The x-ray transitions in Cu- and Ni-like tungsten ions in the 5.19–5.26 Å wavelength range that are relevant as a high-temperature tokamak diagnostic, in particular for JET in the ITER-like wall configuration, have been studied. Tungsten spectra were measured at the upgraded Shanghai- Electron Beam Ion Trap operated with electron-beam energies from 3.16 to 4.55 keV. High-resolution measurements were performed by means of a flat Si 111 crystal spectrometer equipped by a CCD camera. The experimental wavelengths were determined with an accuracy of 0.3–0.4 mÅ. The wavelength of the ground-state transition in Cu-like tungsten from the $3p^{5}3d^{10}4s4d[{(3/2,{(1/2,5/2)}_2]}_{1/2}$ level was measured. All measured wavelengths were compared with those measured from JET ITER-like wall plasmas and with other experiments and various theoretical predictions including cowan, relac, multiconfigurational Dirac-Fock (MCDF), and fac calculations. To obtain a higher accuracy from theoretical predictions, the MCDF calculations were extended by taking into account correlation effects (configuration-interaction approach). It was found that such an extension brings the calculations closer to the experimental values in comparison with other calculations.

The $abinitio$ molecular dynamics (MD) simulations using an atom-centered density matrix propagation method have been carried out to investigate the fragmentation of the ground-state triply charged carbon dioxide, ${\mathrm{CO}}_2{}^{3+}\to {\mathrm{C}}^{+}$ + ${\mathrm{O}}_{\text{a}}{}^{+}$ + ${\mathrm{O}}_{\text{b}}{}^{+}$. Ten thousands of trajectories have been simulated. By analyzing the momentum correlation of the final fragments, it is demonstrated that the sequential fragmentation dominates in the three-body dissociation, consistent with our experimental observations which were performed by electron collision at impact energy of 1500 eV. Furthermore, the MD simulations allow us to have detailed insight into the ultrafast evolution of the molecular bond breakage at a very early stage, within several tens of femtoseconds, and the result shows that the initial nuclear vibrational mode plays a decisive role in switching the dissociation pathways.

Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum-information resources. With the use of the second-order density matrix constructed via exact diagonalization of the microscopic Hamiltonian, and an analytic Hubbard-type model, we explore here the systematic evolution of characteristic interference patterns in the two-body momentum and spatial correlation maps of two entangled ultracold fermionic atoms in a double well, for the entire attractive- and repulsive-interaction range. We uncover quantum-statistics-governed bunching and antibunching, as well as interaction-dependent interference patterns, in the ground and excited states, and interpret our results in light of the Hong-Ou-Mandel interference physics, widely exploited in photon indistinguishability testing and quantum-information science.

We derive the universal relations for an ultracold two-component Fermi gas with a spin-orbit coupling (SOC) ${\sum }_{\alpha ,\beta =x,y,z}{\lambda }_{\alpha \beta }{\sigma }_{\alpha }{p}_{\beta }$, where $p_{x,y,z}$ and ${\sigma }_{x,y,z}$ are the single-atom momentum and Pauli operators for pseudospin, respectively, and the SOC intensity ${\lambda }_{\alpha \beta }$ could take an arbitrary value. We consider the system with an $s$-wave short-range interspecies interaction, and ignore the SOC-induced modification for the value of the scattering length. Using the first-quantized approach developed by Tan [S. Tan, Phys. Rev. Lett. 107, 145302 (2011)], we obtain the short-range and high-momentum expansions for the one-body real-space correlation function and momentum distribution function, respectively. For our system these functions are a $2\times 2$ matrix in the pseudospin basis. We find that the leading-order ($1/k^4$) behavior of the diagonal elements of the momentum distribution function, i.e., $n_{\uparrow \uparrow }\left(\mathbf{k}\right)$ and $n_{\downarrow \downarrow }\left(\mathbf{k}\right)$, are not modified by the SOC. However, the SOC can significantly modify the large-$k$ behaviors of the distribution difference $\delta n\left(\mathbf{k}\right)\equiv n_{\uparrow \uparrow }\left(\mathbf{k}\right)-n_{\downarrow \downarrow }\left(\mathbf{k}\right)$ as well as the nondiagonal elements of the momentum distribution function, i.e., $n_{\uparrow \downarrow }\left(\mathbf{k}\right)$ and $n_{\downarrow \uparrow }\left(\mathbf{k}\right)$. In the absence of the SOC, the leading order of $\delta n\left(\mathbf{k}\right)$, $n_{\uparrow \downarrow }\left(\mathbf{k}\right)$, and $n_{\downarrow \uparrow }\left(\mathbf{k}\right)$ is $O(1/k^6)$. When SOC appears, it can induce a term on the order of $1/k^5$ for these elements. We further derive the adiabatic relation and the energy functional. Our results show that the SOC can induce an additional term in the energy functional, which describes the contribution from the SOC to the total energy. In addition, the form of the adiabatic relation for our system is not modified by the SOC. Our results are applicable for the systems with any type of single-atom trapping potential, which could be either diagonal or nondiagonal in the pseudospin basis.

Previous attempts to derive the differential Jones matrix (DJM, $N)$ by Jones [Jones, J. Opt. Soc. Am. 38, 671 (1948)] for a twisted crystal and the integral Jones matrix (IJM, $J)$ by Chandrasekhar and Rao [Chandrasekhar and Rao, Acta Crystallogr. A 24, 445 (1968)] for a cholesteric liquid crystal resulted in Jones matrices, which are valid for the spectral range except the selective light reflection band. We argue that the limitation of their validity is rooted in two key assumptions used in both approaches, namely, (1) local (nonrotated) DJM $N^0$ and the elementary IJM $J^0$ (to which the cholesteric is split) are those of a uniform nematic and (2) under rotation of the coordinate system, $N^0$ and $J^0$ obey the similarity transformation rule, namely, $N=R{N}^0{R}^{-1}$ and $J=R{J}^0{R}^{-1}$, where $R$ is the rotation matrix. We show that both of these assumptions are of limited applicability for a cholesteric, being justified only for weak twist. In our approach, the DJM and IJM are derived for a cholesteric without these assumptions. To derive the cholesteric DJM, we have established the relation between the diagonal form $N^{0d}$ of $N^0$ and Mauguin solutions [Mauguin, Bull. Soc. Fr. Mineral. Crystallogr. N° 3, 71 (1911)] of Maxwell equations for eigenwaves propagating in the cholesteric. Namely, the eigenvalues of $N^0$ appear to be the wave numbers for the two eigenwaves propagating in the sample. Then the form of $N^0$ reconstructs from its diagonal form $N^{0d}$. Our DJM and IJM, derived for a general case of any ellipticity value of the eigenwaves, correspond to an optically anisotropic plate possessing gyrotropy, linear birefringence, and Jones dichroism. In the limiting approximations of circularly polarized eigenwaves and that corresponding to the Mauguin regime, the DJM and IJM reduce to those known from the literature. We found that the form of the transformation rule for the local DJM $N^0$ under rotation of the coordinate system depends on the regime of light propagation, being different from the similarity transformation rule alluded to above, but reduces to it at weak twist corresponding to the Mauguin regime.

Elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate phase reveals a unique physical configuration of interacting light and matter waves. However, the joint coherent dynamics of the optical excitation induced by an incident photon is influenced by the presence of incoherent scattering channels. For a sample of sufficient length the excitation transports as a polariton wave and the propagation Green's function obeys the scattering equation which we derive. The polariton dynamics could be tracked in the outgoing channel of the scattered photon as we show via numerical solution of the scattering equation for one-dimensional geometry. The results are analyzed and compared with predictions of the conventional macroscopic Maxwell theory for light scattering from a nondegenerate atomic sample of the same density and size.

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

A possible alternative to the standard model of measurement-based quantum computation (MBQC) is offered by the sequential model of MBQC—a particular class of quantum computation via ancillae. Although these two models are equivalent under ideal conditions, their relative resilience to noise in practical conditions is not yet known. We analyze this relationship for various noise models in the ancilla preparation and in the entangling-gate implementation. The comparison of the two models is performed utilizing both the gate infidelity and the diamond distance as figures of merit. Our results show that in the majority of instances the sequential model outperforms the standard one in regard to a universal set of operations for quantum computation. Further investigation is made into the performance of sequential MBQC in experimental scenarios, thus setting benchmarks for possible cavity-QED implementations.

We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in Jachymski et al. [Phys. Rev. Lett. 120, 013401 (2018)], is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic-field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect the transmission. We illustrate our findings with concrete examples of experimental relevance, demonstrating that for large atom fluences $N$ a sensitivity of the order of 1 nT/$\sqrt{N}$ for the field strength and 100 nT/(mm $\sqrt{N}$) for the gradient can be reached with our scheme.

We propose a method to convert measured positronium annihilation rates in gaseous xenon into total and differential cross sections of positronium-xenon collisions in an ultralow-energy region of less than 80 meV where their experimental determinations as functions of the positronium kinetic energy are extremely difficult. This method makes it possible to determine not only the $s$-wave collisional parameters but also the $p$-wave and $d$-wave parameters. We have found a small positive value of the scattering length, $A_0=2.06\pm 0.10a_0$, which indicates that the positronium-xenon interaction in this energy region is repulsive and suggests that it is dominated by the scattering amplitude of the positron rather than that of the electron. An extrapolation of the analytical result into the experimentally inaccessible energy regions from 80 meV to 1.0 eV indicates that there should not be a Ramsauer-Townsend minimum but rather a peak in the total cross section at an energy of approximately 0.4 eV.

Weak measurement enables faithful amplification and high-precision measurement of small physical parameters and is under intensive investigation as an effective tool in metrology and for addressing foundational questions in quantum mechanics. Here we demonstrate weak-value amplification using the asymmetric spectral response of Fano resonance as the pointer arising naturally in precisely designed metamaterials, namely, waveguided plasmonic crystals. The weak coupling between the polarization degree of freedom and the spectral response of Fano resonance arises due to a tiny shift in the asymmetric spectral response between two orthogonal linear polarizations. By choosing the preselected and postselected polarization states to be nearly mutually orthogonal, we observe both real and imaginary weak-value amplifications manifested as a spectacular shift of the Fano-resonance peak and narrowing (or broadening) of the resonance linewidth, respectively. The remarkable control and tunability of Fano resonance in a single device enabled by weak-value amplification may enhance active Fano-resonance–based applications in the nano-optical domain. In general, weak measurements using Fano-type spectral response broadens the domain of applicability of weak measurements using natural spectral line shapes as a pointer in a wide range of physical systems.

We report on the catalystlike effect of orbital angular momentum (OAM) on local spin-state conversion within the tightly focused radially polarized beams associated with optical spin-orbit interaction. It is theoretically demonstrated that the incident OAM can lead to a conversion of purely transverse spin state to a three-dimensional spin state on the focal plane. This conversion can be conveniently manipulated by altering the sign and value of the OAM. By comparing the total OAM and spin angular momentum (SAM) on the incident plane to those on the focal plane, it is indicated that the incident OAM have no participation in the angular momentum intertransfer, and just play a role as a catalyst of local SAM conversion. Such an effect of OAM sheds new light on the optical spin-orbit interaction in tight-focusing processes. The resultant three-dimensional spin states may provide more degrees of freedom in optical manipulation and spin-dependent directive coupling.

An exact formula of a two-time correlation function is derived for an open quantum system which interacts with a Gaussian thermal reservoir. It is provided in terms of functional derivative with respect to fictitious fields. A perturbative expansion and its diagrammatic representation are developed, where the small expansion parameter is related to a correlation time of the Gaussian thermal reservoir. The two-time correlation function of the lowest order is equivalent to that calculated by means of the quantum regression theorem. The result clearly shows that the violation of the quantum regression theorem is caused by a finiteness of the reservoir correlation time. By making use of an exactly solvable model consisting of a two-level system and a set of harmonic oscillators, it is shown that the two-time correlation function up to the first order is a good approximation to the exact one.

Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit (${}^{174}\mathrm{Yb}^{+}$) to a hyperfine qubit (${}^{171}\mathrm{Yb}^{+}$) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using ${}^{174}\mathrm{Yb}^{+}$ if the magnetic field can be stabilized with fluctuations smaller than $10\mu \mathrm{G}$.

Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both $(2\times 2)$-dimensional and $(3\times 3)$-dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible $(2\times 2)$-dimensional as well as $(3\times 3)$-dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.