We investigate the entanglement of $n$-mode $n$-partite Gaussian fermionic states (GFS). First, we identify a reasonable definition of separability for GFS and derive a standard form for mixed states, to which any state can be mapped via Gaussian local unitaries (GLU). As the standard form is unique, two GFS are equivalent under GLU if and only if their standard forms coincide. Then, we investigate the important class of local operations assisted by classical communication (LOCC). These are central in entanglement theory as they allow one to partially order the entanglement contained in states. We show, however, that there are no nontrivial Gaussian LOCC (GLOCC) among pure $n$-partite (fully entangled) states. That is, any such GLOCC transformation can also be accomplished via GLU. To obtain further insight into the entanglement properties of such GFS, we investigate the richer class of Gaussian stochastic local operations assisted by classical communication (SLOCC). We characterize Gaussian SLOCC classes of pure $n$-mode $n$-partite states and derive them explicitly for few-mode states. Furthermore, we consider certain fermionic LOCC and show how to identify the maximally entangled set of pure $n$-mode $n$-partite GFS, i.e., the minimal set of states having the property that any other state can be obtained from one state inside this set via fermionic LOCC. We generalize these findings also to the pure $m$-mode $n$-partite (for $m>n$) case.

We introduce a method to dispersively detect alkali-metal atoms in radio-frequency-dressed states. In particular, we use dressed detection to measure populations and population differences of atoms prepared in their clock states. Linear birefringence of the atomic medium enables atom number detection via polarization homodyning, a form of common path interferometry. In order to achieve low technical noise levels, we perform optical sideband detection after adiabatic transformation of bare states into dressed states. The balanced homodyne signal then oscillates independently of field fluctuations at twice the dressing frequency, thus allowing for robust, phase-locked detection that circumvents low-frequency noise. Using probe pulses of two optical frequencies, we can detect both clock states simultaneously and obtain population difference as well as the total atom number. The scheme also allows for difference measurements by direct subtraction of the homodyne signals at the balanced detector, which should technically enable quantum noise limited measurements with prospects for the preparation of spin squeezed states. The method extends to other Zeeman sublevels and can be employed in a range of atomic clock schemes, atom interferometers, and other experiments using dressed atoms.

We report on three-dimensional (3D) electron momentum distributions from single ionization of helium by a laser pulse consisting of two counter-rotating circularly polarized fields (390 and 780 nm). A pronounced 3D low-energy structure and subcycle interferences are observed experimentally and reproduced numerically using a trajectory-based semiclassical simulation. The orientation of the low-energy structure in the polarization plane is verified by numerical simulations solving the time-dependent Schrödinger equation.

We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e., a maximally entangled state of two qubits). The amount of randomness is certified through the observation of Bell nonlocal correlations. To attain this result we implemented a high-purity entanglement source and a nonprojective three-outcome measurement. Our implementation achieves a gain of 27% of randomness as compared with the standard methods using projective measurements. Additionally, we estimate the amount of randomness certified in a one-sided device-independent scenario, through the observation of Einstein-Podolsky-Rosen steering. Our results prove that nonprojective quantum measurements allow extending the limits for nonlocality-based certified randomness generation using current technology.

In a recent work on quantum state preparation, Sørensen and co-workers [Nature (London) 532, 210 (2016)] explore the possibility of using video games to help design quantum control protocols. The authors present a game called “Quantum Moves” (https://www.scienceathome.org/games/quantum-moves/) in which gamers have to move an atom from A to B by means of optical tweezers. They report that, “players succeed where purely numerical optimization fails.” Moreover, by harnessing the player strategies, they can “outperform the most prominent established numerical methods.” The aim of this Rapid Communication is to analyze the problem in detail and show that those claims are untenable. In fact, without any prior knowledge and starting from a random initial seed, a simple stochastic local optimization method finds near-optimal solutions which outperform all players. Counterdiabatic driving can even be used to generate protocols without resorting to numeric optimization. The analysis results in an accurate analytic estimate of the quantum speed limit which, apart from zero-point motion, is shown to be entirely classical in nature. The latter might explain why gamers are reasonably good at the game. A simple modification of the BringHomeWater challenge is proposed to test this hypothesis.

We propose a protocol based on coherent states and linear optics operations for solving the appointment-scheduling problem. Our main protocol leaks strictly less information about each party's input than the optimal classical protocol, even when considering experimental errors. Along with the ability to generate constant-amplitude coherent states over two modes, this protocol requires the ability to transfer these modes back-and-forth between the two parties multiple times with very low losses. The implementation requirements are thus still challenging. Along the way, we develop tools to study quantum information cost of interactive protocols in the finite regime.

We propose to use the energy absorption spectroscopy to measure the kinetic coefficients of unitary Fermi gases in a uniform potential. We show that, in our scheme, the energy absorption spectrum is proportional to the dynamic structure factor of the system. The profile of the spectrum depends on the shear viscosity $\eta$, the thermal conductivity $\kappa$, and the superfluid bulk viscosity ${\xi }_3$. We show that extraction of these coefficients from the spectrum is achievable in present experiments.

Do experiments based on superconducting loops segmented with Josephson junctions (e.g., flux qubits) show macroscopic quantum behavior in the sense of Schrödinger's cat example? Various arguments based on microscopic and phenomenological models were recently adduced in this debate. We approach this problem by adapting (to flux qubits) the framework of large-scale quantum coherence, which was already successfully applied to spin ensembles and photonic systems. We show that contemporary experiments might show quantum coherence more than 100 times larger than experiments in the classical regime. However, we argue that the often-used demonstration of an avoided crossing in the energy spectrum is not sufficient to make a conclusion about the presence of large-scale quantum coherence. Alternative, rigorous witnesses are proposed.

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

Nuclear-spin-dependent parity violation (NSD-PV) effects in atoms and molecules arise from $Z^0$ boson exchange between electrons and the nucleus and from the magnetic interaction between electrons and the parity-violating nuclear anapole moment. It has been proposed to study NSD-PV effects using an enhancement of the observable effect in diatomic molecules [D. DeMille et al., Phys. Rev. Lett. 100, 023003 (2008)]. Here we demonstrate highly sensitive measurements of this type, using the test system ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$. We show that systematic errors associated with our technique can be suppressed to at least the level of the present statistical sensitivity. With $\sim 170$ h of data, we measure the matrix element $W$ of the NSD-PV interaction with uncertainty $\delta W/\left(2\pi \right)<0.7$ Hz for each of two configurations where $W$ must have different signs. This sensitivity would be sufficient to measure NSD-PV effects of the size anticipated across a wide range of nuclei.

We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive conditions on the external force that allow for a “semiadiabatic” regime in which semiclassical equations of motion can apply, leading to Bloch oscillations between the edges of a pseudo-Brillouin-zone. We verify this semiclassical theory by comparing to the results of an exact numerical solution. Interesting features appear in the semiclassical dynamics for the quasicrystal for a particle driven in a cyclic trajectory around the corner of the pseudo-Brillouin-zone: The particle fails to return to its initial state, providing a realization of a “spiral holonomy” in the dynamics. We show that there can appear anomalous velocity contributions, associated with nonzero Berry curvature. We relate these to the Berry phase associated with the spiral holonomy, and show how the Berry curvature can be accessed from the semiclassical dynamics. Finally, by identifying the pseudo-Brillouin-zone as a higher genus surface, we show that the Chern number classification for periodic systems can be extended to a quasicrystal, thereby determining a topological index for the system.

We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for ${\chi }^{\left(2\right)}$-interaction based quantum computation in multimode Fock bases: the ${\chi }^{\left(2\right)}$ parity-check code, the ${\chi }^{\left(2\right)}$ embedded error-correcting code, and the ${\chi }^{\left(2\right)}$ binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via ${\chi }^{\left(2\right)}$ Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The ${\chi }^{\left(2\right)}$ binomial code is of special interest because, with $m\le N$ identified from channel monitoring, it can correct $m$-photon-loss errors, or $m$-photon-gain errors, or $(m-1)\mathrm{th}$-order dephasing errors using logical qudits that are encoded in $O\left(N\right)$ photons. In comparison, other bosonic QEC codes require $O\left(N^2\right)$ photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the ${\chi }^{\left(2\right)}$ parity-check code and the ${\chi }^{\left(2\right)}$ embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our ${\chi }^{\left(2\right)}$ QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.

We present precise frequency measurement of the $2{}^{1}S_0\text{−}3{}^{1}D_2$ two-photon transition in ${}^4\mathrm{He}$ at 1009 nm. The laser source at 1009 nm is stabilized on an optical frequency comb to perform the absolute frequency measurement. The absolute frequency of $2{}^{1}S_0\text{−}3{}^{1}D_2$ transition is experimentally determined to be 594 414 291.803(13) MHz with a relative uncertainty of $1.6\times {10}^{-11}$, which is more precise than previous determinations by a factor of 25. In combination with the theoretical ionization energy of the $3{}^{1}D_2$ state, the ionization energy of the $2{}^{1}S_0$ state is determined to be 960 332 040.823(24) MHz. In addition, the deduced $2{}^{1}S_0$ and $2{}^{3}S_1$ Lamb shifts are 2806.864(24) MHz and 4058.130(24) MHz, respectively, which are 1.6 times better than previous determinations, and the fine structure $3{}^{3}D_1\text{−}3{}^{1}D_2$ is determined to be 101 143.889(29) MHz, improving the precedent determination by a factor of 11.

We study the ground-state physics of a single-component Haldane model on a hexagonal two-leg ladder geometry with a particular focus on strongly interacting bosonic particles. We concentrate our analysis on the regime of less than one particle per unit cell. As a main result, we observe several Meissner-like and vortex-fluid phases, both for a superfluid as well as a Mott-insulating background. Furthermore, we show that for strongly interacting bosonic particles, an unconventional vortex-lattice phase emerges, which is stable even in the regime of hard-core bosons. We discuss the mechanism for its stabilization for finite interactions by a means of an analytical approximation. We show how the different phases may be discerned by measuring the nearest- and next-nearest-neighbor chiral currents as well as their characteristic momentum distributions.

We provide a simple construction of bipartite entangled states that are positive under partial transposition and hence undistillable. The construction makes use of the properties of the projectors onto the symmetric and antisymmetric subspaces of the Hilbert space of two identical systems. The resulting states can be considered as generalizations of the celebrated Werner states.

It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low-frequency modes) $|011\rangle \to i|100\rangle \to -|011\rangle$. We have analyzed a recent scheme proposed by Xia et al. [Phys. Rev. Lett. 116, 023601 (2016)] to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e., for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a $\pi$ phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro [Phys. Rev. A 73, 062305 (2006)] and by Gea-Banacloche [Phys. Rev. A 81, 043823 (2010)] one of us.

Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. We report the results of the calculations of the rate of laser-induced electric quadrupole transitions between a large set of ro-vibrational states of ${\mathrm{H}}_2^{+}$. The hyperfine and Zeeman structure of the $E2$ transition spectrum and the effects of the laser polarization are treated in detail. The treatment is generally applicable to molecules in ${}^2\mathrm{\Sigma }$ states. We also present the nuclear spin-electron spin-coupling constants, computed with a precision ten times higher than previously obtained.

Ultrashort electron pulses are crucial for time-resolved electron diffraction and microscopy of the fundamental light-matter interaction. In this work, we study experimentally and theoretically the generation and characterization of attosecond electron pulses by optical-field-driven compression and streaking at dielectric or absorbing interaction elements. The achievable acceleration and deflection gradient depends on the laser-electron angle, the laser's electric and magnetic field directions, and the foil orientation. Electric and magnetic fields have similar contributions to the final effect and both need to be considered. Experiments and theory agree well and reveal the optimum conditions for highly efficient, velocity-matched electron-field interactions in the longitudinal or transverse direction. We find that metallic membranes are optimum for light-electron control at mid-infrared or terahertz wavelengths, but dielectric membranes are excellent in the visible and near-infrared regimes and are therefore ideal for the formation of attosecond electron pulses.

Using Landau's theory of two-fluid hydrodynamics, we investigate first and second sounds propagating in a two-dimensional (2D) Bose gas. We study the temperature and interaction dependence of both sound modes and show that their behavior exhibits a deep qualitative change as the gas evolves from the weakly interacting to the strongly interacting regime. Special emphasis is placed on the jump of both sounds at the Berezinskii-Kosterlitz-Thouless transition, caused by the discontinuity of the superfluid density. We find that the excitation of second sound through a density perturbation becomes weaker and weaker as the interaction strength increases as a consequence of the decrease in the thermal expansion coefficient. Our results could be relevant for future experiments on the propagation of sound on the Bose-Einstein condensate (BEC) side of the BCS-BEC crossover of a 2D superfluid Fermi gas.

We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing the concept of contravariant operator-valued measures. Our approach is applied to the theory of array detectors, which is a challenging task as the finite dimensionality of the POVM substantially restricts the available information about quantum states. Our geometric technique allows for a direct estimation of expectation values of different observables, which are typically not accessible with such detection schemes. In addition, we also demonstrate the applicability of our method to quantum-state reconstruction with unbalanced homodyne detection.