Ultracold molecule production via a resonant oscillating magnetic field

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Channel Selection of Ultracold Atom-Molecule Scattering in Dynamic Magnetic Fields

We demonstrate that final states of ultracold molecules by scattering with atoms can be selectively produced using dynamic magnetic fields of multiple frequencies. We develop a multifrequency Floquet coupled channel method to study the channel selection by dynamic magnetic field control, which can be interpreted by a generalized quantum Zeno effect for the selected scattering channels. In particular, we use an atom-molecule spin-flip scattering to show that the transition to certain final states of the molecules in the inelastic scattering can be suppressed by engineered coupling between the Floquet states.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Evidence for the association of triatomic molecules in ultracold 23Na40K + 40K mixtures

Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics and quantum simulation with molecules^1-3. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in a mixture of ultracold atoms and diatomic molecules by using a Feshbach resonance between them^4,5. Although ultracold atom-diatomic-molecule Feshbach resonances have been observed recently^6,7, using these resonances to form triatomic molecules remains challenging. Here we report on evidence of the association of triatomic molecules near the Feshbach resonance between ²³Na⁴⁰K molecules in the rovibrational ground state and ⁴⁰K atoms. We apply a radio-frequency pulse to drive the free-bound transition in ultracold mixtures of ²³Na⁴⁰K and ⁴⁰K and monitor the loss of ²³Na⁴⁰K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature. The observation that the distance between the association feature and the atomic transition changes with the magnetic field provides strong evidence for the formation of triatomic molecules. The binding energy of the triatomic molecules is estimated from the measurements. Our work contributes to the understanding of the complex ultracold atom-molecule Feshbach resonances and may open up an avenue towards the preparation and control of ultracold triatomic molecules.

Quantum register of fermion pairs

Quantum control of motion is central for modern atomic clocks¹ and interferometers². It enables protocols to process and distribute quantum information^3,4, and allows the probing of entanglement in correlated states of matter⁵. However, the motional coherence of individual particles can be fragile to maintain, as external degrees of freedom couple strongly to the environment. Systems in nature with robust motional coherence instead often involve pairs of particles, from the electrons in helium, to atom pairs⁶, molecules⁷ and Cooper pairs. Here we demonstrate long-lived motional coherence and entanglement of pairs of fermionic atoms in an optical lattice array. The common and relative motion of each pair realize a robust qubit, protected by exchange symmetry. The energy difference between the two motional states is set by the atomic recoil energy, is dependent on only the mass and the lattice wavelength, and is insensitive to the noise of the confining potential. We observe quantum coherence beyond ten seconds. Modulation of the interactions between the atoms provides universal control of the motional qubit. The methods presented here will enable coherently programmable quantum simulators of many-fermion systems⁸, precision metrology based on atom pairs and molecules^9,10 and, by implementing further advances^11-13, digital quantum computation using fermion pairs¹⁴.

Topological pumping of a 1D dipolar gas into strongly correlated prethermal states

Long-lived excited states of interacting quantum systems that retain quantum correlations and evade thermalization are of great fundamental interest. We create nonthermal states in a bosonic one-dimensional (1D) quantum gas of dysprosium by stabilizing a super-Tonks-Girardeau gas against collapse and thermalization with repulsive long-range dipolar interactions. Stiffness and energy-per-particle measurements show that the system is dynamically stable regardless of contact interaction strength. This enables us to cycle contact interactions from weakly to strongly repulsive, then strongly attractive, and finally weakly attractive. We show that this cycle is an energy-space topological pump (caused by a quantum holonomy). Iterating this cycle offers an unexplored topological pumping method to create a hierarchy of increasingly excited prethermal states.

A digital feedback controller for stabilizing large electric currents to the ppm level for Feshbach resonance studies

Magnetic Feshbach resonances are a key tool in the field of ultracold quantum gases, but their full exploitation requires the generation of large, stable magnetic fields up to 1000 G with fractional stabilities of better than 10^-4. Design considerations for electromagnets producing these fields, such as optical access and fast dynamical response, mean that electric currents in excess of 100 A are often needed to obtain the requisite field strengths. We describe a simple digital proportional-integral-derivative current controller constructed using a field-programmable gate array and off-the-shelf evaluation boards that allows for gain scheduling, enabling optimal control of current sources with non-linear actuators. Our controller can stabilize an electric current of 337.5 A to the level of 7.5 × 10^-7 in an averaging time of 10 min and with a control bandwidth of 2 kHz.

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses

The molecular association process in a thermal gas of ^{85}Rb is investigated where the effects of the envelope of the radio-frequency field are taken into account. For experimentally relevant parameters our analysis shows that with increasing pulse length the corresponding molecular conversion efficiency exhibits low-frequency interference fringes which are robust under thermal averaging over a wide range of temperatures. This dynamical interference phenomenon is attributed to Stückelberg phase accumulation between the low-energy continuum states and the dressed molecular state which exhibits a shift proportional to the envelope of the radio-frequency pulse intensity.

Effective Atom-Molecule Conversions Using Radio Frequency Fields

The present study is inspired by the Wieman group experiment [Phys. Rev. Lett. 2005, 95, 190404], in which they use a slow modulated magnetic field to effectively transfer rubidium atoms into cold molecules near a Feshbach resonance. We develop a time-dependent collision theory based on two channel model potentials to study the atom-molecule population transfer induced by a single-color radio frequency field in an ultracold ⁸⁷ Rb gas. Wave-packet dynamical simulations allow an investigation of both bound-bound transitions and free-bound transitions. The effects of temperature, detuning and the RF amplitude on the population transfer are discussed in detail. Some of our simulations suggest that oscillatory atom-molecule conversion could originate from the long coherence time of the wave packet. This coherence time is unusually long in ultracold gases because the collision energy is typically quite well-defined.

Ultracold Dipolar Molecules Composed of Strongly Magnetic Atoms

In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two-dimensional geometry can be reduced by using the anisotropy of the dipole-dipole interaction and that this reduction follows a universal dipolar behavior.

Inducing Resonant Interactions in Ultracold Atoms with a Modulated Magnetic Field

In systems of ultracold atoms, pairwise interactions can be resonantly enhanced by a new mechanism that does not rely upon a magnetic Feshbach resonance. In this mechanism, interactions are controlled by tuning the frequency of an oscillating parallel component of the magnetic field close to the transition frequency between the scattering atoms and a two-atom bound state. The real part of the resulting s-wave scattering length a is resonantly enhanced when the oscillation frequency is close to the transition frequency. The resonance parameters can be controlled by varying the amplitude of the oscillating field. The amplitude also controls the imaginary part of a, which arises because the oscillating field converts atom pairs into molecules. The real part of a can be made much larger than the background scattering length without introducing catastrophic atom losses from the imaginary part. For the case of a shallow bound state in the scattering channel, the dimensionless resonance parameters are universal functions of the dimensionless oscillation amplitude.

Quantum Dynamics with Spatiotemporal Control of Interactions in a Stable Bose-Einstein Condensate

Optical control of atomic interactions in quantum gases is a long-sought goal of cold atom research. Previous experiments have been hindered by rapid decay of the quantum gas and parasitic deformation of the trap potential. We develop and implement a generic scheme for optical control of Feshbach resonances which yields long quantum gas lifetimes and a negligible parasitic dipole force. We show that fast and local control of interactions leads to intriguing quantum dynamics in new regimes, highlighted by the formation of van der Waals molecules and localized collapse of a Bose condensate.

Feshbach-stabilized insulator of bosons in optical lattices

Feshbach resonances-namely, resonances between an unbound two-body (atomic) state and a bound (molecular) state, differing in magnetic moment-are a unique tool to tune the interaction properties of ultracold atoms. Here we show that the spin-changing interactions, coherently coupling the atomic and molecular states, can act as a novel mechanism to stabilize an insulating phase-the Feshbach insulator-for bosons in an optical lattice close to a narrow Feshbach resonance. Making use of quantum Monte Carlo simulations and mean-field theory, we show that the Feshbach insulator appears around the resonance, preventing the system from collapsing when the effective atomic scattering length becomes negative. On the atomic side of the resonance, the transition from condensate to Feshbach insulator has a characteristic first-order nature, due to the simultaneous loss of coherence in the atomic and molecular components. These features appear clearly in the ground-state phase diagram of, e.g., ^{87}Rb around its 414 G resonance, and they are therefore directly amenable to experimental observation.

Association of atoms into universal dimers using an oscillating magnetic field

In a system of ultracold atoms near a Feshbach resonance, pairs of atoms can be associated into universal dimers by an oscillating magnetic field with a frequency near that determined by the dimer binding energy. We present a simple expression for the transition rate that takes into account many-body effects through a transition matrix element of the contact. In a thermal gas, the width of the peak in the transition rate as a function of the frequency is determined by the temperature. In a dilute Bose-Einstein condensate of atoms, the width is determined by the inelastic scattering rates of a dimer with zero-energy atoms. Near an atom-dimer resonance, there is a dramatic increase in the width from inelastic atom-dimer scattering and from atom-atom-dimer recombination. The recombination contribution provides a signature for universal tetramers that are Efimov states consisting of two atoms and a dimer.

Rabi oscillations between atomic and molecular condensates driven with coherent one-color photoassociation

We demonstrate coherent one-color photoassociation of a Bose-Einstein condensate, which results in Rabi oscillations between atomic and molecular condensates. We attain atom-molecule Rabi frequencies that are comparable to decoherence rates by driving photoassociation of atoms in an ^{88}Sr condensate to a weakly bound level of the metastable 1S0+3P1 molecular potential, which has a long lifetime and a large Franck-Condon overlap integral with the ground scattering state. Transient shifts and broadenings of the excitation spectrum are clearly seen at short times, and they create an asymmetric excitation profile that only displays Rabi oscillations for blue detuning from resonance.

Quadrupole response of a weakly bound bosonic trimer

The inelastic response of a bosonic trimer is explored in the confines of the Borromean region. To this end we model the interaction between the external field and the bosonic system as a photoabsorptionlike process and study the response of the trimer in the quadrupole approximation. We utilize the hyperspherical-harmonics expansion to solve the Schrödinger equation and the Lorentz integral transform method to calculate the reaction. It is found that the magnitude of the response function and corresponding sum rules increase exponentially when approaching the 3-body threshold. It is also found that this increase is governed by unnatural exponents. The connection between our results and radio-frequency experiments in ultracold atom systems is made.

Rotons in interacting ultracold bose gases

In three dimensions, noninteracting bosons undergo Bose-Einstein condensation at a critical temperature, T(c), which is slightly shifted by ΔT(c), if the particles interact. We calculate the excitation spectrum of interacting Bose systems, (4)He and (87)Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related. We also suggest two experimental avenues to observe rotons in condensates. These results, based upon a path-integral Monte Carlo approach, provide a microscopic explanation of the shift in the critical temperature and also show that a roton minimum does emerge in the excitation spectrum of particles with a structureless, short-range, two-body interaction.

Nuclear-spin-independent short-range three-body physics in ultracold atoms

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, 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-spin independent.

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on the magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with theoretical expectations. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that, for energies in a gap of the lattice band structure, the molecules cannot dissociate.

p-Wave Feshbach molecules

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 the 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 ml=+/-1 and ml=0 angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasibound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier.

Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas

We report on the observation of ultracold heteronuclear Feshbach molecules. Starting with a 87Rb Bose-Einstein condensate and a cold atomic gas of 85Rb, we utilize previously unobserved interspecies Feshbach resonances to create up to 25,000 molecules. Even though the 85Rb gas is nondegenerate, we observe a large molecular conversion efficiency due to the presence of a quantum degenerate 87Rb 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 265.44+/-0.15 G and 372.4+/-1.3 G. We also directly measure the small binding energy of the molecules through resonant magnetic-field association.