We investigate the decay of highly excited states of ultracold fermions in a three-dimensional optical lattice. Starting from a repulsive Fermi-Hubbard system near half filling, we generate additional doubly occupied sites (doublons) by lattice modulation. The subsequent relaxation back to thermal equilibrium is monitored over time. The measured absolute doublon lifetime covers 2 orders of magnitude. In units of the tunneling time $h/J$ it is found to depend exponentially on the ratio of on-site interaction energy $U$ to kinetic energy $J$. We argue that the dominant mechanism for the relaxation is a simultaneous many-body process involving several single fermions as scattering partners. A many-body calculation is carried out using diagrammatic methods, yielding fair agreement with the data.

We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.

We study the scaling behavior of dispersion potentials and forces under very general conditions. We prove that a rescaling of an arbitrary geometric arrangement by a factor $a$ changes the atom–atom and atom–body potentials in the long-distance limit by factors $1/a^7$ and $1/a^4$, respectively, and the Casimir force per unit area by $1/a^4$. In the short-distance regime, electric and magnetic bodies lead to different scaling behavior. As applications, we present scaling functions for two atom–body potentials and display the equipotential lines of a plate-assisted two-atom potential.

We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium—unlike the direction of the torque—can be predicted based on the sign of the force between two slabs of the same material.

We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing the evolution of such a system may be described either by a nonlocal master equation with a memory kernel or equivalently by an equation which is local in time. These two descriptions are complementary: if one is simple, the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point “$t_0$.” This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular; nevertheless, the corresponding dynamics is perfectly regular. Remarkably, the singularities of the generator may lead to interesting physical phenomena such as the revival of coherence or sudden death and revival of entanglement.

Localization properties of noninteracting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy dependent mobility edges are analytically predicted in this model and verified with numerical calculations. The results are then mapped to the continuum Schrödinger equation, and an approximate analytical expression for the localization phase diagram and the energy dependent mobility edges in the ground band is obtained.

We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity ${\chi }_{N+1}/{\chi }_N$ that governs the bosonic character of a pair of fermions when $N$ such pairs approximately share the same wave function. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity ${\chi }_{N+1}/{\chi }_N$ approaches its ideal bosonic value.

We report a calculation of the fine-structure splitting in light heliumlike atoms, which accounts for all quantum electrodynamical effects up to order ${\alpha }^5\mathrm{Ry}$. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine-structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.

The dilemma of identifying the correct form for the momentum of light in a medium has run for a century and has been informed by many distinguished contributions, both theoretical and experimental. We show that both the Abraham and Minkowski forms of the momentum density are correct, with the former being the kinetic momentum and the latter the canonical momentum. This identification allows us to explain why the experiments supporting each of the rival momenta gave the results that they did. The inclusion of dispersion and absorption provides an interesting subtlety, but does not change our conclusion.

The temperature dependence of the magnetic-resonance spectra of nitrogen-vacancy (${\mathrm{NV}}^{-}$) ensembles in the range of 280–330 K was studied. Four samples prepared under different conditions were analyzed with ${\mathrm{NV}}^{-}$ concentrations ranging from 10 ppb to 15 ppm. For all samples, the axial zero-field splitting (ZFS) parameter $D$ was found to vary significantly with temperature, $T$, as $dD/dT=-74.2(7)\mathrm{kHz}/\mathrm{K}$. The transverse ZFS parameter $E$ was nonzero (between 4 and 11 MHz) in all samples, and exhibited a temperature dependence of $dE/(EdT)=-1.4(3)\times {10}^{-4}{\mathrm{K}}^{-1}$. The results might be accounted for by considering local thermal expansion. The temperature dependence of the ZFS parameters presents a significant challenge for diamond magnetometers and may ultimately limit their bandwidth and sensitivity.

We have constructed an optical clock with a fractional frequency inaccuracy of , based on quantum logic spectroscopy of an ion. A simultaneously trapped ion serves to sympathetically laser cool the ion and detect its quantum state. The frequency of the clock transition is compared to that of a previously constructed optical clock with a statistical measurement uncertainty of . The two clocks exhibit a relative stability of , and a fractional frequency difference of , consistent with the accuracy limit of the older clock.

We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to $1/N$ can be tolerated using $N$-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising considering recent progress in atom-photon entanglement and in photon hyperentanglement.

Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to changes in parameters, and one is left to make adjustments by hand. We explain this difficulty by interpreting the fitting process as a generalized interpolation procedure. By considering the manifold of all model predictions in data space, we find that cross sections have a hierarchy of widths and are typically very narrow. Algorithms become stuck as they move near the boundaries. We observe that the model manifold, in addition to being tightly bounded, has low extrinsic curvature, leading to the use of geodesics in the fitting process. We improve the convergence of the Levenberg-Marquardt algorithm by adding geodesic acceleration to the usual step.

Monopolar charge disorder effects are studied in the context of fluctuation-induced interactions between neutral dielectric slabs. It is shown that quenched bulk charge disorder gives rise to an additive contribution to the net interaction force which decays as the inverse distance between the slabs and may thus completely mask the standard Casimir–van der Waals force at large separations. By contrast, annealed (bulk or surface) charge disorder leads to a net interaction force whose large-distance behavior agrees with the universal Casimir force between ideal conductors, which scales as the inverse cubic distance, and the dielectric properties enter only in the subleading corrections.

We report the observation of vortex nucleation in a rotating optical lattice. A ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.

We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits $k$, the distance of the code $d$, and the number of particles $n$. It is shown that $k{d}^2=O(n)$ where the coefficient in $O(n)$ depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. The analogous tradeoff for the classical information storage is $k\sqrt{d}=O(n)$.

We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size $\ell$, our algorithm runs in time $\log \ell$ compared to ${\ell }^6$ needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high $Q$ harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring a large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker’s position Hilbert space is increased. We observed a non-Gaussian distribution of the walker’s final position, thus characterizing a faster spread of the photon wave packet in comparison to the classical random walk. The walk is realized for many different coin settings and initial states, opening the way for the implementation of a quantum-walk-based search algorithm.

We present the proposition of an experiment in which the multiphoton quantum superposition consisting of $\mathcal{N}\approx {10}^5$ particles generated by a quantum-injected optical parametric amplifier, seeded by a single-photon belonging to an Einstein-Podolsky-Rosen entangled pair, is made to interact with a mirror-Bose-Einstein condensate (BEC) shaped as a Bragg interference structure. The overall process will realize a macroscopic quantum superposition involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in spacelike separated distant places.