The transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We develop a projector operator method able to derive, in this case, a generalized Smoluchowski equation for the position variable. We show that this explicitly non-Markovian equation can be written as a systematic expansion involving higher-order derivatives. We use the latter to compute arbitrary moments of the spatial distribution and analyze their multifractal properties.

Recently, anomalous superdiffusion of ultracold ${}^{87}\mathrm{Rb}$ atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and $x\sim t^{3/2}$ scaling, the latter related to Obukhov’s model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.

We study the quantum electrodynamics vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel’dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis.

We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom’s Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces.

I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cramér-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a Heisenberg error limit that scales with the average energy and a limit similar to the quantum Cramér-Rao bound that scales with the energy variance. These results are further illustrated by applying the bound to a few examples of optical phase estimation, which show that a quantum Ziv-Zakai bound can be much higher and thus tighter than a quantum Cramér-Rao bound for states with highly non-Gaussian photon-number statistics in certain regimes and also stay close to the latter where the latter is expected to be tight.

The Abraham force exerted by a time-dependent electromagnetic field on neutral, polarizable matter has two contributions. The one induced by a time-varying magnetic field and a static electric field is reported here for the first time. We discuss our results in the context of the radiative momentum in matter. Our observations are consistent with Abraham’s and Nelson’s versions for radiative momentum.

We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasilocal; i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables’ support. The precision increases exponentially with the diameter of the considered subsystem. Hence, time evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations in the Schrödinger picture, our result can be used to rigorously bound finite-size effects.

Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation. Openness of the system’s dynamics creates decoherence, leading to strong mixing. We present a method to analytically solve the asymptotic dynamics of coined, percolated quantum walks for a general graph structure. For the case of a circle and a linear graph we derive the explicit form of the asymptotic states. We find that a rich variety of asymptotic evolutions occur: not only the fully mixed state, but other stationary states; stable periodic and quasiperiodic oscillations can emerge, depending on the coin operator, the initial state, and the topology of the underlying graph.

Single molecular magnets (SMMs) are among the potential systems for quantum memory and quantum information processing. Quantum coherence and oscillation are critical for these applications. The ground-state quantum coherence and Rabi oscillations of the SMM ${\mathrm{V}}_{15}$ ($[{\mathrm{V}}_{15}^{\mathrm{IV}}{\mathrm{As}}_6^{\mathrm{III}}{\mathrm{O}}_{42}({\mathrm{H}}_2\mathrm{O}){]}^{6-}$) have been studied in this context. We have affirmatively measured at 2.4 K the Rabi quantum oscillations and coherence time $T_2$ for the ground states of the ${\mathrm{V}}_{15}$ ion of collective spin $S=1/2$, in addition to confirming the previously reported results for the $S=3/2$ excited states. The oscillations of $S=3/2$ and $S=1/2$ states are of different frequencies, and so can be separately selected for purposive manipulations. $T_2$ of $188\pm 4\mathrm{ns}$ ($S=3/2$) and $149\pm 10\mathrm{ns}$ ($S=1/2$) are much less than $T_1\sim 12\mu \mathrm{s}$ and are further extendible via various approaches for qubit implementations.

Multipartite entanglement is a key concept in quantum mechanics for which, despite the experimental progress in entangling three or more quantum devices, there is still no general quantitative theory that exists. In order to characterize the robustness of multipartite entanglement, one often employs generalized Werner states, that is, mixtures of a Greenberger-Horne-Zeilinger (GHZ) state and the completely unpolarized state. While two-qubit Werner states have been instrumental for various important advancements in quantum information, as of now there is no quantitative account for such states of more than two qubits. By using the GHZ symmetry introduced recently, we find exact results for tripartite entanglement in three-qubit generalized Werner states and, moreover, the entire family of full-rank mixed states that share the same symmetries.

We introduce two forms of correlations on two $d$-level (qudit) systems for entanglement detection. The correlations can be measured via experimentally tractable two local measurement settings and their separable bounds are determined by discrete Fourier-based uncertainty relations. They are useful to estimate lower bounds of the Schmidt number in order to clarify generation of a genuine qudit entanglement. We also present inseparable conditions for multiqudit systems associated with the qudit stabilizer formalism as another role of the correlations on the inseparability problem.

We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked $\log (n)$ entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in “$q$-sampling” protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.

Tap-proof long-distance quantum communication requires a deep understanding of the strong losses in transmission channels. Here we provide a rigorous treatment of the effects of beam wandering, one of the leading disturbances in atmospheric channels, on the quantum properties of light. From first principles we derive the probability distribution of the beam transmissivity, with the aim to completely characterize the quantum state of light. It turns out that beam wandering may preserve nonclassical effects, such as entanglement, quadrature and photon number squeezing, much better than a standard attenuating channel of the same losses.

We report on the experimental investigation of an individual pseudomolecule using trapped ions with adjustable magnetically induced $J$-type coupling between spin states. Resonances of individual spins are well separated and are addressed with high fidelity. Quantum gates are carried out using microwave radiation in the presence of thermal excitation of the pseudomolecule’s vibrations. Demonstrating controlled-NOT gates between non-nearest neighbors serves as a proof-of-principle of a quantum bus employing a spin chain. Combining advantageous features of nuclear magnetic resonance experiments and trapped ions, respectively, opens up a new avenue toward scalable quantum information processing.

The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow degrees of freedom in a system of two magnetically coupled driven colloidal particles. The apparent entropy production based on the observation of just one particle obeys a fluctuation theorem–like symmetry with a slope of 1 in the short time limit. For longer times, we find a constant slope, but different from 1. We present theoretical arguments for a generic linear behavior both for small and large apparent entropy production but not necessarily throughout. By fine-tuning experimental parameters, such an intermediate nonlinear behavior can indeed be recovered in our system as well.

Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by a measurement device, and that different detection schemes result in different types of jumps (or diffusion). Here we propose experimental tests to rigorously prove the detector dependence of the stochastic evolution of an individual atom. The tests involve no special preparation of the atom or field, and the required efficiency can be as low as $\eta \approx 58\%$.

We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterflylike spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.

We develop an experimental technique for rf association of Efimov trimers from a three-atom continuum. We apply it to probe the lowest accessible Efimov energy level in bosonic lithium in the region where strong deviations from the universal behavior are expected, and provide a quantitative study of this effect. The position of the Efimov resonance at the atom-dimer threshold, measured using a different experimental technique, concurs with the rf association results.

In this Letter we study the nonlocal properties of permutation symmetric states of $n$ qubits. We show that all these states are nonlocal, via an extended version of the Hardy paradox and associated inequalities. Natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different nonlocal features. Belonging to a given entanglement class will guarantee the violation of associated Bell inequalities which see the persistence of correlations to subsets of players, whereas there are states outside that class which do not violate.

We propose the measurement of cavity-enhanced parity-nonconserving (PNC) optical rotation in several transitions of metastable Xe and Hg, including Xe ${(}^2{P}_{3/2}^o)6s{}^2[3/2{]}_2^o\to {(}^2{P}_{1/2}^o)6s{}^2[1/2{]}_1^o$ and Hg $6s6p{}^{3}P_2^o\to 6s6p{}^{1}P_1^o$, with calculated amplitude ratios of $E_1^{\mathrm{PNC}}/M1=11\times {10}^{-8}$ and $10\times {10}^{-8}$, respectively. We demonstrate the use of a high-finesse bow-tie cavity with counterpropagating beams and a longitudinal magnetic field, which allows the absolute measurement of chiral optical rotation, with a path length enhancement of about ${10}^4$, necessary for PNC measurement from available column densities of ${10}^{14}{\mathrm{cm}}^{-2}$ for metastable Xe or Hg. Rapid PNC-signal reversal, allowing robust background subtraction, is achieved by shifting the cavity resonance to an opposite polarization mode or by inverting the magnetic field. The precise measurement of isotope and nuclear-spin dependent $E_1^{\mathrm{PNC}}$ amplitudes provides a sensitive low-energy test of the standard model.