We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single-photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the average fidelity between the expected and reconstructed states is computed for qubits, qutrits, and entangled qubits.

The largest hyperfine interaction coefficients in the hydrogen molecular ion ${\mathrm{HD}}^{+}$, i.e., the electron-proton and electron-deuteron spin-spin scalar interactions, are calculated with estimated uncertainties slightly below 1 ppm. The ${\left(Z\alpha \right)}^2{E}_F$ relativistic correction for which a detailed derivation is presented, QED corrections up to the order ${\alpha }^3{ln}^2\left(\alpha \right)$ along with an estimate of higher-order terms, and nuclear structure corrections are taken into account. Improved results are also given for the electron-proton interaction coefficient in ${\mathrm{H}}_2^{+}$, in excellent agreement with rf spectroscopy experiments. In ${\mathrm{HD}}^{+}$, a $4\sigma$ difference is found in the hyperfine splitting of the $(v,L)=(0,3)\to (9,3)$ two-photon transition that was recently measured with high precision. The origin of this discrepancy is unknown.

We present a theoretical study of temporal, spectral, and spatial reshaping of intense, ultrafast x-ray pulses propagating through a resonant medium. Our calculations are based on the solution of a three-dimensional time-dependent Schrödinger-Maxwell equation, with the incident x-ray photon energy on resonance with the core-level $1s\text{−}3p$ transition in neon. We study the evolution of the combined incident and medium-generated field, including the effects of stimulated emission, absorption, ionization, and Auger decay, as a function of the input pulse energy and duration. We find that stimulated Raman scattering between core-excited states $1s^{-1}3p$ and $2p^{-1}3p$ occurs at high x-ray intensity, and that the emission around this frequency is strongly enhanced when also including the similar $1s^{-1}\text{−}2p^{-1}$ response of the ion. We also explore the dependence of x-ray self-induced transparency (SIT) and self-focusing on the pulse intensity and duration, and we find that the stimulated Raman scattering plays an important role in both effects. Finally, we discuss how these nonlinear effects may potentially be exploited as control parameters for pulse properties of x-ray free-electron laser sources.

We investigate theoretically the imprints of light-induced potentials (LIPs) on the dissociation dynamics of ${\mathrm{O}}_2{}^{+}$ molecular ions, as observable in angle-resolved fragment kinetic-energy-release (KER) spectra. Following the vibrational and rotational dynamics of the initial pump-laser-excited cationic nuclear wave packet, while accounting for the dipole coupling between the ${\mathrm{O}}_2{}^{+}\left(a{}^4{\mathrm{\Pi }}_u\right)$ and ${\mathrm{O}}_2{}^{+}\left(f{}^4{\mathrm{\Pi }}_g\right)$ electronic states in 800-nm 40-fs probe-laser pulses with peak intensities between ${10}^{13}$ and ${10}^{14} \mathrm{W}/{\mathrm{cm}}^2$, we calculate angle-resolved KER spectra which reveal characteristic energy- and angle-dependent fringe structures. These fringes shift downward in energy as the molecular alignment angle $\theta$ relative to the probe-pulse polarization direction increases from 0 to $\pi /2$. The angle-dependent shifts in the KER fringes increase for larger probe-pulse peak intensities and follow the angle and light-wave-intensity dependence of the vibrational spectrum in the associated Floquet bond-hardening well, which is a manifestation of transient ${\mathrm{O}}_2{}^{+}$ nuclear-probability trapping in the LIP during dissociation. By examining the rovibrational dynamics of the dissociating molecular cation near the light-induced conical intersection (LICI) in the cationic LIP surface at $\theta =\pi /2$, we identify related angle-dependent structures in the KER spectra, suggesting a means for assessing the significance of LICIs in molecular dissociation pathways.

Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. We introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman transitions can be understood as a special case. We also show that the SG interferometer can keep high contrast against a misalignment in position and momentum caused by the field gradient.

We study the stationary and nonstationary measurement of a classical force driving a mechanical oscillator coupled to an electromagnetic cavity under two-tone driving. For this purpose, we develop a theoretical framework based on the signal-to-noise ratio to quantify the sensitivity of linear spectral measurements. Then we consider stationary force sensing and study the necessary conditions to minimize the added force noise. We find that imprecision noise and back-action noise can be arbitrarily suppressed by manipulating the amplitudes of the input coherent fields; however, the force noise power spectral density cannot be reduced below the level of thermal fluctuations. Therefore, we consider a nonstationary protocol that involves nonthermal dissipative state preparation followed by a finite time measurement, which allows one to perform measurements with a signal-to-noise ratio much greater than the maximum possible in a stationary measurement scenario. We analyze two different measurement schemes in the nonstationary transient regime: a back-action-evading measurement, which implies modifying the drive asymmetry configuration upon arrival of the force, and a nonstationary measurement that leaves the drive asymmetry configuration unchanged. Conditions for optimal force noise sensitivity are determined, and the corresponding force noise power spectral densities are calculated.

The Hartmann-Hahn technique allows sensitivity enhancement of magnetic resonance imaging and spectroscopy by coupling the spins under study to another spin species that is externally driven. Here we theoretically study the coupled spins' dynamics and find that for a certain region of driving parameters the system becomes unstable. The required conditions for making this region of instability becoming experimentally accessible are discussed.

Superconducting cavities with high quality factors play an essential role in circuit quantum electrodynamics and quantum computing. In measurements of the intrinsic loss rates of high frequency modes, it can be challenging to design an appropriate coupling to the measurement circuit in such a way that the resulting signal is sufficiently strong but also that this coupling does not lead to an unwanted loading circuit, obscuring the intrinsic internal loss rates. Here, we propose and demonstrate a spectroscopic probe of high-Q resonators based on the phenomena of electromagnetically induced transparency (EIT) between the resonator and qubit in the weak dispersive coupling regime. Applying a sideband drive signal to the qubit, we observe an interference dip originated from EIT in the qubit spectroscopy, originating from the quantum interference between the qubit probe signal and sideband transition. From the width and the depth of the dip, we are able to extract the single-photon linewidth of the resonator from an analytical model. Working in a previously unexplored regime in which the qubit has a larger linewidth than the resonator reduces the technical challenge of making a high-coherence qubit and is advantageous for remaining in the weakly invasive limit of coupling to the resonator. Furthermore, the sideband and the dispersive coupling between the resonator and the qubit can be tuned $insitu$ controlling the strength of the sideband drive power. This in situ tuneability allows the technique to be applied for efficient measurement of the resonator loss rate for any quality factor below a fixed upper bound, on the order of ${10}^8$ for our device, allowing a wide range of quality factors to be probed using a single design.

Coherent states are normally used to describe the state of a laser field in experiments that generate and detect squeezed states of light. Nevertheless, since the laser field absolute phase is unknown, its quantum state can be described by a statistical mixture of coherent states with random phases, which is equivalent to a statistical mixture of Fock states. Here we describe single-mode squeezed vacuum experiments using this mixed quantum state for the laser field. Representing the laser state in the Fock basis, we predict the usual experimental results without using the squeezing concept in the analysis and concluding that no squeezed state is generated in the experiments. We provide a general physical explanation for the noise reduction in the experiments in terms of a better definition of the relative phase between the signal and local oscillator fields. This explanation is valid in any description of the laser field (in terms of coherent or Fock states), thus providing a deeper understanding of the phenomenon.

The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this Rapid Communication we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to the violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not only in quantum theory but in no-signaling theories as well.

We quantify the maximum amount of entanglement of formation (EoF) that can be achieved by continuous-variable states under passive operations, which we refer to as the EoF potential. Focusing, in particular, on two-mode Gaussian states we derive analytical expressions for the EoF potential for specific classes of states. For more general states, we demonstrate that this quantity can be upper bounded by the minimum amount of squeezing needed to synthesize the Gaussian modes, a quantity called squeezing of formation. Our work, thus, provides a link between nonclassicality of quantum states and the nonclassicality of correlations.

Canonical forms of two-qubits under the action of stochastic local operations and classical communications (SLOCC) offer great insight for understanding nonlocality and entanglement shared by them. They also enable geometric picture of two-qubit states within the Bloch ball. It has been shown [Phys. Rev. A 64, 010101(R) (2001)] that an arbitrary two-qubit state gets transformed under SLOCC into one of the two different canonical forms. One of these happens to be the Bell diagonal form of two-qubit states and the other a nondiagonal canonical form is obtained for a family of rank deficient two-qubit states. The method employed by Verstraete et al. [Phys. Rev. A 64, 010101(R) (2001)] required highly nontrivial results on matrix decompositions in $n$-dimensional spaces with an indefinite metric. Here we employ an entirely different approach—inspired by the methods developed by Rao et al. [J. Mod. Opt. 45, 955 (1998)] in classical polarization optics—which leads naturally towards the identification of two inequivalent SLOCC invariant canonical forms for two-qubit states. In addition, our approach results in a simple geometric visualization of two-qubit states in terms of their SLOCC canonical forms.

We present an experimental realization of a 16 element, temporal-array, photon-number-resolving (PNR) detector, which is a multiplexed single-photon detector that splits an input signal over multiple time bins, and the time bins are detected using two superconducting nanowire single-photon detectors (SNSPD). A theoretical investigation of the PNR capabilities of the detector is performed and it is concluded that, compared to a single-photon detector, our array detector can resolve one order of magnitude higher mean photon numbers, given the same number of input pulses to measure. This claim is experimentally verified and we show that the detector can accurately predict photon numbers between ${10}^{-3}$ and ${10}^2$. Our present detector is incapable of single-shot photon-number measurements with high precision since its effective quantum efficiency is $49\%$. Using SNSPDs with a higher quantum efficiency the PNR performance will improve, but the photon-number resolution will still be limited by the array size.

Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to reach quantum advantage in approximately solving the Unit-Disk Maximum Independent Set problem. Using noisy simulations of Rydberg platforms of up to 26 atoms interacting through realistic van der Waals interactions, we compute the average approximation ratio that can be attained with a simple quantum annealing-based heuristic within a fixed temporal computational budget. Based on estimates of the correlation lengths measured in the engineered quantum state, we extrapolate the results to large atom numbers and compare them to a simple classical approximation heuristic. We find that approximation ratios of at least $\approx 0.84$ are within reach for near-future noise levels. Not taking into account further classical and quantum algorithmic improvements, we estimate that quantum advantage could be reached by attaining a number of controlled atoms of $\sim 8000$ for a time budget of 2 s, and $\sim 1000–1200$ for a time budget of 0.2 s, provided the coherence levels of the system can be improved by a factor 10 while maintaining a constant repetition rate.

The ionization and dissociation of ammonia by impact of protons is investigated experimentally in a wide range of energies from 125 to 2700 keV. Coincidence measurements are used to separate single from multiple ionization. The role of the charge sign of the projectile was analyzed for the ionization by comparing the proton with previous electron data. The energy dependence of the single and multiple-ionization cross sections allowed us to evaluate the role of second-order mechanisms. For single ionization, the role of a two-step mechanism was inferred. The double-ionization cross section showed that postcollisional deexcitation takes over the two-step sequential ionization above 800 keV. Triple ionization is prompted mostly by postcollisional Auger decay.

The thermal electron-emission rate constant for ${\mathrm{C}}_{60}{}^{-}$ has been deduced for internal energies from 9.7 to 14.1 eV from storage ring measurements of the decays of ions reheated with single-photon absorption. The thermal radiation from the ions is quantified from the data with respect to continuous cooling and discrete photon quenching.

Relativistic and correlation effects in endohedrally confined atoms ($A@{\mathrm{C}}_{60}$) have been investigated using many-body techniques. The endohedral environment is approximated as an atom trapped in a spherically symmetric Gaussian annular square well model potential. The objective of the work is to present Shannon entropy as an indicator of (i) correlation effects and (ii) relativistic effects in confined atoms. The correlation energy in $\mathrm{Be}@{\mathrm{C}}_{60}$ is studied as a function of the depth of the confining potential to give some idea as to how Shannon's correlation entropy is sensitive to the minimum location of correlation energy. To see the prominent relativistic effects in the confined atom, Shannon's relativistic entropy of the valence subshell of $\mathrm{Ba}@{\mathrm{C}}_{60}$ is scrutinized for different confinement parameters. The influence of relativistic and correlation effects on the Shannon entropy of confined atoms is illustrated.

Impulsive laser excitation of molecules can create rotational wave packets that lead to transient alignment or orientation. We present a theoretical analysis of the signatures of post-pulse field-free time-dependent alignment and orientation of diatomic molecules in time-resolved nonresonant x-ray scattering. This shows that alignment and its time dependence due to the interference terms of the rotational wave packet are visible in the x-ray scattering signal whereas signatures of orientation and its time dependence are absent. To that end, we discuss the time dependence of the coherent rotational motion associated with electronically resonant one-photon excitations. We illustrate our findings with calculated two-dimensional scattering signals for the sodium fluoride molecule (NaF) in the gas phase.

The ab initio $R$-matrix with time method has recently been extended to allow simulation of fully nonperturbative multielectron processes in molecules driven by ultrashort arbitrarily polarized strong laser fields. Here we demonstrate the accuracy and capabilities of the current implementation of the method for two targets: We study single-photon and multiphoton ionization of ${\mathrm{H}}_2$ and one-photon and strong-field ionization of ${\mathrm{H}}_2\mathrm{O}$ and compare the results to available experimental and theoretical data as well as our own time-independent $R$-matrix calculations. We obtain a highly accurate description of total and state-to-state single-photon ionization of ${\mathrm{H}}_2\mathrm{O}$ and, using a simplified coupled-channel model, we show that state coupling is essential to obtain qualitatively correct results and that its importance as a function of laser intensity changes. We find that electron correlation plays a more important role at low intensities (up to approximately 50 $\text{TW}/{\mathrm{cm}}^2$).