Laboratoire de Physique et Modélisation des Milieux Condensés

Quantum thermodynamics defines the ideal quantum thermoelectric, with maximum possible efficiency at finite power output. However, such an ideal thermoelectric is challenging to implement experimentally. Instead, here we consider two types of thermoelectrics regularly implemented in experiments: (i) finite-height potential barriers or quantum point contacts, and (ii) double-barrier structures or single-level quantum dots. We model them with Landauer scattering theory as (i) step transmissions and(ii) Lorentzian transmissions, respectively. We optimize their thermodynamic efficiency for any given power output, when they are used as thermoelectric heat engines or refrigerators. The Lorentzian's efficiency is excellent at vanishing power, but we find that it is poor at the finite powers of practical interest. In contrast, the step transmission is remarkably close to ideal efficiency (typically within 15\%) at all power outputs. The step transmission is also close to ideal in the presence of phonons and other heat leaks, for which the Lorentzian performs very poorly. Thus, a simple nanoscale thermoelectric - made with a potential barrier or quantum point contact - is almost as efficient as an ideal thermoelectric.

We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to $N = 96$ qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.

The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are nonanalytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of $\mathrm{SU}(n)$ models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.

The authors find that the SU($N$) Fermi-Hubbard model on two sites can be mapped to the Lipkin-Meshkov-Glick model. It admits a Bethe ansatz solution and exhibits a quantum phase transition in the large-$N$ limit that could be experimentally accessible using current technologies involving SU($N$) ultracold atoms or molecules.

We study spontaneous photon decay into multiple photons triggered by strong nonlinearities in an experimental simulator of a bosonic quantum impurity model. Previously, spectroscopic signatures of photon conversion were reported and evidenced as resonances in the many-body spectrum of these systems. Here, we report on the observation of multimode fluorescence of a small Josephson junction embedded in a high impedance superconducting transmission line. Measurement of the down-converted photons is achieved using state-of-the-art broadband parametric amplifiers. Photon triplet emission is explicitly demonstrated at a given frequency as the counterpart of inelastic photon decay at 3× the emission frequency. These results open exciting prospects for the burgeoning field of many-body quantum optics and offer a direct signature of the ultrastrong light-matter coupling.

We have developed an efficient method for performing density matrix renormalization group (DMRG) simulations of the SU(N) Fermi-Hubbard chain with open boundary conditions, fully leveraging the SU(N) symmetry of the problem. This method extends a previously developed approach for the SU(N) Heisenberg model and relies on the systematic use of the semi-standard Young tableaux (SSYT) basis in a DMRG algorithm `a la White. Specifically, the method aligns the site-by-site growth process of the infinite-size part of the DMRG, in its original formulation, with the site-by-site construction of the SSYT (or Gelfand-like) basis, based on the chain of unitary subgroups $U(1)\subset U(2) \subset U(3) \subset U(4)\cdots $. We give special emphasis to the calculation of the symmetry-resolved reduced matrix elements of the hopping terms between the left and the right block, which makes direct use of the basis of SSYT and of the Gelfand-Tsetlin coefficients, offering a computational advantage in scaling with N compared to alternative methods that rely on summing over Clebsch-Gordan coefficients. Focusing on the model with homogeneous hopping between nearest neighbors, we have calculated the ground state energy as a function of U, i.e the atom-atom interaction amplitude, up to N=6 for filling 1/N (one particle per site in average), and for one atom (resp. hole) away from filling 1/N, alllowing us to compute the charge gaps, and to estimate in the thermodynamical limit, the critical value $U_c$, separating the Mott insulator from the metallic phase. Central charges c are extracted from the entanglement entropy using the Calabrese-Cardy formula, and are consistent with the theoretical predictions: c=N-1, expected from the $SU(N)_1$ Wess-Zumino-Witten CFTs in the spin sector for the Mott phase, and c=N in the metallic phase, reflecting the presence of one additional (charge) gapless critical mode.

Many systems, classical or quantum, closed or open, exhibit universal statistical properties. Exciton-polariton condensates, being intrinsically driven-dissipative, offer a promising platform for observing non-equilibrium universal features. By conducting extensive numerical simulations of an incoherently pumped and interacting condensate coupled to an exciton reservoir we show that the effective nonlinearity of the condensate phase dynamics can be finely adjusted across a broad range, by varying the exciton-polariton interaction strength, allowing one to probe three main universal regimes with parameters accessible in current experiments: the weakly nonlinear Edwards-Wilkinson (EW) regime, where the phase fluctuations dominate, but the phase profile does not become rough, the strongly non-linear Kardar-Parisi-Zhang regime, where the condensate phase fluctuations grow in a superdiffusive manner leading to roughening of the phase, and a vortex-dominated phase emerging at stronger interactions, where both density and phase dynamics play significant roles. Our results provide a unified picture of the phase diagram of 2d exciton-polariton condensates under incoherent pumping, and shed light on recent experimental and numerical observations.

We propose a universal framework for classifying quantum states based on their scale-resolved correlation structure. Using the recently introduced information lattice, which provides an operational definition of the total amount of correlations at each scale, we define intrinsic characteristic length scales of quantum states. We analyze ground and midspectrum eigenstates of the disordered interacting Kitaev chain, showing that our framework provides a novel unbiased approach to quantum matter.

We show how to perform exact diagonalizations of SU(N) Fermi-Hubbard models on L-site clusters separately in each irreducible representation (irrep) of SU(N). Using the representation theory of the unitary group U(L), we demonstrate that a convenient orthonormal basis, on which matrix elements of the Hamiltonian are very simple, is given by the set of semistandard Young tableaux (or, equivalently, the Gelfand-Tsetlin patterns) corresponding to the targeted irrep. As an application of this color factorization, we study the robustness of some SU(N) phases predicted in the Heisenberg limit upon decreasing the on-site interaction U on various lattices of size L≤12 and for 2≤N≤6. In particular, we show that a long-range color ordered phase emerges for intermediate U for N=4 at filling 1/4 on the triangular lattice.

In this Perspective, we discuss thermal imbalance and the associated electron-mediated thermal transport in quantum electronic devices at very low temperatures. We first present the theoretical approaches describing heat transport in nanoscale conductors at low temperatures, in which quantum confinement and interactions play an important role. We then discuss the experimental techniques for generating and measuring heat currents and temperature gradients on the nanoscale. Eventually, we review the most important quantum effects on heat transport and discuss implications for quantum technologies and future directions in the field.