We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-$\frac{1}{2}$ fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact $\text{SO}(3,2)$ algebra. The degeneracy of the physical spectrum only involves an infinite, so-called singleton representation. In the branch where orbital and spin angular momentum are aligned, the full representation appears, constituting a three-dimensional analog of Landau levels. Antialigning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem.

Imperfect devices in commercial quantum key distribution systems open security loopholes that an eavesdropper may exploit. An example of one such imperfection is the wavelength-dependent coupling ratio of the fiber beam splitter. Utilizing this loophole, the eavesdropper can vary the transmittances of the fiber beam splitter at the receiver's side by inserting lights with wavelengths different from what is normally used. Here, we propose a wavelength attack on a practical continuous-variable quantum key distribution system using homodyne detection. By inserting light pulses at different wavelengths, this attack allows the eavesdropper to bias the shot-noise estimation even if it is done in real time. Based on experimental data, we discuss the feasibility of this attack and suggest a prevention scheme by improving the previously proposed countermeasures.

We report the production of ${}^{87}\mathrm{RbCs}$ Feshbach molecules in a crossed-beam dipole trap. A mixture of ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ is cooled close to quantum degeneracy before an interspecies Feshbach resonance at 197 G is used to associate up to $\sim 5000$ molecules with a temperature of $\sim 300$ nK. The molecules are confined in the dipole trap with a lifetime of 0.21(1) s, long enough for future experiments exploring optical transfer to the absolute ground state. We have measured the magnetic moment of the Feshbach molecules in a magnetic bias field range between 181 and 185 G to demonstrate the ability to control the character of the molecular state. In addition, we have performed Feshbach spectroscopy in a field range from 0 to 1200 G and located three previously unobserved resonances at high magnetic fields.

We have analyzed the angular distributions of the photoelectrons emitted upon photoionization of rare gases by a comb of harmonics in the extreme ultraviolet range, in the presence of a “dressing” infrared (IR) field with controlled delay $\tau$, stabilized down to about $\pm 60$ as. The measurements have been performed with the help of the coincidence momentum imaging technique. We evidence marked differences in the measured angular distributions of the photoelectrons, depending on the number of IR photons exchanged. Joined to a theoretical interpretation, these observations bring new insights into the dynamics of this class of two-color photoionization processes that are a key step towards studying photoionization in the time domain, with attosecond time resolution.

We propose a scheme of feed-forward control and its reversal for protecting quantum state against decoherence. Before the noise channel our pre-weak measurement and feed-forward are simply to change the protected state into the state almost immune to the noise channel, and after the channel our reversed operations and post-weak measurements are simply to restore the protected state. Unlike most previous state protection schemes, ours only concerns the noise channel and does not care about the protected state. We show that our scheme can effectively protect unknown states, nonorthogonal states, and entangled states against amplitude damping noise. Our scheme has the merit of protecting quantum states against heavy amplitude damping noise, and can perfectly protect some specific nonorthogonal states in an almost deterministic way, which might find some applications in current quantum communication technology. And it is most important that our scheme is experimentally available with current technology.

A variational $R$-matrix approach combined with multichannel quantum defect theory is used for a computational study of triplet gerade states of H${}_2$. Electron-ion reaction (quantum defect) matrices are calculated as functions of internuclear distance and energy for the bound and continuum ranges including singly and doubly excited configurations built on the $1{\sigma }_g$ ($X^{+}{}^2{\Sigma }_g{}^{+}$) and $1{\sigma }_u$ ($A^{+}{}^2{\Sigma }_u{}^{+}$) core states of the H${}_2{}^{+}$ ion. It is shown how these matrices can be reduced to effective quantum defect functions adapted to the analysis of high-resolution spectra in the bound range. These $R$-matrix effective quantum defects are finally adjusted to the available experimental data [Sprecher et al., J. Phys. Chem. A 117, 9462 (2013)], producing agreement with experiment to within $0.5$ cm${}^{-1}$, nearly as good as obtained by Sprecher et al. In addition, the $R$-matrix calculations predict the evolution of the quantum defects for higher energies, in a range extending far into the electronic continuum.

Based on the results of numerical simulations we study scattering effects in single and double photoionization of the helium dimer. To this end we use a planar two-active-electron model of the helium dimer and abridged Hamiltonians in which different interactions between the electrons and the laser field and/or between the charged particles are removed from the full Hamiltonian. By comparing photoelectron angular distributions obtained in respective numerical simulations we are able to identify the role of the Coulomb interactions between the electrons and between the electrons and the nuclei for the primary as well as the knock-off electron in the processes.

We generalize the concept of population for non-Hermitian systems in different ways and identify the one best suited to characterize adiabaticity. An approximate adiabaticity criterion consistent with this choice is also worked out. Examples are provided for different processes involving two-level atoms with decay.

We demonstrate cooling of the motion of a single neutral atom confined by a dipole trap inside a high-finesse optical resonator. Cooling of the vibrational motion results from electromagnetically induced transparency (EIT)–like interference in an atomic $\Lambda$-type configuration, where one transition is strongly coupled to the cavity mode and the other is driven by an external control laser. Good qualitative agreement with the theoretical predictions is found for the explored parameter ranges. Further, we demonstrate EIT cooling of atoms in the dipole trap in free space, reaching the ground state of axial motion. By means of a direct comparison with the cooling inside the resonator, the role of the cavity becomes evident by an additional cooling resonance. These results pave the way towards a controlled interaction among atomic, photonic, and mechanical degrees of freedom.

Topological objects can influence each other if the underlying homotopy groups are non-Abelian. Under such circumstances, the topological charge of each individual object is no longer a conserved quantity and can be transformed to each other. Yet we can identify the conservation law by considering the backaction of topological influence. We develop a general theory of topological influence and backaction based on the commutators of the underlying homotopy groups. In the case of the topological influence of a half-quantum vortex on a point defect, we point out that the topological backaction from the point defect is a twisting of the vortex. The total twist of the vortex line compensates for the change in the point-defect charge to conserve the total charge. We use this theory to classify charge transfers in condensed matter systems and show that a non-Abelian charge transfer can be realized in a spin-2 Bose-Einstein condensate.

We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A 87, 033814 (2013)]. For a range of the nonlinear interaction strength about a special value, degeneracies or near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity loss, gives rise to an essentially closed cycle of excitations and photon emissions within these subspaces. Consequently, the cavity output field is strongly antibunched, while over this range of nonlinear strengths the atomic population undergoes an abrupt inversion. We develop a quantum-trajectory-based description of the system that models its key properties very well, and use a simple dressed-state picture to explain the novel structure of the cavity fluorescence spectrum. We also present numerical results for a potential realization of the system using a rubidium atom coupled strongly to a high-finesse optical cavity mode.

We study the nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semiclassical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semiclassical density of states; one static ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semiclassical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semiclassical results describe very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore, the semiclassical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

The nonintegrable Dicke model and its integrable approximation, the Tavis-Cummings model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the previous paper by focusing on the statistical properties of the quantum fluctuations in the energy spectrum and their relation with the excited-state quantum phase transitions. These properties are compared with the dynamics observed in the semiclassical versions of the models. The presence of chaos for different energies and coupling constants is exhibited, employing Poincaré sections and Peres lattices in the classical and quantum versions, respectively. A clear correspondence between the classical and quantum result is found for systems containing between $\mathcal{N}=80$ and 200 atoms. A measure of the Wigner character of the energy spectrum for different couplings and energy intervals is also presented employing the statistical Anderson-Darling test. It is found that in the Dicke model, for any coupling, a low-energy regime with regular states is always present. The richness of the onset of chaos is discussed both for finite quantum systems and for the semiclassical limit, which is exact when the number of atoms in the system tends to infinite.

This paper shows how one can reconstruct an unknown $n$-qubit state by only a single apparatus. Its core is a redistribution of the information within an extended Hilbert space by coupling the unknown system with an assistant system through only a pairwise interaction, which results in a one-to-one mapping between the unknown density matrix elements and the probabilities of the occurrence of the eigenvalues of a single, factorized observable of the composite system. In such an interaction configuration, which is more feasible in experiments, the quality of the measurement only depends on that of the subsystem consisting a of one-qubit system coupled to a one-qubit assistant. We analyze in detail the performance of this procedure and experimentally implement it for reconstructing an unknown two-qubit state using a four-nuclear-spin system.

Several approaches to the semiclassical dynamics of fermions have been proposed in the past. The main subject under discussion was the inclusion of the Pauli principle, i.e., the fact that two electrons with parallel spins must be in orthogonal states. In the past, this was sometimes achieved by adding repulsive Pauli potentials or by using antisymmetric trial states. In this article we show that (a) the use of semiclassical propagators based on classical trajectories is sufficient to account for the Pauli principle, but (b) a semiclassical wave-function approach is not satisfactory.

We consider an implementation of a two-qubit entangling gate between trapped ions controlled by fully overlapping laser pulses. We particularly address the role of a relative phase between the pulses in the gate design. Though, in general, the relative phase determines the exact form of the two-qubit operation, it is shown that it affects only its single qubit part and has no effect on its entangling content. Based on a general canonical decomposition of the evolution operator we demonstrate that the controlled-not (cnot) gate can be decomposed in terms of a two-qubit entangled gate and single qubit phase gates. Our study shows that any relative phase errors in two-qubit operations related to phase fluctuations of the external fields can be successfully corrected locally by single-qubit operations, which are usually easy to implement.

In this paper, we propose a quantum key distribution (QKD) protocol based on only a two-dimensional Hilbert space encoding a quantum system and independent devices between the equipment for state preparation and measurement. Our protocol is inspired by the fully device-independent quantum key distribution (FDI-QKD) protocol and the measurement-device-independent quantum key distribution (MDI-QKD) protocol. Our protocol only requires the state to be prepared in the two-dimensional Hilbert space, which weakens the state preparation assumption in the original MDI-QKD protocol. More interestingly, our protocol can overcome the detection loophole problem in the FDI-QKD protocol, which greatly limits the application of FDI-QKD. Hence our protocol can be implemented with practical optical components.

The influence of inner electrons on the ionization dynamics in strong laser fields is investigated in a wavelength regime where the inner electron dynamics is usually assumed to be negligible. The role of inner electrons is of particular interest for the application of frozen-core approximations and pseudopotentials in time-dependent density functional theory (TDDFT) and the single-active-electron (SAE) approximation in strong-field laser physics. Results of TDDFT and SAE calculations are compared with exact ones obtained by the numerical ab initio solution of the three-electron time-dependent Schrödinger equation for a lithium model atom. It is found that dynamical antiscreening, i.e., a particular form of dynamical core polarization, may substantially alter the ionization rate in the single-photon regime. Requirements for the validity of the approximations in the single and multiphoton ionization domain are identified.

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\delta$-interacting repulsive bosons. By using a recently proposed variational method, we here obtain the exact nonthermal steady state of the system in the thermodynamic limit and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a standard implementation of the generalized Gibbs ensemble fails.