Sympathetic cooling with two atomic species in an optical trap

Method and computer library for calculation of the Boltzmann collision integrals on discrete momentum lattice

We present a general and numerically efficient method for calculation of collision integrals for interacting quantum gases on a discrete momentum lattice. Here we employ the original analytical approach based on Fourier transform covering a wide spectrum of solid-state problems with various particle statistics and arbitrary interaction models, including the case of momentum-dependent interaction. The comprehensive set of the transformation principles is given in detail and realized as a computer Fortran 90 library FLBE (Fast Library for Boltzmann Equation).

A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate

This manuscript introduces a discrete technique to estimate the solution of a double-fractional two-component Bose–Einstein condensate. The system consists of two coupled nonlinear parabolic partial differential equations whose solutions are two complex functions, and the spatial fractional derivatives are interpreted in the Riesz sense. Initial and homogeneous Dirichlet boundary data are imposed on a multidimensional spatial domain. To approximate the solutions, we employ a finite difference methodology. We rigorously establish the existence of numerical solutions along with the main numerical properties. Concretely, we show that the scheme is consistent in both space and time as well as stable and convergent. Numerical simulations in the one-dimensional scenario are presented in order to show the performance of the scheme. For the sake of convenience, A MATLAB code of the numerical model is provided in the appendix at the end of this work.

Impact of higher-order nonlinearity on modulational instability in two-component Bose-Einstein condensates

We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.

Tailored Single-Atom Collisions at Ultralow Energies

We employ collisions of individual atomic cesium (Cs) impurities with an ultracold rubidium (Rb) gas to probe atomic interaction with hyperfine- and Zeeman-state sensitivity. Controlling the Rb bath's internal state yields access to novel phenomena observed in interatomic spin exchange. These can be tailored at ultralow energies, owing to the excellent experimental control over all relevant energy scales. First, detecting spin-exchange dynamics in the Cs hyperfine-state manifold, we resolve a series of previously unreported Feshbach resonances at magnetic fields below 300 mG, separated by energies as low as h×15  kHz. The series originates from a coupling to molecular states with binding energies below h×1  kHz and wave function extensions in the micrometer range. Second, at magnetic fields below ≈100  mG, we observe the emergence of a new reaction path for alkali atoms, where in a single, direct collision between two atoms two quanta of angular momentum can be transferred. This path originates from the hyperfine analog of dipolar spin-spin relaxation. Our work yields control of subtle ultralow-energy features of atomic collision dynamics, opening new routes for advanced state-to-state chemistry, for controlling spin exchange in quantum many-body systems for solid-state simulations, or for determination of high-precision molecular potentials.

Dipolar Quantum Mixtures of Erbium and Dysprosium Atoms

We report on the first realization of heteronuclear dipolar quantum mixtures of highly magnetic erbium and dysprosium atoms. With a versatile experimental setup, we demonstrate binary Bose-Einstein condensation in five different Er-Dy isotope combinations, as well as one Er-Dy Bose-Fermi mixture. Finally, we present first studies of the interspecies interaction between the two species for one mixture.

Sensing Static Forces with Free-Falling Nanoparticles

Miniaturized mechanical sensors rely on resonant operation schemes, unsuited to detect static forces. We demonstrate a nanomechanical sensor for static forces based on an optically trapped nanoparticle in vacuum. Our technique relies on an off-resonant interaction of the particle with a weak static force, and a resonant readout of the displacement caused by this interaction. We demonstrate a sensitivity of 10 aN to static gravitational and electric forces. Our work provides a tool for the closer investigation of short-range forces, and marks an important step towards the realization of matter-wave interferometry with macroscopic objects.

Bright-dark and dark-dark solitons in coupled nonlinear Schrödinger equation with PT-symmetric potentials

We explore different nonlinear coherent structures, namely, bright-dark (BD) and dark-dark (DD) solitons in a coupled nonlinear Schrödinger/Gross-Pitaevskii equation with defocusing/repulsive nonlinearity coefficients featuring parity-time ( PT)-symmetric potentials. Especially, for two choices of PT-symmetric potentials, we obtain the exact solutions for BD and DD solitons. We perform the linear stability analysis of the obtained coherent structures. The results of this linear stability analysis are well corroborated by direct numerical simulation incorporating small random noise. It has been found that there exists a parameter regime which can support stable BD and DD solitons.

Two-stage crossed beam cooling with ⁶Li and ¹³³Cs atoms in microgravity

Applying the direct simulation Monte Carlo (DSMC) method developed for ultracold Bose-Fermi mixture gases research, we study the sympathetic cooling process of 6Li and 133Cs atoms in a crossed optical dipole trap. The obstacles to producing 6Li Fermi degenerate gas via direct sympathetic cooling with 133Cs are also analyzed, by which we find that the side-effect of the gravity is one of the main obstacles. Based on the dynamic nature of 6Li and 133Cs atoms, we suggest a two-stage cooling process with two pairs of crossed beams in microgravity environment. According to our simulations, the temperature of 6Li atoms can be cooled to T = 29.5 pK and T/TF = 0.59 with several thousand atoms, which propose a novel way to get ultracold fermion atoms with quantum degeneracy near pico-Kelvin.

Versatile cold atom source for multi-species experiments

We present a dual-species oven and Zeeman slower setup capable of producing slow, high-flux atomic beams for loading magneto-optical traps. Our compact and versatile system is based on electronic switching between different magnetic field profiles and is applicable to a wide range of multi-species experiments. We give details of the vacuum setup, coils, and simple electronic circuitry. In addition, we demonstrate the performance of our system by optimized, sequential loading of magneto-optical traps of lithium-6 and cesium-133.

Dynamics of single neutral impurity atoms immersed in an ultracold gas

We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows us to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.

Sympathetic cooling in an optically trapped mixture of alkali and spin-singlet atoms

We report on the realization of a stable mixture of ultracold lithium and ytterbium atoms confined in a far-off-resonance optical dipole trap. We observe sympathetic cooling of 6Li by 174Yb and extract the s-wave scattering length magnitude |a(6Li-174Yb)|=(13±3)a0 from the rate of interspecies thermalization. Using forced evaporative cooling of 174Yb, we achieve reduction of the 6Li temperature to below the Fermi temperature, purely through interspecies sympathetic cooling.

Thermodynamical approach to sympathetic cooling of neutral particles

We present a "toy" classical model for sympathetic cooling of the neutral Brownian particle in the frame of robust thermodynamical approach. The cooling time is expressed with the parameters of the Brownian particle and the particles from the cooling reservoir. Qualitative and numerical estimations of the model confirm that the sympathetic cooling can be efficient for heavy neutral molecules and clusters.

Collisional stability of 40K immersed in a strongly interacting Fermi gas of 6Li

We investigate the collisional stability of a sample of 40K atoms immersed in a tunable spin mixture of 6Li atoms. In this three-component Fermi-Fermi mixture, we find very low loss rates in a wide range of interactions as long as molecule formation of 6Li is avoided. The stable fermionic mixture with two resonantly interacting spin states of one species together with another species is a promising system for a broad variety of phenomena in few- and many-body quantum physics.

Formation of ultracold polar molecules in the rovibrational ground state

Ultracold LiCs molecules in the absolute ground state X1Sigma+, v'' = 0, J'' = 0 are formed via a single photoassociation step starting from laser-cooled atoms. The selective production of v'' = 0, J'' = 2 molecules with a 50-fold higher rate is also demonstrated. The rotational and vibrational state of the ground state molecules is determined in a setup combining depletion spectroscopy with resonant-enhanced multiphoton ionization time-of-flight spectroscopy. Using the determined production rate of up to 5 x 10(3) molecules/s, we describe a simple scheme which can provide large samples of externally and internally cold dipolar molecules.

Double species Bose-Einstein condensate with tunable interspecies interactions

We produce Bose-Einstein condensates of two different species, 87Rb and 41K, in an optical dipole trap in proximity of interspecies Feshbach resonances. We discover and characterize two Feshbach resonances, located around 35 and 79 G, by observing the three-body losses and the elastic cross section. The narrower resonance is exploited to create a double species condensate with tunable interactions. Our system opens the way to the exploration of double species Mott insulators and, more in general, of the quantum phase diagram of the two-species Bose-Hubbard model.

Discrete vector on-site vortices

We study discrete vortices in coupled discrete nonlinear Schrödinger equations. We focus on the vortex cross configuration that has been experimentally observed in photorefractive crystals. Stability of the single-component vortex cross in the anti-continuum limit of small coupling between lattice nodes is proved. In the vector case, we consider two coupled configurations of vortex crosses, namely the charge-one vortex in one component coupled in the other component to either the charge-one vortex (forming a double-charge vortex) or the charge-negative-one vortex (forming a, so-called, hidden-charge vortex). We show that both vortex configurations are stable in the anti-continuum limit, if the parameter for the inter-component coupling is small and both of them are unstable when the coupling parameter is large. In the marginal case of the discrete two-dimensional Manakov system, the double-charge vortex is stable while the hidden-charge vortex is linearly unstable. Analytical predictions are corroborated with numerical observations that show good agreement near the anti-continuum limit, but gradually deviate for larger couplings between the lattice nodes.

Controlling collisions of ultracold atoms with dc electric fields

It is demonstrated that elastic collisions of ultracold atoms forming a heteronuclear collision complex can be manipulated by laboratory practicable dc electric fields. The mechanism of electric field control is based on the interaction of the instantaneous dipole moment of the collision pair with external electric fields. It is shown that this interaction is dramatically enhanced in the presence of a p-wave shape or Feshbach scattering resonance near the collision threshold, which leads to novel electric-field-induced Feshbach resonances.

Experimental investigation of ultracold atom-molecule collisions

Ultracold collisions between Cs atoms and Cs2 dimers in the electronic ground state are observed in an optically trapped gas of atoms and molecules. The Cs2 molecules are formed in the triplet ground state by cw photoassociation through the outer well of the 0-(g) (P3/2) excited electronic state. Inelastic atom-molecule collisions converting internal excitation into kinetic energy lead to a loss of Cs2 molecules from the dipole trap. Rate coefficients are determined for collisions involving Cs atoms in either the F=3 or F=4 hyperfine ground state, and Cs2 molecules in either highly vibrationally excited states (nu'=32-47) or in low vibrational states (nu'=4-6) of the a3 summation(u)+ triplet ground state. The rate coefficients beta approximately 10(-10) cm3/s are found to be largely independent of the vibrational and rotational excitation indicating unitary limited cross sections.

Vector solitons with an embedded domain wall

We present a class of soliton solutions to a system of two coupled nonlinear Schrödinger equations, with an intrinsic domain wall (DW) which separates regions occupied by two different fields. The model describes a binary mixture of two Bose-Einstein condensates (BECs) with interspecies repulsion. For the attractive or repulsive interactions inside each species, we find solutions which are bright or dark solitons in each component, while for the opposite signs of the intraspecies interaction, a bright-dark soliton pair is found (each time, with the intrinsic DW). These solutions can arise in the context of discrete lattices, and most of them can be supported in continuum settings by an external parabolic trap. The stability of the solitons with intrinsic DWs is examined, and the evolution of unstable ones is analyzed. We also briefly discuss the possibility of generating such families of solutions in the presence of linear coupling between the components, and an application of the model to bimodal light propagation in nonlinear optics.

Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases

We report on the observation of sympathetic cooling of a cloud of fermionic 6Li atoms which are thermally coupled to evaporatively cooled bosonic 87Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud is colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |amx|=20(+9)(-6)aB. We found that the presence of residual rubidium atoms in the |2, 1> and the |1, -1> Zeeman substates gives rise to important losses due to inelastic collisions.

Cooling dynamics of ultracold two-species Fermi-Bose mixtures

We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow one to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.