Considering the parity symmetry related to the Dirac equation, the interplay between energy localization and the temporal evolution of parity-defined quantum superpositions is investigated for fermions in a magnetic field. The unitary evolution of Dirac cat states is obtained by initializing either even or odd principal quantum numbers in the equivalent harmonic oscillator basis in relativistic Landau levels. Quantum operators feature well-defined selection rules for states thus identified, exhibiting a permanent revival structure. Our analysis is specialized for the survival probability function and for the expectation values of spinor matrix operators, which are identified as quantifiers of spin-parity correlations encoded in Dirac bispinors. In such a context, the time-evolving quantum state also imprints a signature on the energy expansion. Namely, frequencies associated with revivals are doubled for each revival order, being observed up to a so-called super revival timescale. Results show that Dirac cat states exhibit a fractional revival structure, which works as a probe of suppressions and regenerations of intrinsic correlations driven by the discrete spin-parity degrees of freedom of Dirac bispinors.

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasimonochromatic optical beam (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling intrinsic to the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion and which belongs to the recently studied class of “space-time wave packets.” We show that the predicted transformation from a quasimonochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.

We investigate theoretically the dynamics of 1-norm geometric quantum correlations and their classical counterparts in a two-qubit system. Both qubits are initially prepared in Bell-diagonal states and locally coupled to separated thermal squeezed baths or a common squeezed thermal bath via energy-preserving interactions. We then unveil the effects of reservoir squeezing on the abrupt changes in the evolution of geometric correlations. It is found that adequately tuning the squeezing phase can efficiently suppress the dephasing rate and delay the appearance of sudden transitions in geometric correlations. Further, we show that the squeezing phase of the bath renders a different avenue to enhance the finite time interval for frozen quantum correlation. On the other hand, in this context, we show that the squeezing strength of the reservoir exhibits a negative role. In addition, in the common bath case, we observe the steady-state correlations and decoherence-free subspace, which can be governed via squeezing parameters. Moreover, the abrupt change from a decaying regime to a constant nonzero value in classical correlation signals the emergence of a pointer-state basis. We show that the emergence of a pointer-state basis can be delayed by suitably adjusting the bath squeezing parameters. Remarkably, we find the optimal value of the squeezing phase, which introduces maximum retardation in the appearance of a pointer-state basis.

Quantum circuits performing arithmetic operations are critical in quantum computing because of the need for such operations in proven quantum algorithms. Although quantum computers are becoming increasingly resourceful, the number of qubits currently available is still limited. Furthermore, these qubits are heavily affected by internal and external noise. It has been proven that quantum circuits built using Clifford $+T$ gates can be made fault tolerant. However, the use of the $T$ gates comes at a very high cost. If the number of $T$ gates used in a circuit is not optimized, the cost of the circuit will be increased excessively. As a consequence, it is essential to optimize the circuits so that they are as resource efficient as possible and also noise tolerant. This paper presents the design of a circuit to perform the multiplication of two integers. The circuit is built using only Clifford $+T$ gates for compatibility with error detection and correction codes. It outperforms the circuits in the state of the art in terms of $T$ count and $T$ depth.

High-fidelity single- and multiqubit operations compose the backbone of quantum information processing. This fidelity is based on the ability to couple single- or two-qubit levels in an extremely coherent and precise manner. A necessary condition for coherent quantum evolution is a highly stable local oscillator driving these transitions. Here we study the effect of fast noise, that is, noise at frequencies much higher than the local oscillator linewidth, on the fidelity of one- and two-qubit gates in a trapped-ion system. We analyze and measure the effect of fast noise on single-qubit operations, including resonant $\pi$ rotations and off-resonant sideband transitions. We further numerically analyze the effect of fast phase noise on the Mølmer-Sørensen two-qubit gate. We find a unified and simple way to estimate the performance of all of these operations through a single parameter given by the noise power spectral density at the qubit response frequency. While our analysis focuses on phase noise and on trapped-ion systems, it is relevant for other sources of fast noise as well as for other qubit systems in which spinlike qubits are coupled by a common bosonic field. Our analysis can help in guiding the design of quantum hardware platforms and gates, improving their fidelity towards fault-tolerant quantum computing.

Ion transport is an essential operation in some models of quantum information processing, where fast ion shuttling with minimal motional excitation is necessary for efficient high-fidelity quantum logic. While fast and cold ion shuttling has been demonstrated, the dynamics and specific trajectory of an ion during diabatic transport have not been studied in detail. Here we describe a position-dependent optical deshelving technique useful for sampling an ion's position throughout its trajectory and we demonstrate the technique on fast linear transport of a ${}^{40}{\text{Ca}}^{+}$ ion in a surface-electrode ion trap. At high speed, the trap's electrode filters strongly distort the transport potential waveform. With this technique, we observe deviations from the intended constant-velocity (100-m/s) transport: We measure an average speed of 82(2) m/s and a peak speed of 251(6) m/s over a distance of 120 $\mu \mathrm{m}$.

Quantum entanglement of atoms enables precision measurement and frequency metrology beyond the standard quantum limit that is imposed by the quantum projection noise. Here we propose employing entangled atoms in the synchronous differential measurement to enhance the detection sensitivity of spatially dependent frequency shift. Two ways of engineering entangled atoms are studied. The synchronous comparison between two pixels within an entangled atomic cloud leads to a sensitivity enhancement factor of 1.4 over the standard quantum limit. The sensitivity enhancement becomes saturated for a large number of atoms. In contrast, the synchronous comparison between two independent pixels that are individually composed of entangled atoms allows for a strong sensitivity enhancement by a factor of, for example, about 10 with ${10}^3$ entangled atoms in each pixel, corresponding to a reduction of the averaging time by a factor of about ${10}^2$. A large atom number may further elevate the sensitivity. Our work paves the way towards the entanglement-enhanced detection of gravitational redshift by means of the in situ imaging spectroscopy.

We consider a system of composite bosons given by strongly bound fermion pairs tunneling through sites that form a low-dimensional network. It has been shown that the ground state of this system can have condensatelike properties in the very dilute regime for two-dimensional lattices but displays fermionization for one-dimensional lattices. Studying graphs with fractal dimensions, we explore intermediate situations between these two cases and observe a correlation between increasing dimension and increasing condensatelike character. However, this is only the case for graphs for which the average path length grows with power smaller than 1 in the number of sites and which have an unbounded circuit rank. We thus conjecture that these two conditions are relevant for condensation of composite bosons in arbitrary networks and should be considered jointly with the well-established criterion of high entanglement between constituents.

We successfully fabricated silicon-on-insulator (SOI) photonic crystal (PhC) slabs in which electromagnetic topological band gaps and edge modes were materialized for symmetric transverse-electric-like modes. Because the structure of our specimens can be regarded as symmetric about the horizontal middle plane of the PhC slab, their symmetric and antisymmetric eigenmodes were rigorously separated, so we could achieve genuine photonic band gaps for the former. We fabricated those specimens by electron beam lithography of the top Si layer of SOI wafers and successive plasma-enhanced chemical vapor deposition of a ${\mathrm{SiO}}_2$ capping layer. We confirmed the complete common band gap of topologically trivial and nontrivial PhCs and the topological edge modes on the boundary between them by angle-resolved reflection spectroscopy in the mid-infrared range. This is an observation of the common band gap and edge modes that materialized in symmetric PhC slabs without a membrane structure, that is, without the etching of a sacrificial layer under the PhC to increase the refractive-index contrast and the width of the common band gap.

Atom-photon dressed states are a basic concept of quantum optics. Here, we demonstrate that the non-Hermiticity of an open cavity can be harnessed to form the dressed bound states (DBSs) and identify two types of DBSs, the vacancylike DBS and Friedrich-Wintgen DBS, in a microring resonator operating at a chiral exceptional point. With the analytical DBS conditions, we show that the vacancylike DBS occurs when an atom couples to the standing-wave mode that is a node of the photonic wave function and characterized by null spectral density at cavity resonance. However, the Friedrich-Wintgen DBS can be accessed by continuously tuning the system parameters, such as the atom-photon detuning, and evidenced by a vanishing Rabi peak in the emission spectrum, an unusual feature in the strong-coupling anticrossing. We also demonstrate the quantum-optics applications of the proposed DBSs. Our work exhibits quantum state control through non-Hermiticity of open quantum system and presents a clear physical picture of DBSs at chiral exceptional points, which holds great potential for building high-performance quantum devices for sensing, photon storage, and nonclassical light generation.

We study the photon blockade at exceptional points for a non-Hermitian optomechanical system coupled to the driven whispering-gallery-mode microresonator with two nanoparticles under the weak optomechanical coupling approximation, where exceptional points emerge periodically by controlling the relative angle of the nanoparticles. We find that conventional photon blockade occurs at exceptional points for the eigenenergy resonance of the single-excitation subspace driven by a laser field and discuss the physical origin of conventional photon blockade. Under the weak driving condition, we analyze the influences of the different parameters on conventional photon blockade. We investigate conventional photon blockade at nonexceptional points, which exists at two optimal detunings due to the eigenstates in the single-excitation subspace splitting from one (coalescence) at exceptional points to two at nonexceptional points. Unconventional photon blockade can occur at nonexceptional points, while it does not exist at exceptional points since the destructive quantum interference cannot occur due to the two different quantum pathways to the two-photon state not being formed. The realization of photon blockade in our proposal provides a viable and flexible way for the preparation of single-photon sources in the non-Hermitian optomechanical system.

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

It is shown that there are anomalous bound-state solutions to the two-body Dirac equation for an electron and a positron interacting via an electromagnetic potential. These anomalous solutions have quantized coordinates at nuclear distances (fermi) and are orthogonal to the usual atomic positronium bound states as shown by a simple extension of the Bethe-Salpeter equation. It is shown that the anomalous states have many properties which correspond to those of neutrinos.

We investigate the ionization momentum spectrum of a bound system composed of two oppositely charged particles, which interact via electromagnetic forces, under nonrelativistic Compton scattering. Our analysis focuses on positronium, a unique system that can be experimentally realized. We find that as the incident photon energy increases, the ionization momentum spectrum of positrons and electrons converges to their respective bound-state momentum distributions. This property distinguishes positronium from the hydrogen atom and can be attributed to the mass ratio $R_m$ of the two particles in the system. We provide a detailed analysis of the effect of $R_m$ and demonstrate the existence of hydrogenlike atoms with $R_m\ne 1$ that exhibit similar behavior in Compton scattering. Such atoms correspond to exotic systems found in nature.

In a recent experiment [P. Weckesser et al., Nature (London) 600, 429 (2021)], the quantum $s$-wave regime was attained for an alkali-metal and alkaline-earth atom-ion combination $\left({\mathrm{LiBa}}^{+}\right)$. We investigate possible outcomes from the interaction of this ion-atom pair at quantum regimes from a theoretical point of view. For this purpose, Born-Oppenheimer potential energy surfaces are constructed for the three lowest dissociation channels of the ${\left(\mathrm{Ba}\text{−}\mathrm{Li}\right)}^{+}$ molecular system using a multireference configuration interaction electronic-structure calculation. We present elastic, spin-exchange (SE), and diffusion cross sections in different energy regimes. The collisional properties of this system are calculated in terms of the scattering phase shifts and scattering cross sections, and the semiclassical behavior at a relatively high energy limit is also examined. For SE collisions, phase locking is obtained towards lower partial waves.

A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches $5\times {10}^{-14}$ at ${10}^3$ s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.

Photon addition and subtraction render Gaussian states non-Gaussian. We provide a quantitative analysis of the change in nonclassicality produced by these processes by analyzing the Wigner negativity and quadrature coherence scale (QCS) of the resulting states. The QCS is a recently introduced measure of nonclassicality [Phys. Rev. Lett. 122, 080402 (2019); Phys. Rev. Lett. 124, 090402 (2020)], which we show to undergo a relative increase under photon addition and subtraction that can be as large as 200%. This implies that the degaussification and the concomitant increase of nonclassicality come at a cost. Indeed, the QCS is proportional to the decoherence rate of the state so that the resulting states are considerably more prone to environmental decoherence. Our results are quantitative and rely on explicit and general expressions for the characteristic and Wigner functions of photon-added and -subtracted single- and multimode Gaussian states for which we provide a simple and straightforward derivation. These expressions further allow us to certify the quantum non-Gaussianity of the photon-subtracted states with positive Wigner function.

The violation of contextuality inequalities shows a strong conflict between the noncontextual hidden variable theory and quantum mechanics. A single qutrit is the simplest indivisible quantum system that can allow a state-dependent contextuality test with five observables and a state-independent contextuality test with 13 observables. For any qutrit states, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated [P. Kurzynski and D. Kaszlikowski, Phys. Rev. A 86, 042125 (2012)]. In this paper, we demonstrate the violation of this inequality using single-photon experiments. Our experiments not only enrich the tests of quantum contextuality, but also deepen the understanding of the physical nature of quantum mechanics.

The Duan-Lukin-Cirac-Zoller (DLCZ) scheme is a potential method to establish remote entanglements and realize large-scale quantum networks. Here we propose a DLCZ-like scheme based on the noiseless photon echo in rare-earth ion-doped crystals. Correlated photon pairs with a controllable delay can be created by the direct optical rephasing. Theoretical analysis indicates that the protocol is efficient in the low-optical-depth regime. This protocol could be feasibly implemented to establish long-lived quantum correlations between a photon and a spin-wave excitation in rare-earth ion-doped crystals.

The study of positive muon ${\mu }^{+}$-He scattering plays an important role in precision experiments involving positive muons. In this paper, we employed the confined variational method to investigate $S$-wave ${\mu }^{+}$-He scattering with scattering momenta below $0.1a_0^{-1}$, where $a_0$ denotes the Bohr radius. Our approach yielded accurate $S$-wave phase shifts and scattering lengths. By utilizing the modified effective range formula, we determined the $S$-wave scattering lengths to be $-12.3a_0$ and $-10.6a_0$ for ${\mu }^{+}\text{−}{}^4\mathrm{He}$ and ${\mu }^{+}\text{−}{}^3\mathrm{He}$ scattering, respectively. Furthermore, we examined the distortion effects on helium induced by ${\mu }^{+}$.