arXiv subjects

Jérôme Dubail

Publications and source records attributed to Jérôme Dubail.

At least 19 recordsLinked to original sources

arXiv2026

Free fermion models with an operator entanglement growing as $O(\sqrt{t})$

We study the time evolution of the Operator Space Entanglement Entropy (OSEE) of one-dimensional number-conserving free fermions subject to a random space- and time-dependent evolution. It is known that, in free-fermion systems without randomness, the OSEE of \emph{local} operators grows at most \emph{logarithmically} in time. Here we show that, in the presence of randomness, the OSEE of local spin operators involving a Jordan-Wigner string grows as $\mathcal O(\sqrt t)$, for all values of the Rényi index. We establish this in two models: a Brownian Hamiltonian and a brick-wall matchgate circuit. We also consider the OSEE of the evolution operator, and we show that it also grows as $\mathcal O(\sqrt{t})$, in contrast with the linear growth generically expected without randomness. We analytically compute the average entropies of the two operators by mapping the quantum models to the symmetric simple exclusion process, relying on an assumption of self-averaging which we support numerically. We also consider two other types of randomness: random evolution in time that keeps spatial translation invariance, and quenched disorder. In the former case, we find that the OSEE also grows as $\sqrt{t}$. In the latter case, we find that the entropy grows as $\mathcal O( \log \log t)$ for Hamiltonian evolution both for local operators with a Jordan-Wigner string and for the evolution operator, whereas it remains bounded at all times in the brick-wall matchgate circuit.

quant-ph↗

arXiv2026

Enhanced localization length in a disordered one-dimensional band via cavity coupling to delocalized states

We investigate the localization properties of cavity-coupled electronic states in disordered systems, motivated by recent proposals of cavity-mediated hopping in quantum Hall systems. We first introduce a minimal two-band model in which localized states in a disordered one-dimensional band are coupled, through a homogeneous cavity mode, to an excited band of delocalized states. Combining perturbation theory with a transfer-matrix approach, we show that cavity-assisted hopping between localized states decays exponentially with distance, implying that the eigenstates remain localized even beyond the perturbative regime. Nevertheless, the corresponding localization length increases with the light-matter coupling strength and can extend over several lattice sites in the single-electron ultrastrong-coupling regime. We then study a disordered Landau band coupled to a cavity mode within the framework developed in Refs.[1,2]. We find that the effective cavity-mediated coupling between edge states also decays exponentially with distance, but with a localization length that can reach micrometer scales for experimentally realistic parameters. By analyzing the inverse participation ratio, we show that this enhanced coupling is predominantly mediated by the most extended states of the upper Landau band. Our results demonstrate that, while cavity-induced hopping in disordered quantum Hall systems remains exponentially localized, the associated localization length can become sufficiently large for the corresponding states to exhibit effectively delocalized behavior on mesoscopic length scales.

cond-mat.mes-hall↗

arXiv2025

Experimental Investigation of a Bipartite Quench in a 1D Bose gas

Long wavelength dynamics of 1D Bose gases with repulsive contact interactions can be captured by Generalized HydroDynamics (GHD) which predicts the evolution of the local rapidity distribution. The latter corresponds to the momentum distribution of quasiparticles, which have infinite lifetime owing to the integrability of the system. Here we experimentally investigate the dynamics for an initial situation that is the junction of two semi-infinite systems in different stationary states, a protocol referred to as `bipartite quench' protocol. More precisely we realise the particular case where one half of the system is the vacuum state. We show that the evolution of the boundary density profile exhibits ballistic dynamics obeying the Euler hydrodynamic scaling. The boundary profiles are similar to the ones predicted with zero-temperature GHD in the quasi-BEC regime, with deviations due to non-zero entropy effects. We show that this protocol, provided the boundary profile is measured with infinite precision, permits to reconstruct the rapidity distribution of the initial state. For our data, we extract the initial rapidity distribution by fitting the boundary profile and we use a 3-parameter ansatz that goes beyond the thermal assumption. Finally, we investigate the local rapidity distribution inside the boundary profile, which, according to GHD, presents, on one side, features of zero-entropy states. The measured distribution shows the asymmetry predicted by GHD, although unelucidated deviations remain.

cond-mat.quant-gas↗

arXiv2025

Accuracy of time-dependent GGE under weak dissipation

Unitary integrable models typically relax to a stationary Generalized Gibbs Ensemble (GGE), but in experimental realizations dissipation often breaks integrability. In this work, we use the recently introduced time-dependent GGE (t-GGE) approach to describe the open dynamics of a gas of bosons subject to atom losses and gains. We employ tensor network methods to provide numerical evidence of the exactness of the t-GGE in the limit of adiabatic dissipation, and of its accuracy in the regime of weak but finite dissipation. That accuracy is tested for two-point functions via the rapidity distribution, and for more complicated correlations through a non-Gaussianity measure. We combine this description with Generalized Hydrodynamics and we show that it correctly captures transport at the Euler scale. Our results demonstrate that the t-GGE approach is robust in both homogeneous and inhomogeneous settings.

cond-mat.quant-gas↗

arXiv2024

Effects of atom losses on a one-dimensional lattice gas of hardcore bosons

Atom losses occur naturally during cold atoms experiments. Since this phenomenon is unavoidable, it is important to understand its effect on the remaining atoms. Here we study a gas of hard-core bosons on a lattice subject to $K$-body losses (where $K=1,2,3,\dots$ is the number of atoms lost in each loss event), and in particular we investigate the effect of losses on the rapidity distribution $ρ(k)$ of the atoms. Under the assumption that losses are weak enough so that the system relaxes between two loss events, we are able to determine the loss functional $F[ρ](k)$ encoding the loss process for $K$-body losses. We derive closed expressions for the cases of one- and two-body losses, and show their effects on the evolution of the total number of particles. Then we add a harmonic trapping potential and study the evolution of the position-dependent rapidity distribution of this system by solving numerically the evolution equation for one-, two- and three-body losses.

cond-mat.quant-gas↗

arXiv2024

Multifractality in the interacting disordered Tavis-Cummings model

We analyze the spectral and transport properties of the interacting disordered Tavis-Cummings model at half excitation filling. We demonstrate that a Poissonian level statistics coexists with eigenfunctions that are multifractal (extended, but non-ergodic) in the Hilbert space, for all strengths of light-matter interactions. This is associated with a lack of thermalization for a local perturbation. We find that the bipartite entanglement entropy grows logarithmically with time, similarly to many-body localized systems, while the spin imbalance tends to zero for strong coupling, in analogy to ergodic phases. We show that these effects are due to the combination of finite interactions and integrability of the model. When a small integrability-breaking perturbation (nearest-neighbor hopping) is introduced, typical eigenfunctions become ergodic, seemingly turning the system into a near-perfect conductor, contrary to the single-excitation noninteracting case. We propose a realization of this model with cold atoms.

quant-ph↗

arXiv2023

More on symmetry resolved operator entanglement

The `operator entanglement' of a quantum operator $O$ is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global $U(1)$ conservation law, and on operators $O$ with a well-defined $U(1)$ charge, for which it is possible to resolve the operator entanglement of $O$ according to the $U(1)$ symmetry. We employ the notion of symmetry resolved operator entanglement (SROE) introduced in [PRX Quantum 4, 010318 (2023)] and extend the results of the latter paper in several directions. Using a combination of conformal field theory and of exact analytical and numerical calculations in critical free fermionic chains, we study the SROE of the thermal density matrix $ρ_β= e^{- βH}$ and of charged local operators evolving in Heisenberg picture $O = e^{i t H} O e^{-i t H}$. Our main results are: i) the SROE of $ρ_β$ obeys the operator area law; ii) for free fermions, local operators in Heisenberg picture can have a SROE that grows logarithmically in time or saturates to a constant value; iii) there is equipartition of the entanglement among all the charge sectors except for a pair of fermionic creation and annihilation operators.

cond-mat.stat-mech↗

arXiv2023

Anomalous diffusion in the Long-Range Haken-Strobl-Reineker model

We analyze the propagation of excitons in a $d$-dimensional lattice with power-law hopping $\propto 1/r^α$ in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent $α_{\rm cr} = (d+2)/2$. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for $α\leqα_{\rm cr}$, while for $α> α_{\rm cr}$ the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Lévy-flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any $α$, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.

quant-ph↗

arXiv2023

Relaxation of phonons in the Lieb-Liniger gas by dynamical refermionization

We investigate the Lieb-Liniger gas initially prepared in an out-of-equilibrium state that is Gaussian in terms of the phonons. Because the phonons are not exact eigenstates of the Hamiltonian, the gas relaxes to a stationary state at very long times. Thanks to integrability, that stationary state needs not be a thermal state. We characterize the stationary state of the gas after relaxation and compute its phonon population distribution. Technically, this follows from the mapping between the exact eigenstates of the Lieb-Liniger Hamiltonian and those of a non-interacting Fermi gas -- a mapping provided by the Bethe equations -- , as well as on bosonization formulas valid in the low-energy sector of the Hilbert space. We apply our results to the case where the initial state is an excited coherent state for a single phonon mode, and we compare them to exact results obtained in the hard-core limit.

cond-mat.quant-gas↗

arXiv2023

Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model

We investigate the non-equilibrium dynamics of a one-dimensional spin-1/2 XXZ model at zero-temperature in the regime $|Δ|< 1$, initially prepared in a product state with two domain walls i.e, $|\downarrow\dots\downarrow\uparrow\dots\uparrow\downarrow\dots\downarrow\rangle$. At early times, the two domain walls evolve independently and only after a calculable time a non-trivial interplay between the two emerges and results in the occurrence of a split Fermi sea. For $Δ=0$, we derive exact asymptotic results for the magnetization and the spin current by using a semi-classical Wigner function approach, and we exactly determine the spreading of entanglement entropy exploiting the recently developed tools of quantum fluctuating hydrodynamics. In the interacting case, we analytically solve the Generalized Hydrodynamics equation providing exact expressions for the conserved quantities. We display some numerical results for the entanglement entropy also in the interacting case and we propose a conjecture for its asymptotic value.

cond-mat.stat-mech↗

arXiv2022

Gradient corrections to the local density approximation in the one-dimensional Bose gas

The local density approximation (LDA) is the central technical tool in the modeling of quantum gases in trapping potentials. It consists in treating the gas as an assembly of independent mesoscopic fluid cells at equilibrium with a local chemical potential, and it is justified when the correlation length is larger than the size of the cells. The LDA is often regarded as a crude approximation, particularly in the ground state of the one-dimensional (1D) Bose gas, { where the correlation length is "therefore said to be" infinite (in the sense that correlation functions decay as a power law).} Here we take another look at the LDA. The local density $ρ(x)$ is viewed as a functional of the trapping potential $V(x)$, to which one applies a gradient expansion. The zeroth order in that expansion is the LDA. The first-order correction in the gradient expansion vanishes due to reflection symmetry. At second order, there are two corrections proportional to $d^2V/dx^2$ and $(dV/dx)^2$, and we propose a method to determine the corresponding coefficients by a perturbative calculation in the Lieb-Liniger model. This leads to an expression for the coefficients in terms of matrix elements of the density operator, which can in principle be evaluated numerically for an arbitrary coupling constant; here we show how to efficiently evaluate the coefficient associated to the curvature of the potential $d^2V/dx^2$, which dominates the deviation to LDA near local minima or maxima of the trapping potential. Both coefficients are evaluated analytically in the limits of infinite repulsion (hard-core bosons) and small repulsion (quasi-condensate).} The corrected LDA density profiles are compared to DMRG calculations, with significant improvement compared to zeroth-order LDA.

cond-mat.quant-gas↗

arXiv2022

Entanglement barrier and its symmetry resolution: theory and experiment

The operator entanglement (OE) is a key quantifier of the complexity of a reduced density matrix. In out-of-equilibrium situations, e.g. after a quantum quench of a product state, it is expected to exhibit an entanglement barrier. The OE of a reduced density matrix initially grows linearly as entanglement builds up between the local degrees of freedom, it then reaches a maximum, and ultimately decays to a small finite value as the reduced density matrix converges to a simple stationary state through standard thermalization mechanisms. Here, by performing a new data analysis of the published experimental results of [Brydges et al., Science 364, 260 (2019)], we obtain the first experimental measurement of the OE of a subsystem reduced density matrix in a quantum many-body system. We employ the randomized measurements toolbox and we introduce and develop a new efficient method to post-process experimental data in order to extract higher-order density matrix functionals and access the OE. The OE thus obtained displays the expected barrier as long as the experimental system is large enough. For smaller systems, we observe a barrier with a double-peak structure, whose origin can be interpreted in terms of pairs of quasi-particles being reflected at the boundary of the qubit chain. As $U(1)$ symmetry plays a key role in our analysis, we introduce the notion of symmetry resolved operator entanglement (SROE), in addition to the total OE. To gain further insights into the SROE, we provide a thorough theoretical analysis of this new quantity in chains of non-interacting fermions, which, in spite of their simplicity, capture most of the main features of OE and SROE. In particular, we uncover three main physical effects: the presence of a barrier in any charge sector, a time delay for the onset of the growth of SROE, and an effective equipartition between charge sectors.

quant-ph↗

arXiv2021

Generalized Hydrodynamics in the 1D Bose gas: theory and experiments

We review the recent theoretical and experimental progress regarding the Generalized Hydrodynamics (GHD) behavior of the one-dimensional Bose gas with contact repulsive interactions, also known as the Lieb-Liniger gas. In the first section, we review the theory of the Lieb-Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb-Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb-Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results on GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atoms experiments: the experimental realization of the Lieb-Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions.

cond-mat.quant-gas↗

arXiv2021

Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy

We apply the theory of Quantum Generalized Hydrodynamics (QGHD) introduced in [Phys. Rev. Lett. 124, 140603 (2020)] to derive asymptotically exact results for the density fluctuations and the entanglement entropy of a one-dimensional trapped Bose gas in the Tonks-Girardeau (TG) or hard-core limit, after a trap quench from a double well to a single well. On the analytical side, the quadratic nature of the theory of QGHD is complemented with the emerging conformal invariance at the TG point to fix the universal part of those quantities. Moreover, the well-known mapping of hard-core bosons to free fermions, allows to use a generalized form of the Fisher-Hartwig conjecture to fix the non-trivial spacetime dependence of the ultraviolet cutoff in the entanglement entropy. The free nature of the TG gas also allows for more accurate results on the numerical side, where a higher number of particles as compared to the interacting case can be simulated. The agreement between analytical and numerical predictions is extremely good. For the density fluctuations, however, one has to average out large Friedel oscillations present in the numerics to recover such agreement.

cond-mat.quant-gas↗

arXiv2021

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider $SU(2)_k$ as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size $L$ the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on $L$ but only on the dimension of the representation. Moreover, a $\log\log L$ contribution to the Rényi entropies exhibits a universal form related to the underlying symmetry group of the model, i.e. the dimension of the Lie group.

hep-th↗

arXiv2021

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

We consider the non-equilibrium dynamics of the entanglement entropy of a one-dimensional quantum gas of hard-core particles, initially confined in a box potential at zero temperature. At $t=0$ the right edge of the box is suddenly released and the system is let free to expand. During this expansion, the initially correlated region propagates with a non-homogeneous profile, leading to the growth of entanglement entropy. This setting is investigated in the hydrodynamic regime, with tools stemming from semi-classical Wigner function approach and with recent developments of quantum fluctuating hydrodynamics. Within this framework, the entanglement entropy can be associated to a correlation function of chiral twist-fields of the conformal field theory that lives along the Fermi contour and it can be exactly determined. Our predictions for the entanglement evolution are found in agreement with and generalize previous results in literature based on numerical calculations and heuristic arguments.

cond-mat.stat-mech↗

arXiv2021

Large Random Arrowhead Matrices: Multifractality, Semi-Localization, and Protected Transport in Disordered Quantum Spins Coupled to a Cavity

We provide an exact solution of large random arrowhead Hamiltonians with diagonal disorder, a minimal model for inhomogeneously broadened quantum emitters coupled to a cavity mode. We find that the distribution of energy spacing can be continuously tuned between Poisson statistics and a distribution that is very close to semi-Poisson statistics - the latter being usually associated to the critical point of "Anderson" localization-delocalization transitions. We demonstrate that all the eigenstates - including two polaritons and a continuum of dark states - are multifractal, which indicates the existence of a critical "semi-localized" phase for all values of the light-matter coupling strength, where dark states are localized over multiple, arbitrarily-distant sites. By computing the escape probability from an initial site, we find that the system has a peculiar diffusive-like behavior with an escape probability growing linearly with time for any finite coupling strength, and that the escape rate can be controlled by selecting the energy of the initial site. The escape rate averaged over the disorder configurations is found to exhibit a maximum for intermediate coupling strengths, before saturating at a lower value in the collective strong coupling limit - a "cavity protection" effect. Surprisingly, we show that the saturation value increases with the disorder, indicating that the cavity does not only protect transport against disorder but can also turn the latter into an ally improving transport. We finally investigate the system in a two-terminal configuration, and show that the steady-state excitation current exhibits similar features as the escape probability, thereby extending our cavity-protected transport scenario to out-of-equilibrium situations. We finally demonstrate that dark states can provide the major contribution to long-distance transport in disordered systems.

quant-ph↗

arXiv2021

Breakdown of Tan's relation in lossy one-dimensional Bose gases

In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as $\sim 1/|p|^4$ at large momentum $p$. Tan's relation connects the amplitude of that $1/|p|^4$ tail to the adiabatic derivative of the energy with respect to the gas' coupling constant or scattering length. Here it is shown that the relation breaks down in the one-dimensional Bose gas with contact repulsion, for a peculiar class of stationary states. These states exist thanks to the infinite number of conserved quantities in the system, and they are characterized by a rapidity distribution which itself decreases as $1/|p|^4$. In the momentum distribution, that rapidity tail adds to the usual Tan contact term. Remarkably, atom losses, which are ubiquitous in experiments, do produce such peculiar states. The development of the tail of the rapidity distribution originates from the ghost singularity of the wavefunction immediately after each loss event. This phenomenon is discussed for arbitrary interaction strengths, and it is supported by exact calculations in the two asymptotic regimes of infinite and weak repulsion.

cond-mat.quant-gas↗