Nonlinear and nonlocal effects are discussed in the interaction of laser fields with thermal Rydberg atoms in an electromagnetically induced transparency configuration. We assume that the system's steady state adiabatically follows the time variation in the dipole-dipole interactions due to the atomic motion and use a continuum description for the atomic medium. Based on these approximations, we obtain an analytical form for the nonlocal nonlinear atomic response of the thermal medium and study it for different parameter cases. We further propose a generalized model to describe the modulational instability (MI) in absorptive nonlinear media, in order to understand the propagation dynamics in the thermal Rydberg medium. Interestingly, this model predicts that at short propagation distances, each wave component exhibits the MI effect in absorptive nonlinear media, unlike in the purely dispersive case.

We report observation of anomalous fluorescence spectral features in the environs of a two-photon transition in a rubidium vapor when excited with two different wavelength lasers that are both counterpropagating through the vapor. These features are characterized by an unusual trade-off between the detunings of the driving fields. Three different hypothetical processes are presented to explain the observed spectra: a simultaneous three-atom and four-photon collision, a four-photon excitation involving a light field produced via amplified spontaneous emission, and population pumping perturbing the expected steady-state spectra. Numerical modeling of each hypothetical process is presented, supporting the population pumping process as the most plausible mechanism.

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY $\text{spin-}\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady-state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectory simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.

Among the many facets of quantum correlations, bound entanglement has remained one the most enigmatic phenomena, despite the fact that it was discovered in the early days of quantum information. Even its detection has proven to be difficult, let alone its precise quantitative characterization. In this work, we present the exact quantification of entanglement for a two-parameter family of highly symmetric two-qutrit mixed states, which contains a sizable part of bound entangled states. We achieve this by explicitly calculating the convex-roof extensions of the linear entropy as well as the concurrence for every state within the family. Our results provide a benchmark for future quantitative studies of bipartite entanglement in higher-dimensional systems.

Kapitza-Dirac scattering of nonrelativistic electrons from counterpropagating bichromatic laser waves of linear polarization is studied. The focus lies on the electronic spin dynamics in the Bragg regime when the laser fields possess a frequency ratio of 2. To this end, the time-dependent Pauli equation is solved numerically, both in coordinate space and momentum space. Our numerical results are corroborated by analytical derivations. We demonstrate that, for certain incident electron momenta, the scattering crucially relies on the electron spin which undergoes characteristic Rabi-like oscillations. A parameter regime is identified where the Rabi oscillations reach maximum amplitude. We also briefly discuss spin-dependent Kapitza-Dirac scattering of protons.

By presenting the evolution of a quantum state with the trajectories of the Majorana stars on the Bloch sphere, the Majorana's stellar provides an intuitive geometric picture to study a quantum system with high-dimensional Hilbert space. We study the Berry phase and quantum entanglement by distributions and motions of these stars on the Bloch sphere. It is shown that both of these unique characters of quantum state can be perfectly represented by the Majorana stars. The former is expressed by the solid angles of Majorana star loops and the distance between stars. For the latter, the distances between stars are also found to be a tool for measuring and classifying the multiparticle entanglement of a symmetric multiqubit pure state. To demonstrate our theory, we study a typical spin model which is equivalent to an interacting boson model or an interacting multiqubit system. The self-trapping phenomenon within is also discussed via the Majorana stars.

We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnot${}^N$ gate on $N+1$ hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.

Quantities invariant under local unitary transformations are of natural interest in the study of entanglement. This paper deduces and studies a particularly simple quantity that is constructed from a combination of two standard permutations of the density matrix, namely, realignment and partial transpose. This bipartite quantity, denoted here as $R_{12}$, vanishes on large classes of separable states including classical-quantum correlated states, while being maximum for only maximally entangled states. It is shown to be naturally related to the 3-tangle in three-qubit states via their two-qubit reduced density matrices. Upper and lower bounds on concurrence and negativity of two-qubit density matrices for all ranks are given in terms of $R_{12}$. Ansatz states satisfying these bounds are given and verified using various numerical methods. In the rank-2 case, it is shown that the states satisfying the lower bound on $R_{12}$ versus concurrence define a class of three-qubit states that maximize the tripartite entanglement (the 3-tangle) given an amount of entanglement between a pair of them. The measure $R_{12}$ is conjectured, via numerical sampling, to be always larger than the concurrence and negativity. In particular, this is shown to be true for the physically interesting case of $X$ states.

We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons ($A$) and one distinguishable particle ($B$). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, $\mathcal{A}=m_B/m_A$, between particles $B$ and $A$ are varied from 0.01 to 100, providing a number of bound states decreasing from 8 to 2. Energies and mean-square radii of these states are analyzed for small $\mathcal{A}$ by use of the Born-Oppenheimer potential between the two heavy $A$ particles. For large $\mathcal{A}$ the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When $\mathcal{A}$ approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound $AB$ dimers and one loosely bound $A$ particle.

We completed a measurement of the Stark shift within the ${}^{115}\mathrm{In}6s_{1/2}\to 6p_{1/2}$ excited-state transition using two-step laser spectroscopy in an indium atomic beam. By combining this measurement with recent experimental results we determine the scalar polarizability ${\alpha }_0$ of the $6p_{1/2}$ state to be $7683\pm 43a_0^3$ (in atomic units), a result which agrees very well with recent theoretical calculations. In this experiment, one laser, stabilized to the $5p_{1/2}\to 6s_{1/2}410$ nm transition, was directed transversely to the atomic beam, while a second, overlapping laser was scanned across the 1343 nm $6s_{1/2}\to 6p_{1/2}$ transition. We utilized two-tone frequency-modulation spectroscopy of the infrared laser beam to measure the second-step absorption in the interaction region, where the optical depth is less than ${10}^{-3}$. In the course of our experimental work we also determined the hyperfine splitting within the $6p_{1/2}$ state, improving upon the precision of an existing measurement.

Variational ab initio $R$-matrix theory combined with generalized multichannel quantum defect theory is used to calculate singly excited Rydberg states of the hydrohelium molecular ion, ${\mathrm{HeH}}^{+}$, for ${}^{1,3}\mathrm{\Sigma }^{+},{}^{1,3}\mathrm{\Pi },{}^{1,3}\mathrm{\Delta },{}^{1,3}\mathrm{\Phi }$, and ${}^{1,3}\mathrm{\Gamma }$ symmetry. Bound levels are calculated for $n$ values up to $n\approx 10$, and continuum states up to $\approx 3$ eV above the ${\mathrm{HeH}}^{2+}$ threshold. The calculations span the range of internuclear distances $R$ from 1 to 5 bohrs. The present work follows a preliminary study on the ${}^{1,3}\mathrm{\Delta }$ states of ${\mathrm{HeH}}^{+}$ [Bouhali, Bezzaouia, Telmini, and Jungen, EPJ Web Conf. 84, 04004 (2015)] which was also based on $R$-matrix theory. Further—although limited to rather small $R$ values—the present work extends the recent ab initio computations of Jungen and Jungen [Mol. Phys. 113, 2333 (2015)] to higher excitation energies which are not accessible to standard quantum-chemical methods. Where a comparison with the calculations of Jungen and Jungen and other older results can be made, namely for $n\le 5$, very good agreement with previous ab initio results is obtained.

We study few-cycle, strong-field dissociation of aligned ${\mathrm{H}}_2^{+}$ by solving the time-dependent Schrödinger equation including rotation. We examine the dependence of the final angular distribution, the kinetic energy release spectrum, and the total dissociation yield on the initial nuclear angular distribution. In particular, we look at the dependence on the relative angle ${\theta }_0$ between the laser polarization and the symmetry axis of a well-aligned initial distribution, as well as the dependence on the delay between the “pump” pulse that prepares the alignment and the few-cycle probe pulse. Surprisingly, we find the dissociation probability for ${\theta }_0={90}^{\circ }$ can be appreciable even though the transitions involved are purely parallel. We therefore address the limits of the commonly held “ball-and-stick” picture for molecules in intense fields as well as the validity of the axial recoil approximation.

We show how robust statistical features of a many-particle quantum state's two-point correlations after transmission through a multimode random scatterer can be used as a sensitive probe of the injected particles' mutual indistinguishability. This generalizes Hong-Ou-Mandel interference as a diagnostic tool for many-particle transmission signals across multimode random scatterers. Furthermore, we show how, from such statistical features of the many-particle interference pattern, information can be deduced on the temporal structure of the many-particle input state, by inspection of the many-particle interference with an additional probe particle of tunable distinguishability.

We propose and demonstrate a method for quantum-state tomography of qudits encoded in the quantum polarization of $N$-photon states. This is achieved by distributing $N$ photons nondeterministically into three paths and their subsequent projection, which for $N=1$ is equivalent to measuring the Stokes (or Pauli) operators. The statistics of the recorded $N$-fold coincidences determines the unknown $N$-photon polarization state uniquely. The proposed, fixed setup manifestly rules out any systematic measurement errors due to moving components and allows for simple switching between tomography of different states, which makes it ideal for adaptive tomography schemes.

An essential element of classical computation is the “if-then” construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand, quantum theory prevents the existence of an analogous universal construct accepting a control qubit and an arbitrary quantum gate as its input. Nevertheless, there are controllable sets of quantum gates for which such a construct exists. Here we provide a necessary and sufficient condition for a set of unitary transformations to be controllable, and we give a complete characterization of controllable sets in the two-dimensional case. This result reveals an interesting connection between the problem of controllability and the problem of extracting information from an unknown quantum gate while using it.

We introduce a model of a non-Gaussian quantum channel that stems from the composition of two physically relevant processes occurring in open quantum systems, namely, amplitude damping and dephasing. For it we find input states approaching zero output entropy while respecting the input energy constraint. These states fully exploit the infinite dimensionality of the Hilbert space. Upon truncation of the latter, the minimum output entropy remains finite, and optimal input states for such a case are conjectured thanks to numerical evidence.

We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least-squares optimization. In contrast to related previous contributions suffering from the problem of reading out the optimal parameters of the fit, our scheme focuses on the machine-learning task of guessing the output corresponding to a new input given examples of data points. Furthermore, we adapt the algorithm to process nonsparse data matrices that can be represented by low-rank approximations, and significantly improve the dependency on its condition number. The prediction result can be accessed through a single-qubit measurement or used for further quantum information processing routines. The algorithm's runtime is logarithmic in the dimension of the input space provided the data is given as quantum information as an input to the routine.

The antihydrogen formation by charge exchange between cold antiprotons and Rydberg positronium ${\text{P}}_s^{*}$ is studied by using the classical trajectory Monte Carlo method. In the absence of external magnetic field the cross section scaled by the fourth power of the ${\text{P}}_s^{*}$ principal quantum number $n_{{\text{P}}_s}$ shows a universal behavior as a function of the ratio $k_v$ between the velocity of the ${\text{P}}_s$ center of mass and that of the positron in the classical circular orbit. At low velocity, below about $k_v\simeq 0.2–0.3$, we show for Rydberg positronium that the cross section increases as $1/k_v^2$ or, in an equivalent way, as $1/E_{{\text{P}}_s}^{\text{cm}}$ with $E_{{\text{P}}_s}^{\text{cm}}$ being the ${\text{P}}_s^{*}$ center-of-mass energy. In this regime the distribution of the principal quantum number of the antihydrogen state is narrow and it shows a peak at about $\sqrt{2}{n}_{{\text{P}}_s}$ while at higher $k_v$ values a broad distribution of antihydrogen states is produced. The study of the collision process in the presence of moderate magnetic field (0.5–2 T) shows that there is an experimentally interesting region of $k_v$ with the cross section slightly higher than that in the absence of field. However the presence of a magnetic field changes significantly the cross section behavior as a function of $k_v$, especially at low velocities, where reductions of the cross sections and deviations from the $1/k_v^2$ ($1/E_{{\text{P}}_s}^{\text{cm}}$) are observed. Our calculations show a dependance of the cross section upon the angle between the magnetic field and the flight direction of the incoming ${\text{P}}_s^{*}$.

This paper presents a full three-dimensional (3D) comparison between experiment and theory for 24 MeV ${\mathrm{O}}^{8+}$ single ionization of the $2s$ ground state of lithium and the $2p$ excited state. Two theoretical approximations are examined: the three-body continuum distorted-wave (3DW) and three-body continuum distorted-wave–eikonal initial state (3DW-EIS). Normally, there is a significant difference between these two approaches and the 3DW-EIS is in much better agreement with experiment. In this case, there is very little difference between the two approaches and both are in very good agreement with experiment. For the excited $2p$ state, the 3D cross sections would exhibit a mirror symmetry about the scattering plane if all three magnetic sublevels were excited in equal proportions. For the present experiment, the $2p_{+1}(m=+1)$ sublevel is dominantly excited (quantization axis is the incident beam direction) and for this case there is a magnetic dichroism which is observed both experimentally and theoretically.