We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-$Z$ gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persistency, which are related to measurement based quantum computation. The presence of multipartite entanglement is instead revealed by the use of witness operators which are subsequently adapted to study nonlocal properties through the violation of suitable Bell inequalities. We also present results on the entanglement detection of particular randomized graph states, by deriving explicit thresholds for entanglement and nonlocality in terms of the noise parameter that characterizes the controlled-$Z$ gates exploited for their generation. Finally, we propose a method to further improve the detection of genuine multipartite entanglement in this class of states.

Ionization by an attosecond pulse launches an electron wave packet in the continuum which contains rich information about the pulse, the parent system, and the ionization dynamics. This emission process is not instantaneous in the sense that the electrons take a finite time to leave the potential. This time is closely related to the Wigner time. In this paper we introduce the stereo Wigner time delay, which measures the relative delay between electrons emitted to the left and right in an asymmetric system. We present a theoretical study of the delay in photoemission for a small asymmetric molecular system using the streaking technique. The stereo Wigner time delay shows advantages compared to previous schemes. Our numerical calculation shows that such a measurement removes the infrared laser-Coulomb coupling, which has been problematic in the interpretation of the measured delay in photoemission from atomic systems.

We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.

We present a detailed analysis of the multimode quantum state embedded in an optical frequency comb generated by a synchronously pumped optical parametric oscillator (SPOPO) [J. Roslund, R. Medeiros de Araújo, S. Jiang, C. Fabre, and N. Treps, Nat. Photon. 8, 109 (2014)]. The full covariance matrix of the state is obtained with homodyne detection where the local oscillator is spectrally controlled with pulse-shaping techniques. The resulting matrix reveals genuine multipartite entanglement. Additionally, the beam is comprised of several independent eigenmodes that correspond to specific pulse shapes. The experimental data is confirmed with numerical simulations. Finally, the potential to create continuous-variable cluster states from the quantum comb is analyzed. Multiple cluster states are shown to be simultaneously embedded in the SPOPO state, and these states can be revealed by a suitable basis change applied to the measured covariance matrix.

The persistent $a_{\mu }\equiv (g-2)/2$ anomaly in the muon sector could be due to new physics visible in the electron sector through a sub-ppb (parts per ${10}^9$) measurement of the anomalous magnetic moment of the electron $a_e$. Driven by recent results on the electron mass [S. Sturm et al., Nature 506, 467 (2014)], we reconsider the sources of uncertainties that limit our knowledge of $a_e$ including current advances in atom interferometry. We demonstrate that it is possible to attain the level of precision needed to test $a_{\mu }$ in the naive scaling hypothesis on a time scale similar to next-generation $g-2$ muon experiments at Fermilab and JPARC. In order to achieve this level of precision, knowledge of the quotient $h/M$, i.e., the ratio between the Planck constant and the mass of the atom employed in the interferometer, will play a crucial role. We identify the most favorable isotopes to achieve an overall relative precision below ${10}^{-10}$.

We present a simple, experimentally realizable method to make coherent three-body interactions dominate the physics of an ultracold lattice gas. Our scheme employs either lattice modulation or laser-induced tunneling to reduce or turn off two-body interactions in a rotating frame, promoting three-body interactions arising from multiorbital physics to leading-order processes. This approach provides a route to strongly correlated phases of lattice gases that are beyond the reach of previously proposed dissipative three-body interactions. In particular, we study the mean-field phase diagram for spinless bosons with three- and two- body interactions and provide a roadmap to dimer states of varying character in one dimension. This toolkit should be immediately applicable in state-of-the-art cold-atom experiments.

We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincaré sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincaré sphere and the location of the zero-intensity point.

We present a quantum theory of ion-atom interactions that is applicable at energies comparable to or smaller than the atomic hyperfine splitting and takes proper account of the effects of identical nuclei. The theory reveals the subtlety and the complexity of cold ion-atom interactions including the change of threshold behavior due to hyperfine splitting and the existence of a large number and a variety of scattering resonances between hyperfine thresholds. We show how this complexity is described, efficiently and at a quantitative level, using a multichannel quantum-defect theory that we present here for ion-atom interactions. Such an efficient description is a key enabling element to understand few-body and many-body quantum systems involving ions.

We use a microscopic quantum optical model to compute the spectrum of quantum vacuum emission from strong laser pulses propagating in nonlinear optical media. Similarities and differences with respect to the emission of analog white holes as predicted by quantum field theory in curved spacetime are highlighted. Conceptual issues related to the role played by the material dispersion and to the presence or absence of the horizon are clarified. Critical comparison with available experimental data is made.

We demonstrate and analyze a strongly driven quantum pendulum in the angular motion of state-selected and laser-aligned carbonyl sulfide molecules. Raman couplings during the rising edge of a 50-ps laser pulse create a wave packet of pendular states, which propagates in the confining potential formed by the polarizability interaction between the molecule and the laser field. This wave-packet dynamics manifests itself as pronounced oscillations in the degree of alignment with a laser-intensity-dependent period.

Highly elongated quasi-one-dimensional cold-atom samples have been studied extensively over the past years experimentally and theoretically. This work determines the energy spectrum of two identical fermions and a third distinguishable particle as functions of the mass ratio $\kappa$ and the free-space $s$-wave scattering length $a_{3\text{D}}$ between the identical fermions and the distinguishable third particle in a cylindrically symmetric waveguide whose symmetry axis is chosen to be along the $z$ axis. We focus on the regime where the mass of the identical fermions is equal to or larger than that of the third distinguishable particle. Our theoretical framework accounts explicitly for the motion along the transverse confinement direction. In the regime where excitations in the transverse direction are absent (i.e., for states with projection quantum number $M_{\text{rel}}=0$), we determine the binding energies for states with odd parity in $z$. These full three-dimensional energies deviate significantly from those obtained within a strictly one-dimensional framework when the $s$-wave scattering length is of the order of or smaller than the oscillator length in the confinement direction. If transverse excitations are present, we predict the existence of a class of universal three-body bound states with $|M_{\text{rel}}|=1$ and positive parity in $z$. These bound states arise on the positive $s$-wave scattering length side if the mass ratio $\kappa$ is sufficiently large. Implications of our results for ongoing cold-atom experiments are discussed.

We present an entirely linear all-optical method of cavity scale factor enhancement that relies on mode coupling between the orthogonal polarization modes of a single optical cavity, eliminating the necessity of using an atomic medium to produce the required anomalous dispersion, which decreases the dependence of the scale factor on temperature and increases signal-to-noise ratio by reducing absorption and nonlinear effects. The use of a single cavity results in common mode rejection of the noise and drift that would be present in a system of two coupled cavities. We show that the scale-factor-to-mode-width ratio is increased above unity for this system, and demonstrate tuning of the scale factor by (i) directly varying the polarization mode coupling via rotation of an intracavity half-wave plate, and (ii) coherent control of the cavity reflectance which is achieved simply by varying the incident polarization superposition. These tuning methods allow us to closely approach the critical anomalous dispersion condition and achieve unprecedented enhancements in scale factor and in the scale-factor-to-mode-width ratio. Based on these findings, we propose an adaptation of the traditional optical cavity gyroscope that takes advantage of polarization mode coupling to enhance the gyro scale factor, and demonstrate how the bandwidth of the scale factor enhancement for this gyroscope can be effectively broadened in comparison with fast-light gyroscopes based on atomic media.

Surface-enhanced coherent nonlinear optical signals can dramatically improve detection sensitivity of spectroscopic imaging techniques. Large enhancement factors (EFs) of many orders of magnitude are expected for coherent Raman scattering of molecules in local fields of plasmonic nanostructures. However, only small EFs, several orders of magnitude less than the predicted values, were experimentally observed. To understand this discrepancy we measured the spatial variation of the shape of surface-enhanced coherent anti-Stokes Raman scattering (SECARS) spectra of pyridazine on randomly aggregated gold nanoparticles. We developed a model to simulate the dependence of SECARS spectra on the position and linewidth of the surface plasmon resonance, and attribute small (and even negative) EFs to local destructive interference. We report measurements of nanoscale phase effects in SECARS, and propose strategies to increase experimental EFs towards theoretical predictions.

We propose an interferometric method to measure ${\mathbb{Z}}_2$ topological invariants of time-reversal invariant topological insulators realized with optical lattices in two and three dimensions. We suggest two schemes which both rely on a combination of Bloch oscillations with Ramsey interferometry and can be implemented using standard tools of atomic physics. In contrast to topological Zak phase and Chern number, defined for individual one-dimensional and two-dimensional Bloch bands, the formulation of the ${\mathbb{Z}}_2$ invariant involves at least two Bloch bands related by time-reversal symmetry which one must keep track of in measurements. In one of our schemes this can be achieved by the measurement of Wilson loops, which are non-Abelian generalizations of Zak phases. The winding of their eigenvalues is related to the ${\mathbb{Z}}_2$ invariant. We thereby demonstrate that Wilson loops are not just theoretical concepts but can be measured experimentally. For the second scheme we introduce a generalization of time-reversal polarization which is continuous throughout the Brillouin zone. We show that its winding over half the Brillouin zone yields the ${\mathbb{Z}}_2$ invariant. To measure this winding, our protocol only requires Bloch oscillations within a single band, supplemented by coherent transitions to a second band which can be realized by lattice shaking.

We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare-earth element holmium. Atoms are loaded from an atomic beam source and captured in six-beam ${\sigma }_{+}-{\sigma }_{-}$ molasses using a strong $J=15/2\leftrightarrow J=17/2$ cycling transition at $\lambda =410.5$ nm. Due to the small difference in hyperfine splittings and Landé $g$ factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio $<$${10}^{-5}$, which is adequate for state-resolved measurements on hyperfine encoded qubits.

Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on ${}^6$Li, ${}^{39}$K, and ${}^{133}$Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero crossing for both broad and narrow resonances. However, the effective-range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic-field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to “splitting” the ground-state Fermi-sea-like quantum number configuration, are zero-entropy states which display interesting properties more normally associated with ground states. Using a numerically exact method based on integrability, we study these states' excitation spectrum, density correlations, and momentum distribution functions. These correlations display power-law asymptotics and are shown to be accurately described by an effective multicomponent Tomonaga-Luttinger liquid theory whose parameters are obtained from the Bethe ansatz. The nonuniversal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.

We investigate experimentally the backscattering properties of an array of atoms that is evanescently coupled to an optical nanofiber in the strongly nonparaxial regime. We observe that the power and the polarization of the backscattered light depend on the nanofiber-guided excitation field in a way that significantly deviates from the predictions of a simple model based on two-level atoms and a scalar waveguide. Even though it has been widely used in previous experimental and theoretical studies of waveguide-coupled quantum emitters, this simple model is thus in general not adequate even for a qualitative description of such systems. We develop an ab initio model that includes the multilevel structure of the atoms and the full vectorial properties of the guided field and find very good agreement with our data.

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

We present an experimental and theoretical study of modal nonlinear dynamics in a specially designed dual-mode semiconductor Fabry-Pérot laser with a saturable absorber. At zero bias applied to the absorber section, we have found that with increasing device current, single-mode self-pulsations evolve into a complex dynamical state where the total intensity experiences regular bursts of pulsations on a constant background. Spectrally resolved measurements reveal that in this state the individual modes of the device can follow highly symmetric but oppositely directed spiraling orbits. Using a generalization of the rate equation description of a semiconductor laser with saturable absorption to the multimode case, we show that these orbits appear as a consequence of the interplay between the material dispersion in the gain and absorber sections of the laser. Our results provide insights into the factors that determine the stability of multimode states in these systems, and they can inform the development of semiconductor mode-locked lasers with tailored spectra.