Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

We derive an analytical formula for the covariance $\mathrm{cov}(A,B)$ of two smooth linear statistics $A=\sum _{i}a({\lambda }_i)$ and $B=\sum _{i}b({\lambda }_i)$ to leading order for $N\to \infty$, where $\{{\lambda }_i\}$ are the $N$ real eigenvalues of a general one-cut random-matrix model with Dyson index $\beta$. The formula, carrying the universal $1/\beta$ prefactor, depends on the random-matrix ensemble only through the edge points $[{\lambda }_{-},{\lambda }_{+}]$ of the limiting spectral density. For $A=B$, we recover in some special cases the classical variance formulas by Beenakker and by Dyson and Mehta, clarifying the respective ranges of applicability. Some choices of $a(x)$ and $b(x)$ lead to a striking decorrelation of the corresponding linear statistics. We provide two applications—the joint statistics of conductance and shot noise in ideal chaotic cavities, and some new fluctuation relations for traces of powers of random matrices.

We reconsider the large $N$ asymptotics of Harish-Chandra—Itzykson—Zuber integrals. We provide, using Dyson’s Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin’s equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

We show that a distinguishable mobile impurity inside a one-dimensional many-body state at zero temperature generally does not behave like a quasiparticle. Instead, both the impurity dynamics as well as the ground state of the bath are fundamentally transformed by a diverging number of zero-energy excitations being generated, leading to what we call infrared-dominated (ID) dynamics. Combining analytics and density matrix renormalization group numerics, we provide a general formula for the power law governing ID dynamics at zero momentum, discuss a threshold beyond which quasiparticle dynamics may occur again, and study the competition between the ID and quasiparticle universality classes at larger impurity momenta.

We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS Ansätzes.

We propose a technique for engineering momentum-dependent dissipation in Bose-Einstein condensates with nonlocal interactions. The scheme relies on the use of momentum-dependent dark states in close analogy to velocity-selective coherent population trapping. During the short-time dissipative dynamics, the system is driven into a particular finite-momentum phonon mode, which in real space corresponds to an ordered structure with nonlocal density-density correlations. Dissipation-induced ordering can be observed and studied in present-day experiments using cold atoms with dipole-dipole or off-resonant Rydberg interactions. Because of its dissipative nature, the ordering does not require artificial breaking of translational symmetry by an optical lattice or harmonic trap. This opens up a perspective of direct cooling of quantum gases into strongly interacting phases.

We present heat-transport measurements conducted with a vacuum-operated scanning thermal microscope to study the thermal conductance of monolayers of nine different alkane thiols self-assembled on Au(111) surfaces as a function of their length (2 to 18 methylene units). The molecular thermal conductance is probed in a confined area with a diameter below 10 nm in the contact between a silicon tip and the self-assembled monolayer. This yields a $\mathrm{p}{\mathrm{WK}}^{-1}$ sensitivity per molecule at a tip temperature of $200–300°\mathrm{C}$ versus the gold at room temperature. We found a conductance variance of up to a factor of 3 as a function of alkane chain length, with maximum conductance for a chain length of four carbon atoms.

Using the transfer-matrix method, we numerically compute the precise position of the mobility edge of atoms exposed to a laser speckle potential and study its dependence versus the disorder strength and correlation function. Our results deviate significantly from previous theoretical estimates using an approximate, self-consistent approach of localization. In particular, we find that the position of the mobility edge in blue-detuned speckles is much lower than in the red-detuned counterpart, pointing out the crucial role played by the asymmetric on-site distribution of speckle patterns.

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this Letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low-energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the low-energy ES and the Rényi entropies can mislead entirely, while for quantum Hall systems, the ES has much less universal content than assumed to date.

Quantum correlations are at the heart of many applications in quantum information science and, at the same time, they form the basis for discussions about genuine quantum effects and their difference to classical physics. On one hand, entanglement theory provides the tools to quantify correlations in information processing and many results have been obtained to discriminate useful entanglement, which can be distilled to a pure form, from bound entanglement, being of limited use in many applications. On the other hand, for discriminating quantum phenomena from their classical counterparts, Schrödinger and Bell introduced the notions of steering and local hidden variable models. We provide a method to generate systematically bound entangled quantum states which can still be used for steering and, therefore, to rule out local hidden state models. This sheds light on the relations between the various views on quantum correlations and disproves a widespread conjecture known as the stronger Peres conjecture. For practical applications, it implies that even the weakest form of entanglement can be certified in a semidevice independent way.

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

The efficient implementation of many-body interactions in superconducting circuits allows for the realization of multipartite entanglement and topological codes, as well as the efficient simulation of highly correlated fermionic systems. We propose the engineering of fast multiqubit interactions with tunable transmon-resonator couplings. This dynamics is obtained by the modulation of magnetic fluxes threading superconducting quantum interference device loops embedded in the transmon devices. We consider the feasibility of the proposed implementation in a realistic scenario and discuss potential applications.

We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels $N$ that can be accessed by the measurement apparatus via projective measurements. We provide exact bounds for small $N$ that exceed the known bound for the Leggett-Garg inequality, and we show that in the limit $N\to \infty$ the Leggett-Garg inequality can be violated up to its algebraic maximum.

We demonstrate the role of interactions in driving the relaxation of an isolated integrable quantum system following a sudden quench. We consider a family of integrable hard-core lattice anyon models that continuously interpolates between noninteracting spinless fermions and strongly interacting hard-core bosons. A generalized Jordan-Wigner transformation maps the entire family to noninteracting fermions. We find that, aside from the singular free-fermion limit, the entire single-particle density matrix and, therefore, all one-body observables relax to the predictions of the generalized Gibbs ensemble (GGE). This demonstrates that, in the presence of interactions, correlations between particles in the many-body wave function provide the effective dissipation required to drive the relaxation of all one-body observables to the GGE. This relaxation does not depend on translational invariance or the tracing out of any spatial domain of the system.

The feasibility of obtaining exact analytical results in the realm of QED in the presence of a background electromagnetic field is almost exclusively limited to a few tractable cases, where the Dirac equation in the corresponding background field can be solved analytically. This circumstance has restricted, in particular, the theoretical analysis of QED processes in intense laser fields to within the plane wave approximation even at those high intensities, achievable experimentally only by tightly focusing the laser energy in space. Here, within the Wentzel-Kramers-Brillouin approximation, we construct analytically single-particle electron states in the presence of a background electromagnetic field of general space-time structure in the realistic assumption that the initial energy of the electron is the largest dynamical energy scale in the problem. The relatively compact expression of these states opens, in particular, the possibility of investigating analytically strong-field QED processes in the presence of spatially focused laser beams, which is of particular relevance in view of the upcoming experimental campaigns in this field.