Rotating Binary Bose-Einstein Condensates and Vortex Clusters in Quantum Droplets.

Quantum droplets may form out of a gaseous Bose-Einstein condensate, stabilized by quantum fluctuations beyond mean field. Determining the ground state of a rotating binary condensate, we show that multiple singly quantized vortices may form in these droplets at moderate angular momenta in two dimensions. Droplets carrying these precursors of an Abrikosov lattice remain self-bound for certain timescales after switching off an initial harmonic confinement. Intriguingly, we find evidence of a metastable persistent current in these new types of binary condensates. We discuss how this finding can be used to experimentally generate vortex-carrying quantum droplets.

Quantum Szilard Engine with Attractively Interacting Bosons.

We show that a quantum Szilard engine containing many bosons with attractive interactions enhances the conversion between information and work. Using an ab initio approach to the full quantum-mechanical many-body problem, we find that the average work output increases significantly for a larger number of bosons. The highest overshoot occurs at a finite temperature, demonstrating how thermal and quantum effects conspire to enhance the conversion between information and work. The predicted effects occur over a broad range of interaction strengths and temperatures.

Few-Body Precursor of the Higgs Mode in a Fermi Gas.

We demonstrate that an undamped few-body precursor of the Higgs mode can be investigated in a harmonically trapped Fermi gas. Using exact diagonalization, the lowest monopole mode frequency is shown to depend nonmonotonically on the interaction strength, having a minimum in a crossover region. The minimum deepens with increasing particle number, reflecting that the mode is the few-body analogue of a many-body Higgs mode in the superfluid phase, which has a vanishing frequency at the quantum phase transition point to the normal phase. We show that this mode mainly consists of coherent excitations of time-reversed pairs, and that it can be selectively excited by modulating the interaction strength, using, for instance, a Feshbach resonance in cold atomic gases.

Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap.

We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.

Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases.

We introduce a density functional formalism to study the ground-state properties of strongly correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Because of its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.

Total current blockade in an ultracold dipolar quantum wire.

Cold-atom systems offer a great potential for the future design of new mesoscopic quantum systems with properties that are fundamentally different from semiconductor nanostructures. Here, we investigate the quantum-gas analogue of a quantum wire and find a new scenario for the quantum transport: Attractive interactions may lead to a complete suppression of current in the low-bias range, a total current blockade. We demonstrate this effect for the example of ultracold quantum gases with dipolar interactions.

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

Complexity of quantum states in the two-dimensional pairing model.

It is known that many-fermion systems, such as complex atoms and nuclei, reveal (at some level of excitation energy) local signatures of quantum chaos similar to the predictions of random matrix theory. Here, we study the gradual development of such signatures in a model system of up to 16 fermions interacting through short-range pairing-type forces in a two-dimensional harmonic trap. We proceed from the simplest characteristics of the level spacing distribution to the complexity of eigenstates, strength, and correlation functions. For increasing pairing strength, at first, chaotic signatures gradually appear. However, when the pairing force dominates the Hamiltonian, we see a regression towards regularity. We introduce a "phase correlator" that allows us to distinguish the complexity of a quantum state that originates from its collective nature, from the complexity originating from quantum chaos.

Bosonic and fermionic dipoles on a ring.

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.

Tunable Wigner states with dipolar atoms and molecules.

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.

Mixtures of Bose gases confined in a ring potential.

The rotational properties of a mixture of two distinguishable Bose gases that are confined in a ring potential provide novel physical effects that we demonstrate in this study. Persistent currents are shown to be stable for a range of the population imbalance between the two components at low angular momentum. At higher values of the angular momentum, even small admixtures of a second species of atoms make the persistent currents highly fragile.

Cold fermionic atoms in two-dimensional traps: pairing versus Hund's rule.

The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.

Energy gaps and interaction blockade in confined quantum systems.

We investigate universal properties of strongly confined particles that turn out to be dramatically different from what is observed for electrons in atoms and molecules. For a large class of harmonically confined systems, such as small quantum dots and optically trapped atoms, many-body particle addition and removal energies, and energy gaps, are accurately obtained from single-particle eigenvalues. Transport blockade phenomena are related to the derivative discontinuity of the exchange-correlation functional. This implies that they occur very generally, with Coulomb blockade being a particular realization of a more general phenomenon. In particular, we predict a van der Waals blockade in cold atom gases in traps.

Mixtures of Bose gases under rotation.

We examine the rotational properties of a mixture of two Bose gases. Considering the limit of weak interactions between the atoms, we investigate the behavior of the system under a fixed angular momentum. We demonstrate a number of exact results in this many-body system.

Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids.

The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results are analysed as a function of the total angular momentum of the system. Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5, etc is the system fully polarized. The lowest energy states exhibit spin waves, domains, and localization, depending on the angular momentum. Vortices exist only at excited polarized states. The high angular momentum limit shows localization of electrons and separation of the charge and spin excitations.

Electron-hole duality and vortex rings in quantum dots.

In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for fermions in a rotating trap the vortices appear as holes in the Fermi sea. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunneling spectroscopy. We use the duality picture to show that these oscillations are caused by the localization of vortices in rings.

Universal vortex formation in rotating traps with bosons and fermions.

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.

Spontaneous magnetism of quantum dot lattices.

The magnetism of square lattices of quantum dots with up to 12 electrons per dot is studied using the spin-density functional formalism. At small values of the lattice constant, all lattices are nonmagnetic and gapless. When the lattice constant is increased, the shell structure of the single dots governs the magnetism of the lattice. At closed shells, the lattices are nonmagnetic and have a gap at the Fermi level. At the beginning and at the end of a shell, they become ferromagnetic and stay gapless up to large values of the lattice constant. Antiferromagnetism was observed only at midshell after a band gap was opened.

Weakly interacting Bose-Einstein condensates under rotation: mean-field versus exact solutions.

We consider a weakly interacting, harmonically trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.