Manuel Valiente

Strongly interacting confined quantum systems in one dimension.

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional (1D) systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that 1D fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and antiferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice

Topological quantum matter can be realized by subjecting engineered systems to time-periodic modulations. In analogy with static systems, periodically driven quantum matter can be topologically classified by topological invariants, whose non-zero value guarantees the presence of robust edge modes. In the high-frequency limit of the drive, topology is described by standard topological invariants, such as Chern numbers. Away from this limit, these topological numbers become irrelevant, and novel topological invariants must be introduced to capture topological edge transport. The corresponding edge modes were coined anomalous topological edge modes, to highlight their intriguing origin. Here we demonstrate the experimental observation of these topological edge modes in a 2D photonic lattice, where these propagating edge states are shown to coexist with a quasi-localized bulk. Our work opens an exciting route for the exploration of topological physics in time-modulated systems operating away from the high-frequency regime.

Two-particle states in the Hubbard model

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.

Scattering resonances and two-particle bound states of the extended Hubbard model

We present a complete derivation of two-particle states of the one-dimensional extended Bose–Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interaction-bound states which are not present in the Hubbard model with the on-site interaction alone.

Fractional energy states of strongly interacting bosons in one dimension

We study two-component bosonic systems with strong inter-species and vanishing intra-species interactions. A new class of exact eigenstates is found with energies that are not sums of the single-particle energies with wave functions that have the characteristic feature that they vanish over extended regions of coordinate space. This is demonstrated in an analytically solvable model for three equal mass particles, two of which are identical bosons, which is exact in the strongly interacting limit. We numerically verify our results by presenting the first application of the stochastic variational method to this kind of system. We also demonstrate that the limit where both inter- and intra-component interactions become strong must be treated with extreme care as these limits do not commute. Moreover, we argue that such states are generic also for general multi-component systems with more than three particles. The states can be probed using the same techniques that have recently been used for fermionic few-body systems in quasi-1D.

Simulating an interacting gauge theory with ultracold Bose gases

We show how density dependent gauge potentials can be induced in dilute gases of ultracold atoms using light-matter interactions. We study the effect of the resulting interacting gauge theory and show how it gives rise to novel topological states in the ultracold gas. We find in particular that the onset of persistent currents in a ring geometry is governed by a critical number of particles. The density-dependent gauge potential is also found to support chiral solitons in a quasi-one-dimensional ultracold Bose gas.

Universal properties of Fermi gases in arbitrary dimensions

We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tans distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for non-integer dimensions interpolates between the known results in integer dimensions 1, 2 and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from D=2, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

Bound states of dipolar bosons in one-dimensional systems

We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole?dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as a function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three-, four- and five-body problems in two or more tubes. Our results indicate that in the weakly coupled limit the intertube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.

Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension

The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached analytically. To illustrate this analytical approach we consider a simple system of three distinguishable particles, which can be addressed experimentally. For this system we show that for infinite repulsion the energy spectrum is sixfold degenerate. We also show that this degeneracy is partially lifted for finitely large repulsion for which we find and describe corresponding wave functions.

Quantum spin transistor with a Heisenberg spin chain.

Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements.