Jonas Cremon

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.

Signatures of Wigner localization in epitaxially grown nanowires

It was predicted by Wigner in 1934 that an electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made toward the detection of electronic Wigner states, their clear and direct experimental verification still remains a challenge. Here we address signatures of Wigner molecule formation in the transport properties of InSb nanowire quantum-dot systems, where a few electrons may form localized states depending on the size of the dot (i.e., the electron density). Using a configuration interaction approach combined with an appropriate transport formalism, we are able to predict the transport properties of these systems, in excellent agreement with experimental data. We identify specific signatures of Wigner state formation, such as the strong suppression of the antiferromagnetic coupling, and are able to detect the onset of Wigner localization, both experimentally and theoretically, by studying different dot sizes. (Less)

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.

Spin-orbit-enhanced Wigner localization in quantum dots

We investigate quantum dots with Rashba spin-orbit coupling in the strongly-correlated regime. We show that the presence of the Rashba interaction enhances the Wigner localization in these systems, making it achievable for higher densities than those at which it is observed in Rashba-free quantum dots. Recurring shapes in the pair distribution functions of the yrast spectrum, which might be associated with rotational and vibrational modes, are also reported.

Vortices in Bose-Einstein condensates: Finite-size effects and the thermodynamic limit

For a weakly interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasiperiodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state. (Less)

Test of a Jastrow-type Wavefunction for a Trapped Few-body System in One Dimension

For a system with interacting quantum mechanical particles in a one-dimensional harmonic oscillator, a trial wavefunction with simple structure based on the solution of the corresponding two-particle system is suggested and tested numerically.With the inclusion of a scaling parameter for the distance between particles, at least for the very small systems tested here the ansatz gives a very good estimate of the ground state energy, with the error being of the order of ~1 % of the gap to the first excited state.

Coreless vortices in rotating two-component quantum droplets

The rotation of a quantum liquid induces vortices to carry angular momentum. When the system is composed of multiple components that are distinguishable from each other, vortex cores in one component may be filled by particles of the other component, and coreless vortices form. Based on evidence from computational methods, here we show that the formation of coreless vortices occurs very similarly for repulsively interacting bosons and fermions, largely independent of the form of the particle interactions. We further address the connection to the Halperin wave functions of non-polarized quantum Hall states.

Wigner-localized states in spin-orbit-coupled bosonic ultracold atoms with dipolar interaction

We investigate the occurence of Wigner-localization phenomena in bosonic dipolar ultracold few-body systems with Rashba-like spin-orbit coupling. We show that the latter strongly enhances the effects of the dipole-dipole interactions, allowing to reach the Wigner-localized regime for strengths of the dipole moment much smaller than those necessary in the spin-orbit-free case.

Vortices in fermion droplets with repulsive dipole-dipole interactions

Vortices are found in a fermion system with repulsive dipole-dipole interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator potential. Such systems have much in common with electrons in quantum dots, where rotation is induced via an external magnetic field. In contrast to the Coulomb interactions between electrons, the (externally tunable) anisotropy of the dipole-dipole interaction breaks the rotational symmetry of the Hamiltonian. This may cause the otherwise rotationally symmetric exact wave function to reveal its internal structure more directly.