Spekkens' toy theory is a noncontextual hidden variable model with an epistemic restriction, a constraint on what the observer can know about the reality. In reproducing many features of quantum mechanics in an essentially classical model, it clarified our understanding of what behavior can be truly considered intrinsically quantum. In this work, we show that Spekkens' theory can be also used to help understanding aspects of quantum computation—in particular, an important subroutine in fault-tolerant quantum computation called state injection. State injection promotes fault-tolerant quantum circuits, which are usually limited to the classically efficiently simulatable stabilizer operations, to full universal quantum computation. We show that the limited set of fault-tolerant operations used in standard state-injection circuits can be realized within Spekkens' theory, and that state injection leads to nonclassicality in the form of contextuality. To achieve this, we extend prior work connecting Spekkens' theory and stabilizer quantum mechanics, showing that subtheories of the latter can be represented within Spekkens' theory, in spite of the contextuality in qubit stabilizer quantum mechanics. The work shines light on the relationship between quantum computation and contextuality.

We study the decoherence dynamics of a quantum Ising lattice of finite size with a transverse dissipative interaction, namely, the coupling with the bath is assumed perpendicular to the direction of the spins interaction and parallel to the external magnetic field. In the limit of small transverse field, the eigenstates and spectrum are obtained by a strong-coupling expansion, from which we derive the Lindblad equation in the Markovian limit. At temperature lower than the energy gap and for weak dissipation, the decoherence dynamics can be restricted to take only the two degenerate ground states and the first excited subspace into account. The latter is formed by pairs of topological excitations (domain walls or kinks), which are quantum delocalized along the chain due to the small magnetic field. We find that some of these excited states form a relaxation-free subspace, namely, they do not decay to the ground states.

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\mathcal{H}}_0$ of the system, and targeting a unique dark state in ${\mathcal{H}}_0$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\mathcal{H}}_0$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.

We examine the role of quantum error correction (QEC) in achieving pretty good quantum state transfer over a class of one-dimensional spin Hamiltonians. Recasting the problem of state transfer as one of information transmission over an underlying quantum channel, we identify an adaptive QEC protocol that achieves pretty good state transfer. Using an adaptive recovery and approximate QEC code, we obtain explicit analytical and numerical results for the fidelity of transfer over ideal and disordered one-dimensional Heisenberg chains. In the case of a disordered chain, we study the distribution of the transition amplitude, which in turn quantifies the stochastic noise in the underlying quantum channel. Our analysis helps us to suitably modify the QEC protocol so as to ensure pretty good state transfer for small disorder strengths and indicates a threshold beyond which QEC does not help in improving the fidelity of state transfer.

Different mechanisms for the dication production of molecular nitrogen and oxygen are reported here. It is shown that the ${\mathrm{N}}_2$ dication is produced by direct double ionization, or TS-2, while the ${\mathrm{O}}_2$ dication results primarily from an inner valence shell single ionization followed by a postcollisional Auger decay. In order to unveil these different characteristics of both production pathways, absolute cross-sectional measurements for the homoisotopic ${{\mathrm{N}}_2}^{2+}$ and ${{\mathrm{O}}_2}^{2+}$ by electron impact with energy ranging between 200 and 900 eV were measured. The separation of the doubly ionized parent molecules from the singly ionized fragments ${\mathrm{N}}^{+}$ and ${\mathrm{O}}^{+}$ was possible by employing the delayed extraction time-of-flight technique. The reasons for the two pure different pathways are discussed in the light of the present data, showing that while the single-ionization dication production process is impossible for nitrogen due to the energy levels limitations of its molecular orbitals, the direct double-ionization channel is strongly inhibited for oxygen due to geometrical constraints of its molecular orbitals orientation.

Inspired by Wannier's threshold law, we recognize that collision-complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the classical foundations of ultracold reactions and to help bring calculations currently beyond the capabilities of quantum mechanics within reach. A classical method with a simplified model of many-body interactions is provided for the determination of the collision-complex lifetime and demonstrated for a reduced-dimensional system, as preliminary to the calculation of collision-complex lifetimes in the full-dimensional system.

We investigate a conjecture used in recent experiments to reconstruct the complete dynamics of Fano autoionization processes out of measured spectral amplitudes [Gruson et al., Science 354, 734 (2016); Beaulieu et al., Science 358, 1288 (2017); Busto et al., J. Phys. B: At. Mol. Opt. Phys. 51, 044002 (2018)]. The validity of the conjecture is established analytically within the formalism of Fano, and tested numerically on model atoms displaying adjustable autoionizing states. A general condition for which the conjecture is valid, beyond the Fano case, is then derived.

In solids, crystal field splitting refers to the lifting of atomic orbital degeneracy by the surrounding ions through the static electric field. Similarly, we show that the degenerated $d$ orbitals, which were derived in the harmonic oscillator approximation, are split into a low-lying $d_{x^2+y^2}$ singlet and a $d_{x^2-y^2/xy}$ doublet by the high-order Taylor polynomials of triangular optical potential. The low-energy effective theory of the orbital Mott insulator at $2/3$ filling is generically described by the Heisenberg-compass model, where the antiferro-orbital exchange interactions of compass type depend on the bond orientation and are geometrically frustrated in the triangular lattice. While, for the square optical lattice, the degenerated $d$ orbitals are split into a different multiplet structure, i.e., a low-lying $d_{x^2\pm y^2}$ doublet and a $d_{xy}$ singlet, which has its physical origin in the $C_{4v}$ point group symmetry of square optical potential. Our results build a bridge between ultracold atom systems and solid-state systems for the investigation of $d$-orbital physics.

Backscattering depolarization of nonspherical particles plays a critical role in active Light Detection And Ranging (LiDAR) retrievals of cloud or aerosol parameters, as well as in particle characterization techniques. However, the interpretation of backscattering light from particles is a challenging research subject. This paper addresses the depolarization of nearly spherical particles by using the Debye series approach. Specifically, the T matrix is represented as an infinite sum of terms; the terms in the expansion are correspondingly associated with diffraction and reflection ($p=0$), and multiple transmissions ($p>0$) from the particle to the medium as waves undergo internal reflections. We found that the enhanced depolarization for optically soft particles stems from multiple transmissions. However, this is mostly from the transmission after one internal reflection ($p=2$), when the refractive index is larger than 1.3. Moreover, the interference among multiple transmissions was found to play an essential role in suppressing the depolarization ratio as the refractive index approaches unity. These findings have implications in interpreting the backscattering optical properties of atmospheric aerosols and hydrosols in water.

Multiwavelength quantum cascade lasers (QCLs) as coherent optical sources at mid- and far-IR spectral regions can be tailored regarding their dynamic and modulation response, output power, and stability condition of each spectral component under optical injection locking. Based on a developed model fitted to experimental data of a dual-wavelength mid-infrared (mid-IR), we show that an injection ratio threshold exists for each wavelength after which a stable-locking is obtained. While the uninjected wavelength imposes a long turn-on delay and an increased threshold current before its extinction, the injection-locked wavelength may experience output powers and modulation bandwidths about twice as large as the free-running values at moderate injection ratios. This idea provides a tunability viewpoint for spectral and power-dependent switching applications of multiwavelength and broadband QCLs.

When building a parametric down-conversion photon-pair source with spectrally separable photons, e.g., for making high-purity heralded single photons, two practical issues must be accounted for: the design of the experiment, and its characterization. To address experiment design, we study the impact on spectral separability of realistic (sech-shaped and chirped) pump fields, realistic nonlinear crystals with fabrication imperfections, and undesirable PDC generation far from the central PMF peak coming from nonlinearity shaping methods. To address experiment characterization, we study the effect of discretization and spectral range of the measured biphoton joint spectrum, the difference between inferring separability from the joint spectral amplitude versus the joint spectral intensity, and advantages of interference experiments for purity characterization over methods based on the joint spectral intensity. This study will be of practical interest to researchers building the next generation of nonlinear sources of separable photon pairs.

A Bacon-Shor code is a subsystem quantum error-correcting code on an $L\times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $2L(L-1)$ weight-2 gauge operators. Here, we show that the stabilizers can be measured directly and fault tolerantly with bare ancillary qubits by constructing circuits that follow the pattern of gauge operators. We then examine the implications of this method for small quantum error-correcting codes by comparing distance-3 versions of the rotated surface code and the Bacon-Shor code with the standard depolarizing model and in the context of a trapped-ion quantum computer. We find that for a simple circuit of prepare, error correct, and measure, the Bacon-Shor code outperforms the surface code by requiring fewer qubits, taking less time, and having a lower error rate.

As shown recently [H. F. Hofmann, Phys. Rev. A 96, 020101(R) (2017)], it is possible to demonstrate that quantum particles do not move along straight lines in free space by increasing the probability of finding the particles within narrow intervals of position and momentum beyond the “either/or” limit of 0.5 using constructive quantum interference between a component localized in position and a component localized in momentum. The probability of finding the particle in a corresponding spatial interval at a later time then violates the lower bound of the particle propagation inequality which is based on the validity of Newton's first law. In this paper, the problem of localizing the two state components in their respective target intervals is addressed by introducing a set of three coefficients that describe the localization of arbitrary wave functions quantitatively. This characterization is applied to a superposition of Gaussians, obtaining a violation of the particle propagation inequality by more than 5% if the width of the Gaussian wave function is optimized along with the size of the position and momentum intervals. It is shown that the violation of the particle propagation inequality originates from the fundamental way in which quantum interferences relate initial position and momentum to the future positions of a particle, indicating that the violation is a fundamental feature of causality in the quantum limit.

The dynamics of a wave in an open quantum system can be described by the eigenstates of the non-Hermitian Hamiltonian, provided that it is not at an exceptional point. Naively, one would expect that the decay of the energy eigenstates directly determines the decay of the total wave intensity. We show, however, that this is not the case for systems with localized losses. Instead, the nonorthogonality of the energy eigenstates plays an important role. It can to a large extent compensate for the initial decay of the eigenstates leading to a transient power-law decay of the wave intensity with a potentially large exponent.

We single out a class of states possessing only the three-tangle but distributed all over four qubits. This is a three-site analog of states from the $W$ class. The latter possess exclusively globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits for which all possible SL invariants vanish, and hence which are part of the $\mathrm{SL}$ null cone. Instead, they will possess a certain unitary invariant. In analyzing the three-tangle of rank-two reduced density matrices of these states, we manage to show that in this particular case we reach the convex roof exactly. As an interesting by-product this solution is extended in the rank-two case to a homogeneous polynomial SL-invariant measure of entanglement of degree $2m$, if there are two states which correspond to an at most $n$-fold degenerate solution in the zero polytope for $0<n<m$ that can be combined with the convexified minimal characteristic curve at an $(2m-n)$-fold zero yielding a decomposition of $\rho$. If more than one such state does exist in the zero polytope, a minimization must be performed. If no decomposition of $\rho$ is obtained in this way, it provides a better lower bound than the lowest convexified curve.

The development of quantum network relies on high-quality entanglement between remote quantum nodes. In reality the unavoidable decoherence limits the quality of entangled quantum nodes, however, entanglement distillation can overcome this problem. Here we propose an experimentally feasible scheme of continuous-variable entanglement generation, storage, and distillation between distant quantum nodes, which only requires the atomic ensemble quantum memory and balanced homodyne detection (BHD). Initially one copy of a bipartite entangled state of light, suffering phase fluctuations during the distributions, is stored in two distant atomic ensembles so that the atomic ensembles are entangled. Within the storage lifetime, by distributing and storing another copy of entangled optical modes in these two atomic ensembles, the distillation on entangled atomic spin waves can be implemented based on the post-selection of the BHD result. Our scheme provides a highly entangled state between remote quantum nodes for downstream applications, and enables the extension to multipartite entanglement distillation in a large-scale quantum network.

Up to the present, although experimental studies about the polarizabilities of alkali-metal Rydberg atoms have involved the states with principal quantum numbers $n\le 80$, theoretical calculations are limited to the states with $n\le 50$. In this work, we calculate the scalar and tensor polarizabilities of the $n{S}_{1/2}$, $n{P}_{1/2,3/2}$, and $n{D}_{3/2,5/2}$ Rydberg states of Rb with principal quantum number $n$ up to 140 employing a model potential and the $B$-spline expansion technique. We obtain the polarizabilities that are in good agreement with the existing theoretical and experimental data.

Synchrotron radiation is commonly known to be completely linearly polarized when observed in the orbital plane of the synchrotron motion. Under actual experimental conditions, however, the degree of polarization of the synchrotron radiation may be lower than the ideal 100%. We demonstrate that even tiny impurities of polarization of the incident radiation can drastically affect the polarization of the elastically scattered light. We propose to use this effect as a precision tool for the diagnostics of the polarization purity of the synchrotron radiation. Two variants of the diagnostics method are proposed. The first one is based on the polarization measurements of the scattered radiation and relies on theoretical calculations of the transition amplitudes. The second one involves simultaneous measurements of the polarization and the cross sections of the scattered radiation and is independent of theoretical amplitudes.

We study the retrieval of the angular dependence of the photoionization transition dipole phase of an attosecond XUV pulse in order to reconstruct the whole photoelectron wave packet after the photoemission process. Using a one-electron model Ar atom, we show that the full electron wave packet can be reconstructed from IR-free photoelectron angular distributions and the streaking electron spectra in an IR-dressed XUV photoionization, with photoelectrons along the common polarization direction of the two pulses. The method relies on the validity of the strong-field approximation so it is valid only for higher energy photoelectrons. We also point out that a single photoionization group time delay is not enough to represent a photoemission process; instead, a complete characterization of the electron wave packet requires the retrieval of the spectral phase over the whole bandwidth of the wave packet.