Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible---thanks to tremendous progress in cooling, trapping, and manipulating ultracold samples---to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.
In this paper, the condensate fraction and the critical atom number and its corresponding critical temperature of condensate ultracold boson atoms trapped in optical box traps, are investigated. The semiclassical approximation is employed in this study. The boxes traps are modeled by a general power-law potential. The deviation of the boxes traps from an ideal boxes traps are discussed. The out come results furnish useful quantitative theoretical results for the future BEC experiments in such traps
We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP) which allows the generation of a large variety of traps and waveguides for ultracold atoms. Multiple traps can be coupled through controllable tunneling barriers or merged altogether. We present analytical expressions for pancake-, cigar-, and ring- shaped traps. The ring-geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of controllable diameter, and thus a tunable sensitivity of the interferometer.
We discuss the suitability of holographically generated optical potentials for the investigation of superfluidity in ultracold atoms. By using a spatial light modulator and a feedback enabled algorithm we generate a smooth ring with variable bright regions that can be dynamically rotated to stir ultracold atoms and induce superflow. We also comment on its future integration into a cold atoms experiment.
We show that conical intersections can be created in laboratory coordinates by dressing a parabolic trap for ultracold atoms or molecules with a combination of optical and static magnetic fields. The resulting ring trap can support single-particle states with half-integer rotational quantization and many-particle states with persistent flow. Two well-separated atomic or molecular states are brought into near-resonance by an optical field and tuned across each other with an inhomogeneous magnetic field. Conical intersections occur at the nodes in the optical field.
We theoretically investigate magnetic properties of a unitary Fermi gas in a harmonic trap. Including strong pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a trap potential within the local density approximation (LDA), we calculate the local spin susceptibility $χ(T,r)$ above the superfluid phase transition temperature $T_{\rm c}$. We show that the formation of preformed singlet Cooper pairs anomalously suppresses $χ(T,r)$ in the trap center near $T_{\rm c}$. We also point out that, in the unitarity limit, the spin-gap temperatur…
We study the virial relations for ultracold trapped two component Fermi gases in the case of short finite range interactions. Numerical verifications for such relations are reported through the BCS-BEC crossover. As an intermediate step, it is necessary to evaluate the partial derivatives of the many body energy with respect to the inverse of the scattering length and with respect to the interaction range. They are found to have extreme values at the unitary limit. The virial results are used to check the quality of the variational wave function involved in the calculations.
We study theoretically the collective modes of a two-component Fermi gas with attractive interactions in a quasi-one-dimensional harmonic trap. We focus on an imbalanced gas in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Using a mean-field theory, we study the response of the ground state to time-dependent potentials. For potentials with short wavelengths, we find dramatic signatures in the large-scale response of the gas which are characteristic of the FFLO phase. This response provides an effective way to detect the FFLO state in experiments.
We propose a method to measure the superfluid fraction of an atomic gas. The method involves the use of a vector potential generated by optical beams with non-zero angular momentum to simulate uniform rotation. The induced change in angular momentum of the atomic gas can be measured spectroscopically. This allows a direct determination of the superfluid fraction.
We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-li…
We theoretically investigate single particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-Condensation) crossover regime of an ultracold Fermi gas. Including strong pairing fluctuations within a $T$-matrix approximation, as well as effects of a harmonic trap potential in the local density approximation, we calculate the local photoemission spectrum in the normal state. Recently, JILA group has measured this quantity in a $^{40}$K Fermi gas, in order to examine homogeneous single-particle properties of this system. Comparing our results with this experiment, we show tha…
Using the time-dependent density matrix renormalization group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass wh…
The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an a…
The striped state of ultracold bosons with Rashba spin-orbit coupling in a homogeneous infinite system has, as we show, a constant particle flow, which in a finite-size system would accumulate particles at the boundaries; it is thus not a physical steady state of the system. We propose, as a variational ansatz, a condensate wave function for a weakly trapped system which behaves similarly to the striped state near the center, but does not have particle flow at the boundaries. This state has a line of unquantized coreless vortices. We show, by minimizing the total energy, that our modified stri…
A vortex in a Bose-Einstein condensate on a ring undergoes quantum dynamics in response to a quantum quench in terms of partial symmetry breaking from a uniform lattice to a biperiodic one. Neither the current, a macroscopic measure, nor fidelity, a microscopic measure, exhibit critical behavior. Instead, the symmetry memory succeeds in identifying the point at which the system begins to forget its initial symmetry state. We further identify a symmetry energy difference in the low lying excited states which trends with the symmetry memory.
We derive the ground-state energy for a small number of ultracold atoms in an isotropic harmonic trap using effective quantum field theory (EFT). Atoms are assumed to interact through pairwise energy-independent and energy-dependent delta-function potentials with strengths proportional to the scattering length $a$ and effective range volume $V$, respectively. The calculations are performed systematically up to order $l^{-4}$, where $l$ denotes the harmonic oscillator length. The effective three-body interaction contains a logarithmic divergence in the cutoff energy, giving rise to a non-univer…
We present accurate results based on Quantum Monte Carlo simulations of two-component bosonic systems on a square lattice and in the presence of an external harmonic confinement. Starting from hopping parameters and interaction strengths which stabilize the Ising antiferromagnetic phase in the homogeneous case and at half integer filling factor, we study how the presence of the harmonic confinement challenge the realization of such phase. We consider realistic trapping frequencies and number of particles, and establish under which conditions, i.e. total number of particles and population imbal…
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density-matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superflu…
We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms $<1 μ$m away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate ultracold atoms with quantum electronic devices to give extreme sensitivity and control: for example, activating a single quantized conductance channel in the 2DEG can split a Bose-Einstein condensate (BEC) for atom interferometry. In turn, the BEC offers unique structural and functional imaging of quantum devices and transport in heterostructures and graphene.
We present two novel dressed inductive ring trap geometries, ideal for atom interferometry or studies of superfluidity and well-suited to utilisation in atom chip architectures. The design permits ring radii currently only accessible via near-diffraction-limited optical traps, whilst retaining the ultra-smooth magnetic potential afforded by inductive traps. One geometry offers simple parallel implementation of multiple rings, whereas the other geometry permits axial beam-splitting of the torus suitable for whole-ring atom interferometry.
We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schroedinger equation for this system, and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach reso…
We report on the compensation of excess micromotion due to parasitic rf-electric fields in a Paul trap. The parasitic rf-electric fields stem from the Paul trap drive but cause excess micromotion, e.g. due to imperfections in the setup of the Paul trap. We compensate these fields by applying rf-voltages of the same frequency but adequate phases and amplitudes to Paul trap electrodes. The magnitude of micromotion is probed by studying elastic collision rates of the trapped ion with a gas of ultracold neutral atoms. Furthermore, we demonstrate that also reactive collisions can be used to quantif…
We have analytically explored finite size and interparticle interaction corrections to the average energy of a harmonically trapped Fermi gas below and above the Fermi temperature, and have obtained a better fitting for the excess energy reported by DeMarco and Jin [Science $\textbf{285}$, 1703 (1999)]. We have presented a perturbative calculation within a mean field approximation.
We have formulated and experimentally demonstrated an improved algorithm for design of arbitrary two-dimensional holographic traps for ultracold atoms. Our method builds on the best previously available algorithm, MRAF, and improves on it in two ways. First, it allows for creation of holographic atom traps with a well defined background potential. Second, we experimentally show that for creating trapping potentials free of fringing artifacts it is important to go beyond the Fourier approximation in modelling light propagation. To this end, we incorporate full Helmholtz propagation into our cal…
We show that simple laser configurations can give rise to "optical flux lattices", in which optically dressed atoms experience a periodic effective magnetic flux with high mean density. These potentials lead to narrow energy bands with non-zero Chern number. Optical flux lattices will greatly facilitate the achievement of the quantum Hall regime for ultracold atomic gases.
We find a new physical regime in the trapped Bose-Hubbard Hamiltonian using time-evolving block decimation. Between Mott-insulating and superfluid phases, the latter induced by trap compression, a spatially self-organized state appears in which non-local entropy signals entanglement between spatially distant superfluid shells. We suggest a linear rather than harmonic potential as an ideal way to observe such a self-organized system. We also explore both quantum information and thermal entropies in the superfluid regime, finding that while the former follows the density closely the latter can b…
We study a system of periodic Bose condensed atoms coupled to cavity photons using the input-output formalism. We show that the cavity will either act as a through pass Lorentzian filter when the superfluid fraction of the condensate is minimum or completely reflect the input field when the superfluid fraction is maximum. We show that by monitoring the ratio between the transmitted field and the reflected field, one can estimate the superfluid fraction.
We investigate the ground state properties and tunneling dynamics of ultracold dipolar bosons in a one dimensional triple well trap from a few-body ab-initio perspective. Our focus is primarily on the distinctive features of dipolar bosons compared to the contact interacting bosons. Formation of intra-well localization is observed for very strong dipolar interaction. General population rearangement as well as fragmentation and localization effects have been found, depending strongly on the particle number. The energy spectrum for two particles exhibits avoided crossings that lead to several di…
We explore the possibility of detecting many-body entanglement using time-of-flight (TOF) momentum correlations in ultracold atomic fermi gases. In analogy to the vacuum correlations responsible for Bekenstein-Hawking black hole entropy, a partitioned atomic gas will exhibit particle-hole correlations responsible for entanglement entropy. The signature of these momentum correlations might be detected by a sensitive TOF type experiment.
We theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase tra…
The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic, as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space…
The immersion of a single ion confined by a radiofrequency trap in an ultracold atomic gas extends the concept of buffer gas cooling to a new temperature regime. The steady state energy distribution of the ion is determined by its kinetics in the radiofrequency field rather than the temperature of the buffer gas. Moreover, the finite size of the ultracold gas facilitates the observation of back-action of the ion onto the buffer gas. We numerically investigate the system's properties depending on atom-ion mass ratio, trap geometry, differential cross-section, and non-uniform neutral atom densit…
We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the ato…
We study collisions in an optically trapped, pure sample of ultracold Cs$_2$ molecules in various internal states. The molecular gas is created by Feshbach association from a near-degenerate atomic gas, with adjustable temperatures in the nanokelvin range. We identify several narrow loss resonances, which point to the coupling to more complex molecular states and may be interpreted as Feshbach resonances in dimer-dimer interactions. Moreover, in some molecular states we observe a surprising temperature dependence in collisional loss. This shows that the situation cannot be understood in terms …
Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructive or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase-imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as m…
Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that the corrections induced by the finite range of interactions can become especially important in the vicinity of narrow Feshbach resonances and suggest realistic schemes of their experimental detection. The interplay of confinement and interactions can lead to effective transparency where the one-dimensional interactions are weak in a wide range of parameters…
We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $χ_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $χ_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing f…
Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 10…
High-density and ultracold atomic gases have emerged as promising media for storage of individual photons for quantum memory applications. In this paper we provide an overview of our theoretical and experimental efforts in this direction, with particular attention paid to manipulation of light storage (a) through complex recurrent optical scattering processes in very high density gases (b) by an external control field in a characteristic electromagnetically induced transparency configuration.
We report on deviations beyond the Born-Oppenheimer approximation in the potassium inter-atomic potentials. Identifying three up-to-now unknown $d$-wave Feshbach resonances, we significantly improve the understanding of the $^{39}$K inter-atomic potentials. Combining these observations with the most recent data on known inter- and intra-isotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear case appear.
We present measurements of interspecies thermalization between ultracold samples of $^{133}$Cs and either $^{174}$Yb or $^{170}$Yb. The two species are trapped in a far-off-resonance optical dipole trap and $^{133}$Cs is sympathetically cooled by Yb. We extract effective interspecies thermalization cross sections by fitting the thermalization measurements to a rate equation model, giving $σ_{\mathrm{Cs^{174}Yb}} = \left(5 \pm 2\right) \times 10^{-13} \, \mathrm{cm^{2}}$ and $σ_{\mathrm{Cs^{170}Yb}} = \left(18 \pm 8\right) \times 10^{-13} \, \mathrm{cm^{2}}$. We perform quantum scattering calcu…
Bose-Fermi mixtures have been recently realized and invesitigated in ultracold atomic experiments. We formulate quantum Monte Carlo simulation of Bose-Fermi mixtures on the (3+1)-dimensional lattice. As its first application, we analyze the boson-fermion pair correlation and the phase diagram of the Bose-Einstein condensation.
The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant and scattering states are included on an equal footing, and we argue …
We describe a hybrid vacuum system in which a single ion or a well defined small number of trapped ions (in our case Ba$^+$ or Rb$^+$) can be immersed into a cloud of ultracold neutral atoms (in our case Rb). This apparatus allows for the study of collisions and interactions between atoms and ions in the ultracold regime. Our setup is a combination of a Bose-Einstein condensation (BEC) apparatus and a linear Paul trap. The main design feature of the apparatus is to first separate the production locations for the ion and the ultracold atoms and then to bring the two species together. This schem…
Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photo-excitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecu…
We analyze the phase structure of mass- and spin-imbalanced unitary Fermi gases in harmonic traps. To this end, we employ Density Functional Theory in the local density approximation. Depending on the values of the control parameters measuring mass and spin imbalance, we observe that three regions exist in the trap, namely: a superfluid region at the center, surrounded by a mixed region of resonantly interacting spin-up and spin-down fermions, and finally a fully polarized phase surrounding the previous two regions. We also find regimes in the phase diagram where the existence of a superfluid …
We propose a one-dimensional Hamiltonian $H_{1D}$ which supports Majorana fermions when $d_{x^{2}-y^{2}}$-wave superfluid appears in the ultracold atomic system and obtain the phase-separation diagrams both for the time-reversal-invariant case and time-reversal-symmetry-breaking case. From the phase-separation diagrams, we find that the single Majorana fermions exist in the topological superfluid region, and we can reach this region by tuning the chemical potential $μ$ and spin-orbit coupling $α_{R}$. Importantly, the spin-orbit coupling has realized in ultracold atoms by the recent experiment…
We report on the design, implementation, and performance of a compact two-dimensional magneto-optical trap (2D MOT) for cesium. In a small-volume vacuum chamber, the setup uses cesium dispensers in close proximity to the trapping region of the 2D MOT and operates at low vapor pressures in the $10^{-9}$ torr range. We achieve a cold atom flux of $4 \times 10^8$ atoms/s that is comparable to the performance of more complex atomic sources. The setup is simple to construct and can be adapted to a broad range of atomic species.
Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex format…
Standard lattice formulations of non-relativistic Fermi gases with two spin components suffer from a sign problem in the cases of repulsive contact interactions and attractive contact interactions with spin imbalance. We discuss the nature of this sign problem and the applicability of stochastic quantisation with complex Langevin evolution in both cases. For repulsive interactions, we find that the results converge, using adaptive step size scaling and a Gaussian regulator to modify the lattice action. We present results on density profiles and correlations of a harmonically trapped system in …
Spatial adiabatic passage processes for ultracold atoms trapped in tunnel-coupled cylindrically symmetric concentric potentials are investigated. Specifically, we discuss the matter-wave analogue of the rapid adiabatic passage (RAP) technique for a high fidelity and robust loading of a single atom into a harmonic ring potential from a harmonic trap, and for its transport between two concentric rings. We also consider a system of three concentric rings and investigate the transport of a single atom between the innermost and the outermost rings making use of the matter-wave analogue of the stimu…
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could b…
We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact pseudopotential with complex scattering length and investigate the properties of eigenergies and eigenfunctions for different trap states as a function of real and imaginary part of the scattering length. In the analyzed case the eigenenergies take complex values, and their imaginary part can be interpreted in terms of decay rates. Then we introduce the model of …
