We measure the coherent scattering of low-intensity, near-resonant light by a cloud of laser-cooled two-level rubidium atoms with a size comparable to the wavelength of light. We isolate a two-level atomic structure by applying a 300-G magnetic field. We measure both the temporal and the steady-state coherent optical response of the cloud for various detunings of the laser and for atom numbers ranging from 5 to 100. We compare our results to a microscopic coupled-dipole model and to a multimode, paraxial Maxwell-Bloch model. In the low-intensity regime, both models are in excellent agreement, thus validating the Maxwell-Bloch model. Comparing to the data, the models are found in very good agreement for relatively low densities ($n/k^3\lesssim 0.1$), while significant deviations start to occur at higher density. This disagreement indicates that light scattering in dense, cold atomic ensembles is still not quantitatively understood, even in pristine experimental conditions.

Collective responses of localized surface plasmon resonances, known as surface lattice resonances (SLRs) in metal nanoparticle arrays, can lead to high quality factors ($\sim 100$), large local-field enhancements, and strong light-matter interactions. SLRs have found many applications in linear optics, but little work of the influence of SLRs on nonlinear optics has been reported. Here we show how SLRs could be utilized to enhance nonlinear optical interactions. We devote special attention to the sum-frequency, difference-frequency, and third-harmonic generation processes because of their potential for the realization of novel sources of light. We also demonstrate how such arrays could be engineered to enhance higher-order nonlinear optical interactions through cascaded nonlinear processes. In particular, we demonstrate how the efficiency of third-harmonic generation could be engineered via cascaded second-order responses.

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a “beam shifter” at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.

A generic computational imaging setup is considered which assumes sequential illumination of a semitransparent object by an arbitrary set of structured coherent illumination patterns. For each incident illumination pattern, all transmitted light is collected by a photon-counting bucket (single-pixel) detector. The transmission coefficients measured in this way are then used to reconstruct the spatial distribution of the object's projected transmission. It is demonstrated that the square of the spatial resolution of such a setup is usually equal to the ratio of the image area to the number of linearly independent illumination patterns. If the noise in the measured transmission coefficients is dominated by photon shot noise, then the ratio of the square of the mean signal to the noise variance is proportional to the ratio of the mean number of registered photons to the number of illumination patterns. The signal-to-noise ratio in a reconstructed transmission distribution is always lower if the illumination patterns are nonorthogonal, because of spatial correlations in the measured data. Examples of imaging methods relevant to the presented analysis include conventional imaging with a pixelated detector, computational ghost imaging, compressive sensing, super-resolution imaging, and computed tomography.

We study the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist of multipulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multipeak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solutions. Our analysis is based on a generic model of mode locking that consists of a time-delayed dynamical system, but also on a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, which is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

We show how an upper bound for the ability to discriminate any number $N$ of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master-equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an $N$-dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple nonorthogonal quantum states as a semidefinite programming problem. We provide three realistic examples of multihypothesis testing with open quantum systems.

Interconnecting optical photons with superconducting circuits is a challenging problem but essential for building long-range superconducting quantum networks. We propose a hybrid quantum interface between the microwave and optical domains where the propagation of a single-photon pulse along a nanowaveguide is controlled in a coherent way by tuning the electromagnetically induced transparency window with the quantum state of a flux qubit mediated by the spin in a nanodiamond. The qubit can route a single-photon pulse using the nanodiamond into a quantum superposition of paths without the aid of an optical cavity—simplifying the setup. By preparing the flux qubit in a superposition state our cavityless scheme creates a hybrid state-path entanglement between a flying single optical photon and a static superconducting qubit.

We show that quantum Reed-Solomon codes constructed from classical Reed-Solomon codes can approach the capacity on the quantum erasure channel of $d$-level systems for large dimension $d$. We study the performance of one-way quantum repeaters with these codes and obtain a significant improvement in key generation rate compared to previously investigated encoding schemes with quantum parity codes and quantum polynomial codes. We also compare the three generations of quantum repeaters using quantum Reed-Solomon codes and identify parameter regimes where each generation performs the best.

Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In our framework, we consider Gaussian operations as free operations, and non-Gaussian operations as resources. We define entanglement-assisted non-Gaussianity generating power and show that it is a monotone that is nonincreasing under the set of free superoperations, i.e., concatenation and tensoring with Gaussian channels. For conditional unitary maps, this monotone can be analytically calculated. As examples, we show that the non-Gaussianity of ideal photon-number subtraction and photon-number addition equal the non-Gaussianity of the single-photon Fock state. Based on our non-Gaussianity monotone, we divide non-Gaussian operations into two classes: (i) the finite non-Gaussianity class, e.g., photon-number subtraction, photon-number addition, and all Gaussian-dilatable non-Gaussian channels; and (ii) the diverging non-Gaussianity class, e.g., the binary phase-shift channel and the Kerr nonlinearity. This classification also implies that not all non-Gaussian channels are exactly Gaussian dilatable. Our resource theory enables a quantitative characterization and a first classification of non-Gaussian operations, paving the way towards the full understanding of non-Gaussianity.

The magnetic dipole ($M1$) line strength between the fine-structure levels of the ground configurations in B-, F-, Al-, and Cl-like ions are calculated for the four elements argon, iron, molybdenum, and tungsten. Systematically enlarged multiconfiguration Dirac-Hartree-Fock (MCDHF) wave functions are employed to account for the interelectronic interaction with the Breit interaction included in first-order perturbation theory. The QED corrections are evaluated to all orders in $\alpha Z$ utilizing an effective potential approach. The calculated line strengths are compared with the results of other theories. The $M1$ transition rates are reported using accurate energies from the literature. Moreover, the lifetimes in the range of millisecond to picosecond are predicted including the contributions from the transition rate due to the $E2$ transition channel. The discrepancies of the predicted rates from those available from the literature are discussed and a benchmark data set of theoretical lifetimes is provided to support future experiments.

We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single-component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counterflowing channels, we seed a line of quantized vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behavior of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantized vortices. From this we demonstrate a straightforward method to measure the effective viscosity of a turbulent quantum fluid in a system with a moderate number of vortices, within the range of current experimental capabilities.

An experimental proposal for realizing spin-orbit (SO) coupling of pseudospin 1 in the ground manifold ${}^1\mathrm{\Sigma }(\upsilon =0)$ of (bosonic) bialkali polar molecules is presented. The three spin components are composed of the ground rotational state and two substates from the first excited rotational level. Using hyperfine resolved Raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. The properties of Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar interactions are further explored. In addition to the SO-coupling-induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using SO-coupled rotating polar molecules with dipolar interactions.

We propose an experimental scheme to generate, in a heralded fashion, arbitrary quantum superpositions of two-mode optical states with a fixed total photon number $n$ based on weakly squeezed two-mode squeezed state resources (obtained via weak parametric down-conversion), linear optics, and photon detection. Arbitrary $d$-level (qudit) states can be created this way where $d=n+1$. Furthermore, we experimentally demonstrate our scheme for $n=2$. The resulting qutrit states are characterized via optical homodyne tomography. We also discuss possible extensions to more than two modes concluding that, in general, our approach ceases to work in this case. For illustration and with regards to possible applications, we explicitly calculate a few examples such as NOON states and logical qubit states for quantum error correction. In particular, our approach enables one to construct bosonic qubit error-correction codes against amplitude damping (photon loss) with a typical suppression of $\sqrt{n}-1$ losses and spanned by two logical codewords that each correspond to an $n$-photon superposition for two bosonic modes.

Long-distance quantum optical communications usually require efficient wave-mixing processes to convert the wavelengths of single photons. Many quantum applications based on electromagnetically induced transparency (EIT) have been proposed and demonstrated at the single-photon level, such as quantum memories, all-optical transistors, and cross-phase modulations. However, EIT-based four-wave mixing (FWM) in a resonant double-$\mathrm{\Lambda }$ configuration has a maximum conversion efficiency (CE) of 25% because of absorptive loss due to spontaneous emission. An improved scheme using spatially modulated intensities of two control fields has been theoretically proposed to overcome this conversion limit. In this study, we first demonstrate wavelength conversion from 780 to 795 nm with a 43% CE by using this scheme at an optical density (OD) of 19 in cold ${}^{87}\mathrm{Rb}$ atoms. According to the theoretical model, the CE in the proposed scheme can further increase to 96% at an OD of 240 under ideal conditions, thereby attaining an identical CE to that of the previous nonresonant double-$\mathrm{\Lambda }$ scheme at half the OD. This spatial-light-modulation-based FWM scheme can achieve a near-unity CE, thus providing an easy method of implementing an efficient quantum wavelength converter for all-optical quantum information processing.

The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present Rapid Communication we determine the dimensionality $D$ for which the Efimov effect can exist for different values of the mass ratio $\mathcal{A}=m_B/m_A$ for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit. In addition, we provide a prediction for the Efimov discrete scaling factor $exp(\pi /s)$ as a function of a wide range of values of $\mathcal{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.

We investigate the nonequilibrium quantum heat transfer in a quantum thermal transistor, constructed by a triangle-coupled spin-boson system in a three-terminal setup. By exploiting the nonequilibrium noninteracting blip approximation approach combined with full counting statistics, we obtain the steady-state thermal transport, such as heat currents. We identify the giant heat amplification feature in a strong coupling regime, which results from the negative differential thermal conductance with respect to the gate temperature. Analysis shows that the strong coupling between the gate qubit and corresponding gate thermal bath plays the crucial role in exhibiting these far-from-equilibrium features. These results would have potential implications in designing efficient quantum thermal transistors in the future.

The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.

The energy splittings for $J=1$, $F=3/2$, $|m_F|=3/2$ hyperfine levels of the ${}^3{\mathrm{\Delta }}_1$ electronic state of ${}^{180}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ ion are calculated as functions of the external variable electric and magnetic fields within two approaches. In the first one, the transition to the rotating frame is performed, whereas in the second approach, the quantization of rotating electromagnetic field is performed. Calculations are required for understanding possible systematic errors in the experiment to search for the electron electric dipole moment ($e\mathrm{EDM}$) with the ${}^{180}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ ion.

The $K\beta$ x-ray spectra of the elements from Ca to Ge have been systematically investigated using a high-resolution antiparallel double-crystal x-ray spectrometer. Each $K{\beta }_{1,3}$ natural linewidth has been corrected using the instrumental function of this type of x-ray spectrometer, and the spin doublet energies have been obtained from the peak position values in $K{\beta }_{1,3}$ x-ray spectra. For all studied elements the corrected $K{\beta }_1$ x-ray lines FWHM increase linearly as a function of $Z$. However, for $K{\beta }_3$ x-ray lines this dependence is generally not linear in the case of $3d$ elements but increases from Sc to Co elements. It has been found that the contributions of satellite lines are considered to be $\left[KM\right]$ shake processes. Our theoretically predicted synthetic spectra of Ca, Mn, Cu, and Zn are in very good agreement with our high-resolution measurements, except in the case of Mn, due to the open-shell valence configuration effect (more than 7000 transitions for diagram lines and more than $100000$ transitions for satellite lines) and the influence of the complicated structure of the metallic Mn.