We perform a free-space measurement and control of the refractive index of a single trapped ion in the presence of quantum interference effects. The single atom refractive index is characterized by the Faraday rotation of a laser field tightly focused onto a trapped and laser-cooled barium ion. It is tuned using the internal ion state that is optically controlled via a $V$ or a $\Lambda$ scheme. Measurements of the phase shift associated with an electromagnetically induced transparency are then performed and the internal state on the qubit transition is read-out with a detection fidelity of ($98\pm 1$)%.

In continuous-variable quantum information processing, detectors are necessarily coarse grained and of finite range. We discuss how, especially, the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security when missed data outside the detector range are ignored. We demonstrate that a straightforward worst-case analysis is sufficient to avoid false positive statements about entanglement. We show that, for our worst-case analysis, entropic separability or security criteria are much superior to variance-based criteria.

We present a theoretical study of the two-dimensional ultracold Bose gas in the presence of disorder and bichromatic pseudodisorder in an optical lattice, to which we apply a synthetic magnetic field. We demonstrate that, in the ballistic-transport regime, this leads to positive magnetoresistance and that, in the diffusive and strong-localization regimes, can also lead to negative magnetoresistance. We propose experimental scenarios to observe these effects.

We propose a nonlinear atom-optics experiment to create diffraction catastrophes threaded by quantized vortex skeletons in Bose-Einstein-condensed matter waves. We show how atom-optical aberrations induced in trapped Bose-Einstein condensates evolve into specific caustic structures due to imperfect focusing. Vortex skeletons, whose cross sections are staggered vortex lattices, are observed to nucleate inside the universal diffraction catastrophes. Our observations shed further light on the structure and dynamics of Bose novae and suggest applications of matter wave diffraction catastrophes, including the detection of the order parameter pairing symmetry in cold gas experiments.

Laser modes may coalesce into a mode-locked state that enables femtosecond pulse compression. The nature of the interaction and the interaction time play fundamental roles in the onset of this collective state, but the investigation of the transition dynamics is technically challenging because phases are not always experimentally accessible. This is even more difficult for random lasers, a kind of disordered laser in which energies in play are much smaller than in the ordered macroscopic case. Here we investigate experimentally and numerically the dynamics of the phase-locking transition in a random laser. We developed an experimental setup able to pump individual modes with different pulse durations and found that the mode-locked regime builds only for quasicontinuous pumping, resulting in an emission linewidth dependent on the pump duration. Numerical simulation confirms experimental data.

When measuring the phase of quantum states of light, the optimal single-shot measurement implements a projection on the unphysical phase states. If we want to improve the precision further we need to accept a reduced probability of success, either by implementing a probabilistic measurement or by probabilistically manipulating the measured quantum state by means of noiseless amplification. We analyze the limits of this approach by finding the optimal probabilistic measurement that, for a given rate of success, maximizes the precision with which the phase can be measured.

I clarify here the relation between Leggett's concept of crypto-nonlocality and the better known notions of Bell's local causality and quantum separability, emphasizing that these are three genuinely different concepts. In particular, I show that while the correlations of separable quantum states clearly satisfy the assumptions of crypto-nonlocality, the opposite is not true: there exist entangled states whose correlations are always compatible with Leggett's crypto-nonlocality.

We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables, $\widehat{A}$ and $\widehat{B}$, the eigenstates of which form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.

Constructing compact quantum circuits for universal quantum gates on solid-state systems is crucial for quantum computing. We present some compact quantum circuits for a deterministic solid-state quantum computing, including the cnot, Toffoli, and Fredkin gates on the diamond NV centers confined inside cavities, achieved by some input-output processes of a single photon. Our quantum circuits for these universal quantum gates are simple and economic. Moreover, additional electron qubits are not employed, but only a single-photon medium. These gates have a long coherent time. We discuss the feasibility of these universal solid-state quantum gates, concluding that they are feasible with current technology.

We propose a probabilistic scheme to prepare a maximally entangled state between a pair of two-level atoms coupled to a leaking cavity mode in circuit QED, without requiring precise time control of the system evolution and initial atomic state. We show that the steady state of this dissipative system is a mixture of two parts, where the atoms are either in their ground state or in a maximally entangled one. Then, by applying a weak probe field to the cavity mode, we are able to discriminate those states without disturbing the atomic system, i.e., to perform a quantum nondemolition measurement via the cavity transmission. In this scheme, one has maximum cavity transmission only when the atomic system is in an entangled state, so that a single click in the detector is enough to be sure that the atoms are in a maximally entangled state. Our scheme relies on an interference effect as it happens in an electromagnetically induced transparency phenomenon so that it works even in the limit of a cavity decay rate much stronger than the atom-field coupling.

Magic-state distillation is a fundamental technique for realizing fault-tolerant universal quantum computing and produces high-fidelity Clifford eigenstates, called magic states, which can be used to implement the non-Clifford $\pi /8$ gate. We propose an efficient protocol for distilling other nonstabilizer states that requires only Clifford operations, measurement, and magic states. One critical application of our protocol is efficiently and fault-tolerantly implementing arbitrary, non-Clifford, single-qubit rotations in, on average, constant online circuit depth and polylogarithmic (in precision) offline resource cost, resulting in significant improvements over state-of-the-art decomposition techniques. Finally, we show that our protocol is robust to noise in the resource states.

Recent work [Phys. Rev. Lett. 109, 266404 (2012)] showed that the exact exchange-correlation potential of time-dependent density-functional theory generically displays dynamical step structures. These have a spatially nonlocal and time-nonlocal dependence on the density in real-time dynamics. The steps are missing in the usual approximations, which consequently yield inaccurate dynamics. Yet these same approximations often yield good linear response spectra. Here we investigate whether the steps appear in the linear response regime, when the response is calculated from a real-time dynamics simulation, by examining the exact correlation potential of model two-electron systems at various times. We find there are no step structures in regions where the system response is linear. Step structures appear in the correlation potential only in regions of space where the density response is nonlinear; these regions, having exponentially small density, do not contribute to the observables measured in linear response.

Angle-resolved photoelectron spectra of low-temperature sodium clusters Na${}_{33{}^{-}}$ and Na${}_{34{}^{-}}$ have been measured as a function of photon energy. The experiments in combination with density functional theory calculations demonstrate that despite the strongly oblate shape of the clusters, most of the occupied valence orbitals are close to angular-momentum eigenstates. Some states, however, exhibit a strongly mixed character. This mixing follows the selection rules $\Delta l=\pm 2$ and $\Delta m=0$, which result from the approximate symmetry of the cluster deformation.

Solid parahydrogen ($p$-H${}_2$) is known to support long-lived coherences, of the order of 100 ps, which enables high-resolution spectroscopy in the time domain. Rotational Raman-type excitations to sublevels of $J=2$ are delocalized due to electric-quadrupole–quadrupole coupling in $p$-H${}_2$ crystals, and the resulting states can be characterized as rotons. Wave packets of rotons exhibit molecular alignment with respect to laboratory coordinates. Here the concept of field-free molecular alignment, induced by strong ultrashort laser pulses, is extended into a molecular solid case. We derive a solid-state analog for the gas-phase alignment measure and illustrate the time-dependent alignment degree in $p$-H${}_2$ crystals by numerical simulations. To underscore the Raman gain effect of the solid, general properties of the field-free alignment are revisited by comparing gaseous $p$-H${}_2$ with N${}_2$. The interplay between the polarization direction of the excitation pulses and the axis directionality of the crystal is shown to affect the alignment dynamics via the spatial ($M=0,\pm 1,\pm 2$) composition of the roton wave packets. We simulate experimental traces by incorporating the induced alignment degree in the calculation of heterodyne-detected realization of femtosecond pump-probe optical Kerr effect spectroscopy. With the help of dispersed, two-dimensional resolved images of the calculated signal we reproduce the experiment as a whole. To that end, the effects of probe chirp, shape, and power must be explored in detail. We find good agreement with previous experiments and unravel the ambiguity of tracing back the wave-packet composition from the signal; in particular, we find that the effect of quantum phase factors of all the components should be taken into account when explaining the signal properties.

We exploit the relationship between high harmonic generation (HHG) and the molecular photorecombination dipole to extract the molecular-frame differential photoionization cross section (PICS) in the extreme ultraviolet (XUV) for molecular nitrogen. A shape resonance and a Cooper-type minimum are reflected in the pump-probe time delay measurements of different harmonic orders, where high-order rotational revivals are observed in N${}_2$. We observe the energy- and angle-dependent Cooper minimum and shape resonance directly in the laboratory-frame HHG yield by achieving a high degree of alignment, $\langle {\cos }^2\theta \rangle \ge 0.8$. The interplay between PICS and rotational revivals is confirmed by simulations using the quantitative rescattering theory. Our method of extracting molecular-frame structural information points the way to similar measurements in more complex molecules.

We propose an analysis of the time-optimal control of SU(2) quantum operations. By using the Pontryagin maximum principle, we show how to determine the optimal trajectory for reaching a given target state. Explicit analytical solutions are given for two specific examples. We discuss the role of the detuning in the construction of the optimal synthesis.

A scheme to realize an electron interferometer using low-intensity, bichromatic laser pulses as beam splitter is proposed. The splitting process is based on a modification of the Kapitza-Dirac effect, which produces a momentum kick for electrons with a specific initial momentum. A full interferometric setup in Ramsey-Bordé configuration is theoretically analyzed.

We investigate the sympathetic relaxation of a free-standing, vibrating carbon nanotube that is mounted on an atom chip and is immersed in a cloud of ultracold atoms. Gas atoms colliding with the nanotube excite phonons via a Casimir-Polder potential. We use Fermi's golden rule to estimate the relaxation rates for relevant experimental parameters and develop a fully dynamic theory of relaxation for the multimode phononic field embedded in a thermal atomic reservoir. Based on currently available experimental data, we identify the relaxation rates as a function of atom density and temperature that are required for sympathetic ground-state cooling of carbon nanotubes.

We determine the relative stability of different ground-state phases of spin-imbalanced populations of attractive fermions in square lattices. The ground state is determined within Hartree-Fock-Bogoliubov theory, with care taken to remove finite-size effects. The phases are systematically characterized by the symmetry of the order parameter and their real- and momentum-space structures. For quarter- to half-filled lattices, where the Fermi surfaces are most distorted from their spherical counterpart in the continuum, we predominantly find unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase exists when the ordering wave vector is diagonally directed. Charge and pairing order coexist, rather than compete, and are responsible for the opening of the gap on different portions of the Fermi surface. A variational determination of the correct pair momentum of the Larkin-Ovchinikov phases shows that phase separation does not occur in the considered regime of density and magnetization.