In a recent paper [A. Unnikrishnan et al., Phys. Rev. Lett. 122, 240501 (2019)], a quantum anonymous communication protocol was proposed in the presence of malicious agents and an untrusted source. Here, we point out that malicious agents can change the generated anonymous entanglement between the sender and the receiver without being detected, which means that the correctness of the generated anonymous entanglement should be reexamined. The way to check the above correctness is discussed.

We propose the generation of effective three-body interactions in superconducting circuits by coupling qubits or resonators to a bus qubit. Such interactions are characterized by energy exchange between two qubits or resonators depending on the state of the bus qubit. We show that a controlled-iswap (-$\sqrt{\mathrm{i}swap}$) gate can be naturally implemented based on the three-body interactions and it can be used to construct a quantum Fredkin (controlled-swap) gate. A generalized Fredkin gate which controls the swapping of photons between two resonators can be realized in a similar way. It can be used to generate the entangled state of a high number of photons. This proposal is promising to be demonstrated with superconducting circuits previously reported and will stimulate the implementation of multiqubit quantum gates based on many-body interactions.

We have measured the absolute frequency of the $2{}^{1}S_0–3{}^{1}D_2$ two-photon transitions in ${}^3\mathrm{He}$ at 1009 nm based on a cesium frequency standard through an optical frequency comb. The measured frequencies are 594 384 961.072(19) MHz for the $2{}^{1}S_{0,1/2}–3{}^{1}D_{2,5/2}$ transition and 594 384 821.209(15) MHz for the $2{}^{1}S_{0,1/2}–3{}^{1}D_{2,3/2}$ transition with relative uncertainties of $2.5\times {10}^{-11}$ and $3.9\times {10}^{-11}$, respectively. The determination of the $2{}^{1}S_0–3{}^{1}D_2$ two-photon transition frequency, without hyperfine effect, in ${}^3\mathrm{He}$ is 594 384 761.556(12) MHz. The deduced isotope shift between ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ is 29.530246(18) GHz. The difference of the squares of the nuclear charge radii is deduced to be $1.059\left(25\right){\mathrm{fm}}^2$. Finally, by combining other precise measured transitions, we are able to derive the $3{}^{3}D_1–3{}^{1}D_2$ separation in ${}^3\mathrm{He}$ to be 101 058 203(56) kHz, which is an improvement by a factor of 89 compared to previous work.

A variational theory called free-complement (FC) $s_{ij}$ theory for solving the Schrödinger equation of atoms and molecules using only one- and two-electron integrals over Slater or Gaussian functions is proposed. It is derived from the scaled Schrödinger equation [Phys Rev. Lett. 93, 030403 (2004)] by replacing the two-electron part $r_{ij}$ of the scaling $g$ operator with $s_{ij}=r_{ij}^2$, both of which solve the divergence difficulty inherent to the original Schrödinger equation by avoiding the interelectron collisions. The $s_{ij}$ function can be rewritten with only one-electron functions so that when the initial wave function of the FC theory is composed of only one-electron functions, the FC wave function including $s_{ij}$ can be rewritten with only one-electron functions. Therefore, the variational calculations of the FC $s_{ij}$ theory can be performed with only one- and two-electron integrals. However, in comparison with the $r_{ij}$ function, the $s_{ij}$ function behaves less efficiently when two electrons come close to each other: the electron-electron cusp condition is not satisfied with the FC $s_{ij}$ theory, though the wave function has explicit $r_{ij}$ dependence. On the other hand, the electron-nuclear cusp condition is satisfied, even with the Gaussian functions, for the presence of the electron-nuclear function $r_{iA}$ in the $g$ operator. Test applications of the FC $s_{ij}$ theory were done to He, Li, and the ${}^{5}S^{\mathrm{o}} {\mathit{sp}}^3$ state of carbon atom and to hydrogen molecule using the local-molecular orbital (MO)- and valence bond (VB)-type initial functions. We examined both Slater and Gaussian functions. As the order of the FC theory increased, the wave functions were improved and the energies approached from a few kcal/mol to less than 1 kcal/mol accuracies relative to the known exact values. Thus, with the FC $s_{ij}$ theory, the Schrödinger equation was solved to less than 1 kcal/mol accuracy for all the systems examined. The costs for the $s_{ij}$ calculations were much smaller than those of the $r_{ij}$ theory. However, for the ${}^{5}S^{\mathrm{o}} {\mathit{sp}}^3$ state of the carbon atom, we observed that the convergence rate became slow when the calculation came close to $\sim 1$ kcal/mol accuracy. This suggests that for the FC $s_{ij}$ theory, the calculations would become easier if the required accuracy is within a few kcal/mol for the absolute energy. Actually, what we need in chemical studies are mostly related to the difference energy, whose accuracy could be better than that of the absolute energy with the robust variational method. Two lines of future studies were suggested.

We report Doppler-free two-photon absorption of ${\mathrm{N}}_2\mathrm{O}$ at $\lambda =4.53\mu \mathrm{m}$, measured by cavity ring-down spectroscopy. High power was achieved by optical self-locking of a quantum cascade laser to a linear resonator of finesse $\mathcal{F}=22730$, and accurate laser detuning over a 400-MHz range was measured relative to an optical frequency comb. At a sample pressure of $p=0.13\mathrm{kPa}$, we report a large two-photon cross section per molecule of ${\sigma }_{13}^{\left(2\right)}=8.0\times {10}^{-41}\mathrm{c}{\mathrm{m}}^4\mathrm{s}$ for the $Q\left(18\right)$ rovibrational transition at a resonant frequency of ${\nu }_0=66179400.8\mathrm{MHz}$.

We present a theoretical investigation of the radiative recombination of twisted electrons into bound states of initially bare ions. Special emphasis is placed on the magnetic sublevel population of the residual hydrogenlike ions under the assumption that emitted photons remain unobserved. We show that this sublevel population strongly depends on the position of an ion within the incident electron wave front. To better understand this position dependence, detailed calculations are presented for the electron capture into $1s_{1/2}$ and $2p_{3/2}$ ionic states. The results of the calculations show that the structured beams of hydrogenlike ions can be produced in collisions with Bessel electrons at ion storage rings. Having multiple-ring intensity profiles and complex spin patterns, these structured beams can become a valuable tool for future ion collision studies.

We theoretically investigate a Bose-Einstein condensate confined by a rotating harmonic trap whose rotation axis is not aligned with any of its principal axes. The principal axes of the Thomas-Fermi density profiles of the resulting stationary solutions are found to be tilted with respect to those of the rotating trap, representing an extra degree of freedom that is associated with the existence of additional branches of stationary solutions for any given rotation axis alignment. By linearizing the time-dependent theory about the stationary states, we obtain a semianalytical prediction of their dynamical instability at high rotation frequencies against collective modes arising from environmental perturbations. Comparing the stationary states to direct simulations of the Gross-Pitaevskii equation, we predict the nucleation of quantum vortices in the dynamically unstable rotational regime. These vortex lines are aligned along the rotation axis despite the tilting of the rotating trap although the background density profile is tilted with respect to the trapping and rotation axes.

We investigate the formation of trimers in an infinite one-dimensional lattice model of hard-core particles with single-particle hopping $t$ and and nearest-neighbor two-body $U$ and three-body $V$ interactions of relevance to Rydberg atoms and polar molecules. For sufficiently attractive $U\le -2t$ and positive $V>0$ a large trimer is stabilized, which persists as $V\to \infty$, while both sufficiently attractive $U$ and $V$ bind a small trimer. The excited state above this small trimer is also bound and has a large extent; its behavior as $V\to -\infty$ resembles that of the large ground-state trimer. These large bound states appear to admit a continuum description. Furthermore, we find that in the limit $V\gg t,U<-2t$ the bound-state behavior qualitatively evolves with larger $\left|U\right|$ from a state described by the scattering of three far separated particles to a state of a compact dimer scattering with a single particle.

In recent years, several works have demonstrated the advantage of photon-subtracted Gaussian states for various quantum optics and information protocols. In most of these works, the relation between the advantages and the usual increasing energy of the quantum state related to photon subtraction was not clearly investigated. In this paper, we study the performance of an interferometer injected with multiphoton-annihilated squeezed vacuum states mixed with coherent states for both single- and correlated-phase estimations. For single-phase estimation, although the use of multiphoton-annihilated squeezed vacuum states at low mean photons per mode provides an advantage compared to classical strategy, when the total input energy is held fixed, the advantage due to photon subtraction is completely lost. However, for the correlated case in the analogous scenario, some advantage appears to come from both the energy rise and improvement in photon statistics. In particular quantum enhanced sensitivity with photon-subtracted states appears more robust to losses, showing an advantage of about $30\%$ with respect to the squeezed vacuum state in the case of a realistic value of the detection efficiency.

We study the interaction of laser pulses carrying orbital angular momentum (OAM) with structural asymmetry quantum-dot molecules characterized by four energy levels. We demonstrate how the interdot tunneling endows exchange of optical vortices between different frequencies. We consider a case where a weak probe beam has an optical vortex and thus has a zero intensity at the center. The presence of tunneling coupling generates an additional weak laser beam with the same vorticity as that of the incident vortex beam. We analyze conditions for the vortex of the initial beam to be transferred efficiently to the generated beam. The propagation of Laguerre-Gaussian (LG) beams possessing OAM states characterized by both azimuthal and radial indices is then investigated for the case where the strong control beam is also an OAM mode. It is shown that the conservation of OAM states is always satisfied over the OAM exchange process. Yet, an abnormal case is observed in which the radial index induces some intensity patterns of the generated beam which differs from a pure LG beam of incident beams. Analytical solutions are provided to elucidate such effects induced by radial indices on propagation characteristics of OAM beams. When superimposing two initially present weak OAM modes, it is observed that the resulting optical vortices move about the beam axis as the light propagates, forming a sort of “constellation” around the center. The shift in axis of such a composite pulse is due to the effect of interdot tunneling which is controlled by an external electric voltage. The optical angular momenta may add a new degree of freedom in the study of solid systems suitable for quantum technologies.

It has long been recognized as a difficult problem to determine whether the observed statistical correlations between two classical variables arise from causality or from common causes. Recent research has shown that, in a quantum theoretical framework, the mechanisms of entanglement and quantum coherence provide advantages in tackling this problem. In some particular cases, quantum common causes and quantum causality can be effectively distinguished by using observations alone. However, these solutions do not apply to all cases. There still exist a large class of cases in which quantum common causes and quantum causality cannot be distinguished. In this paper, along the line of considering unitary transformation as causality in the quantum world, we formally show that quantum common causes and quantum causality are universally separable. Based on the analysis, we further provide a general method to discriminate the two.

We propose a method for enacting the unitary time propagation of two interacting neutrons at leading order of chiral effective-field theory by efficiently encoding the nuclear dynamics into a single multilevel quantum device. The emulated output of the quantum simulation shows that, by applying a single gate that draws on the underlying characteristics of the device, it is possible to observe multiple cycles of the nuclear dynamics before the onset of decoherence. Owing to the signal's longevity, we can then extract spectroscopic properties of the simulated nuclear system. This allows us to validate the encoding of the nuclear Hamiltonian and the robustness of the simulation in the presence of quantum-hardware noise by comparing the extracted spectroscopic information to exact calculations. This work paves the way for transformative calculations of the dynamical properties of nuclei on near-term quantum devices.

Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole–dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with $>0.999$ fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups.

We analyze neutral atom Rydberg $C_Z$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity $\mathcal{F}>0.999$ by using adiabatic rapid passage pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity $\mathcal{F}=0.997$. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room-temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion.

We report modulation-transfer spectroscopy (MTS) on the $6\mathit{s}6\mathit{p}{}^{3}P_0\leftrightarrow 6\mathit{s}7\mathit{s}{}^{3}S_1$ transition in neutral ytterbium (Yb) isotopes in a hollow cathode lamp. The MTS dispersive signals show an effective linewidth of 70 MHz, contributed primarily by the pressure broadening. MTS has demonstrated the capability of completely resolving all isotopic lines, except the one in low-abundance ${}^{168}\mathrm{Yb}$. Frequency measurements of the isotope-stabilized laser are performed using an optical comb, and systematic shifts therein are corrected. We have examined the relative isotope shifts, and the hyperfine constants for the $6\mathit{s}7\mathit{s}{}^{3}S_1$ state are given as $\mathit{A}\left({}^{171}\mathrm{Yb}\right)=6837.83\left(19\right)$ MHz, $\mathit{A}\left({}^{173}\mathrm{Yb}\right)=-1891.46\left(7\right)$ MHz and $\mathit{B}\left({}^{173}\mathrm{Yb}\right)=-0.62\left(16\right)$ MHz. Our results are in reasonable agreement with previously reported values and essentially resolve the existing discrepancies.

Ground-state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-$1/2$ one-dimensional (1D) Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasiparticle transformation by allowing for Cooper pairing to exist between all possible single-particle states and accounts for the effects of the inhomogeneous trapping potential as well as the mean-field Hartree potential. This provides an unbiased framework to describe inhomogeneous densities and pairing correlations in the FFLO state of a confined 1D gas. In a harmonic trap, numerical minimization of the HFB ground-state energy yields a spatially oscillating order parameter reminiscent of the FFLO state. However, we find that this state has almost no imprint in the local fermion densities (consistent with experiments that found no evidence of the FFLO phase). In contrast, for a hard-wall geometry, we find a strong signature of the spatial oscillations of the FFLO pairing amplitude reflected in the local in situ densities. In the hard-wall case, the excess spins are strongly localized near regions where there is a node in the pairing amplitude, creating an unmistakable crystalline modulation of the density.

We present a theoretical study of Fano interference effects in few-photon transport. Under appropriate conditions, a local defect in an optical waveguide induces a highly asymmetric transmission line shape, characteristic of Fano interference. For a two-level emitter placed adjacent to such a defect, here modeled as a partially transmitting element, we find an analytical expression for the full-time evolution of single-photon wave packets and the emitter excitation probability. We show how the partially transmitting element affects the emitter lifetime and shifts the spectral position of the effective system resonances. Using input-output formalism, we determine the single- and two-photon $S$ matrices for both a two-level emitter and a cavity-emitter system coupled to a waveguide with a partially transmitting element. We show how the Fano interference effect can be exploited for the implementation of a Hong-Ou-Mandel switch in analogy with a tunable linear or nonlinear beam splitter.

The physics of Markovian open quantum systems can be described by quantum master equations. These are dynamical equations that incorporate the Hamiltonian and jump operators and generate the system's time evolution. Reconstructing the system's Hamiltonian and its coupling to the environment from measurements is important both for fundamental research and for performance evaluation of quantum machines. Here we introduce a method that reconstructs the dynamical equation of open quantum systems, directly from a set of expectation values of selected observables. We benchmark our technique both by a simulation and experimentally, by measuring the dynamics of a trapped ${}^{88}{\text{Sr}}^{+}$ ion qubit under spontaneous photon scattering.

The main challenges in achieving high-fidelity quantum gates are to reduce the influence of control errors caused by imperfect Hamiltonians and the influence of decoherence caused by environment noise. To overcome control errors, a promising proposal is nonadiabatic holonomic quantum computation, which has attracted much attention in both theories and experiments. While the merit of holonomic operations resisting control errors has been well exploited, an important issue following is how to shorten the evolution time needed for realizing a holonomic gate so as to avoid the influence of environment noise as much as possible. In this paper, we put forward a general approach of constructing Hamiltonians for nonadiabatic holonomic quantum computation, which makes it possible to minimize the evolution time and might open a new horizon for the realistic implementation of nonadiabatic holonomic quantum computation.

In this paper we systematically investigate the stability of the restricted Hartree-Fock (RHF) solutions for all closed-shell atoms and ions up to xenon-like systems by means of a symmetry-adapted Thouless stability matrix. We express the RHF solution and the lowest eigenvalue of the stability matrix in the form of a series in $1/Z$; $Z$ is the nuclear charge. Using Padé and Weniger sequence transformations, we first determine the onset of the pure singlet instability, i.e., the instability preserving all the symmetries of the underlying Hamiltonian, and identify it with the critical charge $Z_c$, i.e., the smallest charge supporting a bound-state RHF solution. This thus finally gives a physical meaning to the pure singlet instability. Consequently, we find that no basis-set-independent RHF solution for any doubly charged anion exists. Second, we determine the onset of instabilities associated with the breaking one of the symmetries of the Hamiltonian and give a simple qualitative criterion for their appearance. In particular, we find that once the shells are no longer filled according to the Aufbau principle for hydrogenic energy levels, cations are generally unstable with respect to monoexcitations violating the spherical symmetry.