All publications from Andrea Trombettoni
Logarithmic negativity of the 1D antiferromagnetic spin-1 Heisenberg model with single-ion anisotropy
Papoyan V.V., Gori G., Papoyan V.V., Trombettoni A., Ananikian N.
We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low-temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behavior of LN is discussed in the B−D plane, including a separating line – ending in a triple point – where the energy density is independent on the size. Finally, results for LN at finite temperature as a function of B and D are presented and commented.
Experimental signature of initial quantum coherence on entropy production
Hernández-Gómez S., Gherardini S., Belenchia A., Trombettoni A., Paternostro M., Fabbri N.
We report on the experimental quantification of the contribution to non-equilibrium entropy production stemming from the quantum coherence content in the initial state of a qubit exposed to both coherent driving and dissipation. Our experimental demonstration builds on the exquisite experimental control of the spin state of a nitrogen-vacancy defect in diamond and is underpinned, theoretically, by the formulation of a generalized fluctuation theorem designed to track the effects of quantum coherence. Our results provide significant evidence of the possibility to pinpoint the genuinely quantum mechanical contributions to the thermodynamics of non-equilibrium quantum processes in an open quantum systems scenario.
Nonequilibrium steady states of long-range coupled harmonic chains
Andreucci F., Lepri S., Ruffo S., Trombettoni A.
We perform a numerical study of transport properties of a one-dimensional chain with couplings decaying as an inverse power r-(1+σ) of the intersite distance r and open boundary conditions, interacting with two heat reservoirs. Despite its simplicity, the model displays highly nontrivial features in the strong long-range regime -1<σ<0. At weak coupling with the reservoirs, the energy flux departs from the predictions of perturbative theory and displays anomalous superdiffusive scaling of the heat current with the chain size. We trace this behavior back to the transmission spectrum of the chain, which displays a self-similar structure with a characteristic σ-dependent fractal dimension.
Can multipartite entanglement be characterized by two-point connected correlation functions?
Lepori L., Trombettoni A., Giuliano D., Kombe J., Yago Malo J., Daley A.J., Smerzi A., Luisa Chiofalo M.
We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.
Strange correlators for topological quantum systems from bulk-boundary correspondence
Lepori L., Burrello M., Trombettoni A., Paganelli S.
"Strange"correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper, we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and nontranslational invariant cases, and in the presence of on-site disorder and long-range couplings, extend the validity of the strange correlator approach for the diagnosis of topological phases of matter and indicate a general procedure for their optimal choice.
Long-range interacting quantum systems
Defenu N., Donner T., Macrì T., Pagano G., Ruffo S., Trombettoni A.
In this review recent investigations are summarized of many-body quantum systems with long-range interactions, which are currently realized in Rydberg atom arrays, dipolar systems, trapped-ion setups, and cold atoms in cavities. In these experimental platforms parameters can be easily changed, and control of the range of the interaction has been achieved. The main aim of the review is to present and identify the common and mostly universal features induced by long-range interactions in the behavior of quantum many-body systems. Discussed are the case of strong nonlocal couplings, i.e., the nonadditive regime, and the one in which energy is extensive, but low-energy, long-wavelength properties are altered with respect to the short-range case. When possible, comparisons with the corresponding results for classical systems are presented. Finally, cases of competition with local effects are also reviewed.
Quantum multicritical behavior for coupled optical cavities with driven laser fields
Hu Y., Zhou Y., Luo W., Trombettoni A., Huang G.
Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.
Quantum simulator of link models using spinor dipolar ultracold atoms
Fontana P., Barros J.C.P., Trombettoni A.
We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a nonperturbative one tied to angular-momentum conservation, and a perturbative one. A comparison with other schemes for (2+1)-dimensional quantum link models present in the literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.
Probing the Degree of Coherence through the Full 1D to 3D Crossover
Shah R., Barrett T.J., Colcelli A., Oručević F., Trombettoni A., Krüger P.
We experimentally study a gas of quantum degenerate Rb87 atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential μ controls the departure of the system from 3D and that the fluctuations are dependent on both μ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.
Villain model with long-range couplings
Giachetti G., Defenu N., Ruffo S., Trombettoni A.
The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.
Fractional dynamics and modulational instability in long-range Heisenberg chains
Laetitia M.Y., Nguenang J.P., Paglan P.A., Dauxois T., Trombettoni A., Ruffo S.
We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent α. We add to the Hamiltonian an anisotropy in the z-direction. In the framework of a semiclassical approach, we use the Holstein–Primakoff transformation to derive an effective long-range discrete nonlinear Schrödinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schrödinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for α<3. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent α.
Interacting two-mode model for ultracold quantum interferometers
Baroni C., Gori G., Chiofalo M.L., Trombettoni A.
Ultracold gases provide an excellent platform for the realization of quantum interferometers. In the case of implementations based on Bose-Einstein condensates in double well potentials, an effective two-mode model allows to study how the interactions among particles affect the sensitivity of the interferometer. In this work we review the properties of such a model and its application to interferometric protocols, focusing on the achievable sensitivity in the presence of interactions turned on. In particular we study the full interferometric sequence when the initial state is a Twin Fock state, which is perfectly number squeezed. We found that in the presence of interactions and for certain values of the holding time in which a phase difference between the two modes is accumulated, the same sensitivity as in the non interacting case is recovered when using the population imbalance between the two wells as observable. Finally, we characterize the behaviour of the sensitivity by looking at the δ-derivative and the variance of the operator used for the measurement and studying the squeezing parameters.
Holographic realization of the prime number quantum potential
Cassettari D., Mussardo G., Trombettoni A.
We report the experimental realization of the prime number quantum potential VN(x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes’s sieve used for the primes. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.
Rethinking Frequency Combs for Infrared Spectroscopy
Cappelli F., Gabrielli T., Consolino L., Sorgi A., Borri S., Roati G., Scazza F., Trombettoni A., Smerzi A., De Rosa M., Ricciardi I., De Natale P.
Frequency combs (FC) underwent a significant miniaturization since the Ti:Sa passively mode-locked laser was introduced. Nowadays, a full FC re-design, e.g. based on ultracold-atoms simulation, can provide access to genuine quantum radiation.
Designing and controlling quantum cascade lasers for quantum technologies: towards a new generation of infrared sub-classical sources
Cappelli F., Borri S., Consolino L., Gabrielli T., Sorgi A., Roati G., Scazza F., Trombettoni A., Giuntini M., Montori A., Siciliani de Cumis M., Bruno N., Smerzi A., Zavatta A., De Rosa M., Ricciardi I., De Natale P.
Laser sources, since their invention, have proved to be the right solution in practically all conceived applications. Recently, the so-called second quantum revolution and quantum technologies like sensing, computing, simulation or communication are triggering a new generation of sub-classical sources to tackle such novel and challenging applications. First concepts and experimental results aimed to endow quantum cascade lasers and other infrared sources with truly quantum properties will be shown.
High-precision anomalous dimension of three-dimensional percolation and spatial profile of the critical giant cluster
Galvani A., Trombettoni A., Gori G.
In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile φ, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Δφ. The latter can be fixed from outcomes of numerical simulations, from which we obtain Δφ=0.47846(71) and the corresponding value of the anomalous dimension η=-0.0431(14). The comparison with values of η determined by using scaling relations is discussed. A test of hyperscaling is also performed.
Cold atoms in space: community workshop summary and proposed road-map
Alonso I., Alpigiani C., Altschul B., Araújo H., Arduini G., Arlt J., Badurina L., Balaž A., Bandarupally S., Barish B.C., Barone M., Barsanti M., Bass S., Bassi A., Battelier B., Baynham C.F.A., Beaufils Q., Belić A., Bergé J., Bernabeu J., Bertoldi A., Bingham R., Bize S., Blas D., Bongs K., Bouyer P., Braitenberg C., Brand C., Braxmaier C., Bresson A., Buchmueller O., Budker D., Bugalho L., Burdin S., Cacciapuoti L., Callegari S., Calmet X., Calonico D., Canuel B., Caramete L.I., Carraz O., Cassettari D., Chakraborty P., Chattopadhyay S., Chauhan U., Chen X., Chen Y.A., Chiofalo M.L., Coleman J., Corgier R., Cotter J.P., Michael Cruise A., Cui Y., Davies G., De Roeck A., Demarteau M., Derevianko A., Di Clemente M., Djordjevic G.S., Donadi S., Doré O., Dornan P., Doser M., Drougakis G., Dunningham J., Easo S., Eby J., Elertas G., Ellis J., Evans D., Examilioti P., Fadeev P., Fanì M., Fassi F., Fattori M., Fedderke M.A., Felea D., Feng C.H., Ferreras J., Flack R., Flambaum V.V., Forsberg R., Fromhold M., Gaaloul N., Garraway B.M., Georgousi M., Geraci A., Gibble K., Gibson V., Gill P., Giudice G.F., Goldwin J., Gould O., Grachov O., Graham P.W., Grasso D., Griffin P.F., Guerlin C., Gündoğan M., Gupta R.K.
We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies.
Possible limits on superconducting quantum computers from spontaneous wave-function collapse models
Vischi M., Ferialdi L., Trombettoni A., Bassi A.
The continuous spontaneous localization (CSL) model is an alternative formulation of quantum mechanics, which introduces a noise-coupled nonlinearly to the wave function to account for its collapse. We consider CSL effects on quantum computers made of superconducting transmon qubits. As a direct effect CSL reduces quantum superpositions of the computational basis states of the qubits: we show the reduction rate to be negligibly small. However, an indirect effect of CSL, dissipation induced by the noise, also leads transmon qubits to decohere, by generating additional quasiparticles. Since the decoherence rate of transmon qubits depends on the quasiparticle density, by computing their generation rate induced by CSL, we can estimate the corresponding quasiparticle density and thus the limit set by CSL on the performances of transmon quantum computers. We show that CSL could spoil the quantum computation of practical algorithms on large devices. We further explore the possibility of testing CSL effects on superconducting devices.
Free fall of a quantum many-body system
Colcelli A., Mussardo G., Sierra G., Trombettoni A.
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses, because its discussion usually requires wavepackets built on the Airy functions-a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds to a change of reference frame from the laboratory frame to the one comoving with the falling system. Using this approach, the quantum mechanics problem of a particle in an external gravitational potential reduces to a much simpler one where there is no longer any gravitational potential in the Schrödinger equation. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential and a two-body interparticle potential that is a function of the distance between the particles. This topic provides a helpful and pedagogical example of a quantum many-body system whose dynamics can be analytically described in simple terms.
Mutual information for fermionic systems
Lepori L., Paganelli S., Franchini F., Trombettoni A.
We study the behavior of the mutual information (MI) in various quadratic fermionic chains, with and without pairing terms and both with short- and long-range hoppings. The models considered include the short-range limit and long-range versions of the Kitaev model as well, and also cases in which the area law for the entanglement entropy is - logarithmically or nonlogarithmically - violated. In all cases surveyed, when the area law is violated at most logarithmically, the MI is a monotonically increasing function of the conformal four-point ratio x. Where nonlogarithmic violations of the area law are present, nonmonotonic features can be observed in the MI, and the four-point ratio, as well as other natural combinations of the parameters, is found not to be sufficient to capture the whole structure of the MI with a collapse onto a single curve. We interpret this behavior as a sign that the structure of peaks is related to a nonuniversal spatial configuration of Bell pairs. For the model exhibiting a perfect volume law, the MI vanishes identically. For the Kitaev model the MI is vanishing for x→0 and it remains zero up to a finite x in the gapped case. In general, a larger range of the pairing corresponds to a reduction of the MI at small x. A discussion of the comparison with the results obtained by the anti-de Sitter/conformal field theory correspondence in the strong-coupling limit is presented.

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