We propose a method to create two-photon states in a controllable way using interaction between the Rydberg atoms during the storage and retrieval of slow light. A distinctive feature of the suggested procedure is that the slow light is stored into a superposition of two atomic coherences under conditions of electromagnetically induced transparency. Interaction between the atoms during the storage period creates entangled pairs of atoms in a superposition state that is orthogonal to the initially stored state. Restoring the slow light from this new atomic state one can produce a two-photon state with a second-order correlation function determined by the atom-atom interaction and the storage time. Therefore the measurement of the restored light allows one to probe the atom-atom coupling by optical means with a sensitivity that can be increased by extending the storage time. As a realization of this idea we consider a many-body Ramsey-type technique which involves $\pi /2$ pulses creating a superposition of Rydberg states at the beginning and the end of the storage period. In that case the regenerated light is due to the resonance dipole-dipole interaction between the atoms in the Rydberg states.

We investigate the finite nuclear mass corrections in the helium atom in order to resolve a significant disagreement between the $2{}^{3}S-2{}^{3}P$ and $2{}^{3}S-2{}^{1}S$ transition isotope shifts. These two transitions lead to discrepant results for the nuclear charge radii difference between ${}^4\mathrm{He}$ and ${}^3\mathrm{He}$. The accurate treatment of the finite nuclear mass effects is quite complicated and requires the use of the quantum field theoretical approach. We derive the ${\alpha }^6{m}^2/M$ correction with the help of nonrelativistic QED and dimensional regularization of the three-body Coulombic system and present accurate numerical results for low-lying states. The previously reported $4\sigma$ discrepancy in the nuclear charge radius difference between ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ from two different atomic isotope shift transitions is confirmed, which calls for verification of experimental transition frequencies.

Given a classical, reversible dynamics over a line of discrete systems, we can define a quantum evolution, which acts on basis states like the classical one but is linearly extended to allow for quantum superpositions. It is a curious fact that in the quantum regime, the speed of propagation of information can sometimes be much greater than in the classical regime. Here we provide optimal bounds on this quantum speedup. In particular we show that over a run of many steps, the quantum propagation neighborhood can only increase by a constant fringe, so that there is no asymptotic increase in speed.

Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be extended by yet another complementary observable. We construct explicit examples of unextendible sets up to dimension 16 and conjecture certain small sets to be unextendible in higher dimensions. Our constructions provide three complementary measurements, only one observable away from the ultimate minimum of two. Almost all our examples in finite dimensions are useful for discriminating pure states from some mixed states, and they help to shed light on the complex topology of the Bloch space of higher-dimensional quantum systems.

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.

We propose a photonic crystal composed of Eaton lenses and invisible lenses, respectively. We show that for certain frequency ranges the photonic crystal of Eaton lenses is transparent, whereas the crystal composed of invisible lenses cannot be penetrated by the light waves. This is exactly the opposite behavior than one can observe within geometrical optics where the Eaton lens works as a perfect retroreflector, while the invisible lens is transparent.

Attosecond delays between photoelectron wave packets emitted from different electronic shells are now well established. Is there any delay between electrons originating from the same electronic shell but leaving the cation in different fine-structure states? This question is relevant for all attosecond photoemission studies involving heavy elements, be it atoms, molecules or solids. We answer this fundamental question by measuring energy-dependent delays between photoelectron wave packets associated with the ${}^{2}P_{3/2}$ and ${}^{2}P_{1/2}$ components of the electronic ground states of ${\mathrm{Xe}}^{+}$ and ${\mathrm{Kr}}^{+}$. We observe delays reaching up to $33\pm 6$ as in the case of Xe. Our results are compared with two state-of-the-art theories. Whereas both theories quantitatively agree with the results obtained for Kr, neither of them fully reproduces the experimental results in Xe. Performing delay measurements very close to the ionization thresholds, we compare the agreement of several analytical formulas for the continuum-continuum delays with experimental data. Our results show an important influence of spin-orbit coupling on attosecond photoionization delays, highlight the requirement for additional theory development, and offer a precision benchmark for such work.

We theoretically investigate the manipulation of the motional states of trapped ground-state atoms using Rydberg dressing via nonresonant laser fields. The forces resulting from Rydberg state interaction between dressed neighboring atoms in an array of microtraps or an optical lattice can strongly couple their motion. We show that intensity modulation of the dressing field allows us to squeeze the relative motion of a pair of atoms and generate nonclassical mechanical states. Extending this pairwise scheme to one-dimensional chains provides flexible control over the mechanical degrees of freedom of the whole system. We illustrate our findings with protocols to manipulate all motional degrees of freedom of a pair of atoms and create entangled states. We also present a method to transfer nonclassical correlations along an atomic chain of nontrivial length. The long-lived nature of motional states, together with the high tunability of Rydberg dressing, makes our proposal feasible for current experimental setups.

We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors, and classical feedforward at each repeater node, but no quantum memories. We show that the quantum-secure key rate has the form $R\left(\eta \right)=D{\eta }^s$ bits per mode, where $\eta$ is the end-to-end channel's transmissivity, and the constants $D$ and $s$ are functions of various device inefficiencies and the resource constraint, such as the number of available photon sources at each repeater node. Even with lossy devices, we show that it is possible to attain $s<1$, and in turn outperform the maximum key rate attainable without quantum repeaters, $R_{\mathrm{direct}}\left(\eta \right)=-{log}_2(1-\eta )\approx (1/ln2)\eta$ bits per mode for $\eta \ll 1$, beyond a certain total range $L$, where $\eta \sim e^{-\alpha L}$ in optical fiber. We also propose a suite of modifications to a recently proposed all-optical repeater protocol that ours builds upon, which lower the number of photon sources required to create photonic clusters at the repeaters so as to outperform $R_{\mathrm{direct}}\left(\eta \right)$, from $\sim {10}^{11}$ to $\sim {10}^6$ photon sources per repeater node. We show that the optimum separation between repeater nodes is independent of the total range $L$ and is around 1.5 km for assumptions we make on various device losses.

Optical microtraps provide a strong spatial confinement for laser-cooled atoms. They can, e.g., be realized with strongly focused trapping light beams or the optical near fields of nanoscale waveguides and photonic nanostructures. Atoms in such traps often experience strongly spatially varying ac Stark shifts which are proportional to the magnetic quantum number of the respective energy level. These inhomogeneous fictitious magnetic fields can cause a displacement of the trapping potential that depends on the Zeeman state. Hitherto, this effect was mainly perceived as detrimental in optical microtraps. However, it also provides a means to probe and to manipulate the motional state of the atoms in the trap by driving transitions between Zeeman states. Furthermore, by applying additional real or fictitious magnetic fields, the state dependence of the trapping potential can be controlled. Here, using laser-cooled atoms that are confined in a nanofiber-based optical dipole trap, we employ this control in order to tune the microwave coupling of motional quantum states. We record corresponding microwave spectra which allow us to infer the trap parameters as well as the temperature of the atoms. Finally, we reduce the mean number of motional quanta in one spatial dimension to $\langle n\rangle =0.3\left(1\right)$ by microwave sideband cooling. Our work shows that the inherent fictitious magnetic fields in optical microtraps expand the experimental toolbox for interrogating and manipulating cold atoms.

The longitudinal (${\mathrm{\Gamma }}_1$) and transverse (${\mathrm{\Gamma }}_2$) decay rates of a two-level quantum system have a profound influence on its evolution. Atomic systems with ${\mathrm{\Gamma }}_2=\frac{1}{2}{\mathrm{\Gamma }}_1$ have been studied extensively, but with the rise of solid-state quantum devices it is also important to consider the effect of stronger transverse relaxation due to interactions with the solid environment. Here we study the quantum dynamics of a single organic dye molecule driven by a laser. We measure the variation of ${\mathrm{\Gamma }}_2$ with temperature and determine the activation energy for thermal dephasing of the optical dipole. Then we measure the second-order correlation function $g^{\left(2\right)}\left(\tau \right)$ of the light emitted by the molecule for various ratios ${\mathrm{\Gamma }}_2/{\mathrm{\Gamma }}_1$ and saturation parameters $S$. We show that the general solution to the optical Bloch equations accurately describes the observed quantum dynamics over a wide range of these parameters, and we discuss the limitations of the various approximate expressions for $g^{\left(2\right)}\left(\tau \right)$ that appear in the literature.

We compute an $O({\alpha }^2{\left(Z\alpha \right)}^6)$ contribution to the hydrogen-atom Lamb shift arising from light-by-light scattering. Analogous diagrams, with one atomic electric field insertion replaced by an external magnetic field, contribute to the gyromagnetic factor of the bound electron at $O({\alpha }^2{\left(Z\alpha \right)}^4)$. We also calculate the contribution to the gyromagnetic factor from the muon magnetic loop.

We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.

We study the excitation of a two-level system (2LS) by quantum light, thereby bringing our previous studies [see Paper I of this series, Phys. Rev. A 94, 063825 (2016)] to a target that is quantum itself. While there is no gain for the quantum state of the target as compared to driving it with classical light, its dynamical features, such as antibunching, can be improved. We propose a chain of two-level systems, i.e., setting the emission of each 2LS as the driving source of the following one, as an arrangement to provide better single-photon sources. At a fundamental level, we discuss the notion of strong coupling between quantum light from a source and its target, and the several versions of the Mollow triplet that follow from various types of driving light. We discuss the Heitler effect of antibunched photons from the scattered light off a laser.

We observe Feshbach resonances in ultracold mixtures of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms in the ${}^{85}\mathrm{Rb}|2,+2\rangle +{}^{87}\mathrm{Rb}|1,+1\rangle$ and ${}^{85}\mathrm{Rb}|2,-2\rangle +{}^{87}\mathrm{Rb}|1,-1\rangle$ scattering channels. The positions and properties of the resonances are predicted and characterized using the semianalytic multichannel quantum-defect theory by Gao. Of particular interest, a number of broad entrance-channel-dominated $p-\mathrm{wave}$ resonances are identified, implicating exciting opportunities for studying a variety of $p-\mathrm{wave}$ interaction–dominated physics.

We investigate the spatiospectral coupling appearing in the spatially resolved high-order-harmonic spectra generated in gases. When ionization is weak, harmonic generation in the far field often exhibits rings surrounding a central spot centered on each odd harmonics in the spatiospectral domain. The nature of these structures is debated. They could stem from interferences between the emission of short and long trajectories, or could be the signature of the temporal and spatial dependence of the longitudinal phase matching of long trajectories (Maker fringes). We conducted spectrally and spatially resolved measurements of the harmonic spectra as a function of pressure, intensity, and ellipticity. In addition, we performed calculations where only a single emission plane is included (i.e., omitting deliberately the longitudinal phase matching), reproducing the features experimentally observed. This study has been completed by the spatiospectral coupling when strong ionization occurs leading to complex patterns which have been compared to calculations using the same model and also show good agreement. We conclude that many spatiospectral structures of the harmonic spectrum can be interpreted in terms of spatial and temporal transverse coherence of the emitting medium without resorting to longitudinal phase matching or quantum phase interference between short and long trajectories.

We report the observation of a clear single-mode instability threshold in continuous-wave Fabry-Perot quantum cascade lasers (QCLs). The instability is characterized by the appearance of sidebands separated by tens of free spectral ranges (FSR) from the first lasing mode, at a pump current not much higher than the lasing threshold. As the current is increased, higher-order sidebands appear that preserve the initial spacing, and the spectra are suggestive of harmonically phase-locked waveforms. We present a theory of the instability that applies to all homogeneously broadened standing-wave lasers. The low instability threshold and the large sideband spacing can be explained by the combination of an unclamped, incoherent Lorentzian gain due to the population grating, and a coherent parametric gain caused by temporal population pulsations that changes the spectral gain line shape. The parametric term suppresses the gain of sidebands whose separation is much smaller than the reciprocal gain recovery time, while enhancing the gain of more distant sidebands. The large gain recovery frequency of the QCL compared to the FSR is essential to observe this parametric effect, which is responsible for the multiple-FSR sideband separation. We predict that by tuning the strength of the incoherent gain contribution, for example by engineering the modal overlap factors and the carrier diffusion, both amplitude-modulated (AM) or frequency-modulated emission can be achieved from QCLs. We provide initial evidence of an AM waveform emitted by a QCL with highly asymmetric facet reflectivities, thereby opening a promising route to ultrashort pulse generation in the mid-infrared. Together, the experiments and theory clarify a deep connection between parametric oscillation in optically pumped microresonators and the single-mode instability of lasers, tying together literature from the last 60 years.

Ultrafast nonlinear spectroscopy, which records transient wave-mixing signals in a medium, is a powerful tool to access microscopic information using light sources in the radio-frequency and optical regimes. The extension of this technique towards the extreme ultraviolet (XUV) or even x-ray regimes holds the promise to uncover rich structural or dynamical information with even higher spatial or temporal resolution. Here, we demonstrate noncollinear wave mixing between weak XUV attosecond pulses and a strong near-infrared (NIR) few-cycle laser pulse in gas phase atoms (one photon of XUV and two photons of NIR). In the noncollinear geometry the attosecond and either one or two NIR pulses interact with argon atoms. Nonlinear XUV signals are generated in a spatially resolved fashion as required by phase matching. Different transition pathways can be identified from these background-free nonlinear signals according to the specific phase-matching conditions. Time-resolved measurements of the spatially gated XUV signals reveal electronic coherences of Rydberg wave packets prepared by a single XUV photon or XUV-NIR two-photon excitation, depending on the applied pulse sequences. These measurements open possible applications of tabletop multidimensional spectroscopy to the study of dynamics associated with valence or core excitation with XUV photons.

We consider the ground-state properties of an extended one-dimensional Bose gas with pointwise attractive interactions. We take the limit where the interaction strength goes to zero as the system size increases at fixed particle density. In this limit, the gas exhibits a quantum phase transition. We compute local correlation functions at zero temperature, both at finite and infinite size. We provide analytic formulas for the experimentally relevant one-point functions $g_2,g_3$ and analyze their finite-size corrections. Our results are compared to the mean-field approach based on the Gross-Pitaevskii equation which yields the exact results in the infinite system size limit, but not for finite systems.

The possible use of high-resolution rovibrational spectroscopy of the hydrogen molecular ions ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$ for an independent determination of several fundamental constants is analyzed. While these molecules had been proposed for the metrology of nuclear-to-electron mass ratios, we show that they are also sensitive to the radii of the proton and deuteron and to the Rydberg constant at the level of the current discrepancies colloquially known as the proton size puzzle. The required level of accuracy, in the ${10}^{-12}$ range, can be reached both by experiments, using Doppler-free two-photon spectroscopy schemes, and by theoretical predictions. It is shown how the measurement of several well-chosen rovibrational transitions may shed light on the proton-radius puzzle, provide an alternative accurate determination of the Rydberg constant, and yield significantly more precise values of the proton-to-electron and deuteron-to-proton mass ratios.