Daniel Cocks

Emulating solid-state physics with a hybrid system of ultracold ions and atoms.

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

Time-reversal-invariant Hofstadter-Hubbard Model with ultracold fermions

We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold-atom experiments. In these experiments, an additional staggered potential and an artificial Rashba-type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi-metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi-metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.

Dissipation through localized loss in bosonic systems with long-range interactions

In recent years, controlled dissipation has proven to be a useful tool for the probing of a quantum system in an ultracold setup. In this paper we consider the dynamics of bosons induced by a dissipative local defect. We address superfluid and supersolid phases close to half filling that are ground states of an extended Bose-Hubbard Hamiltonian. To this end, we solve the master equation using the Gutzwiller approximation and find that in the superfluid phase repulsive nearest-neighbor interactions can lead to enhanced dissipation processes. On the other hand, our mean-field approach indicates that the effective loss rates are significantly suppressed deep in the supersolid phase where repulsive nearest-neighbor interactions play a dominant role. Our numerical results are explained by analytical arguments and, in particular, in the limit of strong dissipation we recover the quantum Zeno effect.

Effects of smooth boundaries on topological edge modes in optical lattices

Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically nontrivial phases of matter with ultracold atoms has become a major focus of cold-atom experiments. However, several obvious differences exist between cold-atom and solid-state systems, for instance the small size of the atomic cloud and the smooth confining potential. In this article we show that sharp boundaries are not required to realize quantum Hall or quantum spin Hall physics in optical lattices and, on the contrary, that edge states in a smooth confinement exhibit additional interesting properties, such as spatially resolved splitting and merging of bulk bands and the emergence of robust auxiliary states in bulk gaps to preserve the topological quantum numbers. In addition, we numerically validate that these states are robust against disorder. Finally, we analyze possible detection methods, with a focus on Bragg spectroscopy, to demonstrate that the edge states can be detected and that Bragg spectroscopy can reveal how topological edge states are connected to the different bulk bands.

Ab-initio electron scattering cross-sections and transport in liquid xenon

Ab-initio electron - liquid phase xenon fully differential cross-sections for electrons scattering in liquid xenon are developed from a solution of the Dirac-Fock scattering equations, using a recently developed framework [1] which considers multipole polarizabilities, a non-local treatment of exchange, and screening and coherent scattering effects. A multi-term solution of Boltzmanns equation accounting for the full anisotropic nature of the differential cross-section is used to calculate transport properties of excess electrons in liquid xenon. The results were found to agree to within 25% of the measured mobilities and characteristic energies over the reduced field range of 10^{-4} to 1 Td. The accuracies are comparable to those achieved in the gas phase. A simple model, informed by highly accurate gas-phase cross-sections, is presented to transform highly accurate gas-phase cross-sections to improve the liquid cross-sections, which was found to enhance the accuracy of the transport coefficient calculations.

Correlated topological phases and exotic magnetism with ultracold fermions

Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter–Hubbard model. We include an additional staggered lattice potential and an artificial Rashba-type spin–orbit coupling term available in experiment. Without interactions, the system can be either a (semi)-metal, a normal or a topological insulator, and we present the non-Abelian generalization of the Hofstadter butterfly. Using a combination of real-space dynamical mean-field theory (RDMFT), analytical arguments, and Monte-Carlo simulations we study the effect of strong on-site interactions. We determine the interacting phase diagram, and discuss a scenario of an interaction-induced transition from a normal to a topological insulator. At half-filling and large interactions, the system is described by a quantum spin Hamiltonian, which exhibits exotic magnetic order due to the interplay of Rashba-type spin–orbit coupling and the artificial time-reversal-invariant magnetic field term. We determine the magnetic phase diagram: both for the itinerant model using RDMFT and for the corresponding spin model in the classical limit using Monte-Carlo simulations.

Electron scattering and transport in liquid argon

The transport of excess electrons in liquid argon driven out of equilibrium by an applied electric field is revisited using a multi-term solution of Boltzmanns equation together with ab initio liquid phase cross-sections calculated using the Dirac-Fock scattering equations. The calculation of liquid phase cross-sections extends previous treatments to consider multipole polarisabilities and a non-local treatment of exchange, while the accuracy of the electron-argon potential is validated through comparison of the calculated gas phase cross-sections with experiment. The results presented highlight the inadequacy of local treatments of exchange that are commonly used in liquid and cluster phase cross-section calculations. The multi-term Boltzmann equation framework accounting for coherent scattering enables the inclusion of the full anisotropy in the differential cross-section arising from the interaction and the structure factor, without an a priori assumption of quasi-isotropy in the velocity distribution function. The model, which contains no free parameters and accounts for both coherent scattering and liquid phase screening effects, was found to reproduce well the experimental drift velocities and characteristic energies.

Self-consistency of electron-THF cross sections using electron swarm techniques

The drift velocity and first Townsend ionization coefficient of electrons in gaseous tetrahydrofuran are measured over the range of reduced electric fields 4-1000 Td using a pulsed-Townsend technique. The measured drift velocities and Townsend ionization coefficients are subsequently used, in conjunction with a multi-term Boltzmann equation analysis, as a further discriminative assessment on the accuracy and completeness of a recently proposed set of electron-THF vapor cross sections. In addition, the sensitivity of the transport coefficients to uncertainties in the existing cross sections is presented. As a result of that analysis, a refinement of the momentum transfer cross section for electron-THF scattering is presented, along with modifications to the neutral dissociation and dissociative electron attachment cross sections. With these changes to the cross section database, we find relatively good self-consistency between the measured and simulated drift velocities and Townsend coefficients.

Polaronic effects in one- and two-band quantum systems

In this work, we study the formation and dynamics of polarons in a system with a few impurities in a lattice immersed in a Bose-Einstein condensate (BEC). This system has been experimentally realized using ultracold atoms and optical lattices. Here, we consider a two-band model for the impurity atoms, along with a Bogoliubov approximation for the BEC, with phonons coupled to impurities via both intraband and interband transitions. We decouple this Frohlich-type term by an extended two-band Lang-Firsov polaron transformation using a variational method. The new effective Hamiltonian with two (polaron) bands differs from the original Hamiltonian by modified coherent transport, polaron energy shifts, and induced long-range interaction. A Lindblad master-equation approach is used to take into account residual incoherent coupling between polaron and bath. This polaronic treatment yields a renormalized interband relaxation rate compared to Fermis golden rule. For a strongly coupled two-band Frohlich Hamiltonian, the polaron is tightly dressed in each band and can not tunnel between them, leading to an interband self-trapping effect.

Advantages of Mass-Imbalanced Ultracold Fermionic Mixtures for Approaching Quantum Magnetism in Optical Lattices

We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a directly observable signature of the ordered state. For the trapped system, we compare our results obtained by real-space DMFT to a local-density approximation. We calculate the entropy for a wide range of parameters and identify regions, in which mass-imbalanced mixtures could have clear advantages over balanced ones for the purpose of obtaining and detecting quantum magnetism.