We investigate the nonlinear mixing of orbital angular momentum in type-II second-harmonic generation with arbitrary topological charges imprinted on two orthogonally polarized beams. Starting from the basic nonlinear equations for the interacting fields, we derive the selection rules determining the set of paraxial modes taking part in the interaction. Conservation of orbital angular momentum naturally appears as the topological charge selection rule. However, a less intuitive rule applies to the radial orders when modes carrying opposite helicities are combined in the nonlinear crystal, an intriguing feature confirmed by experimental measurements.

Several superconducting circuit configurations are examined on the existence of superradiant phase transitions (SRPTs) in thermal equilibrium. For some configurations consisting of artificial atoms, whose circuit diagrams are however not specified, and an LC resonator or a transmission line, we confirm the absence of SRPTs in the thermal equilibrium following the similar analysis as the no-go theorem for atomic systems. We also show some other configurations where the absence of SRPTs cannot be confirmed.

One-dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phase to non-Hermitian systems, a finite system in a nontrivial topological phase displays surface states with exponentially long lifetimes. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-particle sector, by a non-Hermitian “Hamiltonian” of the desired form. We then study, both analytically and numerically, one-dimensional geometries with up to three sites per unit cell and up to a topological winding number $W=2$. For finite-size systems the number of edge modes is a complicated function of $W$ and the system size $N$. However, we find that there are precisely $W$ modes localized at one end of the chain. In such topological phases the qubit's coherence lifetime is exponentially large in the system size. We verify that for $W>1$, at large times, the Lindbladian evolution is approximately a nontrivial unitary. For $W=2$ this results in Rabi-like oscillations of the qubit's coherence measure.

This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions $r^{-\alpha }$, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015)] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for $\alpha \le 2d$ in a $d$-dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016)]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016)] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents $0\le \alpha \le d$. The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)].

Different regimes of collective light scattering are observed when an elongated Bose-Einstein condensate is pumped by two noninterfering beams counterpropagating along its long axis. In the limit of small Rayleigh scattering rates, the presence of a second pump beam suppresses superradiance, whereas at large Rayleigh scattering rates it lowers the effective threshold power for collective light scattering. In the latter regime, the quench dynamics of the two-beam system are oscillatory, compared to monotonic in the single-beam case. In addition, the dependence on power, detuning, and atom number is explored. The observed features of the two-beam system qualitatively agree with the recent theoretical prediction of a supersolid crystalline phase of light and matter at large Rayleigh scattering rates.

Simulating high-weight Hamiltonians can convert local noise on the original Hamiltonian into undesirable nonlocal noise on the simulated Hamiltonian. Here we show how, starting from a two-local Hamiltonian in the presence of non-Markovian noise, a desired computation can be simulated as well as protected using fast pulses, while maintaining an energy gap against the errors created in the process.w

We propose a hybrid quantum repeater based on ancillary coherent field states and material qubits coupled to optical cavities. For this purpose, resonant qubit-field interactions and postselective field measurements are determined which are capable of realizing all necessary two-qubit operations for the actuation of the quantum repeater. We explore both theoretical and experimental possibilities of generating near-maximally-entangled qubit pairs ($F>0.999$) over long distances. It is shown that our scheme displays moderately low repeater rates, between $5\times {10}^{-4}$ and 23 pairs per second, over distances up to 900 km, and it relies completely on current technology of cavity quantum electrodynamics.

We present a systematic study of the phenomena of number squeezing and fragmentation for a repulsive Bose-Einstein condensate (BEC) in a three-dimensional double-well potential over a range of interaction strengths and barrier heights, including geometries that exhibit appreciable overlap in the one-body wave functions localized in the left and right wells. We compute the properties of the condensate with numerically exact, full-dimensional path-integral ground-state (PIGS) quantum Monte Carlo simulations and compare with results obtained from using two- and eight-mode truncated basis models. The truncated basis models are found to agree with the numerically exact PIGS simulations for weak interactions, but fail to correctly predict the amount of number squeezing and fragmentation exhibited by the PIGS simulations for strong interactions. We find that both number squeezing and fragmentation of the BEC show nonmonotonic behavior at large values of interaction strength $a$. The number squeezing shows a universal scaling with the product of number of particles and interaction strength ($Na$), but no such universal behavior is found for fragmentation. Detailed analysis shows that the introduction of repulsive interactions not only suppresses number fluctuations to enhance number squeezing, but can also enhance delocalization across wells and tunneling between wells, each of which may suppress number squeezing. This results in a dynamical competition whose resolution shows a complex dependence on all three physical parameters defining the system: interaction strength, number of particles, and barrier height.

High-dimensional entangled photon pairs have many excellent properties compared to two-dimensional entangled two-photon states, such as greater information capacity, stronger nonlocality, and higher security. Traditionally, the degree of freedom that can produce high-dimensional entanglement mainly consists of angular momentum and energy time. In this paper, we propose a type of high-dimensional energy-time-entangled qudit, which is different from the traditional model with an extended propagation path. In addition, our method mainly focuses on the generation with multiple frequency modes, while two- and three-dimensional frequency-entangled qudits are examined as examples in detail through the linear or nonlinear optical response of the medium. The generation of high-dimensional energy-time-entangled states can be verified by coincidence counts in the damped Rabi oscillation regime, where the paired Stokes–anti-Stokes wave packet is determined by the structure of resonances in the third-order nonlinearity. Finally, we extend the dimension to $N$ in the sequential-cascade mode. Our results have potential applications in quantum communication and quantum computation.

The microwave clock frequency of the $|5s{}^2{S}_{1/2},F=0,m_F=0\rangle \leftrightarrow |5s{}^2{S}_{1/2},F=1,m_F=0\rangle$ transition in the ${}^{113}\mathrm{Cd}^{+}$ ion has been reported as 15 199 862 855.0192(10) Hz [Opt. Lett. 40, 4249 (2015)]. Fractional systematic shift $\left(\beta \right)$ due to the black-body radiation (BBR) arising from the Stark effect in the above, the clock transition was used as $-1.1\times {10}^{-16}$ from our unpublished preliminary estimation. We present here a precise value of $\beta =-1.815\left(77\right)\times {10}^{-16}$ by carrying out rigorous calculations of third-order polarizabilities of the hyperfine levels associated with the clock transition. This is determined by evaluating the matrix elements of the magnetic dipole hyperfine interaction Hamiltonian, electric dipole operator, and energies between many low-lying states of ${}^{113}\mathrm{Cd}^{+}$. We employ all-order relativistic many-body theories in the frameworks of Fock-space coupled-cluster and relativistic multiconfiguration Dirac-Fock methods.

We derive general conditions for the compatibility of channels in general probabilistic theory. We introduce formalism that allows us to easily formulate steering by channels and Bell nonlocality of channels as generalizations of the well-known concepts of steering by measurements and Bell nonlocality of measurements. The generalization does not follow the standard line of thinking stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and Bell nonlocality as entanglement-assisted incompatibility tests. We show that all of the proposed definitions are, in the special case of measurements, the same as the standard definitions, but not all of the known results for measurements generalize to channels. For example, we show that for quantum channels, steering is not a necessary condition for Bell nonlocality. We further investigate the introduced conditions and concepts in the special case of quantum theory and we provide many examples to demonstrate these concepts and their implications.

We report an experimental determination of the ground-state hyperfine constant $A$ of the ${}^{25}\mathrm{Mg}^{+}$ ions by measuring the $|S_{1/2},F=2,m=0\rangle$ to $|S_{1/2},F=3,m=0\rangle$ transition (0-0 transition) frequency of the two ground-state hyperfine energy levels. The frequency is measured by rf resonant method in a Paul trap under a magnetic field of about 0.1 mT. The result is $A=-596.254$ 248 7(42) MHz. Different frequency shifts and uncertainties are evaluated. The main effect is quadratic Zeeman shift. Since the Paul trap is driven by rf on the electrodes, ac magnetic field can be induced by the rf at the site of the ion. The ac magnetic field causes quadratic Zeeman shift for ion frequency standards and also reduces the coherence time when the ion acts as a quantum bit. Precision measurement of this ac magnetic field can help evaluating the related uncertainty when a single-ion optical clock is established on the trap.

We report fully differential photoelectron spectra from an ab initio coupled-channels treatment of ${\mathrm{CO}}_2$. Photoionization by laser pulses centered at wavelengths of 400 and 800 nm is considered, with arbitrary molecular alignment and polarization (linear and elliptic). Calculations reveal significant excited-state channel contributions that are, at certain molecular orientations, an order of magnitude larger than the ground-state channel in the rescattering plateau. A partial washout of the multiphoton structure in the above threshold ionization spectra and of the nodal features in angle-resolved spectra is observed due to ionization to excited-state channels. The qualitative nature of the spectra is determined by ionization thresholds, orbital symmetries, and interchannel coupling, in order of precedence.

We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-$\frac{1}{2}$) Bose gases in a high synthetic magnetic field in the space of the total filling factor and the ratio of the intercomponent coupling $g_{\uparrow \downarrow }$ to the intracomponent one $g>0$. Using exact diagonalization, we find that when the intercomponent coupling is attractive ($g_{\uparrow \downarrow }<0$), the product states of a pair of nearly uncorrelated quantum Hall states are remarkably robust and persist even when $|g_{\uparrow \downarrow }|$ is close to $g$. This contrasts with the case of an intercomponent repulsion, where a variety of spin-singlet quantum Hall states with high intercomponent entanglement emerge for $g_{\uparrow \downarrow }\approx g$. We interpret this marked dependence on the sign of $g_{\uparrow \downarrow }$ in light of pseudopotentials on a sphere, and also explain recent numerical results in two-component Bose gases in mutually antiparallel magnetic fields where a qualitatively opposite dependence on the sign of $g_{\uparrow \downarrow }$ is found. Our results thus unveil an intriguing connection between multicomponent quantum Hall systems and quantum spin Hall systems in minimal setups.

We consider the Riemann problem of evolution of initial discontinuities for the photon fluid propagating in a normal dispersion fiber with account of self-steepening effects. The dynamics of light field is described by the nonlinear Schrödinger (NLS) equation with self-steepening term appearing due to retardation of the fiber material response to variations of the electromagnetic signal. It is shown that evolution dynamics in this case is much richer than that for the NLS equation. Complete classification of possible wave structures is given for all possible jump conditions at the discontinuity.

We show that anti-$\mathcal{PT}$ symmetry can be realized in dissipatively coupled optical systems. Its emergence gives rise to spontaneous phase transitions for the guided and localized photonic eigenmodes in the waveguide and cavity systems studied, respectively. As a ubiquitous feature we demonstrate that constant refraction [analogous to unit refraction in [Nat. Phys. 12, 1139 (2016)]] occurs in the $\mathcal{PT}$-symmetric phase, which leads to several interesting properties for the photonic system, such as flat broadband light transport and dispersion-induced dissipation.

Circular polarization-entangled photons can be used to obtain an enhancement of the precision in a rotation measurement. In this paper, the method of entanglement transformation is used to produce NOON states in circular polarization from a readily generated linear polarization-entangled photon source. Detection of $N$-fold coincidences serves as the postselection and $N$-fold superoscillating fringes are obtained simultaneously. A parity strategy and conditional probabilistic statistics contribute to a better fringe, saturating the angle sensitivity to the Heisenberg limit. The impact of imperfect state preparation and detection is discussed both separately and jointly. For the separated case, the influence of each system imperfection is pronounced. For the joint case, the feasibility region for surpassing the standard quantum limit is given. Our work pushes the state preparation of circular polarization-entangled photons to the same level as that in the case of linear polarization. It is also confirmed that entanglement can be transformed into different frames for specific applications, serving as a useful scheme for using entangled sources.

We put forward a generic method that enables lossless generation of pure single photons with arbitrary shape over any degree of freedom or several degrees of freedom simultaneously. The method exploits pairs of entangled photons. One of the photons is the subject for lossy shaping manipulations followed by a specially designed mode-equalizing measurement. A successful measurement outcome heralds the losslessly shaped second photon. The method has three crucial ingredients that define the quantum state of the shaped photon: the initial bipartite state of the photons, modulation of the first photon, and its mode-equalizing detection. We provide a specific recipe with a combination of these ingredients for achieving any desired pure state of the shaped photon.

We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chessboard pattern, with a difference of $\pi$ between neighboring sites. We show that the lowest-lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the intensity of the light that, because of the nonlinearity, affects the dynamics of the phase fluctuations. We interpret the results using methods of condensed-matter physics, based on an effective description of the optical system. This interpretation sheds light on the phenomena, facilitating the understanding of individual systems and leading to a framework for relating different problems with the same symmetry. In this context, we show that the perturbative excitations of the phase are Nambu-Goldstone bosons of a spontaneously broken $\text{U}\left(1\right)$ symmetry.

Attosecond photoelectron spectroscopy allows the observation of electronic processes on attosecond time scales ($1\text{as}={10}^{-18}$ s), as has been demonstrated in proof-of-principle experiments that probe the electronic dynamics in isolated atoms with unprecedented accuracy. Its recent expansion to solid targets is starting to allow the distinction of ultrafast collective electronic processes in matter with added spatial resolution, probing the electronic band structure and dielectric response in nanoplasmonically enhanced light-induced processes of relevance for photocatalysis, optoelectronics, and light harvesting. Based on a quantum-mechanical model for photoelectron emission by an attosecond pulse train from the $d$ band of a Cu(111) surface into a delayed assisting laser pulse, we calculate two-pathway two-photon interferograms as functions of the photoelectron energy and pulse delay. Our results scrutinize the dependence of observable photoelectron interferograms on the electronic structure of and electron transport in the substrate and agree well with experimental spectra and semiclassical Monte Carlo simulations of Lucchini et al. [Phys. Rev. Lett. 115, 137401 (2015)].