Publications

We present a microscopic theory for quantum thermoelectric and heat transport in the Schwarzian regime of the Sachdev-Ye-Kitaev (SYK) model. As a charged fermion realization of the SYK model in nanostructures, we assume a setup based on a quantum dot connected to the charge reservoirs through weak tunnel barriers. We analyze particle-hole symmetry breaking effects crucial for both Seebeck and Peltier coefficients. We show that the quantum charge and heat transport at low temperatures are defined by the interplay between elastic and inelastic processes such that the inelastic processes provide a leading contribution to the transport coefficients at the temperatures that are smaller compared to the charging energy. We demonstrate that both electric and thermal conductance obey a power law in temperature behavior, while thermoelectric, Seebeck, and Peltier coefficients are exponentially suppressed. This represents selective suppression of only nondiagonal transport coefficients. We discuss the validity of the Kelvin formula in the presence of a strong Coulomb blockade.

We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. This model is intended to mimic the passage of an excitation through (many-body) insulating regions or ergodic bubbles, therefore providing a toy model for the diffusion-subdiffusion transition observed in the disordered Heisenberg model by Žnidarič et al. [Phys. Rev. Lett. 117, 040601 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.040601]. We also present the exact solution of a semiclassical model of conductors and insulators introduced by Agarwal et al. [Phys. Rev. Lett. 114, 160401 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.160401], which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The critical properties of both models, when passing from diffusion to subdiffusion, are interpreted in terms of "Griffiths effects."We show that the finite-size scaling comes from the interplay of three characteristic lengths: One associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. We conjecture that the latter, which grows logarithmically with system size, may potentially be responsible for the fact that heavy-tailed resistance distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.

We consider the problem of symmetry decomposition of the entanglement negativity in free fermionic systems. Rather than performing the standard partial transpose, we use the partial time-reversal transformation which naturally encodes the fermionic statistics. The negativity admits a resolution in terms of the charge imbalance between the two subsystems. We introduce a normalised version of the imbalance resolved negativity which has the advantage to be an entanglement proxy for each symmetry sector, but may diverge in the limit of pure states for some sectors. Our main focus is then the resolution of the negativity for a free Dirac field at finite temperature and size. We consider both bipartite and tripartite geometries and exploit conformal field theory to derive universal results for the charge imbalance resolved negativity. To this end, we use a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in the Riemann surface defining the entanglement. We interestingly find that the entanglement negativity is always equally distributed among the different imbalance sectors at leading order. Our analytical findings are tested against exact numerical calculations for free fermions on a lattice.

We generalise the form factor bootstrap approach to integrable field theories with U(1) symmetry to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are solved for the free massive Dirac and complex boson theories, which are the simplest theories with U(1) symmetry. We present the exact and complete solution for the bootstrap, including vacuum expectation values and form factors involving any type and arbitrarily number of particles. The non-trivial solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. An alternative and compact determination of the novel form factors is also presented. Based on the form factors of the U(1) composite branch-point twist fields, we re-derive earlier results showing entanglement equipartition for an interval in the ground state of the two models.

We develop a semiclassical theory of laser oscillation into a chiral edge state of a topological photonic system endowed with a frequency-dependent gain. As an archetypal model of this physics, we consider a Harper-Hofstadter lattice embedding population-inverted, two-level atoms as a gain material. We show that a suitable design of the spatial distribution of gain and its spectral shape provides flexible mode-selection mechanisms that can stabilize single-mode lasing into an edge state. Implications of our results for recent experiments are outlined.

We study the temporal evolution of the circuit complexity for a subsystem in harmonic lattices after a global quantum quench of the mass parameter, choosing the initial reduced density matrix as the reference state. Upper and lower bounds are derived for the temporal evolution of the complexity for the entire system. The subsystem complexity is evaluated by employing the Fisher information geometry for the covariance matrices. We discuss numerical results for the temporal evolutions of the subsystem complexity for a block of consecutive sites in harmonic chains with either periodic or Dirichlet boundary conditions, comparing them with the temporal evolutions of the entanglement entropy. For infinite harmonic chains, the asymptotic value of the subsystem complexity is studied through the generalised Gibbs ensemble.

We present a comprehensive and systematic study of thermal rectification in a prototypical low-dimensional quantum system - a nonlinear resonator: we identify necessary conditions to observe thermal rectification and we discuss strategies to maximize it. We focus, in particular, on the case where anharmonicity is very strong and the system reduces to a qubit. In the latter case, we derive general upper bounds on rectification which hold in the weak system-bath coupling regime, and we show how the Lamb shift can be exploited to enhance rectification. We then go beyond the weak-coupling regime by employing different methods: (i) including cotunneling processes, (ii) using the nonequilibrium Green's function formalism, and (iii) using the Feynman-Vernon path integral approach. We find that the strong coupling regime allows us to violate the bounds derived in the weak-coupling regime, providing us with clear signatures of high-order coherent processes visible in the thermal rectification. In the general case, where many levels participate to the system dynamics, we compare the heat rectification calculated with the equation of motion method and with a mean-field approximation. We find that the former method predicts, for a small or intermediate anharmonicity, a larger rectification coefficient.

We investigate the ground state properties of one-dimensional hard-core bosons interacting via a variable long-range potential using the density matrix renormalization group. We show that restoring energy extensivity in the system, which is done by rescaling the interaction potential with a suitable size-dependent factor known as Kac's prescription, has a profound influence on the low-energy properties in the thermodynamic limit. While an insulating phase is found in the absence of Kac's rescaling, the latter leads to a new metallic phase that does not fall into the conventional Luttinger liquid paradigm. We discuss a scheme for the observation of this new phase using cavity-mediated long-range interactions with cold atoms. Our findings raise fundamental questions on how to study the thermodynamics of long-range interacting quantum systems.

This paper was published online on 28 September 2017 with a typographical error in a Grant number in the Acknowledgments. In the Acknowledgments, the third to last sentence should read as “S.?R.?W. and E.?M.?S. acknowledge support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Grant No. DE-SC0008696.” The Acknowledgments have been corrected as of 24 March 2021. The Acknowledgments are incorrect in the printed version of the journal.

In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on an N-dimensional sphere, with N→∞, and subjected to a set of randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of infinite-dimensional hard spheres in Euclidean space. We find that the jamming transition with quantum dynamics shows critical exponents different from the classical case. We also find that the quantum jamming transition, unlike the typical quantum critical points, is not confined to the zero-temperature axis, and the classical results are recovered only at T=∞. Our findings have implications for the theory of glasses at ultralow temperatures and for the study of quantum machine-learning algorithms.

Spontaneous collapse models are proposed modifications to quantum mechanics which aim to solve the measurement problem. In this article, we will consider models which attempt to extend a specific spontaneous collapse model, the Ghirardi-Rimini-Weber model (GRW), to be consistent with special relativity. We will present a condition that a relativistic GRW model must meet for three cases: for a single particle, for N distinguishable particles, and for indistinguishable particles. We will then show that this relativistic condition implies that one can have a relativistic GRW model for a single particles or for distinguishable noninteracting, nonentangled particles but not otherwise.

The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum computation and sensing. The mechanisms by which a quantum system approaches its long-time, limiting stationary state are fascinating and, sometimes, quite different from their classical counterparts. In this respect, quantum networks represent mesoscopic quantum systems of interest. In such a case, the graph encodes the elementary quantum systems (say qubits) at its vertices, while the links define the interactions between them. We study here the relaxation to equilibrium for a fully connected quantum network with controlled-not (cnot) gates representing the interaction between the constituting qubits. We give a number of results for the equilibration in these systems, including analytic estimates. The results are checked using numerical methods for systems with up to 15-16 qubits. It is emphasized in which way the size of the network controls the convergency.

The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity.We explicitly study, in two of these proposals, the effects of decoherence on the system's dynamics by monitoring the corresponding degree of entanglement. We identify the required experimental conditions necessary to perform successfully the experiments. In parallel, we account also for the possible effects of the continuous spontaneous localization (CSL) model, which is the most known among the models of spontaneous wavefunction collapse. We find that any value of the parameters of the CSL model would completely hinder the generation of gravitationally induced entanglement.

The characterization and control of quantum effects in the performance of thermodynamic tasks may open new avenues for small thermal machines working in the nanoscale. We study the impact of coherence in the energy basis in the operation of a small thermal machine which can act either as a heat engine or as a refrigerator. We show that input coherence may enhance the machine performance and allow it to operate in otherwise forbidden regimes. Moreover, our results also indicate that, in some cases, coherence may also be detrimental, rendering optimization of particular models a crucial task for benefiting from coherence-induced enhancements.

We investigate superradiantlike dynamics of a nuclear-spin bath in contact with an electron shuttle, modeled as a moving quantum dot trapping a single electron. The dot is shuttled between two external reservoirs, where electron-nuclear flip flops are associated with tunneling events. For an ideal model with uniform hyperfine interaction, realized through an isotopically enriched "nuclear-spin island", we discuss in detail the nuclear spin evolution and its relation to superradiance. We then show that the superradiantlike evolution is robust to various extensions of the initial setup, and derive the minimum shuttling time which allows to escape adiabatic spin evolution. We also discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet and compare our scheme to a model with stationary quantum dot. Finally, we describe the electrical detection of nuclear entanglement in the framework of Monte Carlo wave-function simulations.

We study the motion of an impurity in a two-leg ladder interacting with two fermionic baths along each leg, a simple model bridging cold atom quantum simulators with an idealized description of the basic transport processes in a layered heterostructure. Using the linked-cluster expansion, we obtain exact analytical results for the single-particle Green's function and find that the long-time behavior is dominated by an intrinsic orthogonality catastrophe associated to the motion of the impurity in each one-dimensional chain. We explore both the case of two identical legs as well as the case where the legs are characterized by different interaction strengths: In the latter case, we observe a subleading correction which can be relevant for intermediate-time transport at an interface between different materials. In all the cases, we do not find significant differences between the intra- and interleg Green's functions in the long-time limit.

We consider heterostructures obtained by stacking layers of two s-wave superconductors with significantly different coupling strengths in the weak- and strong-coupling regimes. The weak- and strong-coupling superconductors are chosen with similar critical temperatures for bulk systems. Using dynamical mean-field theory methods, we find a ubiquitous enhancement of the superconducting critical temperature for all the heterostructures where a single layer of one of the two superconductors is alternated with a thicker multilayer of the other. Two distinct physical regimes can be identified as a function of the thickness of the larger layer: (i) an inherently inhomogeneous superconductor characterized by the properties of the two isolated bulk superconductors where the enhancement of the critical temperature is confined to the interface and (ii) a bulk superconductor with an enhanced critical temperature extending to the whole heterostructure. We characterize the crossover between these regimes in terms of the competition between two length scales connected with the proximity effect and the pair coherence.

We study the models of Kafri et al. (KTM) and Tilloy and Diósi (TD), both of which implement gravity between quantum systems through a continuous measurement and feedback mechanism. The first model is for two particles, moving in one dimension, where the Newtonian potential is linearized. The second is applicable to any quantum system, within the context of Newtonian gravity. We address the issue of how to generalize the KTM model for an arbitrary finite number of particles. We find that the most straightforward generalizations are either inconsistent or are ruled out by experimental evidence. We also show that the TD model does not reduce to the KTM model under the approximations, which define the latter model. We then argue that under the simplest conditions, the TD model is the only viable implementation of a full-Newtonian interaction through a continuous measurement and feedback mechanism.