arXiv subjects

Emanuele Levi

Publications and source records attributed to Emanuele Levi.

At least 19 recordsLinked to original sources

arXiv2019

Coherence, entanglement and quantumness in closed and open systems with conserved charge, with an application to many-body localisation

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.

cond-mat.stat-mech↗

arXiv2017

Non-adiabatic quantum state preparation and quantum state transport in chains of Rydberg atoms

Motivated by recent progress in the experimental manipulation of cold atoms in optical lattices, we study three different protocols for non-adiabatic quantum state preparation and state transport in chains of Rydberg atoms. The protocols we discuss are based on the blockade mechanism between atoms which, when excited to a Rydberg state, interact through a van der Waals potential, and rely on single-site addressing. Specifically, we discuss protocols for efficient creation of an antiferromagnetic GHZ state, a class of matrix product states including a so-called Rydberg crystal and for the state transport of a single-qubit quantum state between two ends of a chain of atoms. We identify system parameters allowing for the operation of the protocols on timescales shorter than the lifetime of the Rydberg states while yielding high fidelity output states. We discuss the effect of positional disorder on the resulting states and comment on limitations due to other sources of noise such as radiative decay of the Rydberg states. The proposed protocols provide a testbed for benchmarking the performance of quantum information processing platforms based on Rydberg atoms.

quant-ph↗

arXiv2017

Terahertz-driven phase transition applied as a room-temperature terahertz detector

There are few demonstrated examples of phase transitions that may be driven directly by terahertz-frequency electric fields, and those that are known require field strengths exceeding 1 MVcm$^{-1}$. Here we report a room-temperature phase transition driven by a weak ($\ll 1$ Vcm$^{-1}$), continuous-wave terahertz electric field. The system consists of caesium vapour under continuous optical excitation to a high-lying Rydberg state, which is resonantly coupled to a nearby level by the terahertz electric field. We use a simple model to understand the underlying physical behaviour, and we demonstrate two protocols to exploit the phase transition as a narrowband terahertz detector: the first with a fast (20 $μ$s) nonlinear response to nano-Watts of incident radiation, and the second with a linearised response and effective noise equivalent power (NEP) $\leq 1$ pWHz$^{-1/2}$. The work opens the door to a new class of terahertz devices controlled with low field intensities and operating around room temperature.

physics.atom-ph↗

arXiv2016

Quantum non-equilibrium dynamics of Rydberg gases in the presence of dephasing noise of different strengths

In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically-constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum Master equation. We interpolate between the coherent and the strongly dephased regime by defining a generalised concept of a blockade length. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include the existence of a time-dependent Rydberg blockade radius, and a growth of the density of excitations which is compatible with the power-law behaviour expected in the classical limit.

quant-ph↗

arXiv2016

Localization phenomena in interacting Rydberg lattice gases with position disorder

Disordered systems provide paradigmatic instances of ergodicity breaking and localization phenomena. Here we explore the dynamics of excitations in a system of Rydberg atoms held in optical tweezers. The finite temperature produces an intrinsic uncertainty in the atomic positions, which translates into quenched correlated disorder in the interatomic interaction strengths. In a simple approach, the dynamics in the many-body Hilbert space can be understood in terms of a one-dimensional Anderson-like model with disorder on every other site, featuring both localized and delocalized states. We conduct an experiment on an eight-atom chain and observe a clear suppression of excitation transfer. Our experiment accesses a regime which is described by a two-dimensional Anderson model on a "trimmed" square lattice. Our results thus provide a concrete example in which the absence of excitation propagation in a many-body system is directly related to Anderson-like localization in the Hilbert space, which is believed to be the mechanism underlying many-body localization.

cond-mat.quant-gas↗

arXiv2016

Non-equilibrium universality in the dynamics of dissipative cold atomic gases

The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The well-established concept at or near equilibrium, universality, can also characterize the physics of systems out of equilibrium. The most fundamental instance of a genuine non-equilibrium phase transition is the directed percolation universality class, where a system switches from an absorbing inactive to a fluctuating active phase. Despite being known for several decades it has been challenging to find experimental systems that manifest this transition. Here we show theoretically that signatures of the directed percolation universality class can be observed in an atomic system with long range interactions. Moreover, we demonstrate that even mesoscopic ensembles --- which are currently studied experimentally --- are sufficient to observe traces of this non-equilibrium phase transition in one, two and three dimensions.

cond-mat.stat-mech↗

arXiv2016

Robustness of many-body localization in the presence of dissipation

Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system---an interacting fermionic chain subject to quenched disorder---in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions make signatures of non-ergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.

cond-mat.str-el↗

arXiv2016

Role of interactions in a dissipative many-body localized system

Recent experimental and theoretical efforts have focused on the effect of dissipation on quantum many-body systems in their many-body localized (MBL) phase. While in the presence of dephasing noise such systems reach a unique ergodic state, their dynamics is characterized by slow relaxation manifested in non-exponential decay of self-correlations. Here we shed light on a currently much debated issue, namely the role of interactions for this relaxation dynamics. We focus on the experimentally relevant situation of the evolution from an initial charge density wave in the presence of strong dephasing noise. We find a crossover from a regime dominated by disorder to a regime dominated by interactions, with a concomitant change of time correlators from stretched exponential to compressed exponential form. The strongly interacting regime can be explained in terms of nucleation and growth dynamics of relaxing regions - reminiscent of the kinetics of crystallization in soft matter systems - and should be observable experimentally. This interaction-driven crossover suggests that the competition between interactions and noise give rise to a much richer structure of the MBL phase than anticipated so far.

cond-mat.str-el↗

arXiv2015

Emergent devil's staircase without particle-hole symmetry in Rydberg quantum gases with competing attractive and repulsive interactions

The devil's staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically such staircase has an explicit particle-hole symmetry, i.e., the staircase at more than half-filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e. a non-convex potential. In the classical limit the ground state features generalized Wigner crystals that --- depending on the filling fraction --- are either composed of dimer particles or dimer holes which results in an emergent complete devil's staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region, where the density-density correlations suggest the emergence of quasi long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.

cond-mat.quant-gas↗

arXiv2015

Crystalline structures and frustration in a two-component Rydberg gas

We study the static behavior of a gas of atoms held in a one-dimensional lattice where two distinct electronically high-lying Rydberg states are simultaneously excited by laser light. We focus on a situation where interactions of van-der-Waals type take place only among atoms that are in the same Rydberg state. We analytically investigate at first the so-called classical limit of vanishing laser driving strength. We show that the system exhibits a surprisingly complex ground state structure with a sequence of compatible to incompatible transitions. The incompatibility between the species leads to mutual frustration, a feature which pertains also in the quantum regime. We perform an analytical and numerical investigation of these features and present an approximative description of the system in terms of a Rokhsar-Kivelson Hamiltonian which permits the analytical understanding of the frustration effects even beyond the classical limit.

physics.atom-ph↗

arXiv2015

Crystalline structures in a one-dimensional two-component lattice gas with $1/r^α$ interactions

We investigate the ground state of a one-dimensional lattice system that hosts two different kinds of excitations (species) which interact with a power-law potential. Interactions are only present between excitations of the same kind and the interaction strength can be species-dependent. For the case in which only one excitation is permitted per site we derive a prescription for determining the ground state configuration as a function of the filling fractions of the two species. We show that depending on the filling fractions compatible or incompatible phases emerge. Furthermore, we discuss in detail the case in which one species is strongly and the other one weakly interacting. In this case the configuration of the strongly interacting (strong) species can be considered frozen and forms an effective inhomogeneous lattice for the other (weak) species. In this limit we work out in detail the microscopic ground state configuration and show that by varying the density of the weak species a series of compatible--incompatible transitions occurs. Finally we determine the stability regions of the weak species in the compatible phase and compare it with numerical simulations.

cond-mat.stat-mech↗

arXiv2015

Dynamics of many-body localisation in a translation invariant quantum glass model

We study the real-time dynamics of a translationally invariant quantum spin chain, based on the East kinetically constrained glass model, in search for evidence of many-body localisation in the absence of disorder. Numerical simulations indicate a change, controlled by a coupling parameter, from a regime of fast relaxation---corresponding to thermalisation---to a regime of very slow relaxation. This slowly relaxing regime is characterised by dynamical features usually associated with non-ergodicity and many-body localisation (MBL): memory of initial conditions, logarithmic growth of entanglement entropy, and non-exponential decay of time-correlators. We show that slow relaxation is a consequence of sensitivity to spatial fluctuations in the initial state. While numerics indicate that certain relaxation timescales grow markedly with size, our finite size results are consistent both with an MBL transition, expected to only occur in disordered systems, or with a pronounced quasi-MBL crossover.

cond-mat.stat-mech↗

arXiv2014

Entanglement Entropy of Non Unitary Conformal Field Theory

In this letter we show that the Rényi entanglement entropy of a region of large size $\ell$ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as $S_n \sim \frac{c_{\mathrm{eff}}(n+1)}{6n} \log \ell$, where $c_{\mathrm{eff}}=c-24Δ>0$ is the effective central charge, $c$ (which may be negative) is the central charge of the conformal field theory and $Δ\neq 0$ is the lowest holomorphic conformal dimension in the theory. We also obtain results for models with boundaries, and with a large but finite correlation length, and we show that if the lowest conformal eigenspace is logarithmic ($L_0 = ΔI + N$ with $N$ nilpotent), then there is an additional term proportional to $\log(\log \ell)$. These results generalize the well known expressions for unitary models. We provide a general proof, and report on numerical evidence for a non-unitary spin chain and an analytical computation using the corner transfer matrix method for a non-unitary lattice model. We use a new algebraic technique for studying the branching that arises within the replica approach, and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non-unitary models.

hep-th↗

arXiv2014

Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain

We study the connection between the cumulants of a time-integrated observable of a quantum system and the PT-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken PT-symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetisation in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where PT-symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of PT -symmetry implies that all cumulants are sub-linear in time, a behaviour usually associated to the absence of decorrelation.

cond-mat.stat-mech↗

arXiv2014

Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states

We introduce a class of spin models with long-range interactions---in the sense that they extend significantly beyond nearest neighbors---whose ground states can be constructed analytically and have a simple matrix product state representation. This enables the detailed study of ground state properties, such as correlation functions and entanglement, in the thermodynamic limit. The spin models presented here are closely related to lattice gases of strongly interacting polar molecules or Rydberg atoms which feature an excluded volume or blockade interaction. While entanglement is only present between spins that are separated by no more than a blockade length, we show that non-classical correlations can extend much further and analyze them through quantum discord. We furthermore identify a set of seemingly critical points where the ground state approaches a crystalline state with a filling fraction that is given by the inverse of the blockade length. We analyze the scaling properties in the vicinity of this parameter region and show that the correlation length possesses a non-trivial dependence on the blockade length.

cond-mat.str-el↗

arXiv2013

Universal corrections to the entanglement entropy in gapped quantum spin chains: a numerical study

We carry out a numerical study of the bi-partite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the anti-ferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behaviour of the entropy. We numerically confirm that, in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to the Bessel function K0(2mr) where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted in publications involving two of the current authors for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behaviour following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

hep-th↗

arXiv2012

Composite branch-point twist fields in the Ising model and their expectation values

We investigate a particular two-point function of the $n$-copy Ising model. That is, the correlation function $\vev{\E(r)\T(0)}$ involving the energy field and the branch-point twist field. The latter is associated to the symmetry of the theory under cyclic permutations of its copies. We use a form factor expansion to obtain an exact integral representation of $\vev{\E(r)\T(0)}$ and find its complete short distance expansion. This allows us to identify all the fields contributing in the short distance massive OPE of the correlation function under examination, and fix their expectation values, conformal structure constants and massive corrections thereof. Most contributions are given by the composite field $:\E\T:$ and its derivatives. We find all non-vanishing form factors of this latter operator.

hep-th↗

arXiv2011

Arguments towards a c-theorem from branch-point twist fields

A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale. The c-theorem establishes that c(r) is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points. At those points c(r) becomes the central charge of the conformal field theory which describes the critical point. In this letter we argue that a different function proposed by Calabrese and Cardy, defined in terms of the two-point function of a branch point twist field and the trace of the stress-energy tensor, has exactly the same qualitative features as c(r).

hep-th↗