Feshbach resonances in rubidium 87: precision measurement and analysis

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

Shaped Microwave Field in a Three-Level Closed Loop Dense Atomic System

In this work, we investigate the atomic properties of a three-level system under the effect of a shaped microwave field. The system is simultaneously driven by a powerful laser pulse and a weak constant probe that drives the ground state to an upper level. Meanwhile, an external microwave field drives the upper state to the middle transition with shaped waveforms. Hence, two situations are considered: one in which the atomic system is controlled by a strong laser pump and a classical constant microwave field, and another in which both the microwave and pump laser fields are shaped. Finally, for sake of comparison, we investigate the tanh-hyperbolic, the Gaussian and the power of the exponential microwave form in the system. Our results reveal that shaping the external microwave field has a significant impact on the absorption and dispersion coefficient dynamics. In comparison with the classical scenario, where usually the strong pump laser is considered to have a major role in controlling the absorption spectrum, we show that shaping the microwave field leads to distinct results.

Analysis of a q-deformed hyperbolic short laser pulse in a multi-level atomic system

A fast laser pulse with a q-deformed hyperbolic function shape is investigated in a Multi-level atomic system. Therefore, we first derive the exact solution of the Bloch equations describing a two-level atom excited by a q-deformed laser pulse with dephasing and time-dependent detuning. Next, we analyze the dynamic of the atomic population inversion at resonance and off-resonance of a Rubidium 87 three-level atom driven by a classical weak field and a strong q-deformed control laser. Finally, in order to get a deeper insight of the probe field’s absorption and dispersion properties, we investigate the coherence’s dependence on the q-deformation. Our work demonstrates that, the dynamic of the atomic system can be fully controlled through the manipulation of the asymmetry scaling parameter q of the q-deformed hyperbolic laser wave-form.

Observation of topological phase with critical localization in a quasi-periodic lattice

Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce topology from trivial band structures, wherein topological invariants are shared by completely localized states. Here we experimentally investigate a fundamentally distinct scenario where topology is identified in a critically localized regime, with eigenstates neither fully extended nor completely localized. Adopting the technique of momentum-lattice engineering for ultracold atoms, we implement a one-dimensional, generalized Aubry-André model with both diagonal and off-diagonal quasi-periodic disorder in momentum space, and characterize its localization and topological properties through dynamic observables. We then demonstrate the impact of interactions on the critically localized topological state, as a first experimental endeavor toward the clarification of many-body critical phase, the critical analogue of the many-body localized state.

Quantum Bubbles in Microgravity

The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.

Fast In Situ Observation of Atomic Feshbach Resonances by Photoassociative Ionization

We propose and experimentally investigate a scheme for observing Feshbach resonances in atomic quantum gases in situ and with a high temporal resolution of several tens of nanoseconds. The method is based on the detection of molecular ions, which are optically generated from atom pairs at small interatomic distances. As a test system we use a standard rubidium gas (^{87}Rb) with well known magnetically tunable Feshbach resonances. The fast speed and the high sensitivity of our detection scheme allows us to observe a complete Feshbach resonance within one millisecond and without destroying the gas.

A Dual-Species Bose-Einstein Condensate with Attractive Interspecies Interactions

We report on the production of a 41 K- 87 Rb dual-species Bose–Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime; i.e., for negative values of the interspecies scattering length a 12 . The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of a 12 . After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components possibly experiencing different potentials.

Observation of Broad d-Wave Feshbach Resonances with a Triplet Structure

High partial-wave (l≥2) Feshbach resonance (FR) in an ultracold mixture of ^{85}Rb-^{87}Rb atoms is investigated experimentally aided by a partial-wave insensitive analytic multichannel quantum-defect theory. Two "broad" resonances from coupling between d waves in both the open and closed channels are observed and characterized. One of them shows a fully resolved triplet structure with a splitting ratio well explained by the perturbation to the closed channel due to interatomic spin-spin interaction. These tunable "broad" d-wave resonances, especially the one in the lowest-energy open channel, could find important applications in simulating d-wave coupling dominated many-body systems. In addition, we find that there is generally a time and temperature requirement, associated with tunneling through the angular momentum barrier, to establish and observe resonant coupling in nonzero partial waves.

Above-threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider

Ultracold atomic gases have realized numerous paradigms of condensed matter physics, where control over interactions has crucially been afforded by tunable Feshbach resonances. So far, the characterization of these Feshbach resonances has almost exclusively relied on experiments in the threshold regime near zero energy. Here, we use a laser-based collider to probe a narrow magnetic Feshbach resonance of rubidium above threshold. By measuring the overall atomic loss from colliding clouds as a function of magnetic field, we track the energy-dependent resonance position. At higher energy, our collider scheme broadens the loss feature, making the identification of the narrow resonance challenging. However, we observe that the collisions give rise to shifts in the center-of-mass positions of outgoing clouds. The shifts cross zero at the resonance and this allows us to accurately determine its location well above threshold. Our inferred resonance positions are in excellent agreement with theory.

Studies on energy-dependent scattering of ultracold atoms were previously carried out near zero collision energies. Here, the authors observe a magnetic Feshbach resonance in ultracold Rb collisions for above-threshold energies and their method can also be used to detect higher partial wave resonances.

An accurate potential model for the a3Σu+ state of the alkali dimers Na2, K2, Rb2, and Cs2

A modified semi-empirical Tang-Toennies potential model is used to describe the a³Σ_u⁺ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth D_e, well location R_e, and the harmonic vibrational frequency ω_e of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na₂, K₂, Rb₂, and Cs₂, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li₂ and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li₂ less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

Universal Three-Body Physics in Ultracold KRb Mixtures

Ultracold atomic gases have recently become a driving force in few-body physics due to the observation of the Efimov effect. While initially observed in equal mass systems, one expects even richer few-body physics in the heteronuclear case. In previous experiments with ultracold mixtures of potassium and rubidium, an unexpected nonuniversal behavior of Efimov resonances was observed. In contrast, we measure the scattering length dependent three-body recombination coefficient in ultracold heteronuclear mixtures of ^{39}K-^{87}Rb and ^{41}K-^{87}Rb and do not observe any signatures of Efimov resonances for accessible scattering lengths in either mixture. Our results show good agreement with our theoretical model for the scattering dependent three-body recombination coefficient and reestablish universality across isotopic mixtures.

Efimov Resonance and Three-Body Parameter in a Lithium-Rubidium Mixture

We study collisional heating in a cold ^{7}Li-^{87}Rb mixture near a broad Feshbach resonance at 661 G. At the high field slope of the resonance, we find an enhanced three-body recombination rate that we interpret as a heteronuclear Efimov resonance. With improved Feshbach spectroscopy of two further resonances, a model for the molecular potentials has been developed that now consistently explains all known Feshbach resonances of the various Li-Rb isotope mixtures. The model is used to determine the scattering length of the observed Efimov state. Its value of -1870a_{0} Bohr radii supports the currently discussed assumption of universality of the three-body parameter also in heteronuclear mixtures.

Interactions and collisions of discrete breathers in two-species Bose-Einstein condensates in optical lattices

The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.

Optical kagome lattice for ultracold atoms with nearest neighbor interactions

We propose a scheme to implement an optical kagome lattice for ultracold atoms with controllable s-wave interactions between nearest neighbor sites and a gauge potential. The atoms occupy three different internal atomic levels with electromagnetically induced coupling between the levels. We show that by appropriately shifting the triangular lattice potentials, experienced by atoms in different levels, the kagome lattice can be realized using only two standing waves, generating a highly frustrated quantum system for the atoms.

Multipole polarizabilities and long-range interactions of the fluorine atom

The polarizabilities of the ground state of fluorine are determined by the box-based B-spline configuration-interaction method. The ground-state static and tensor polarizabilities are calculated as alpha(d) = 3.49a(0)(3) and alpha(2) = 0.303a(0)(3), respectively. The resulting excitation matrix elements are employed to compute the interatomic dispersion interactions for the HF and F(2) molecules.

Strong dissipation inhibits losses and induces correlations in cold molecular gases

Atomic quantum gases in the strong-correlation regime offer unique possibilities to explore a variety of many-body quantum phenomena. Reaching this regime has usually required both strong elastic and weak inelastic interactions because the latter produce losses. We show that strong inelastic collisions can actually inhibit particle losses and drive a system into a strongly correlated regime. Studying the dynamics of ultracold molecules in an optical lattice confined to one dimension, we show that the particle loss rate is reduced by a factor of 10. Adding a lattice along the one dimension increases the reduction to a factor of 2000. Our results open the possibility to observe exotic quantum many-body phenomena with systems that suffer from strong inelastic collisions.

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.

39K Bose-Einstein condensate with tunable interactions

We produce a Bose-Einstein condensate of 39K atoms. Condensation of this species with a naturally small and negative scattering length is achieved by a combination of sympathetic cooling with 87Rb and direct evaporation, exploiting the magnetic tuning of both inter- and intraspecies interactions at Feshbach resonances. We explore the tunability of the self-interactions by studying the expansion and the stability of the condensate. We find that a 39K condensate is interesting for future experiments requiring a weakly-interacting Bose gas.

Confinement effects on the stimulated dissociation of molecular Bose-Einstein condensates

We show that a molecular Bose-Einstein condensate in a trap is stabilized against stimulated dissociation if the trap size is smaller than the resonance healing length (Planck's 2/2mgsqrt[n]);1/2. The condensate shape determines the critical atom-molecule coupling frequency. We discuss an experiment for triggering dissociation by a sudden change of coupling or trap parameters. This effect demonstrates one of the unique collective features of "superchemistry" in that the yield of a chemical reaction depends critically on the size and shape of the reaction vessel.

Unitary quantum three-body problem in a harmonic trap

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short-range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.

Enhanced sensitivity to fundamental constants in ultracold atomic and molecular systems near Feshbach resonances

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 models, 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) on the level of can be detected near a narrow magnetic or an optical Feshbach resonance by monitoring the scattering length on the 1% level. Derived formulas may also be used to estimate the isotopic shift of the scattering length.

Zero-temperature phases of many-atom Bose systems

We show that a many-atom Bose system at zero temperature has, in general, a liquid phase in addition to its well-known gaseous phase. A universal phase diagram is presented that is applicable to all Bose systems with a -C6/r6 type of interaction at large interparticle separations. We show that the predicted phase structure has implications on the stability of a gaseous Bose-Einstein condensate (BEC) even at dilute densities that are routinely achieved under existing experimental conditions. We also predict that should have a gaseous BEC phase below a critical density of 5.58 x 10(15) 1/cm3.

Creating ground state molecules with optical feshbach resonances in tight traps

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.

Atomic quantum dots coupled to a reservoir of a superfluid Bose-Einstein condensate

We study the dynamics of an atomic quantum dot, i.e., a single atom in a tight optical trap which is coupled to a superfluid reservoir via laser transitions. Quantum interference between the collisional interactions and the laser induced coupling results in a tunable dot-bath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spin-boson model with Ohmic coupling, which exhibits a dissipative phase transition and allows us to directly measure atomic Luttinger parameters.

Observation of heteronuclear Feshbach resonances in a mixture of bosons and fermions

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543+/-2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding (-281+/-15)a(0) and (-54+/-12)a(0), respectively. The width of the loss feature at 543 G is 3.7+/-1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions.

Interferometric determination of the s and d-wave scattering amplitudes in 87Rb

We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging in free space. From the interference between s- and d- partial waves in the differential scattering pattern we extract the corresponding phase shifts. The method does not require knowledge of the atomic density. This allows us to infer accurate values for the s- and d-wave scattering amplitudes from the zero-energy limit up to the first Ramsauer minimum using only the van der Waals C6 coefficient as theoretical input. For the 87Rb triplet potential, the method reproduces the scattering length with an accuracy of 6%.

Imaging of s and d partial-wave interference in quantum scattering of identical bosonic atoms

We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.

Atom-molecule coexistence and collective dynamics near a feshbach resonance of cold fermions

Degenerate Fermi gas interacting with molecules near a Feshbach resonance is unstable with respect to the formation of a mixed state, in which atoms and molecules coexist as a coherent superposition. A theory of this state is developed using a mapping to the Dicke model, treating the molecular field in the single mode approximation. The results are accurate in the strong coupling regime relevant for current experimental efforts. The exact solution of the Dicke model is exploited to study stability, phase diagram, and nonadiabatic dynamics of the molecular field in the mixed state.

Dynamics of F=2 spinor Bose-Einstein condensates

We experimentally investigate and analyze the rich dynamics in F=2 spinor Bose-Einstein condensates of 87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of 10(-12) cm(3) s(-1) for spin-changing collisions within the F=2 manifold and spin-dependent loss rates in the range of 10(-13) cm(3) s(-1) for hyperfine-changing collisions. We observe polar behavior in the F=2 ground state of 87Rb, while we find the F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.

Observation of molecules produced from a Bose-Einstein condensate

Molecules are created from a Bose-Einstein condensate of atomic 87Rb using a Feshbach resonance. A Stern-Gerlach field is applied, in order to spatially separate the molecules from the remaining atoms. For detection, the molecules are converted back into atoms, again using the Feshbach resonance. The measured position of the molecules yields their magnetic moment. This quantity strongly depends on the magnetic field, thus revealing an avoided crossing of two bound states at a field value slightly below the Feshbach resonance. This avoided crossing is exploited to trap the molecules in one dimension.

Gibbons-Hawking effect in the sonic de Sitter space-time of an expanding Bose-Einstein-condensed gas

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a (1+1)-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.

Determination of the s-wave scattering length of chromium

We have measured the deca-triplet s-wave scattering length of the bosonic chromium isotopes 52Cr and 50Cr. From the time constants for cross-dimensional thermalization in ultracold atomic samples, we have determined the magnitudes |a(52Cr)|=(170+/-39)a(0) and |a(50Cr)|=(40+/-15)a(0), where a(0)=0.053 nm. By measuring the rethermalization rate of 52Cr over a wide temperature range and comparing the temperature dependence with the effective-range theory and numerical single-channel calculations, we have obtained strong evidence that the sign of a(52Cr) is positive. Rescaling our 52Cr model potential to 50Cr strongly suggests that a(50Cr) is positive also.