Laboratoire de Physique Théorique et Modélisation

For Dirac electrons the Klein paradox implies that the confinement is difficult to achieve with an electrostatic potential although it can be of great importance for graphene-based devices. Here, ab initio and tight-binding approaches are combined and show that the wave function of Dirac electrons can be localized in rotated graphene bilayers due to the Moire pattern. This localization of wave function is maximum in the limit of the small rotation angle between the two layers.

Extensive scanning tunneling microscopy and spectroscopy experiments complemented by first-principles and parametrized tight binding calculations provide a clear answer to the existence, origin, and robustness of van Hove singularities (vHs) in twisted graphene layers. Our results are conclusive: vHs due to interlayer coupling are ubiquitously present in a broad range (from 1° to 10°) of rotation angles in our graphene on 6H-SiC(000-1) samples. From the variation of the energy separation of the vHs with the rotation angle we are able to recover the Fermi velocity of a graphene monolayer as well as the strength of the interlayer interaction. The robustness of the vHs is assessed both by experiments, which show that they survive in the presence of a third graphene layer, and by calculations, which test the role of the periodic modulation and absolute value of the interlayer distance. Finally, we clarify the role of the layer topographic corrugation and of electronic effects in the apparent moiré contrast measured on the STM images.

We consider, by means of the variational approximation (VA) and direct numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of two-dimensional (2D) and 3D condensates with a scattering length containing constant and harmonically varying parts, which can be achieved with an ac magnetic field tuned to the Feshbach resonance. For a rapid time modulation, we develop an approach based on the direct averaging of the GP equation, without using the VA. In the 2D case, both VA and direct simulations, as well as the averaging method, reveal the existence of stable self-confined condensates without an external trap, in agreement with qualitatively similar results recently reported for spatial solitons in nonlinear optics. In the 3D case, the VA again predicts the existence of a stable self-confined condensate without a trap. In this case, direct simulations demonstrate that the stability is limited in time, eventually switching into collapse, even though the constant part of the scattering length is positive (but not too large). Thus a spatially uniform ac magnetic field, resonantly tuned to control the scattering length, may play the role of an effective trap confining the condensate, and sometimes causing its collapse.

Rotated graphene multilayers form a new class of graphene-related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation angles. For smaller angles, states in the Dirac cones belonging to the two layers interact resulting in the appearance of two Van Hove singularities. States become localized as the rotation angle decreases and the two Van Hove singularities merge into one peak at the Dirac energy. Here we go further and consider bilayers with very small rotation angles. In this case, well-defined regions of AA stacking exist in the bilayer supercell and we show that states are confined in these regions for energies in the [$\ensuremath{-}{\ensuremath{\gamma}}_{t}$, $+{\ensuremath{\gamma}}_{t}$] range with ${\ensuremath{\gamma}}_{t}$ the interplane mean interaction. As a consequence, the local densities of states show discrete peaks for energies different from the Dirac energy.

Abstract The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons—quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital-coupled magnets, such as α-RuCl 3 , may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here, we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmonicity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of α-RuCl 3 and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state.

From its very beginning, quantum theory has been revealing extraordinary and counter-intuitive phenomena, such as wave-particle duality, Schrödinger cats and quantum non-locality. Another paradoxical phenomenon found within the framework of quantum mechanics is the 'quantum Cheshire Cat': if a quantum system is subject to a certain pre- and postselection, it can behave as if a particle and its property are spatially separated. It has been suggested to employ weak measurements in order to explore the Cheshire Cat's nature. Here we report an experiment in which we send neutrons through a perfect silicon crystal interferometer and perform weak measurements to probe the location of the particle and its magnetic moment. The experimental results suggest that the system behaves as if the neutrons go through one beam path, while their magnetic moment travels along the other.

Abstract. We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S 3. The S 2 base space of a suitably oriented S 3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S 7, which also allows for a Hopf fibration, with S 3 fibres and a S 4 base. A main striking result is that suitably oriented S 7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussed 1.

We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate K(t) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the "Thouless time" t_{Th} demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K(t) at t≲t_{Th}. We also report numerical results for K(t) in a generic Floquet spin model, which are consistent with these analytic predictions.

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1 + 1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

We study a simple model of $N$-component fermions with contact interactions which describes fermionic atoms with $N=2F+1$ hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound states made of $N$ fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an $\mathrm{SU}(N)$ symmetry between the hyperfine states.

The physical properties of arbitrary half-integer spins F = N - (1/2) fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F > or = (3/2) depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at (1/2) filling.

We investigate the metal-insulator transition of the one-dimensional $\mathrm{SU}(N)$ Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half filling ${(k}_{F}=\ensuremath{\pi}{/Na}_{0})$ is conjectured for $N>2.$ Expressions for the charge and spin velocities as well as for the Luttinger-liquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger-liquid parameters as a function of the Coulomb interaction $U$ are given for the cases $N=3$ and $N=4.$ Our results strongly support the existence of a Mott-Hubbard transition at a nonzero value of the Coulomb interaction. We find ${U}_{c}\ensuremath{\sim}2.2$ for $N=3$ and ${U}_{c}\ensuremath{\sim}2.8$ for $N=4.$

We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the mean-field limit of these models manifests multistable parameter regions of coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to mean field by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product operators in one- and two-dimensional lattices. Correlations are shown to wash the mean-field bistability in dimension one, leading to a unique steady state. In dimension two and higher, we find that multistability is again possible, provided the thermodynamic limit of an infinitely large lattice is taken first with respect to the longtime limit. Variation of the system parameters results in jumps between the different steady states, each showing a critical slowing down in the convergence of perturbations towards the steady state. Experiments with trapped ions can realize the model and possibly answer open questions in the nonequilibrium many-body dynamics of these quantum systems, beyond the system sizes accessible to present numerics.

The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless region with algebraically decaying correlation functions $\ensuremath{\sim}\mathrm{cos}[(\ensuremath{\pi}{/2a}_{0})x]{x}^{\ensuremath{-}3/2}$. When entering the massive phase, the system displays an approximate SO(6) enlarged symmetry with a dimerization type of ordering consisting in alternating spin and orbital singlets.

The spin-transfer effect is investigated for the vortex state of a magnetic nanodot. A spin current is shown to act similarly to an effective magnetic field perpendicular to the nanodot. Then a vortex with magnetization (polarity) parallel to the current polarization is energetically favorable. Following a simple energy analysis and using direct spin-lattice simulations, we predict the polarity switching of a vortex. For magnetic storage devices, an electric current is more effective to switch the polarity of a vortex in a nanodot than the magnetic field.

The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.

The spectral problem of the Heisenberg XXZ spin-12 chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to N, the length of the chain, and which satisfies a set of Bethe equations with an additional term.

Radon transforms defined on smooth curves are well known and extensively studied in the literature. In this paper, we consider a Radon transform defined on a discontinuous curve formed by a pair of half-lines forming the vertical letter V. If the classical two-dimensional Radon transform has served as a work horse for tomographic transmission and/or emission imaging, we show that this V-line Radon transform is the backbone of scattered radiation imaging in two dimensions. We establish its analytic inverse formula as well as a corresponding filtered back projection reconstruction procedure. These theoretical results allow the reconstruction of two-dimensional images from Compton scattered radiation collected on a one-dimensional collimated camera. We illustrate the working principles of this imaging modality by presenting numerical simulation results.

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalize at late times. We show that the full thermalizing dynamics can be described by the generalized hydrodynamics with diffusion and force terms, and we compare these predictions to numerical simulations. Finally, we provide an explanation for the slow thermalization rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterized by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalization can display prethermal plateau and relaxation dynamics with long polynomial finite-time corrections.

Quantum fluids of light merge many-body physics and nonlinear optics, revealing quantum hydrodynamic features of light when it propagates in nonlinear media. One of the most outstanding evidence of light behaving as an interacting fluid is its ability to carry itself as a superfluid. Here, we report a direct experimental detection of the transition to superfluidity in the flow of a fluid of light past an obstacle in a bulk nonlinear crystal. In this cavityless all-optical system, we extract a direct optical analog of the drag force exerted by the fluid of light and measure the associated displacement of the obstacle. Both quantities drop to zero in the superfluid regime characterized by a suppression of long-range radiation from the obstacle. The experimental capability to shape both the flow and the potential landscape paves the way for simulation of quantum transport in complex systems.