use a magnetic Feshbach resonance to tune the interactions to large attractive values and produce a metastable state pinned by attractive interactions with a lifetime on the order of 10 s. We probe the (de)excitation spectrum via lattice modulation spectroscopy, measuring the interaction dependence of two- and three-body bound-state energies. As a result of increased on-site three-body loss we observe resonance broadening and suppression of tunneling processes that produce three-body occupation.

Bose-Einstein Condensation of Erbium

We report on the achievement of Bose-Einstein condensation of erbium atoms and on the observation of magnetic Feshbach resonances at low magnetic fields. By means of evaporative cooling in an optical dipole trap, we produce pure condensates of 168Er, containing up to 7×10(4) atoms. Feshbach spectroscopy reveals an extraordinary rich loss spectrum with six loss resonances already in a narrow magnetic-field range up to 3 G. Finally, we demonstrate the application of a low-field Feshbach resonance to produce a tunable dipolar Bose-Einstein condensate and we observe its characteristic d-wave collapse.

Towards the production of ultracold ground-state RbCs molecules: Feshbach resonances, weakly bound states, and the coupled-channel model

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 cataloged. Magnetic field modulation spectroscopy was used to observe molecular states bound by up to 2.5 $\text{MHz}\ifmmode\times\else\texttimes\fi{}h$. We have created RbCs Feshbach molecules using two of the resonances. Magnetic moment spectroscopy along the magnetoassociation 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 set up a coupled-channel model of the interaction and have used direct least-squares fitting to refine its parameters to fit the experimental results from the Feshbach molecules, in addition to the Feshbach resonance positions and the spectroscopic results for deeply bound levels. The final model gives a good description of all the experimental results and predicts a large resonance near 790 G, which may be useful for tuning the interspecies scattering properties. Quantum numbers and vibrational wave functions from the model can also be used to choose optimal initial states of Feshbach molecules for their transfer to the rovibronic ground state using stimulated Raman adiabatic passage.

Optical Control of Feshbach Resonances in Fermi Gases Using Molecular Dark States

We propose a general method for optical control of magnetic Feshbach resonances in ultracold atomic gases with more than one molecular state in an energetically closed channel. Using two optical frequencies to couple two states in the closed channel, inelastic loss arising from spontaneous emission is greatly suppressed by destructive quantum interference at the two-photon resonance, i.e., dark-state formation, while the scattering length is widely tunable by varying the frequencies and/or intensities of the optical fields. This technique is of particular interest for a two-component atomic Fermi gas, which is stable near a Feshbach resonance.

Ultracold bosons in the vicinity of a narrow resonance: Shallow dimer and recombination

The different resonant regimes that can be achieved by using a magnetic Feshbach resonance are analyzed with a separable two-channel model. Emphasis is put on the case of narrow resonances in a region of intermediate detuning where a shallow dimer exists and an approximate law including the background scattering length for the three-body recombination rate is derived.

Feshbach resonances in an ultracold mixture of 87Rb and 40K

We report the experimental preparations of the absolute ground states of 87Rb and 40K atoms (|F = 1, mF = 1〉 + |F = 9/2, mF = −9/2〉) by means of the radio-frequency and microwave adiabatic rapid passages, and the observation of magnetic Feshbach resonances in an ultracold mixture of bosonic 87Rb and fermionic 40K atoms between 0 T and 6.0 × 10−2 T, including 7 homonuclear and 4 heteronuclear Feshbach resonances. The resonances are identified by the abrupt trap loss of atoms induced by the strong inelastic three-body collisions. These Feshbach resonances should enable the experimental control of interspecies interactions.

Analytic description of atomic interaction at ultracold temperatures. II. Scattering around a magnetic Feshbach resonance

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 tuning of the effective range and the generalized effective range by a magnetic field.

Multichannel quantum-defect theory for ultracold atom–ion collisions

We develop an analytical model for ultracold atom–ion collisions using the multichannel quantum-defect formalism. The model is based on analytical solutions of the r−4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of atom–ion interaction in the ultracold domain in terms of only three parameters: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher-order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40Ca+ ion and a Na atom, and compared with numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.

Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium

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 200 mT. 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 Feshbach resonances in terms of the asymptotic-bound-state model is presented.

Scattering amplitude of ultracold atoms near thep-wave magnetic Feshbach resonance

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 effective-range theory. In this paper we provide an explicit calculation for the p-wave scattering of two ultracold atoms near the p-wave magnetic Feshbach resonance (PMFR). We show that the low energy p-wave scattering amplitude in the presence of PMFR takes the form $f_1(k)=-1/[ik+1/(\mathcal{V}^{\mathrm{eff}}k^2)+1/(\mathcal{S}^{\mathrm{eff}%}k)+1/\mathcal{R}^{\mathrm{eff}}]$ where $\mathcal{V}^{\mathrm{eff}},$ $% \mathcal{S}^{\mathrm{eff}}$ and $\mathcal{R}^{\mathrm{eff}}$ are $k$% -dependent parameters. Based on this result, we show sufficient conditions for the effective range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the p-wave scattering in the ultracold gases of $^{6}$Li and $^{40}$K when the scattering volume is enhanced by the resonance.