We introduce a fully tunable entangling gate for continuous-variable one-way quantum computation. We present a proof-of-principle demonstration by propagating two independent optical inputs through a three-mode linear cluster state and applying the gate in various regimes. The genuine quantum nature of the gate is confirmed by verifying the entanglement strength in the output state. Our protocol can be readily incorporated into efficient multimode interaction operations in the context of large-scale one-way quantum computation, as our tuning process is the generalization of cluster-state shaping.

We present theoretical and experimental analysis of an interferometric measurement of the in situ phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the in situ phase can be accurately determined. Mean-field estimates and numerical simulations show that the interatomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the in situ phase drop.

The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In particular, we derive tight no-signaling bounds for probabilistic cloning and superreplication that coincide with the corresponding optimal achievable fidelities and rates known. In the context of quantum metrology, we derive the Heisenberg limit from the no-signaling principle for certain scenarios including reference frame alignment and maximum likelihood state estimation. We elaborate on the equivalence of assymptotic phase-covariant cloning and phase estimation for different figures of merit.

Super Efimov states are new kinds of universal three-body bound states predicted for three identical fermions with $p\text{-wave}$ resonant interactions in two dimensions (2D) by a recent field-theoretic calculation [Phys. Rev. Lett. 110, 235301 (2013)]. The binding energies of these states obey a dramatic double exponential scaling $E_n=E_{*}exp\left(-2e^{\pi n/s_0+\theta }\right)$ with universal scaling $s_0=4/3$ and three-body parameters $E_{*}$ and $\theta$. We use the hyperspherical formalism and show that the super Efimov states originate from an emergent effective potential $-1/4{\rho }^2-\left(s_0^2+1/4\right)/{\rho }^2{ln}^2\left(\rho \right)$ at large hyperradius $\rho$. Moreover, for pairwise interparticle potentials with van der Waals tails, our numerical calculation indicates that the three-body parameters $E_{*}$ and $\theta$ are also universal and the ground super Efimov state shall cross the threshold when the $2\mathrm{D}p\text{-wave}$ scattering area is about $-42.0l_{\text{vdW}}^2$, with $l_{\text{vdW}}$ the van der Waals length.

We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a Förster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the Förster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantization axis. Our results show good agreement with the angular dependence $\propto (1-3{cos}^2\theta )$ expected for this resonance. Understanding in detail the angular dependence of resonant interactions is important in view of using Förster resonances for quantum state engineering with Rydberg atoms.

Angular resolved electron energy-loss spectroscopy (EELS) gives access to the momentum and the energy dispersion of electronic excitations and allows one to explore the transition from individual to collective excitations. Dimensionality and geometry thereby play a key role. As a prototypical example we theoretically analyze the case of Buckminster fullerene ${\mathrm{C}}_{60}$ using ab initio calculations based on the time-dependent density-functional theory. Utilizing the non-negative matrix factorization method, multipole contributions to various collective modes are isolated, imaged in real space, and their energy and momentum dependencies are traced. A possible experiment is suggested to access the multipolar excitations selectively via EELS with electron vortex (twisted) beams. Furthermore, we construct an accurate analytical model for the response function. Both the model and the ab initio cross sections are in good agreement with recent experimental data.

We investigate optical frequency transfer over a 1400 km loop of underground fiber connecting Braunschweig and Strasbourg. Largely autonomous fiber Brillouin amplifiers are the only means of intermediate amplification used here. This allows phase-continuous measurements over periods up to several days. Over a measurement period of about three weeks we find a weighted mean of the transferred frequency's fractional offset of $(1.1\pm 0.4)\times {10}^{-20}$. In the best case we find an instability of $6.9\times {10}^{-21}$ and a fractional frequency offset of $4.4\times {10}^{-21}$ at an averaging time of around 30 000 s. These results represent an upper limit for the uncertainty over 1400 km when using a chain of remote Brillouin amplifiers, and allow one to compare the world's best optical clocks.

We consider an error model for quantum computing that consists of “contagious quantum germs” that can infect every output qubit when at least one input qubit is infected. Once a germ actively causes error, it continues to cause error indefinitely for every qubit it infects, with arbitrary quantum entanglement and correlation. Although this error model looks much worse than quasi-independent error, we show that it reduces to quasi-independent error with the technique of quantum teleportation. The construction, which was previously described by Knill, is that every quantum circuit can be converted to a mixed circuit with bounded quantum depth. We also consider the restriction of bounded quantum depth from the point of view of quantum complexity classes.

The rigorous quantum electrodynamic approach is applied for the derivation of the Stark shift of the atomic energy levels induced by blackbody radiation (BBR) within the framework of perturbation theory. The temperature-dependent one-loop self-energy (SE) correction of bound atomic electron states accounting for the number of photons represented by the Planckian frequency-distribution function is examined. According to this approach, the energy shift arises as the real part of self-energy correction while the imaginary part describes the BBR-induced depopulation rate for a given atomic state. Moreover, regularization of the divergent energy denominators arising in the SE correction leads to an additional correction to the level width that has not been considered before and can be explained by the mixing effect of atomic levels in the presence of the BBR-induced mean electric field.

Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wavefront. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics, is well studied and observed in experiments. Here we introduce a theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarily small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power-dependent generalizations of the counterintuitive and hereto-elusive exponentially decaying states in Hamiltonian systems. We theoretically show that nonlinear Gamow vectors play a fundamental role in nonlinear Schroedinger models: They may be used as a generalized basis for describing the dynamics of the shock waves and affect the degree of irreversibility of wave-breaking phenomena. Gamow vectors allow analytical calculation of the amount of breaking of time reversal with a quantitative agreement with numerical solutions. We also show that a nonlocal, nonlinear optical medium may act as a simulator for the experimental investigation of quantum irreversible models, as the reversed harmonic oscillator.

In 1935, Einstein, Podolsky, and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror motion in interferometric gravitational wave detectors was proposed, with the aim of testing quantum theory in the regime of macroscopic objects, and to make available nonclassical probe systems for future tests of modified quantum theories that include (nonrelativistic) gravity. The work presented here builds on these earlier results and proposes a specific Michelson interferometer that includes two high-quality laser mirrors of about 0.1 kg mass each. The mirrors are individually suspended as pendula and located close to each other, and cooled to about 4 K. The physical concepts for the generation of the EPR-entangled center-of-mass motion of these two mirrors are described. Apart from a test of quantum mechanics in the macroscopic world, the setup is envisioned to test predictions of yet-to-be-elaborated modified quantum theories that include gravitational effects.

We develop a temperature measurement of an atomic cloud based on the temporal correlations of fluorescence photons evanescently coupled into an optical nanofiber. We measure the temporal width of the intensity-intensity correlation function due to atomic transit time and use it to determine the most probable atomic velocity, hence the temperature. This technique agrees well with standard time-of-flight temperature measurements. We confirm our results with trajectory simulations.

The x-ray near-field speckle-scanning concept is an approach recently introduced to obtain absorption, phase, and dark-field images of a sample. In this paper, we present ways of recovering from a sample its ultrasmall-angle x-ray scattering distribution using numerical deconvolution. We also show how to access the 2D phase gradient signal from random step scans, the latter having the potential to elude the flat-field correction error. Each feature is explained theoretically and demonstrated experimentally at a synchrotron x-ray facility.

In the spin Hall effect of light (SHEL) with an incident linear polarization, the left circularly polarized (LCP) and the right circularly polarized (RCP) spin components are transversely shifted to opposite sides of the incident plane. We find that each spin component of the reflected or the refracted light is actually the coherent superposition of a pair with the same handedness. The two parts in a pair are generated by both the incident LCP and RCP components, respectively, and have different transverse shifts. Their weighted shifts lead to the overall displacement of the corresponding spin component. This perspective can successfully elucidate the dependence of the SHEL spin separations on the angle of polarization of the incident electric field.

We say that two (or more) state assignments for one and the same quantum system are compatible if they could represent the assignments of observers with differing information about the system. A criterion for compatibility was proposed in [Phys. Rev. A 65, 032315 (2002)]; however, this leaves unanswered the question of whether there are degrees of compatibility which could be represented by some quantitative measure, and whether there is a straightforward procedure whereby the observers can pool their information to arrive at a unique joint state assignment. We argue that such measures are only sensible given some assumption about what kind of information was used in making the state assignments in the first place, and that in general state assignments do not represent all of the information possessed by the observers. However, we examine one particular measure and show that it has a straightforward interpretation, assuming that the information was acquired from a particular type of measurement, and that in this case there is a natural rule for pooling information. We extend this measure to compatibility of states for $k$ observers and show that the value is the solution to a semidefinite program. Similar compatibility measures can be defined for alternative notions of state compatibility, including post-Peierls and equal support compatibilities.

The quasistability of highly exicited H and He atoms in a strong infrared (IR) field is studied based on three-dimensional quantum calculations. The spectra of atoms that survive the IR field show a series of IR-frequency-modulated peaks that extend from deeply bound states all the way to the ionization threshold and above. The atoms that survive mainly consist of highly excited Rydberg states, even after hundreds of the intense IR cycles. Also, they tend to have initial energies that allow emission or absorption of an integer number of IR photons to reach these quasistable states. Peaks above the ionization threshold in the survival spectra indicate the existence of multiphoton-assisted recombination in the intense IR field.

We present a theoretical model allowing precise calculation of the phase shift induced by atom-atom interactions in a light-pulse atom interferometer based on two-photon Raman atom optics. This model is in good agreement with numerical simulations based on solving the Gross-Pitaevskii equation. The atom interferometer exhibits an atom-atom-interaction-induced phase shift when there is asymmetry between the two arms of the interferometer. In the case of a Ramsey-Bordé atom interferometer $(\{\pi /2–\pi /2\}–\{\pi /2–\pi /2\}$ pulse configuration), the asymmetry comes from the fact that the number of atoms in each arm of the interferometer is not constant. In the case of a Mach-Zehnder $(\{\pi /2–\pi –\pi /2\}$ pulse sequence), if the pulses are perfect, the number of atoms is constant in the interferometer. We study the effect due to imperfections of the light pulses as well as the effect due to the expansion of the cloud. Our model leads to precise and simple formulas of the mean-field phase shift as a function of the experimental parameters.

We present a compact atomic clock interrogating ultracold ${}^{87}\mathrm{Rb}$ magnetically trapped on an atom chip. Very long coherence times sustained by spin self-rephasing allow us to interrogate the atomic transition with 85% contrast at 5-s Ramsey time. The clock exhibits a fractional frequency stability of $5.8\times {10}^{-13}$ at 1 s and is likely to integrate into the ${10}^{-15}$ range in less than a day. A detailed analysis of seven noise sources explains the measured frequency stability. Fluctuations in the atom temperature (0.4 nK shot-to-shot) and in the offset magnetic field $(5\times {10}^{-6}$ relative fluctuations shot-to-shot) are the main noise sources together with the local oscillator, which is degraded by the 30% duty cycle. The analysis suggests technical improvements to be implemented in a future second generation setup . The results demonstrate the remarkable degree of technical control that can be reached in an atom chip experiment.

We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and nonseparability. Although these effects are negligible in more conventional optical lattice experiments, they are essential for emerging ultracold-atom developments. We focus in particular on two potentials utilized in current ultracold-atom experiments: arrays of tightly focused optical tweezers and a one-dimensional optical lattice with transverse Gaussian confinement and highly excited transverse modes. Our main numerical tools are discrete variable representations (DVRs), which combine many favorable features of spectral and grid-based methods, such as the computational advantage of exponential convergence and the convenience of an analytical representation of Hamiltonian matrix elements. Optimizations, such as symmetry adaptations and variational methods built on top of DVR methods, are presented and their convergence properties discussed. We also present a quantitative analysis of the degree of nonseparability of eigenstates, borrowing ideas from the theory of matrix product states, leading to both conceptual and computational gains. Beyond developing numerical methodologies, we present results for construction of optimally localized Wannier functions and tunneling and interaction matrix elements in optical lattices and tweezers relevant for constructing effective models for many-body physics.

A quantum-eraser experiment is reported with photon pairs generated by two synchronously pumped parametric down-converters coupled via induced coherence. The complementarity between which-source information and two-photon interference fringe visibility is demonstrated explicitly. Changing the phase in a Mach-Zehnder interferometer allows a continuous transition from wavelike to particlelike behavior of photons.