The Lüders rule provides a way to define a quantum channel given a quantum measurement. Using this construction, we establish an if-and-only-if condition for the existence of a $d$-dimensional symmetric-informationally-complete quantum measurement (a SIC) in terms of a particular depolarizing channel. Moreover, the channel in question satisfies two entropic optimality criteria.

We report the first driving of the $7s{}^2{S}_{1/2}\to 6d{}^2{D}_{3/2}$ and $7s{}^2{S}_{1/2}\to 6d{}^2{D}_{5/2}$ electric quadrupole (E2) transitions in ${\mathrm{Ra}}^{+}$. We measure the frequencies of both E2 transitions and two other low-lying transitions in ${}^{226}\mathrm{Ra}^{+}$ that are important for controlling the radium ion's motional and internal states: $6d{}^2{D}_{3/2}\to 7p{}^2{P}_{3/2}^o$ and $6d{}^2{D}_{5/2}\to 7p{}^2{P}_{3/2}^o$.

Experimental determinations of the absolute differential positronium-formation cross sections near $0^{\circ }$ for Ne, Ar, Kr, and Xe are presented and compared with theory. The degree of forward collimation, expressed by the ratios of the differential-to-integral positronium-formation cross sections, is also computed and compared with theories and other targets. Trends among targets and structures at low energies emerge when considered as a function of the reduced total energy.

We study the subradiant collective states of a periodic chain of two-level atoms with either transversal or longitudinal transition dipole moments with respect to the chain axis. We show that long-lived subradiant states can be obtained for the transversal polarization by properly choosing the chain period for a given number of atoms in the case of no open diffraction channels. While not being robust against the positional disorder along the chain, these highly subradiant states have a linewidth that decreases with the number of atoms much faster than it was shown previously. In addition, our paper shows that similar states are present even if there are additional interaction channels between the atoms, i.e., they interact via the waveguide mode of an optical nanofiber, for instance. We develop a theoretical framework allowing us to describe the spectral properties of the system in terms of contributions from each collective eigenstate and we show that subradiant states manifest themselves in the transmission and reflection spectra, allowing us to observe interaction-induced transparency in a very narrow spectral range. Such long-lived collective states may find potential applications in nanophotonics and quantum optics.

We propose a flexible manipulation on the Goos-Hänchen shift (GHS) via a cavity optomechanical system driven by an external coherent control field and reveal the behavior of the GHS as a result of light-matter interaction. It is achievable for both positive and negative GHSs in our system by tuning the coherent control field strength. The positive shift can flexibly be tuned to a negative shift by changing the cavity length. Furthermore, the control field can be used as a knob to turn the optical cavity on and off for manipulating the GHSs. A devastating suppression of the GHS can be observed due to weaker interaction between the cavity photons and the mechanical resonator by increasing the cavity decay rate. The results have potential applications in light-light manipulation via cavity optomechanical systems.

A two-level quantum emitter interacting with a cavity field is an important model for investigating the photon blockade (PB) effect. Most work on this topic relies on the assumption that the emitter transition frequency is resonant with the fundamental mode frequency of the cavity. In this work we relax this constraint and reexamine the PB effect in a more general emitter-cavity system with arbitrary emitter and cavity detunings from a driving field. The results show that when the signs of the emitter and cavity detunings are the same, a PB occurs only in the strong-coupling regime, but for opposite signs of the emitter and cavity detunings, strong photon antibunching is observed in both the weak- and strong-coupling regimes, and better antibunching is achieved compared with the case when the signs are the same. More interestingly, we find that this PB arises from quantum interference for both weak and strong nonlinearities. These results deepen our understanding of the underlying mechanism of PBs and may contribute to the construction of single-photon sources with higher purity and better flexibility using two-level emitter-cavity systems.

We theoretically study the Talbot effect resulting from Raman-induced grating based on periodic spatial modulation of the Raman gain and dispersion in the field of a standing pump wave. Features of integer and fractional Talbot effects are demonstrated for one- and two-dimensional (1D and 2D) Raman-induced gratings. It is shown that the intensity of diffraction images can increase due to Raman amplification in the grating. Glass-shaped diffraction patterns are demonstrated for 2D gratings. It is also shown that in the vicinity of the Talbot planes there are planes in which the diffraction patterns are spatially compressed and the intensity becomes greater. The results expand the possibility of using the Talbot effect in various applications.

We discuss a protocol for the analog quantum simulation of superradiance and subradiance using a linear chain of $N$ trapped qubit ions with a single sympathetic cooling ion. We develop a simple analytic model that shows the dynamics of the qubit subspace converge to those of a cloud undergoing Dicke superradiance and subradiance. We provide numerical simulations of the full ion chain and show that they converge to the dynamics predicted by our analytic model with no fitting parameters. We also map out the parameter regime needed to reach this convergence.

We use the linear programming algorithm introduced by Akulin et al. [V. M. Akulin, G. A. Kabatiansky, and A. Mandilara, Phys. Rev. A 92, 042322 (2015)] to perform best separable approximation on two-qutrit random density matrices. We combine the numerical results with theoretical methods in order to generate random representative families of positive partial transposed bound entangled (BE) states and analyze their properties. Our results disclose that for the two-qutrit system the BE states have negligible volume and that these form tiny “islands” sporadically distributed over the surface of the polytope of separable states. The detected families of BE states are found to be located under a layer of pseudo-one-copy undistillable negative partial transposed states with the latter covering the vast majority of the surface of the separable polytope.

The bosonic system possessing the identical real-space form as a fermionic Kitaev model usually exhibits the trivial topology since bosonic operators conform to the bosonic commutation relation. However, a nontrivial bosonic Kitaev phase can also emerge under some certain conditions. Here we propose a scheme to induce a topologically nontrivial bosonic Kitaev phase based on a frequency-modulated one-dimensional optomechanical array. We find that the bosonic Kitaev model with pure imaginary tunneling amplitudes induced by effective optomechanical coupling can be mapped into a subspace expanded by two Hermitian quadrature operators in which the bosonic system possesses two isolated analogous Majorana modes. The isolated analogous modes imply that the proposed bosonic Kitaev system possesses a topologically nontrivial phase. Furthermore, we investigate the effects of the modulated partial next-nearest-neighbor (NNN) hopping on the topology of the system, in which the system exhibits distinct topological behavior under different parameter regimes. In particular, the bosonic Kitaev system experiences completely different phase-transition processes with the change of real partial NNN hopping corresponding to an even and odd number of lattice sites. Our scheme provides a flexible and controllable platform to investigate bosonic Kitaev phases and phase transitions both in theory and experiment.

We propose an efficient scheme for implementing the universal controlled-phase gate with logical qubits encoded in the superpositions of $2d$ circularly distributed coherent states ($d$ is a positive integer), which have the advantage of protecting quantum information against the $(d-1)$-photon loss errors. We first demonstrate explicitly how to engineer dispersive interaction between the microwave cavity modes and multilevel transmon ancilla in circuit quantum electro-dynamical (QED) system. With the cat-state qubits, we realize the two-qubit controlled phase gate, and its operation time scales as $1/d$. This means that it will be less susceptible to environmental disturbances if we employ larger $d$ to encode information. Finally, we employ the experimentally reachable parameters in circuit QED system to numerically study the influence of the photon loss, the qubit relaxation, and the Kerr nonlinearity. The average fidelity for a controlled-phase gate has reached 0.9955 for $d=8$ when the system imperfections are considered. The results demonstrate the great potential of our scheme for quantum computation in circuit QED system.

It was recently shown that continuous-time quantum walks on dynamic graphs, i.e., sequences of static graphs whose edges change at specific times, can implement a universal set of quantum gates. This result treated all isolated vertices as having self-loops, so they all evolved by a phase under the quantum walk. In this paper, we permit isolated vertices to be loopless or looped, and loopless isolated vertices do not evolve at all under the quantum walk. Using this distinction, we construct simpler dynamic graphs that implement the Pauli gates and a set of universal quantum gates consisting of the Hadamard, $T$, and controlled-not gates, and these gates are easily extended to multiqubit systems. For example, the $T$ gate is simplified from a sequence of six graphs to a single graph, and the number of vertices is reduced by a factor of 4. We also construct a generalized phase gate, of which $Z$, $S$, and $T$ are specific instances. Finally, we validate our implementations by numerically simulating a quantum circuit consisting of layers of one- and two-qubit gates, similar to those in recent quantum supremacy experiments, using a quantum walk.

Fully differential cross sections for single ionization of helium by fast proton impact in different kinematical regimes in the scattering plane were recently measured in a high-precision experiment [O. Chuluunbaatar et al., Phys. Rev. A 99, 062711 (2019)] and calculated using the first Born approximation. We use the nonperturbative wave-packet convergent close-coupling approach to calculate this process more accurately in all the kinematical regimes considered in the experiment. The obtained results show that the coupling between channels and multiple-scattering effects, combined with a more accurate treatment of the target structure, significantly improves the agreement between theory and experiment, especially in the apparently most difficult regions away from the so-called Bethe ridge, where the deviation in the positions of the binary peak observed in the experiment and calculated using the first Born approximation is largest. We also present fully differential cross sections in the same kinematical regimes but for incident projectile energies of 500 keV and 2 MeV. Corresponding results for the so-called perpendicular and azimuthal planes are also exhibited.

Dynamically rich nature of the high-order harmonic generation process lends itself to a variety of ways to increase photon yield and extend the harmonic cutoff frequency. We show here that high-harmonic generation from an atom confined inside an attractive potential shell can show a dramatic increase in the photon yield in certain cases. We consider an endohedrally confined hydrogen atom inside a ${\mathrm{C}}_{60}$ cage as an example, and consider three distinct physical situations in which the initial state is (1) entirely confined inside the ${\mathrm{C}}_{60}$, (2) partially outside, and (3) mainly localized on the cage wall. We demonstrate that when the atom-cage system starts in a state with a classical turning point outside the ${\mathrm{C}}_{60}$ shell, the high-harmonic photon yield can be enhanced up to 4 orders of magnitude when compared with a free atom in the same initial state. We explain the underlying physical mechanisms in each case using fully three-dimensional quantum simulations. This gives a prime example of how directly coupling an atom to a nanostructure can alter strong field processes in atoms in interesting ways.

We study both theoretically and experimentally the existence and stability of symmetry-protected topological chiral edge states in an all-photonic system mimicking Floquet dynamics of a discrete one-dimensional quantum walk in the presence of Kerr nonlinearity. The system is realized via time multiplexing as two fiber loops of slightly different lengths with a dynamically variable coupling strength. We prove that topological edge states persist in the nonlinear regime for moderate intensities, despite chiral symmetry breaking. Above a certain power threshold, they undergo destabilization, resulting in the radiation into the bulk modes. Finally, we show that the nonlinear interaction with bulk modes can serve as an effective pumping of the topological edge states.

From an effective field theory of electromagnetism in vacuum including all lowest-order nonlinear terms consistent with Lorentz invariance and locality of photon-photon interactions, we derive an effective-medium description of strong background fields as regards their influence on a weak probe. We mainly consider as background a pump beam with well-defined wave vector and polarization. This leads us to define a nonlinear index of vacuum which, in the Euler-Heisenberg model derived from QED, has an optimal value of $1.555\times {10}^{-33}{\mathrm{cm}}^2/\mathrm{W}$ for a linearly polarized pump as seen by a counterpropagating, orthogonally polarized probe. We further generalize the model to include coupling to an axion field. In the limit where the axion mass is much smaller than the typical photon energy, this yields dispersive corrections, and the axionic signature is found to be greatly enhanced for a circularly polarized pump as compared to a linearly polarized one. The formalism here presented points to a simplification of the DeLLight experiment [Sarazin et al., Eur. Phys. J. D 70, 13 (2016)] aiming to measure the deflection of a probe by a tightly focused laser pulse.

We describe a superconducting circuit consisting of a Josephson junction in parallel with a quantum phase slip wire, which implements a Hamiltonian that is periodic in both charge and flux. This Hamiltonian is exactly diagonalizable in a double-Bloch band, and the eigenstates are shown to be code states of the Gottesman-Kitaev-Preskill quantum error correcting code. The eigenspectrum has several critical points, where the linear sensitivity to external charge and flux noise vanishes. The states at these critical points thus hold promise as qubit states that are insensitive to common external noise sources.

We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.

Recent experimental realization of one-dimensional spin-orbit coupling (SOC) for ultracold alkaline-earth(-like) atoms in optical lattice clocks opens a new avenue for exploring exotic quantum matter because of the strongly suppressed heating of atoms from lasers comparing with alkaline-earth atoms. Here we propose a scheme to realize two-dimensional (2D) Rashba and three-dimensional (3D) Weyl types of SOC in a 3D optical lattice clock and explore their topological phases. With 3D Weyl SOC, the system can support topological phases with various numbers as well as types (I or II) of Weyl points. The spin distributions of such topological bands for 2D Rashba and 3D Weyl SOCs can be detected using suitably designed spectroscopic sequences. Our proposal may pave the way for the experimental realization of robust topological quantum matters and their exotic quasiparticle excitations in ultracold atomic gases.

Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the increase of quantum entanglement by local operations were reported, and therefore NHQM was not considered as a fundamental theory. Here we show that these and other no-go principles (including the no-cloning and no-deleting theorems) of conventional quantum mechanics still hold in finite-dimensional non-Hermitian quantum systems, including parity-time symmetric and pseudo-Hermitian cases, if its formalism is properly applied. We have developed a modified formulation of NHQM based on the geometry of Hilbert spaces which is consistent with the conventional quantum mechanics for Hermitian systems. Using this formulation the validity of these principles can be shown in a simple and uniform approach.