We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral properties of the system are scrutinized, in particular, we derive analytic expressions for the degeneracies and their breaking for the lower-energy states at small but finite interactions. We demonstrate that the degeneracy of the low-energy states is independent of the number of particles in the noninteracting limit and also for sufficiently weak interactions. In the strongly interacting regime, we show how the many-body wave function develops holes whenever two particles are at the same position in space to avoid the interaction, a mechanism reminiscent of the Tonks-Girardeau gas in 1D. The evolution of the system as the interaction is increased is studied by means of the density profiles, pair correlations and fragmentation of the ground state for $N=2$, $3$, and $4$ bosons.
An easily scalable toroidal geometry presents an opportunity for creating large scale persistent currents in Bose-Einstein condensates, for studies of the Kibble-Zurek mechanism, and for investigations of toroidally trapped degenerate Fermi gases. We consider in detail the process of isentropic loading of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal regime that exhibits a high degree of system invariance when increasing the radius of the toroid. The heating involved in loading a Bose gas is evaluated analytically and numerically, both above and below the critical …
We report on a general method for the rapid production of quantum degenerate gases. Using 174Yb, we achieve an experimental cycle time as low as (1.6-1.8) s for the production of Bose-Einstein condensates (BECs) of (0.5-1) x 10^5 atoms. While laser cooling to 30\muK proceeds in a standard way, evaporative cooling is highly optimized by performing it in an optical trap that is dynamically shaped by utilizing the time-averaged potential of a single laser beam moving rapidly in one dimension. We also produce large (>10^6) atom number BECs and successfully model the evaporation dynamics over more …
Isothermal compression of a Fermi gas to deep quantum degeneracy
Physikalisches Institut, Eberhard Karls Universität Tübingen（蒂宾根大学物理研究所）；Center for Integrated Quantum Science and Technology, Eberhard Karls Universität Tübingen（蒂宾根大学集成量子科学与技术中心）
We study a system of two bosons of one species and a third boson of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intra-species interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical ansatzs gaining physical insight over the numerically obtained wavefunctions. We show that, for both approaches, i…
Using a system composed of a Quadrupole and Ioffe Configuration (QUIC) trap loaded from a slowed atomic beam, we have performed experiments to observe the Bose-Einstein Condensation of Na atoms. In order to obtain the atomic distribution in the trap, we use an in situ out of resonance absorption image through a probe beam, to determine temperature and density. The phase space density (D) is calculated using the density profile and the temperature. We have followed D as a function of the final evaporation frequency. The results show that at 1.65 MHz we crossed the value for D expected to corres…
We achieve a highly degenerate and strongly interacting Fermi gas in a mixture of the two lowest hyperfine states of $^6$Li by direct evaporative cooling in a high power crossed optical dipole trap. The trap is loaded from a large atom number magneto-optical trap (MOT) which is realized by a laser system of 2.5-watts intracavity-frequency-doubled light output at 671 nm. With this system, we also demonstrate the production of a molecular Bose-Einstein condensates (mBEC), and observe the anisotropic expansion of Fermi gases in the so-called BEC-BCS crossover regime.
One of the challenges for fermionic cold atom experiments in optical lattices is to cool the systems to low enough temperature that they can form quantum degenerate ordered phases. In particular, there has been significant work in trying to find the antiferromagnetic phase transition of the Hubbard model in three dimensions, without success. Here, we attack this problem from a different angle by enhancing the ordering temperature via an increase in the degeneracy of the atomic species trapped in the optical lattice. In addition to developing the general theory, we also discuss some potential s…
In a mixture of two kinds of identical bosons there are two types of pairs, identical bosons' pairs, of either species, and pairs of distinguishable bosons. In the present work fragmentation of pairs in a trapped mixture of Bose-Einstein condensate is investigated using a solvable model, the symmetric harmonic-interaction model for mixtures. The natural geminals for pairs made of identical or distinguishable bosons are explicitly contracted by diagonalizing the intra-species and inter-species reduced two-particle density matrices, respectively. Properties of pairs' fragmentation in the mixture…
We study harmonically trapped one-dimensional atoms subjected to an equal combination of Rashba and Dresselhaus spin-orbit coupling induced by Raman transition. We first examine the wave function and the degeneracy of the single-particle ground state, followed by a study of two weakly interacting bosons or fermions. For the two-particle ground state, we focus on the effects of the interaction on the degeneracy, the spin density profiles, and the density-density correlation functions. Finally we show how these studies help us to understand the many-body properties of the system.
Advanced quantum technologies, such as quantum simulation, computation, and metrology are thriving for the implementation of large-scale configurations of identical quantum systems. Sets of atoms and molecules have the advantage of having identical intrinsic properties but need to be placed in identical environments as well. In this work, we present a strong suppression of dephasing effects and a significant increase of the coherence time for ensembles of neutral atoms in arrays of optical traps. Compensation of the differential Stark shift caused by the optical trapping potential is achieved …
We report quantum degeneracy in a gas of ultra-cold fermionic $^{87}$Sr atoms. By evaporatively cooling a mixture of spin states in an optical dipole trap for 10.5\,s, we obtain samples well into the degenerate regime with $T/T_F=0.26^{+.05}_{-.06}$. The main signature of degeneracy is a change in the momentum distribution as measured by time-of-flight imaging, and we also observe a decrease in evaporation efficiency below $T/T_F \sim 0.5$.
A technique is proposed to cool Fermi gases to the regime of quantum degeneracy based on the expected inhibition of spontaneous emission due to the Pauli principle. The reduction of the linewidth for spontaneous emission originates a corresponding reduction of the Doppler temperature, which under specific conditions may give rise to a runaway process through which fermions are progressively cooled. The approach requires a combination of a magneto-optical trap as a cooling system and an optical dipole trap to enhance quantum degeneracy. This results in expected Fermi degeneracy factors $T/T_F$ …
We report on the realization of a sodium Bose--Einstein condensate (BEC) in a combined red-detuned optical dipole trap, formed by two beams crossing in a horizontal plane and a third, tightly focused dimple trap propagating vertically. We produce a BEC in three main steps: loading of the crossed dipole trap from laser-cooled atoms, an intermediate evaporative cooling stage which results in efficient loading of the auxiliary dimple trap, and a final evaporative cooling stage in the dimple trap. Our protocol is implemented in a compact setup and allows us to reach quantum degeneracy even with re…
We have experimentally produced rubidium Bose-Einstein condensate in an optically-plugged magnetic quadrupole (OPQ) trap. A far blue-detuned focused laser beam with a wavelength of 532 nm is plugged in the center of the magnetic quadrupole trap to increase the number of trapped atoms and suppress the heating. A radio frequency (RF) evaporative cooling in the magneto-optical hybrid trap is applied to decrease the atom temperature into degeneracy. The atom number of the condensate is $1.2(0.4)\times10^5$ and the temperature is below 100 nK. We have also studied characteristic behaviors of the co…
Quantum tunneling introduces a fundamental difference between classical and quantum mechanics. Whenever the classical ground state is non-unique (degenerate), quantum mechanics restore uniqueness thanks to tunneling. A condensate in a rotating trap with a vortex can have such a degenerate classical ground state, a degeneracy that is excluded in the absence of rotation at least when the Gross-Pitaevskii equation applies. If the rotating trap has a center of symmetry, like a figure eight (a peanut), the vortex may be on either side with the same energy yielding a degenerate ground state, a degen…
We analyze the superfluid phase transition of harmonically confined bosons with long-range interaction in both two and three dimensions in a broad parameter range from weak to strong coupling. We observe that the onset of superfluidity occurs in $3D$ at significantly lower temperatures compared to $2D$. This is demonstrated to be a quantum degeneracy effect. In addition, the spatial distribution of superfluidity across the shells of the clusters is investigated. It is found that superfluidity is substantially reduced in the outer layers due to increased correlation effects.
We report on Bose-Einstein condensation (BEC) in a gas of strontium atoms, using laser cooling as the only cooling mechanism. The condensate is formed within a sample that is continuously Doppler cooled to below 1\muK on a narrow-linewidth transition. The critical phase-space density for BEC is reached in a central region of the sample, in which atoms are rendered transparent for laser cooling photons. The density in this region is enhanced by an additional dipole trap potential. Thermal equilibrium between the gas in this central region and the surrounding laser cooled part of the cloud is es…
We demonstrate the fast accumulation of Cr atoms in a conservative potential from a magnetically guided atomic beam. Without laser cooling on a cycling transition, a single dissipative step realized by optical pumping allows to load atoms at a rate of 2*10^7 1/s in the trap. Within less than 100 ms we reach the collisionally dense regime, from which we directly produce a Bose-Einstein condensate with subsequent evaporative cooling. This constitutes a new approach to degeneracy where, provided a slow beam of particles can be produced by some means, Bose-Einstein condensation can be reached for …
We demonstrate experimentally the evaporative cooling of a few hundred rubidium 87 atoms in a single-beam microscopic dipole trap. Starting from 800 atoms at a temperature of 125microKelvins, we produce an unpolarized sample of 40 atoms at 110nK, within 3s. The phase-space density at the end of the evaporation reaches unity, close to quantum degeneracy. The gain in phase-space density after evaporation is 10^3. We find that the scaling laws used for much larger numbers of atoms are still valid despite the small number of atoms involved in the evaporative cooling process. We also compare our re…
We study a strongly interacting system of N identical bosons and one impurity in a one-dimensional trap. First, we assume that the particles have identical masses and analyze the corresponding set-up. After that, we study the influence of a small mass asymmetry on our analysis. In particular, we discuss how the structure of the wave function and the degeneracy in the impenetrable regime depend on the mass ratio and the shape of the trapping potential. To illustrate our findings, we consider a four-body system in a box and in an oscillator. We show that in the former case the system has the sma…
We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters (n=2,3,4), each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. We analyze protocols for coherently transferring ground state clusters into highly correlated states, producing theoretical fidelities in excess of 99%.
This is the second in a pair of articles that classify the configuration space and kinematic symmetry groups for $N$ identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies. The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in term…
We propose a simple idea for realizing a quantum gate with two identical fermions in a double well trap via external optical pulses without addressing the atoms individually. The key components of the scheme are Feshbach resonance and Pauli blocking, which decouple unwanted states from the dynamics. As a physical example we study atoms in the presence of a magnetic Feshbach resonance in a nanoplasmonic trap and discuss the constraints on the operation times for realistic parameters, reaching a fidelity above $99.9\%$ within $42μ$s.
Optical transport of cold atoms to quantum degeneracy
State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室和纳米光电前沿科学中心）
We investigate few-boson systems with resonant interactions in a narrow harmonic trap within an effective theory framework. The size of the model space is identified with the effective theory cutoff. In the universal regime, the interactions of the bosons can be approximated by contact interactions. We investigate the convergence properties of genuine and smeared contact interactions as the size of the model space is increased and present a detailed error analysis. The spectra for few-boson systems with up to 6 identical particles are calculated by combining extrapolations in the cutoff and in…
We consider two heteronuclear atoms interacting with a short-range $δ$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same…
We present an experimental study of electron spin waves in atomic hydrogen gas compressed to high densities of $\sim 5 \times 10^{18}$ cm$^{-3}$ at temperatures ranging from 0.26 to 0.6 K in strong magnetic field of 4.6 T. Hydrogen gas is in a quantum regime when the thermal de Broglie wavelength is much larger than the s-wave scattering length. In this regime the identical particle effects play major role in atomic collisions and lead to the Identical Spin Rotation effect (ISR). We observed a variety of spin wave modes caused by this effect with strong dependence on the magnetic potential cau…
Two identical dipolar atoms moving in a harmonic trap without an external magnetic field are investigated. Using the algebra of angular momentum a semi - analytical solutions are found. We show that the internal spin - spin interactions between the atoms couple to the orbital angular momentum causing an analogue of Einstein - de Haas effect. We show a possibility of adiabatically pumping our system from the s-wave to the d-wave relative motion. The effective spin-orbit coupling occurs at anti-crossings of the energy levels.
We evaluate the impact that nonlinear Zeeman shifts have on resonant radio-frequency (RF) dressed traps in an atom-chip configuration. The degeneracy of the resonance between Zeeman levels is lifted at large intensities of a static field, modifying the spatial dependence of the atomic adiabatic potential. In this context, we find effects that are important for the next generation of atom chips with tight trapping: in particular, that the vibrational frequency of the atom trap is sensitive to the RF frequency and, depending on the sign of the Landé factor, can produce significantly weaker, or t…
Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the $N!$ possible orderings of $N$ particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with gr…
We analyze the ac Stark shift of a cesium atom interacting with far-off-resonance guided light fields in the nanofiber-based two-color optical dipole trap realized by Vetsch \textit{et al.} [Phys. Rev. Lett. \textbf{104}, 203603, (2010)]. Particular emphasis is given to the fictitious magnetic field produced by the vector polarizability of the atom in conjunction with the ellipticity of the polarization of the trapping fields. Taking into account the ac Stark shift, the atomic hyperfine interaction, and a magnetic interaction, we solve the stationary Schrödinger equation at a fixed point in sp…
The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent [1]. These geometric structures, called Pauli crystals, are predicted for a system of $N$ identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of t…
We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $Ω$ optimized through the minimization of the eigenenergy of the desired level. It is shown that within the framework of this approach the well-converged results can be achieved at much smaller dimensions of the Hamiltonian matrix than with the standard approach that uses $Ω=1$. We present calculations for model systems of identical bosons with harmonic and double-well potentials. Our results show promising …
We consider identical quantum bosons with weak contact interactions in a two-dimensional isotropic harmonic trap. When the interactions are turned off, the energy levels are equidistant and highly degenerate. At linear order in the coupling parameter, these degenerate levels split, and we study the patterns of this splitting. It turns out that the problem is mathematically identical to diagonalizing the quantum resonant system of the two-dimensional Gross-Pitaevskii equation, whose classical counterpart has been previously studied in the mathematical literature on turbulence. Our purpose is to…
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and solvability depend on the trap shape, two-body interaction, the number of particles, and the number of spin components. A series of comments are presented that characterize the minimal symmetries possible for a composite system constructed from interacting single particles, with special focus on the contact interaction. For five and more particles with inte…
