We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schrödinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.

The local-constant-field approximation (LCFA) is an essential theoretical tool for investigating strong-field QED phenomena in background electromagnetic fields with complex spacetime structure. In our previous work [Phys. Rev. A 98, 012134 (2018)] we have analyzed the shortcomings of the LCFA in nonlinear Compton scattering at low emitted photon energies for the case of a background plane-wave field. Here, we generalize that analysis to background fields, which can feature a virtually arbitrary spacetime structure. In addition, we provide an explicit and simple implementation of an improved expression of the nonlinear Compton scattering differential probability that solves the main shortcomings of the standard LCFA in the infrared region and is suitable for background electromagnetic fields with arbitrary spacetime structure such as those occurring in particle-in-cell simulations. Finally, we carry out a systematic procedure to calculate the probability of nonlinear Compton scattering per unit of emitted photon light-cone energy and of nonlinear Breit-Wheeler pair production per unit of produced positron light-cone energy beyond the LCFA in a plane-wave background field, which allows us to identify the limits of validity of this approximation quantitatively.

We construct minimum-uncertainty states and a non-negative quasiprobability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relation of the two unitary operators related by the discrete Fourier transformation. It is shown that some assumptions in their proof can be justified by the use of the Perron-Frobenius theorem. The minimum-uncertainty states are the ones that saturate this uncertainty inequality. The continuum limit is closely analyzed by introducing a scale factor in the limiting scheme. Using the minimum-uncertainty states, we construct a non-negative quasiprobability distribution. Its marginal distributions are smeared out. However, we show that this quasiprobability is optimal in the sense that there does not exist a non-negative quasiprobability distribution with sharper marginal properties if the translational covariance in the phase space is assumed. Generally, it is desirable that the quasiprobability is complete, i.e., it contains full information of the state. We show that the obtained quasiprobability is indeed complete if the dimension of the state space is odd, whereas it is not if the dimension is even.

We consider a pair of coupled spins with Ising interaction in the $z$ direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large the available control fields become. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. The results of the present work are not restricted only to spin systems, but are expected also to find applications in other physical systems which can be modeled as interacting spins, for example, coupled quantum dots.

Measuring quantum states provides a means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized source by measuring two incompatible bases [Phys. Rev. X 6, 011020 (2016)]. As coherence is the necessary source for generating randomness, we extend the scheme and propose a framework for quantum random number generation with general uncharacterized coherence resource. The previous scheme can be treated as a special case under the framework by considering a nonlinear uncertainty-relation-based coherence witness. Considering general coherence witnesses, we propose a source-independent random-number generation scheme that achieves a higher randomness generation rate. Our paper highlights the close relation between coherence and random-number generation and may shed light on designing general semi-device-independent quantum information processing protocols.

We use an exact quantum phase model to study the dynamical generation of particle entanglement in a bosonic Josephson junction composed by two coupled and interacting Bose–Einstein condensates. Using analytical arguments, we show that linear coupling can accelerate the creation of entanglement with respect to the well-known one-axis twisting model where coupling is absent. Furthermore, with a numerical analysis of optimal control schemes, we identify the optimal parameters for the fast generation of metrologically useful entanglement on short timescales: the optimal evolution is generated for a specific ratio between the coupling and the interaction strength.

Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This midterm challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing the capability of current trapped-ion architectures in facing one of the most demanding parts of this quest: the implementation of an entangling controlled-NOT (CNOT) gate between encoded logical qubits. We present a detailed comparative study of two alternative strategies for trapped-ion topological color codes, either a transversal or a lattice-surgery approach, characterized by a detailed microscopic modeling of both current technological capabilities and experimental sources of noise afflicting the different operations. Our careful fault-tolerant design, together with a low-resource optimization, allows us to determine via exhaustive numerical simulations the experimental regimes where each of the approaches becomes favorable. We hope that our study thereby contributes to guiding the future development of trapped-ion quantum computers.

We consider the perfect transfer of a state between arbitrary nodes of one-dimensional spin-1/2 chain with optimally engineered couplings. Motivated by the fact that such a system could be used as a data bus for connecting multiple quantum processors, we derive two necessary and sufficient conditions that have to be met in order to perfectly transfer a state between any two nodes and we employ them to examine both open and closed geometries. Analytical calculations and numerical optimizations are performed for both cases in order to determine the reachability of certain target states and to provide optimal values for the couplings which ensure perfect fidelity. An important finding is that even-sized closed chains allow for perfect transfer between any pair of sites and therefore are a promising platform for the implementation of data bus protocols.

We present a classical optics simulation of the one-dimensional Dirac equation for a free particle. Positive- and negative-energy components are represented by orthogonal polarizations of a free propagating beam, while the spatial profile represents the spatial wave function of the particle. Using a completely tunable time parameter, we observed the oscillation of the average value of the Dirac position operator—known as Zitterbewegung. We are also able to measure the so-called mean-position operator which is a single-particle observable and presents no oscillations. Our work opens the way for optical simulation of interesting phenomenon of relativistic systems, as well as condensed-matter physics, without any requirement for specially engineered medium.

Without any assumption on detectors, measurement-device-independent quantum random-number generators (MDI QRNGs) with high generation rates have attracted lots of attention lately. However, the influence of statistical fluctuations on randomness extraction rate has not been taken into full consideration, which is crucial in the practical applications of MDI QRNGs. We propose a solution for MDI QRNGs, study the influence of statistical fluctuations, and apply an optimizing method to solve the lower bound of randomness extraction rate. Then the rate is simulated under reasonable values of some observed parameters, and it displays that the QRNG generates $6\times {10}^4\text{bit}/\text{s}$, if the transmission loss is 10 dB and the number of pulses sent from the source is $N={10}^{12}$. Compared with the rates of other MDI QRNGs, our simulation outputs are with genuine randomness, since the statistical fluctuations of all parameters are considered.

We report an experimental and theoretical study on the electronic structure of methyl iodide. The binding energy spectrum (BES) and electron-momentum profiles (EMPs) of valence orbitals have been measured using a high-sensitivity electron-momentum spectrometer at the impact energy of 1200 eV plus binding energy. Theoretical calculations considering the relativistic and electron correlation effects are performed to illuminate the measured results. For the two outermost orbitals, the relativistic effects are revealed by the experimental and theoretical EMPs for two spin-orbit splitting components ($2e_{3/2}$ and $2e_{1/2}$) and the C-I bonding orbital ($3a_1$). In the inner valence region, satellite structures associated with the ionizations from $2a_1$ and $1a_1$ orbitals are observed in the BES and the pole strengths for the satellites are determined by comparing the measured EMPs with the calculated ones. Moreover, distinct relativistic and electron correlation effects on the EMPs for the $2a_1$ orbital and its satellites have been found.

We study various properties of the $2p{}^{2}P_{1/2}-2p{}^{2}P_{3/2}$ fine-structure splittings in the boronlike ${\mathrm{S}}^{11+}, {\mathrm{Cl}}^{12+}, {\mathrm{Ar}}^{13+}$, and ${\mathrm{K}}^{14+}$ ions and the $4p{}^{2}P_{1/2}-4p{}^{2}P_{3/2}$ fine-structure splittings in the galliumlike ${\mathrm{Nb}}^{10+}, {\mathrm{Mo}}^{11+}, {\mathrm{Tc}}^{12+}$, and ${\mathrm{Ru}}^{13+}$ ions to find out the feasibility of using these highly charged ions as suitable optical atomic clocks. The roles of the electron correlations due to the Dirac-Coulomb-Breit Hamiltonian and accounting for lower-order quantum electrodynamics effects are shown explicitly in the calculations of electron affinities, excitation energies, transition-matrix elements, lifetimes, hyperfine-structure constants, and electric quadrupole moments of the states involved with clock transitions using a relativistic couple-cluster method. We also estimate the most commonly appearing systematic effects in the atomic clock experiments due to the electric quadrupole, the second-order Zeeman, both the dc and ac Stark, and the black-body radiation shifts in the aforementioned fine-structure splittings to demonstrate typical orders of magnitude of fractional frequency shifts.

High-precision spectroscopy of the ${}^1{S}_0{\text{−}}^1{D}_2$ clock transition of ${}^{176}\mathrm{Lu}^{+}$ is reported. Measurements are performed with Hertz level precision with the accuracy of the hyperfine-averaged frequency limited by the calibration of an active hydrogen maser to the SI definition of the second via a GPS link. The measurements also provide accurate determination of the ${}^1{D}_2$ hyperfine structure. Hyperfine structure constants associated with the magnetic octupole and electric hexadecapole moments of the nucleus are considered, which includes a derivation of correction terms from third-order perturbation theory.

The influence of oscillating quadrupole fields on atomic energy levels is examined theoretically, and general expressions for the quadrupole matrix elements are given. The results are relevant to any ion-based clock in which one of the clock states supports a quadrupole moment. Clock shifts are estimated for ${}^{176}\mathrm{Lu}^{+}$ and indicate that coupling to the quadrupole field would not be a limitation to clock accuracy at the $\lesssim {10}^{-19}$ level. Nevertheless, a method is suggested that would allow this shift to be calibrated. This method utilizes a resonant quadrupole coupling that enables the quadrupole moment of the atom to be measured. A proof-of-principle demonstration is given using ${}^{138}\mathrm{Ba}^{+}$, in which the quadrupole moment of the $D_{5/2}$ state is estimated to be $\mathrm{\Theta }=3.229\left(89\right)e{a}_0^2$.

We identify circumstances where the effective descriptions of microscopic physical systems leads to a self-consistent reduced dynamics for a truncated subset of the original variables. The effective Hamiltonian involves unusual Poisson brackets that bring in noncommutative geometry. In idealized models of ring molecules, we find time crystal behavior is widespread.

We introduce a theory for the stability of a condensate in an optical lattice. We show that the understanding of the stability-to-ergodicity transition involves the fusion of monodromy and chaos theory. Specifically, the condensate can decay if a connected chaotic pathway to depletion is formed, which requires swap of separatrices in phase space.

The electromagnetic field of optical vortices is in most cases derived from vector and scalar potentials using either a procedure based on the Lorenz or the Coulomb gauge. The former procedure has been typically used to derive paraxial solutions with Laguerre-Gauss radial profiles, while the latter procedure has been used to derive full solutions of the wave equation with Bessel radial profiles. We investigate the differences in the derivation procedures applying each one to both Bessel and Laguerre-Gauss profiles. We show that the electromagnetic fields thus derived differ in the relative strength of electric and magnetic contributions. The new solution that arises from the Lorenz procedure in the case of Bessel beams restores a field symmetry that previous work failed to resolve. Our procedure is further generalized and we find a spectrum of fields beyond the Lorenz and Coulomb gauge types. Finally, we describe a possible experiment to test our findings.

The parity-time ($\mathcal{P}\mathcal{T}$)-symmetric optical properties are significantly restored for broadband radiation if the width of the field spectrum is substantially less than the width of the spectral line of a resonant medium. This is the so-called quasi-$\mathcal{P}\mathcal{T}$-symmetry for broadband radiation. Under the quasi-$\mathcal{P}\mathcal{T}$-symmetric light-matter interaction, we describe the dynamics of a short spatially localized pulse propagating in the extended medium, when the length of propagation significantly exceeds the pulse size. As an example, the boundary problem of dynamical Bragg diffraction in the Laue geometry for a short laser pulse in a photonic crystal (PhC) with strong material dispersion is solved. It is shown that at exceptional point of the $\mathcal{P}\mathcal{T}$-symmetry breaking, the dynamics and parameters of the pulse change dramatically when the sign of the Bragg angle of incidence ${\theta }_B$ changes. Unidirectional zero Bragg reflection and unidirectional Bragg-diffraction-induced pulse splitting are revealed. At a positive angle, ${\theta }_B>0$, the localized short pulse propagates in a quasi-$\mathcal{P}\mathcal{T}$-symmetric PhC with gain and loss under Bragg diffraction condition as in a conservative transparent homogeneous medium. A change in the sign ${\theta }_B<0$ leads to the appearance of an amplified diffracted pulse. In the case of a small detuning from the exact Bragg condition, at ${\theta }_B<0$, the directions and magnitudes of the group velocities of different field modes change and, as a result, the temporal and spatial diffraction-induced pulse splitting occurs. Such asymmetric dynamics of the pulse propagation in a quasi-$\mathcal{P}\mathcal{T}$-symmetric PhC can be used to effectively control the parameters and dynamics of short optical pulses by small changes in its frequency, in the magnitude of the gain and loss parameter of the medium, etc.

We present a perturbation approach to calculate the optical modes in arbitrary weakly deformed disks. By introducing a small perturbation parameter into the mode equation and interface conditions, the original problem is decomposed into different orders of perturbation problems. In this paper, we focus on the linear perturbation method, which is able to provide good approximations to solutions for arbitrary weakly deformed disks. Our linear perturbation method is able to explain the mode-splitting phenomena of the clockwise and counterclockwise degeneracy. We apply our perturbation method to limaçon and spiral cavities, and the perturbation results agree well with numerical results of the full problem.

We studied the Hanbury Brown and Twiss (HBT) bunching effect of discrete chaotic light sources. It is found that, for periodical discrete chaotic light sources, the HBT bunching effect collapses first but then revives repeatedly at specific transverse distances between two detectors in the far-field detection plane, which is very different from the HBT bunching effect with a spatially continuous chaotic light source. Such transverse revivals of the HBT bunching effect are the result of in-phase superposition of all discrete two-photon eigen modes of the periodical discrete chaotic light sources. In addition to the integer HBT bunching revival, the fractional HBT bunching revival can also be observed with nonperiodical discrete chaotic light sources due to the in-phase constructive interference of parts of the two-photon eigen modes. Experimental verification on both the integer and the fractional HBT bunching revivals are given. The transverse revival and fractional revival of the HBT bunching effect provide an efficient way for imaging processing such as ghost image copy in the detection plane.