We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by $d$-dimensional states, and that rely only upon a simple property of the set of measurements used (the maximal overlap between measurement directions). Using these inequalities we show that the critical detection efficiency above which $n$ von Neumann measurements can demonstrate steering is $1/n$. We show furthermore that using our construction and high-dimensional states allows for steering demonstrations which are also highly robust to depolarizing noise and produce unbounded violations in the presence of loss. Finally, our results provide an explicit means to certify the nonjoint measurability of any set of inefficient von Neuman measurements.

We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are.

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy.

We investigate the four-body Coulomb process of low-energy elastic positronium-hydrogen (Ps-H) scattering below the Ps($n=2$) excitation threshold using scattering wave functions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the ${}^{1,3}H$ wave and obtain highly accurate ${}^{1,3}S$- and ${}^{1,3}P$-wave phase shifts. The complex Kohn variational results compare well to a number of other calculations for this system. We present elastic differential, elastic integrated, and momentum transfer cross sections, and for the singlet, resonances through the ${}^{1}F$ wave. The differential cross section exhibits interesting features, including a change from slightly backward peaked to forward peaked scattering as the energy of the incident positronium increases and rich structure due to multiple resonances near the Ps($n=2$) threshold. We also give a detailed analysis of the scattering lengths and effective ranges using multiple effective range theories.

We present a numerical study for optimization of ultrabroad supercontinuum spectrum by controlling the waveforms of laser fields, with the ultimate goal to generate isolated ultrashort attosecond pulses. Specifically, we extend a derivative-free nonconvex optimization algorithm for maximization of the supercontinnum power spectrum near the high-order harmonic generation (HHG) cutoff. It is found that optimally shaped inhomogeneous two-color mid-infrared laser fields can greatly enhance and extend the high-order harmonic generation plateau. Wavelet time-frequency analysis and classical simulations show that the superposition of resulting hydrogen HHG supercontinuum effectively gives rise to a robust isolated 5-as pulse.

We present ground-state calculations for low-density Fermi gases described by two model interactions, an attractive square-well potential and a Lennard-Jones potential, of varying strength. We use the optimized Fermi-hypernetted chain integral equation method, which has been proved to provide, in the density regimes of interest here, an accuracy of better than 1%. We first examine the low-density expansion of the energy and compare it with the exact answer of H. Huang and C. N. Yang [Phys. Rev. 105, 767 (1957)]. It is shown that a locally correlated wave function of the Jastrow-Feenberg type does not recover the quadratic term in the expansion of the energy in powers of $a_0{k}_F$, where $a_0$ is the vacuum $s$-wave scattering length and $k_F$ the Fermi wave number. The problem is cured by adding second-order perturbation corrections in a correlated basis. Going to higher densities and/or more strongly coupled systems, we encounter an instability of the normal state of the system which is characterized by a divergence of the in-medium scattering length. We interpret this divergence as a phonon-exchange-driven dimerization of the system, similar to what occurs at zero density when the vacuum scattering length $a_0$ diverges. We then study, in the stable regime, the superfluid gap and its dependence on the density and the interaction strength. We identify two corrections to low-density expansions: One is medium corrections to the pairing interaction, and the other is finite-range corrections. We show that the most important finite-range corrections are a direct manifestation of the many-body nature of the system.

We introduce a theoretical approach to determine the spin structure of harmonically trapped atoms with two-body zero-range interactions subject to an equal mixture of Rashba and Dresselhaus spin-orbit coupling created through Raman coupling of atomic hyperfine states. The spin structure of bosonic and fermionic two-particle systems with finite and infinite two-body interaction strength $g$ is calculated. Taking advantage of the fact that the $N$-boson and $N$-fermion systems with infinitely large coupling strength $g$ are analytically solvable for vanishing spin-orbit coupling strength $k_{\mathrm{so}}$ and vanishing Raman coupling strength $\mathrm{\Omega }$, we develop an effective spin model that is accurate to second order in $\mathrm{\Omega }$ for any $k_{\mathrm{so}}$ and infinite $g$. The three- and four-particle systems are considered explicitly. It is shown that the effective spin Hamiltonian, which contains a Heisenberg exchange term and an anisotropic Dzyaloshinskii-Moriya exchange term, describes the transitions that these systems undergo with the change of $k_{\mathrm{so}}$ as a competition between independent spin dynamics and nearest-neighbor spin interactions.

A moving boundary separating two otherwise homogeneous regions of a dielectric is known to emit radiation from the quantum vacuum. An analytical framework based on the Hopfield model, describing a moving refractive-index step in $1+1$ dimensions for realistic dispersive media has been developed by S. Finazzi and I. Carusotto [Phys. Rev. A 87, 023803 (2013)]. We expand the use of this model to calculate explicitly spectra of all modes of positive and negative norms. Furthermore, for lower step heights we obtain a unique set of mode configurations encompassing black-hole and white-hole setups. This leads to a realistic emission spectrum featuring black-hole and white-hole emission for different frequencies. We also present spectra as measured in the laboratory frame that include all modes, in particular a dominant negative-norm mode, which is the partner mode in any Hawking-type emission. We find that the emission spectrum is highly structured into intervals of emission with black-hole, white-hole, and no horizons. Finally, we estimate the number of photons emitted as a function of the step height and find a power law of 2.5 for low step heights.

We use a microscopic model, the mirror-oscillator-field (MOF) model proposed by C. R. Galley, R. O. Behunin, and B. L. Hu [Phys. Rev. A 87, 043832 (2013)], to describe the quantum entanglement between a mirror's center-of-mass (c.m.) motion and a field. In contrast with the conventional approach where the mirror-field entanglement is understood as arising from the radiation pressure of an optical field inducing the motion of the mirror's c.m., the MOF model incorporates the dynamics of the internal degrees of freedom of the mirror that couple to the optical field directly. The major advantage in this approach is that it provides a self-consistent treatment of the three pertinent subsystems (the mirror's c.m. motion, its internal degrees of freedom, and the field) including their back-actions on each other, thereby giving a more accurate account of the quantum correlations between the individual subsystems. The optical and the mechanical properties of a mirror arising from its dynamical interaction with a quantum field are obtained without imposing any boundary conditions on the field additionally, as is done in the conventional way. As one of the new physical features that arise from this self-consistent treatment of the coupled optics and mechanics behavior we observe a coherent transfer of quantum correlations from the field to the mirror via its internal degrees of freedom. We find the quantum entanglement between the optical field and the mirror's center-of-mass motion upon coarse-graining over the internal degree of freedom. Further, we show that in certain parameter regimes the mirror-field entanglement is enhanced when the field interacts resonantly with the mirror's internal degree of freedom, a result which highlights the importance of including the internal structure of the mirror in quantum optomechanical considerations.

Exact Hermite-Gaussian solutions to the Klein-Gordon equation for particle beams are obtained here that depend on the 4-position of the beam waist. These are Bateman-Hillion solutions that are shown to include Gouy phase and preserve their forms under Lorentz transformations. As the wave function contains two time coordinates, the particle current must be interpreted in a constraint space to reduce the number of independent coordinates. The form of the constraint space is not certain except in the nonrelativistic limit, but a trial form is proposed, enabling the observable properties of the beam to be calculated for future comparison to experiment. These results can be relevant in the theoretical development of singular electron optics since it was shown that the Gouy phase is crucial in this field as well as to investigate a possible Gouy phase effect in Zitterbewegung phenomenon of spin-zero particles. Additionally, the traditional argument that beam solutions belong to a complex shifted spacetime is shown to necessitate a corresponding Born reciprocal shift in 4-momentum space.

We report an experimental comparison of critical intensities of nonlinear self-focusing in air with conventional focusing and spatiotemporal focusing schemes. Our results show that the conventional focusing with the focal lens completely filled with the incident beam allows for a higher peak intensity near the focus against the nonlinear self-focusing than the spatiotemporal focusing scheme. This is because in the high-numerical-aperture condition, the focal spot will have a compact size, which results in a high focal intensity. Meanwhile, the Rayleigh length of the focused beam will be substantially shortened, which efficiently postpones the onset of self-focusing.

We investigate the properties of the optical output fields from a cavity optomechanical system, where the cavity is optically driven by a strong coupling field and a weak probe field and the mechanical resonator is driven by a coherent mechanical pump. When the frequency of the mechanical pump matches the frequency difference between the coupling and probe optical fields, due to the interference between the different optical components at the same frequency, we demonstrate that the large positive or negative group delay of the output field at the frequency of probe field can be achieved and tuned by adjusting the phase and amplitude of the mechanical driving field. Moreover, the strength of the output field at the frequency of an optical four-wave-mixing (FWM) field also can be controlled (enhanced and suppressed) by tuning the phase and amplitude of the mechanical pump. We show that the power of the output field at the frequency of the optical FWM field can be suppressed to zero or enhanced so much that it can be comparable with and even larger than the power of the input probe optical field.

Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a specific (classical) computational basis. Recently, by regarding coherence as a physical resource, Baumgratz et al. [Phys. Rev. Lett. 113, 140401 (2014)] presented a comprehensive framework for coherence measures. Here, we propose a quantum coherence measure essentially using the intrinsic randomness of measurement. The proposed coherence measure provides an answer to the open question in completing the resource theory of coherence. Meanwhile, we show that the coherence distillation process can be treated as quantum extraction, which can be regarded as an equivalent process of classical random number extraction. From this viewpoint, the proposed coherence measure also clarifies the operational aspect of quantum coherence. Finally, our results indicate a strong similarity between two types of quantumness—coherence and entanglement.

We study a simple open quantum system with a $\mathcal{PT}$-symmetric defect potential as a prototype in order to illustrate a number of general features of $\mathcal{PT}$-symmetric open quantum systems; however, the potential itself could be mimicked by a number of $\mathcal{PT}$ systems that have been experimentally studied quite recently. One key feature is the resonance in continuum (RIC), which appears in both the discrete spectrum and the scattering spectrum of such systems. The RIC wave function forms a standing wave extending throughout the spatial extent of the system and in this sense represents a resonance between the open environment associated with the leads of our model and the central $\mathcal{PT}$-symmetric potential. We also illustrate that as one deforms the system parameters, the RIC may exit the continuum by splitting into a bound state and a virtual bound state at the band edge, a process which should be experimentally observable. We also study the exceptional points appearing in the discrete spectrum at which two eigenvalues coalesce; we categorize these as either EP2As, at which two real-valued solutions coalesce before becoming complex-valued, and EP2Bs, for which the two solutions are complex on either side of the exceptional point. The EP2As are associated with $\mathcal{PT}$-symmetry breaking; we argue that these are more stable against parameter perturbation than the EP2Bs. We also study complex-valued solutions of the discrete spectrum for which the wave function is nevertheless spatially localized, something that is not allowed in traditional open quantum systems; we illustrate that these may form quasibound states in continuum under some circumstances. We also study the scattering properties of the system, including states that support invisible propagation and some general features of perfect transmission states. We finally use our model as a prototype for the construction of scattering states that satisfy $\mathcal{PT}$-symmetric boundary conditions; while these states do not conserve the traditional probability current, we introduce the $\mathcal{PT}$ current which is preserved. The perfect transmission states appear as a special case of the $\mathcal{PT}$-symmetric scattering states.

A general quantum search algorithm aims to evolve a quantum system from a known source state $|s\rangle$ to an unknown target state $|t\rangle$. It uses a diffusion operator $D_s$ that has the source state as one of its eigenstates and $I_t$, where $I_{\psi }$ denotes the selective phase inversion of the $|\psi \rangle$ state. It evolves $|s\rangle$ to a particular state $|w\rangle$, which we will call the $w$ state, in $O(B/\alpha )$ time steps, where $\alpha$ is $|\langle t|s\rangle |$ and $B$ is a characteristic of the diffusion operator. Measuring the $w$ state gives the target state with a success probability of $O(1/B^2)$, and $O\left(B^2\right)$ applications of the algorithm can boost it from $O(1/B^2)$ to $O\left(1\right)$, making the total time complexity $O(B^3/\alpha )$. In the special case of Grover's algorithm, $D_s$ is $I_s$ and $B$ is very close to 1. A more efficient way to boost the success probability is quantum amplitude amplification provided we can efficiently implement $I_w$. Such an efficient implementation is not known so far. In this paper, we present an efficient algorithm to approximate selective phase inversions of the unknown eigenstates of an operator using a phase estimation algorithm. This algorithm is used to efficiently approximate $I_w$, which reduces the time complexity of general algorithm to $O(B/\alpha )$. Although $O(B/\alpha )$ algorithms are known to exist, our algorithm offers physical implementation advantages.

Potential-functional theory is an intriguing alternative to density-functional theory for solving electronic-structure problems. We derive and solve equations using interacting potential functionals. A semiclassical approximation to exchange in one dimension with hard-wall boundary conditions is found to be almost exact (compared to standard density-functional approximations). The variational stability of this approximation is tested, and its far greater accuracy relative to the local-density approximation demonstrated. Even a fully orbital-free potential-functional calculation yields little error relative to exact exchange, for more than one orbital.

The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of theoretical determinations. The static polarizability is evaluated. Comparing the resulting dynamic polarizability as a function of the photon energy with more elaborate calculations reveals the contributions of inner shell electron excitations. The present results are applied to calculate the long-range interactions between two and three magnesium atoms and the interaction between a magnesium atom and a perfectly conducting metallic plate. Extensive comparisons of prior results for the principal resonance line oscillator strength, for the static polarizability, and for the van der Waals coefficient are given in the Appendix.

We consider the recollision process occurring during the ionization of a neutral atom or molecule by a very strong linearly polarized near-infrared laser field. We find that Coulomb focusing persists even when the Coulomb field of the ion is barely noticeable compared with the laser field. We focus on the consequences of Coulomb focusing for trajectories that maximize the energy exchange upon recollision and thus determine the high-harmonic cutoff. Delayed recollisions proliferate in the strong-field regime and bring back energy slightly above the $3.17U_p$ high-harmonic cutoff (where $U_p$ is the pondermotive energy), in stark contradiction with the strong-field approximation. We investigate the nonlinear-dynamical phase-space structures which underlie this dynamics. It is found that the energetic delayed recollisions are organized by a reduced number of periodic orbits and their invariant manifolds.