The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which grow at infinity. These cannot be expanded in terms of the eigenfunctions of a Hermitian operator, and show different relaxation patterns. Considering the exactly solvable examples of Gaussian and generalized Lévy Ornstein-Uhlenbeck processes (OUPs) we show that the relaxation rates belong to the Hermitian spectrum only if the initial condition belongs to the domain of attraction of the stable distribution defining the noise. While for an ordinary OUP initial conditions leading to nonspectral relaxation can be considered exotic, for generalized OUPs driven by Lévy noise, such initial conditions are the rule.

We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, the micromaser, and a dissipative version of the quantum Ising model. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and, in general, dynamical phases need to be uncovered by observables which are strictly dynamical, e.g., dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.

Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.

Intensive theoretical studies have recently predicted that a Bose-Einstein condensate will exhibit a variety of novel properties if spin-orbit coupling is present. However, an unambiguous fact has also been pointed out: Rashba coupling destroys a condensate of noninteracting bosons even in high dimensions. Therefore, a conceptually important question arises as to whether or not a condensate exists in the presence of interaction and a general type of spin-orbit coupling. Here we show that interaction qualitatively changes the ground state of bosons under Rashba spin-orbit coupling. Any infinitesimal repulsion forces bosons either to condense at one or two momentum states or to form a superfragmented state that is a superposition of infinite numbers of fragmented condensates. The superfragmented state is unstable against the anisotropy of spin-orbit coupling in systems with large numbers of particles, leading to the revival of a condensate in current experiments.

We develop a systematic method of performing corrected gate operations on an array of exchange-coupled singlet-triplet qubits in the presence of both fluctuating nuclear Overhauser field gradients and charge noise. The single-qubit control sequences we present have a simple form, are relatively short, and form the building blocks of a corrected cnot gate when also implemented on the interqubit exchange link. This is a key step towards enabling large-scale quantum computation in a semiconductor-based architecture by facilitating error reduction below the quantum error correction threshold for both single-qubit and multiqubit gate operations.

The spin magnetic moment of a single proton in a cryogenic Penning trap was coupled to the particle’s axial motion with a superimposed magnetic bottle. Jumps in the oscillation frequency indicate spin flips and were identified using a Bayesian analysis.

Previous measurements with a single trapped proton ($p$) or antiproton ($\overline{p}$) detected spin resonance from the increased scatter of frequency measurements caused by many spin flips. Here a measured correlation confirms that individual spin transitions and states are rapidly detected instead. The 96% fidelity and an efficiency expected to approach unity suggests that it may be possible to use quantum jump spectroscopy to measure the $p$ and $\overline{p}$ magnetic moments much more precisely.

We point out an earlier unnoticed implication of quantum indistinguishability, namely, a property which we call “dualism” that characterizes the entanglement of two identical particles (say, two ions of the same species)—a feature which is absent in the entanglement of two nonidentical particles (say, two ions of different species). A crucial application of this property is that it can be used to test quantum indistinguishability without bringing the relevant particles together, thereby avoiding the effects of mutual interaction. This is in contrast to the existing tests of quantum indistinguishability. Such a scheme, being independent of the nature and strength of mutual interactions of the identical particles involved, has potential applications, including the probing of the transition from quantum indistinguishability to classical distinguishability.

We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any $2\otimes d$ system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension $d$ of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.

We study a relativistic $O(N)$ model near the quantum critical point in $2+1$ dimensions for $N=2$ and $N=3$. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a well-defined peak associated with the Higgs mode arbitrarily close to the critical point. The peak fidelity and the amplitude ratio between the critical energy scales on both sides of the transition are determined.

In this Letter we report an observation of interference effects in Compton scattering in the experiment held on the VEPP-2000 collider. Infrared laser radiation was scattered head-on the 990 MeV electrons inside the dipole magnet, where an electron orbit radius is about 140 cm. It was observed that the energy spectrum of backscattered photons, measured by a HPGe detector, differs from that defined by the Klein-Nishina cross section and scattering kinematics of free electrons. The explanation of the effect, proposed in terms of classical electrodynamics, is in agreement with QED calculations.

We demonstrate teleportation of quantum bits between two single atoms in distant laboratories. Using a time-resolved photonic Bell-state measurement, we achieve a teleportation fidelity of $(88.0\pm 1.5)\%$, largely determined by our entanglement fidelity. The low photon collection efficiency in free space is overcome by trapping each atom in an optical cavity. The resulting success probability of 0.1% is almost 5 orders of magnitude larger than in previous experiments with remote material qubits. It is mainly limited by photon propagation and detection losses and can be enhanced with a cavity-based deterministic Bell-state measurement.

Using extensive molecular dynamics simulations we explore the fine-grained phase space structure of systems with long-range interactions. We find that if the initial phase space particle distribution has no holes, the final stationary distribution will also contain a compact simply connected region. The microscopic holes created by the filamentation of the initial distribution function are always restricted to the outer regions of the phase space. In general, for complex multilevel distributions it is very difficult to a priori predict the final stationary state without solving the full dynamical evolution. However, we show that, for multilevel initial distributions satisfying a generalized virial condition, it is possible to predict the particle distribution in the final stationary state using Casimir invariants of the Vlasov dynamics.

Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise is a fundamental challenge in a variety of fields. We propose a new approach to derive closed-form equations for joint and marginal probability density functions of state variables. This approach is based on a so-called large-eddy-diffusivity closure and can be used to model a wide class of non-Markovian processes described by the noise with an arbitrary correlation function. We demonstrate the accuracy of the proposed probability density function method for several linear and nonlinear Langevin equations.

Recent experiments on blinking quantum dots, weak turbulence in liquid crystals, and nanoelectrodes reveal the fundamental connection between $1/f$ noise and power law intermittency. The nonstationarity of the process implies that the power spectrum is random—a manifestation of weak ergodicity breaking. Here, we obtain the universal distribution of the power spectrum, which can be used to identify intermittency as the source of the noise. We solve in this case an outstanding paradox on the nonintegrability of $1/f$ noise and the violation of Parseval’s theorem. We explain why there is no physical low-frequency cutoff and therefore why it cannot be found in experiments.

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering.

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-$1/2$ fermions with imaginary polarization.

We prove basic theorems about the ground states of the $S=1$ Bose-Hubbard model. The results are quite universal and depend only on the coefficient $U_2$ of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if $U_2<0$, is spin-singlet if $U_2>0$, and exhibits “SU(3)-ferromagnetism” if $U_2=0$, and completely determine the degeneracy in each region.

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

We demonstrate an absolute magnetometer based on quantum beats in the ground state of nitrogen-vacancy centers in diamond. We show that, by eliminating the dependence of spin evolution on the zero-field splitting $D$, the magnetometer is immune to temperature fluctuation and strain inhomogeneity. We apply this technique to measure low-frequency magnetic field noise by using a single nitrogen-vacancy center located within 500 nm of the surface of an isotopically pure (99.99% ${}^{12}\mathrm{C}$) diamond. The photon-shot-noise limited sensitivity achieves $38\mathrm{nT}/\sqrt{\mathrm{Hz}}$ for 4.45 s acquisition time, a factor of $\sqrt{2}$ better than the implementation which uses only two spin levels. For long acquisition times ($>10\mathrm{s}$), we realize up to a factor of 15 improvement in magnetic sensitivity, which demonstrates the robustness of our technique against thermal drifts. Applying our technique to nitrogen-vacancy center ensembles, we eliminate dephasing from longitudinal strain inhomogeneity, resulting in a factor of 2.3 improvement in sensitivity.