External Harmonic Confinement Research Articles

Higher-charged vortex solitons in harmonic potential

By introducing external harmonic potential confinement, we investigate the stability of higher-charged vortex solitons in competing cubic–quintic nonlinear medium. Vortex solitons with higher charges (m > 5) become robust in harmonic potential. There are two coexisting branches of different power at the same propagation constant domain. Intriguingly, if topological charge m > 1, we find the inferior branch of solitons is completely unstable, while the superior branch of solitons still exists interval of stability with the enhancement of competing nonlinearity. From the perspective of the numerical results, it reveals a novel approach to access optical vortex mode with higher topological charge.

Dynamics of quantum droplets in an external harmonic confinement

Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross–Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov–Kolokolov (VK) criterion and are found stable.

Itinerant ferromagnetism of two-dimensional repulsive fermions with Rabi coupling

We study a two-dimensional fermionic cloud of repulsive alkali-metal atoms characterized by two hyperfine states which are Rabi coupled. Within a variational Hartree–Fock scheme, we calculate analytically the ground-state energy of the system. Then we determine the conditions under which there is a quantum phase transition with spontaneous symmetry breaking from a spin-balanced configuration to a spin-polarized one, an effect known as itinerant ferromagnetism. Interestingly, we find that the transition appears when the interaction energy per particle exceedes both the kinetic energy per particle and the Rabi coupling energy. The itinerant ferromagnetism of the polarized phase is analyzed, obtaining the population imbalance as a function of interaction strength, Rabi coupling, and number density. Finally, the inclusion of a external harmonic confinement is investigated by adopting the local density approximation. We predict that a single atomic cloud can display population imbalance near the center of the trap and a fully balanced configuration at the periphery.

Broken scale invariance in time-dependent trapping potentials

The response of a cold atom gas with contact interactions to a smoothly varying external harmonic confinement in the non-adiabatic regime is studied. The time variation of the angular frequency is varied such that the system is, for vanishing or infinitely strong contact interactions, scale invariant. The time evolution of the system with broken scale invariance (i.e., the time evolution of the system with finite interaction strength), is contrasted with that for a scale invariant system, which exhibits Efimovian-like expansion dynamics that is characterized by log-periodic oscillations with unique period and amplitude. It is found that the breaking of the scale invariance by the finiteness of the interactions leads to a time dependence of the oscillation period and amplitude. It is argued, based on analytical considerations for atomic gases of arbitrary size and numerical results for two one-dimensional particles, that the oscillation pe riod approaches that of the scale-invariant system at large times. The role of the time-dependent contact in the expansion dynamics is analyzed.

Long-time averaged dynamics of a Bose–Einstein condensate in a bichromatic optical lattice with external harmonic confinement

The dynamics of a Bose–Einstein condensate are examined numerically in the presence of a one-dimensional bichromatic optical lattice (BCOL) with external harmonic confinement in the strongly interacting regime. The condensate is excited by a focusing stirring red laser. Two realizations of the BCOL are considered, one with a rational and the other with an irrational ratio of the two constituting wave lengths. The system is simulated by the time-dependent Gross Pitaevskii equation that is solved using the Crank Nicolson method in real time. It is found that for a weak BCOL, the long-time averaged physical observables of the condensate respond only very weakly (or not at all) to changes in the secondary OL depth V1 showing that under these conditions the harmonic trap plays a dominant role in governing the dynamics. However, for a much larger strength of the BCOL, the response is stronger as it begins to compete with the external harmonic trap, such that the frequency of Bloch oscillations of the bosons rises with V1 yielding higher time-averages. Qualitatively there is no difference between the dynamics of the condensate resulting from the use of a rational or irrational ratio of the wavelengths since the external harmonic trap washes it out. It is further found that in the presence of an external harmonic trap, the BCOL acts in favor of superflow.

Magnetism in Strongly Interacting One-Dimensional Quantum Mixtures.

We consider two species of bosons in one dimension near the Tonks-Girardeau limit of infinite interactions. For the case of equal masses and equal intraspecies interactions, the system can be mapped to a S=1/2 XXZ Heisenberg spin chain, thus allowing one to access different magnetic phases. Using a powerful ansatz developed for the two-component Fermi system, we elucidate the evolution from few to many particles for the experimentally relevant case of an external harmonic confinement. In the few-body limit, we already find clear evidence of both ferromagnetic and antiferromagnetic spin correlations as the ratio of intraspecies and interspecies interactions is varied. Furthermore, we observe the rapid emergence of symmetry-broken magnetic ground states as the particle number is increased. We therefore demonstrate that systems containing only a few bosons are an ideal setting in which to realize the highly sought-after itinerant ferromagnetic phase.

Trapped unitary two-component Fermi gases with up to ten particles

The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground state energy for systems with up to ten particles interacting through finite-range two-body potentials for both even and odd number of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.

Pair condensation of polarized fermions in the BCS–BEC crossover

We investigate a two-component Fermi gas with unequal spin populations along the BCS–BEC crossover. By using the extended BCS equations and the concept of off-diagonal-long-range-order we derive a formula for the condensate number of Cooper pairs as a function of energy gap, average chemical potential, imbalance chemical potential and temperature. Then we study the zero-temperature condensate fraction of Cooper pairs by varying interaction strength and polarization, finding a depletion of the condensate fraction by increasing the population imbalance. We also consider explicitly the presence of an external harmonic confinement and we study, within the local-density approximation, the phase separation between superfluid (SF) and normal phase regions of the polarized fermionic cloud. In particular, we calculate both condensate density profiles and total density profiles from the inner SF core to the normal region passing for the interface, where a finite jump in the density is a clear manifestation of this phase-separated regime. Finally, we compare our theoretical results with the available experimental data on the condensate fraction of polarized 6Li atoms (Zwierlein et al 2006 Science 311 492). These experimental data are in reasonable agreement with our predictions in a suitable range of polarizations, but only in the BCS side of the crossover up to unitarity.

Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices

We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.

Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large $s$-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the $(2,2)$ and $(3,1)$ systems at unitarity as a function of the range ${r}_{0}$ of the underlying two-body potential and extrapolate to the ${r}_{0}\ensuremath{\rightarrow}0$ limit. Our calculations include all states with vanishing and finite angular momentum $L$ (and natural and unnatural parity $\ensuremath{\Pi}$) with relative energy up to 10.5 $\ensuremath{\hbar}\ensuremath{\Omega}$, where $\ensuremath{\Omega}$ denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1$%$ or smaller. The $(2,2)$ and $(3,1)$ energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the $(3,2)$ and $(4,1)$ systems at unitarity.

Few-body bound complexes in one-dimensional dipolar gases and nondestructive optical detection

We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical nondestructive detection scheme that enables in situ observation of the creation and dissociation of the few-body complexes. A detailed description of the expected signal of such measurements is given using the numerically calculated wave functions of the bound states. We also discuss implications on the many-body physics of dipolar systems in tubular geometries, as well as experimental issues related to the external harmonic confinement along the tube and the prospect of applying an in-tube optical lattice to increase the effective dipole strength.

Exact Three-Body Local Correlations for Excited States of the 1D Bose Gas

We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of nonthermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.

Ising antiferromagnet with ultracold bosonic mixtures confined in a harmonic trap

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 imbalance, the antiferromagnetic phase can be observed in the trap.

Tuning the structural and dynamical properties of a dipolar Bose–Einstein condensate: ripples and instability islands

It is now well established that the stability of aligned dipolar Bose gases can be tuned by varying the aspect ratio of the external harmonic confinement. This paper extends this idea and demonstrates that a Gaussian barrier along the strong confinement direction can be employed to tune both the structural properties and dynamical stability of an oblate dipolar Bose gas aligned along the strong confinement direction. In particular, our theoretical mean-field analysis predicts the existence of instability islands immersed in otherwise stable regions of the phase diagram. Dynamical studies indicate that these instability islands, which can be probed experimentally with present-day technology, are associated with the going soft of a Bogoliubov–de Gennes excitation frequency with radial breathing mode character. Furthermore, we find dynamically stable ground state densities with ripple-like oscillations along the radial direction. These structured ground states exist in the vicinity of a dynamical radial roton-like instability.

Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space

The effect of strongly repulsive interactions on the tunneling amplitude of hard-sphere (HS) bosons confined in a simple cubic optical lattice plus tight external harmonic confinement in continuous space is investigated. The quantum variational Monte Carlo (VMC) and the variational path integral (VPI) Monte Carlo techniques are used at zero temperature. The effects of the lattice spacing on the tunneling amplitude are also considered. The occupancies of the lattice sites as a function of the repulsion between the bosons are further revealed. Our chief result is that for a small number of bosons ($N=8$) the overlap of the wave functions in neighboring wells practically does not change with an increase of the repulsive interactions and changes only minimally for a larger number of particles ($N=40$). The tunneling amplitude rises with a reduction in the lattice spacing. In addition, the occupancy of the center of the trap decreases in favor of a rise in the occupancy of the lattice sites at the edges of the trap with increasing HS repulsion. Further, it was found that the energy per particle at certain optical-lattice barrier heights is insensitive to the number of particles and variations in the HS diameter of the bosons. In order to support our results, we compare the VMC results with corresponding VPI results.

Trapped polarized Fermi gas at unitarity

We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging s-wave scattering length. Using the fixed-node diffusion Monte Carlo method, the energies of the normal are determined as functions of the population-imbalance and the number of particles. The energies of the trapped system follow, to a good approximation, a universal curve even for fairly small systems. A simple parameterization of the universal curve is presented and related to the equation of state of the bulk system.

Dilute Bose gases interacting via power-law potentials

Neutral atoms interact through a van der Waals potential which asymptotically falls off as ${r}^{\ensuremath{-}6}$. In ultracold gases, this interaction can be described to a good approximation by the atom-atom scattering length. However, corrections arise that depend on the characteristic length of the van der Waals potential. We parametrize these corrections by analyzing the energies of two- and few-atom systems under external harmonic confinement, obtained by numerically and analytically solving the Schr\"odinger equation. We generalize our results to particles interacting through a longer-ranged potential which asymptotically falls off as ${r}^{\ensuremath{-}4}$.

Pseudopotential treatment of two aligned dipoles under external harmonic confinement

Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, long-range potentials. Here, we replace the long-range potential by a zero-range pseudo-potential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zero-range pseudo-potential description reproduces the energy spectrum of two dipoles interacting through a shape-dependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.

Hartree-Fock Stability and Broken Symmetry Solutions of O2- and S2- Anions in External Confinement

We study the effect of a confining potential on systems that exhibit Hartree-Fock (HF) instabilities, and thus admit broken symmetry (BS) HF solutions, by relying on the O2- and S2- doubly-charged anions as model systems. We find that with the increasing strength of the external harmonic confinement potential, W(r) = 1/2(ωr)2 (with 0.0 ≤ ω < 0.2), the BS solutions are systematically eliminated. We use extended, diffuse, doubly-augmented Gaussian basis sets up to and including d-aug-cc-pV6Z, and find that the number and the character of BS solutions exhibit significant basis set effects. These basis sets were further extended by additional ghost basis functions, located away from the atomic center. The role of the electron correlation effects for the BS HF solutions was examined by the CCSD(T) method. In addition to modelling the confinement by the harmonic-like potential W(r), we also examined a more realistic "confinement", realized by a grid of point charges modelling the crystal structure of MgO. Again, we find that the HF instabilities and the implied BS solutions disappear with the increasing magnitude of the model charges simulating the crystal environment. At the same time, the O2- anion is energetically stabilized with respect to both the O- anion and the neutral oxygen atom.

Collective oscillations of one-dimensional Bose-Einstein gas in a time-varying trap potential and atomic scattering length

The collective oscillations of 1D repulsive Bose gas with external harmonic confinement in two different regimes are studied. The first regime is the mean field regime when the density is high. The second regime is the Tonks-Girardeau regime when the density is low. We investigate the resonances under periodic modulations of the trap potential and the effective nonlinearity. Modulations of the effective nonlinear coefficient result from modulations of the atomic scattering length by the Feshbach resonance method or variations of the transverse trap frequency. In the mean field regime we predict the bistability in the nonlinear oscillations of the condensate. In the Tonks-Girardeau regime the resonance has the character of a linear parametric resonance. In the case of rapid strong modulations of the nonlinear coefficient we find analytical expressions for the nonlinearity managed soliton width and the frequency of the slow secondary oscillations near the fixed point.