The saturated absorption spectrum of the $6P_{3/2}\to 7S_{1/2}$ transition of ${}^{203}\mathrm{Tl}$ and ${}^{205}\mathrm{Tl}$ in a hollow cathode lamp has been observed with a frequency-doubled 1070 nm $\mathrm{Nd}:{\mathrm{GdVO}}_4$ laser. The third-derivative spectrum of the hyperfine components are obtained using the wavelength modulation spectroscopy and used to stabilize the laser frequency. The analysis of the error signal shows that the frequency stability reaches 30 kHz at 1 s averaging time. Such a frequency-stabilized light source at 535 nm can be used for laser cooling of thallium and for investigating the parity non-conservation effect in thallium. The absolute frequencies of hyperfine components are measured with an accuracy of 30 MHz using a precision wavelength meter. Including the pressure shift correction, the center of gravity of the transition frequency is determined to an accuracy of 22 MHz for both isotopes. Meanwhile, the isotope shift derived is in good agreement with earlier measurement.

The proton radius conundrum [Pohl et al., Nature 466, 213 (2010) and , Science 339, 417 (2013)] highlights the need to revisit any conceivable sources of electron-muon nonuniversality in lepton-proton interactions within the standard model. Superficially, a number of perturbative processes could appear to lead to such a nonuniversality. One of these is a coupling of the scattered electron into an electronic vacuum-polarization loop as opposed to a muonic one in the photon exchange of two valence quarks, which is present only for electron projectiles as opposed to muon projectiles. However, we show that this effect actually is part of the radiative correction to the proton's polarizability contribution to the Lamb shift, equivalent to a radiative correction to double scattering. We conclude that any conceivable genuine nonuniversality must be connected with a nonperturbative feature of the proton's structure, e.g., with the possible presence of light sea fermions as constituent components of the proton. If we assume an average of roughly $0.7\times {10}^{-7}$ light sea positrons per valence quark, then we can show that virtual electron-positron annihilation processes lead to an extra term in the electron-proton versus muon-proton interaction, which has the right sign and magnitude to explain the proton radius discrepancy.

Highly excited eigenstates of atoms and ions with open $f$ shell are chaotic superpositions of thousands, or even millions, of Hartree-Fock determinant states. The interaction between dielectronic and multielectronic configurations leads to the broadening of dielectronic recombination resonances and relative enhancement of photon emission due to opening of thousands of radiative decay channels. The radiative yield is close to 100% for electron energy $\lesssim$1 eV and rapidly decreases for higher energies due to opening of many autoionization channels. The same mechanism predicts suppression of photoionization and relative enhancement of the Raman scattering. Results of our calculations of the recombination rate are in agreement with the experimental data for W${}^{20+}$ and Au${}^{25+}$.

Mesoscopic samples of polarized dipolar atoms confined in three spatially separated traps conform an extended Bose-Hubbard Hamiltonian in which different quantum phases appear depending on the competition between tunneling, on-site, and long-range intersite dipole-dipole interactions. Here, by choosing an appropriate configuration of triple wells, we analyze the role played by the anisotropic character inherent to the dipolar interaction in the phase diagram of the system. We further characterize the different phases as well as their boundaries by means of their entanglement properties.

A unified criterion of self-focusing, applicable to both freely propagating beams and waveguide modes, is proposed, with the self-focusing threshold defined as the critical peak power needed to induce a refractive-index step capable of trapping one more spatial mode. For freely propagating beams and high-order waveguide modes, this definition is shown to recover the canonical expression for the critical power of self-focusing routinely used in nonlinear optics. In the limiting case of low-order guided modes, the proposed definition is found to be fully consistent with the earlier criteria of self-focusing in a waveguide.

We study Helmholtz bright soliton splitting at nonlocal nonlinear interfaces. Based on the framework of the Helmholtz theory, we demonstrate that bright soliton breakup depends on angle of incidence, nonlinear refractive index mismatch at the interface, and degree of nonlocality. Interestingly, the change of the degree of nonlocality can introduce collision and oscillation of solitons.

We discuss the dynamics of a hybrid optomechanical setup where a dielectric nanosphere is levitated inside the Fabry-Pérot cavity of a standard optomechanical system with one movable cavity mirror. The nanosphere is coupled to the cavity field and the movable mirror by the optomechanical and Casimir interactions with coupling strengths being dependent on the distance between the levitated nanosphere and cavity mirror. We investigate the steady-state characteristics of the system and the optical spring effect of the nanosphere in detail. We also analyze the effects of the distance-dependent optomechanical coupling and Casimir interaction on the cooling of the levitated nanosphere in the cases of a movable and of a fixed cavity mirror. It is found that in both cases, ground-state cooling of the levitated nanosphere can be approached in a certain range of parameters. Furthermore, in contrast to the case with the fixed mirror, the cooling of the levitated nanosphere with a movable mirror can be optimized with a properly chosen mirror oscillation frequency.

We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong-coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators, we show that the system can classically exhibit bistability and bifurcations, and we explore how these manifest themselves in interference, entanglement, and correlation in the quantum theory, while revealing the impact of decoherence of the mechanical system due to cavity fluctuations and coherent driving.

Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation and photon antibunching can be shown in the quantum regime. Our study presents alternate perspectives for engineering nonlinear quantum dynamics on a chip.

We consider an example of an idealized inhomogeneous metamaterial which, when introduced into a Casimir cavity, reduces the magnitude of the Casimir force. It has recently been argued, however, that Casimir-Lifshitz forces in inhomogeneous media are cutoff dependent; the stress tensor typically yields an infinite Casimir force, even in a case where the force must be zero. We demonstrate that, although the medium is inhomogeneous, it does not contribute any additional scattering events, but simply modifies the effective length of the cavity, and consequently the predicted force in this case is finite and can be stated exactly.

A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.

Recently, laser-induced electron diffraction has been used to image molecular structures with subangstrom precision and exposure times of a few femtoseconds by Blaga et al. [Nature (London) 483, 194 (2012)], who treated molecular ions as neutral molecules in the calculation of differential cross section (DCS) for elastic scattering of electrons by molecular ions. In this work, we investigate the long-range and short-range potential effects in elastic scattering of electrons with ions and atoms. It has been found that for incident electron energies above 100 eV and scattering angles greater than 40${}^{\circ }$, the DCSs of long-range Coulomb potential scattering can be neglected and the DCSs for elastic scattering of electrons with atomic ions and neutral atoms agree well. Therefore, the validity of the treatment in Blaga et al. is verified.

We study the quantum lattice gas model in one dimension introduced by Lesanovsky [Lesanovsky, Phys. Rev. Lett. 108, 105301 (2012)], who showed that the exact ground state and a couple of excited states can be obtained analytically. The Hamiltonian of the model depends solely on the parameter $z$, the meaning of which is a fugacity in the corresponding classical lattice gas model. For small $z$ ($0<z<1$), we prove that there is an energy gap between the ground state and the excited states by applying Knabe's method [Knabe, J. Stat. Phys. 52, 627 (1988)].

In this Rapid Communication, we describe how the presence of the third dimension may break the scale invariance in a two-dimensional Bose gas in a pancake-shaped trap. From the two-dimensional perspective, the possibility of a weak spilling of the atomic density beyond the ground state of the confinement alters the two-dimensional chemical potential; in turn, this correction no longer supports scale invariance. We compare experimental data with numerical and analytic perturbative results and find a good agreement.

It has recently been conjectured that detecting quantum effects such as superposition or entanglement for macroscopic systems always requires high measurement precision. Analyzing an apparent counterexample involving macroscopic coherent states and Kerr or higher-order nonlinearities, we find that while measurements with coarse outcomes can be sufficient, the phase control precision of the necessary nonlinear operations has to increase with the size of the system. This suggests a refined conjecture that either the outcome precision or the control precision of the measurements has to increase with system size.

We generalize the original derivation of transparent, static Schrödinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain previously found transparent potentials as special cases and play a key role in the semiclassical solution of the $(1+1)$-dimensional, fermionic quantum field theories of Gross-Neveu and Nambu–Jona-Lasinio types.

We study the harvesting of quantum and classical correlations from a hot scalar field in a periodic cavity by a pair of spatially separated oscillator-detectors. Specifically, we utilize nonperturbative and exact (non-numerical) techniques to solve for the evolution of the detectors-field system and then we examine how the entanglement, Gaussian quantum discord, and mutual information obtained by the detectors change with the temperature of the field. While (as expected) the harvested entanglement rapidly decays to zero as temperature is increased, we find remarkably that both the mutual information $and$ the discord can actually be increased by multiple orders of magnitude via increasing the temperature. We go on to explain this phenomenon by a variety of means and are able to make accurate predictions of the behavior of thermal amplification. By doing this we also introduce a new perspective on harvesting in general and illustrate that the system can be represented as two dynamically decoupled systems, each with only a single detector. The thermal amplification of discord harvesting represents an exciting prospect for discord-based quantum computation, including its use in entanglement activation.

Calculations of high-harmonic spectra from hydrogen atoms driven by strong two-color orthogonal fields with wavelengths 800 and 400 nm are presented. The azimuthal symmetry of the electron dynamics is broken by the two-color orthogonal fields, and therefore the fully three-dimensional time-dependent Schrödinger equation is solved by using the generalized pseudospectral method. The cycle-averaged collision angles as a function of phase delay between the orthogonal fields are evaluated from the harmonic spectra. The results are in qualitative agreement with a recent experiment with helium atoms. Furthermore, the timing and direction of recollisions during the high-harmonic generation are analyzed in the time-frequency domain to extract electron trajectory information on subcycle time scales. Comparison with recent model calculations is also made.

The time-dependent surface flux method developed for the description of electronic spectra [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012); A. Scrinzi, New J. Phys. 14, 085008 (2012)] is extended to treat dissociation and dissociative ionization processes of H${}_2{}^{+}$ interacting with strong laser pulses. By dividing the simulation volume into proper spatial regions associated with the individual reaction channels and monitoring the probability flux, the joint energy spectrum for the dissociative ionization process and the energy spectrum for dissociation is obtained. The methodology is illustrated by solving the time-dependent Schrödinger equation for a collinear one-dimensional model of H${}_2{}^{+}$ with electronic and nuclear motions treated exactly and validated by comparison with published results for dissociative ionization. The results for dissociation are qualitatively explained by analysis based on dressed diabatic Floquet potential energy curves, and the method is used to investigate the breakdown of the two-surface model.

Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical temperature. Here we apply the auxiliary-field quantum Monte Carlo method to perform ab initio calculations of the temperature dependence of three quantities—the energy-staggering pairing gap, the condensate fraction, and the heat capacity—in a trapped finite-size cold atom system in the unitary limit of infinite scattering length. As the calculations of the energy-staggering pairing gap require the use of the canonical ensemble, we employ an efficient algorithm for the stabilization of particle-number projection that is essential for reaching convergence in the size of the model space. We observe clear signatures of the superfluid phase transition in all three quantities, including a signature of the recently measured $\lambda$ peak in the heat capacity. We also find that the energy-staggering gap does not lead the condensate fraction as the temperature decreases.