The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the probabilities of observing entropy-producing and entropy-consuming fluctuations measured over a finite volume and time span in terms of the rate of entropy production in the system, the measurement volume, and time. We study the fluctuation theorem in computer simulations of planar shear flow. The simulations are performed by employing the method of multiparticle collision dynamics, which captures both thermal fluctuations and hydrodynamic interactions. The main outcome of our analysis is that the fluctuation theorem is verified at any averaging time provided that the measurement volume exhibits a specific dependence on a hydrodynamic time scale.

We present a comprehensive study of the frequency shifts associated with the lattice potential in a Sr lattice clock by comparing two such clocks with a frequency stability reaching $5\times {10}^{-17}$ after a 1 h integration time. We put the first experimental upper bound on the multipolar $M1$ and $E2$ interactions, significantly smaller than the recently predicted theoretical upper limit, and give a 30-fold improved upper limit on the effect of hyperpolarizability. Finally, we report on the first observation of the vector and tensor shifts in a Sr lattice clock. Combining these measurements, we show that all known lattice related perturbations will not affect the clock accuracy down to the ${10}^{-17}$ level, even for lattices as deep as 150 recoil energies.

Tests such as Bell’s inequality and Hardy’s paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy’s paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.

The electric dipole moment (EDM) enhancement factor of atomic Tl is of considerable interest as it has been used in determining the most accurate limit on the electron EDM to date. However, its value varies from $-179$ to $-1041$ in different approximations. In view of the large uncertainties associated with many of these calculations, we perform an accurate calculation employing the relativistic coupled-cluster theory and obtain $-466$, which in combination with the most accurate measurement of Tl EDM [Phys. Rev. Lett. 88, 071805 (2002)] yields a new limit for the electron EDM: $|d_e|<2.0\times {10}^{-27}e\mathrm{cm}$.

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.

We study a paradigmatic system with long-range interactions: the Hamiltonian mean-field (HMF) model. It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the final stationary state has a peculiar core-halo structure. In the thermodynamic limit, HMF is neither ergodic nor mixing. Nevertheless, we find that using dynamical properties of Hamiltonian systems it is possible to quantitatively predict both the spin distribution and the velocity distribution functions in the final stationary state, without any adjustable parameters. We also show that HMF undergoes a nonequilibrium first-order phase transition between paramagnetic and ferromagnetic states.

We analyze the effect of a linear time variation of the interaction strength on a trapped one-dimensional Bose gas confined to an optical lattice. The evolution of different observables such as the experimentally accessible on site particle distribution are studied as a function of the ramp time by using time-dependent numerical techniques. We find that the dynamics of a trapped system typically displays two regimes: For long ramp times, the dynamics is governed by density redistribution, while at short ramp times, local dynamics dominates as the evolution is identical to that of an homogeneous system. In the homogeneous limit, we also discuss the nontrivial scaling of the energy absorbed with the ramp time.

Berry and Keating conjectured that the classical Hamiltonian $H=xp$ is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, on average, as the nontrivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this Letter, we show that the Hamiltonian $H=x(p+{\ell }_p^2/p)$ contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet $L$ functions using different self-adjoint extensions of $H$. We discuss the relation of our work to Polya’s fake zeta function and suggest an experimental realization in terms of the Landau model.

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.

It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit violations of inequalities for noncontextual theories in which compatibility is guaranteed by the fact that measurements are performed on separated qutrits. The inequalities are inspired by the basic building block of the Kochen-Specker proof of quantum contextuality for a qutrit, despite the fact that their proof is completely independent of it.

We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.

We present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponential improvement compared with existing schemes.

The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the deterministic case can be solved in polynomial time, stochastic variants are worst-case intractable. We propose an efficient method to solve stochastic matching problems which combines some features of the survey propagation equations and of the cavity method. We test it on random bipartite graphs, for which we analyze the phase diagram and compare the results with exact bounds. Our approach is shown numerically to be effective on the full range of parameters, and to outperform state-of-the-art methods. Finally we discuss how the method can be generalized to other problems of optimization under uncertainty.

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon’s wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.

The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state probabilistically. Thus far, many approximate cloning machines have been experimentally demonstrated, but probabilistic cloning remains an experimental challenge, as it requires more complicated networks and a higher level of precision control. In this work, we design an efficient quantum network with a limited amount of resources and perform the first experimental demonstration of probabilistic quantum cloning in a NMR quantum computer. In our experiment, the optimal cloning efficiency proposed by Duan and Guo [Phys. Rev. Lett. 80, 4999 (1998)] is achieved.

The exchange coupling between quantum dot spin qubits is isotropic, which restricts the types of quantum gates that can be formed. Here, we propose a method for controlling anisotropic interactions between spins arranged in a bus geometry. The symmetry is broken by an external magnetic field, resulting in $XXZ$-type interactions that can efficiently generate maximally entangled Greenberger-Horne-Zeilinger states or universal gate sets for exchange-only quantum computing. We exploit the $XXZ$ couplings to propose a qubit scheme, based on double dots.

In this Letter we propose a fully scalable randomized benchmarking protocol for quantum information processors. We prove that the protocol provides an efficient and reliable estimate of the average error-rate for a set operations (gates) under a very general noise model that allows for both time and gate-dependent errors. In particular we obtain a sequence of fitting models for the observable fidelity decay as a function of a (convergent) perturbative expansion of the gate errors about the mean error. We illustrate the protocol through numerical examples.

The ability to explore the interior of materials for the presence of inhomogeneities was recently demonstrated by mode synthesizing atomic force microscopy [L. Tetard, A. Passian, and T. Thundat, Nature Nanotech. 5, 105 (2009).]. Proposing a semiempirical nonlinear force, we show that difference frequency ${\omega }_{-}$ generation, regarded as the simplest synthesized mode, occurs optimally when the force is tuned to van der Waals form. From a parametric study of the probe-sample excitation, we show that the predicted ${\omega }_{-}$ oscillation agrees well with experiments. We then introduce the concept of virtual resonance to show that probe oscillations at ${\omega }_{-}$ can efficiently be enhanced.

A high signal-to-noise spectrum covering the largest number of hydrogen lines (90 ${\mathrm{H}}_2$ lines and 6 HD lines) in a high-redshift object was analyzed from an observation along the sight line to the bright quasar source J2123-005 with the Ultraviolet and Visual Echelle Spectrograph on the European Southern Observatory Very Large Telescope (Paranal, Chile). This delivers a constraint on a possible variation of the proton-to-electron mass ratio of $\Delta \mu /\mu =(8.5\pm {3.6}_{\mathrm{stat}}\pm {2.2}_{\mathrm{syst}})\times {10}^{-6}$ at redshift $z_{\mathrm{abs}}=2.059$, which agrees well with a recently published result on the same system observed at the Keck telescope yielding $\Delta \mu /\mu =(5.6\pm {5.5}_{\mathrm{stat}}\pm {2.9}_{\mathrm{syst}})\times {10}^{-6}$. Both analyses used the same robust absorption line fitting procedures with detailed consideration of systematic errors.

We determine the sensitivity of a modern Michelson-Morley resonant-cavity experiment to higher-order nonbirefringent and nondispersive coefficients of the Lorentz-violating standard-model extension. Data from a recent year-long run of the experiment are used to place the first experimental bounds on coefficients associated with nonrenormalizable Lorentz-violating operators.