When nitrogen molecules are irradiated by near-infrared lasers around 1000 nm, significant ${{\mathrm{N}}_2}^{+}$ lasing at 391 nm $[B{}^2{\mathrm{\Sigma }}_u^{+}(v^{″}=0)\to X{}^2{\mathrm{\Sigma }}_g^{+}(v=0)]$ occurs. Here we theoretically investigate the underlying mechanism and identify the formation of population inversion between the $X{}^2{\mathrm{\Sigma }}_g^{+}(v=0)$ and $B{}^2{\mathrm{\Sigma }}_u^{+}(v^{″}=0)$ states within the 900- to 1100-nm wavelength range, which is characterized by distinct multipeak structure. Using time-dependent Floquet theory, we demonstrate that the multipeak structure arises from three-photon Rabi oscillations. These oscillations are modulated by nonadiabatic transitions between Floquet states, which ultimately determines the population inversion dynamics. Furthermore, our simulations successfully reproduce the experimentally observed wavelength-dependent lasing signals and reveal that the rarely observed three-photon Rabi oscillations can be reflected in the pulse-duration dependence of the lasing intensity. This work suggests a strategy for controlling ${{\mathrm{N}}_2}^{+}$ lasing through tailored multiphoton interactions, providing valuable insights into the coherent control of molecular dynamics.

We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in (-out) field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution nonperturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated micro-ring resonator side coupled to an input-output waveguide, but is readily generalizable to other integrated structures, while including a variety of (nonsqueezing) third-order interactions. An example of a single-pump, nondegenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.

Leveraging the sensitive dependence of a giant atom's relaxation rate on its frequency [A. F. Kockum et al., Phys. Rev. A 90, 013837 (2014)], we propose an effective magnetometer model based on a single giant emitter. In this model, the emitter's frequency is proportional to the applied bias magnetic field. The self-interference effect causes the slope of the decay rate to vary linearly with the number of emitter-waveguide coupling points. The giant emitter magnetometer achieves a sensitivity as high as ${10}^{-8}–{10}^{-9}\mathrm{T}/\sqrt{\mathrm{Hz}}$, demonstrating the significant advantages of the self-interference effect compared to small emitters. We hope our proposal will expand the applications of giant emitters in precision measurement and magnetometry.

In recent years, extensive research has been dedicated to the study of parity-time ($\mathcal{PT}$) symmetry, which involves the engineered balance of gain and loss in non-Hermitian optics. Complementary to $\mathcal{PT}$ symmetry, the concept of anti-$\mathcal{PT}$ symmetry has emerged as a natural framework for describing the dynamics of open systems with dissipations. In this work, we study spectral transitions and photon transmission in a linear spinning resonator perturbed by nanoparticles. First, we show that by precisely controlling the nanoparticle perturbations, the eigenvalues (or spectra) of a non-Hermitian system satisfying anti-$\mathcal{PT}$ symmetry can transit to that of a quasiclosed Hermitian system. Second, we outline the essential conditions for constructing a quasiclosed system and analyze its dynamic behavior with respect to photon transmission. By adjusting the rotational angular velocity of the spinning resonator and the strength of the nanoparticle perturbations, the quasiclosed system enables a variety of photon distribution behaviors, which may have significant applications in quantum devices. Our findings offer valuable insights for the design of dissipative quantum devices under realistic conditions and for understanding their responses to external perturbations.

In their paper [Phys. Rev. A 109, 022238 (2024)], Aredes and Saldanha analyze several paradoxes related to weak values and present a “general argument” that aims to show that “realistic interpretations $...$ of weak values lead to inconsistencies.” Although we agree with the identified inconsistencies for the specific weak values analyzed there, in this Comment we demonstrate that the origin of these inconsistencies is not their general argument, which is formally incorrect. We use Bohmian mechanics as a counterexample to confirm that their conclusions are not valid for all weak values and quantum theories. In particular, we show that weak values postselected in position can in fact be interpreted within Bohmian mechanics as properties of quantum systems, detached from any measuring devices, in a consistent and meaningful way.

Seoane et al. [preceding Comment, Phys. Rev. A 111, 066201 (2025)] criticized our work [Phys. Rev. A 109, 022238 (2024)], saying that our argument that realistic interpretations of weak values lead to inconsistencies is not valid for all weak values and quantum theories. This is true. We never intended that the arguments we presented would be valid for all weak values. We believe it is clearly stated in our work that we were dealing only with the weak values related to the quantum paradoxes cited in our paper. Seoane et al. also said in their Comment that the “general argument” we present in our paper is formally incorrect. However, this criticism is related to the interpretation they give to the expression “equivalent,” which is different from the one we use. In this sense, the presented criticisms are a matter of semantics, not of physics.

We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank–Shor–Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard–Popescu–Schumacher–Smolin–Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.

We suggest that the observed large annihilation rates of ortho-positronium ($o$-Ps) in halogen gases are due to the process of dissociative Ps attachment $\mathrm{Ps}+X_2\to \mathrm{Ps}X+X$, where $X$ stands for a halogen atom. This process is similar to dissociative electron attachment which leads to formation of negative ions. We calculate the cross section and rate of this process for the ${\mathrm{F}}_2$ molecule, for which it is exothermic and therefore can occur at room temperature. We start with the Ps-${\mathrm{F}}_2$ scattering calculations which take into account electron exchange and correlations within the framework of the free-electron-gas model. The calculations reveal several resonances. Similar to the process of dissociative electron attachment, a ${\mathrm{\Sigma }}_u$ resonance contributes to the dissociative Ps attachment at thermal energies. We determine the resonance position and width as functions of the internuclear separation and use them as inputs for the local version of the quasiclassical theory of dissociative attachment. Our calculations yield an anomalously large rate constant for the $o$-Ps annihilation process which is only one order of magnitude lower than those observed for ${\mathrm{Br}}_2$ and ${\mathrm{I}}_2$.

We investigate the nonperturbative process of vacuum pair production in a combination of two counterpropagating linearly polarized laser pulses of a finite spatial extent. By means of the locally constant field approximation (LCFA), we calculate the total particle yield for the corresponding four-dimensional setup and compare it with the estimates obtained for simplified low-dimensional scenarios. Within the domain where the LCFA is well justified, we examine a combination of two plane-wave pulses, a standing electromagnetic wave, and a spatially uniform oscillating field and demonstrate that at each of these three levels of approximation, one can accurately predict the actual particle number by multiplying the results by properly chosen volume factors depending on the field parameters. We present closed-form expressions for these factors providing universal prescriptions for evaluating the particle yield. Our final formula connecting the spatially uniform setup with the four-dimensional scenario has a relative uncertainty of the level of $10\%$. The explicit correspondences deduced in this study not only prove the relevance of the approximate predictions, but also allow one to quickly estimate the number of pairs for various realistic scenarios without performing multidimensional LCFA integrations.

We investigate the formation of vortices in quasi-two-dimensional dipolar Bose-Einstein condensates (BECs) through the interplay between two-body contact and long-ranged dipole-dipole interactions (DDIs), as both interactions can be tuned from repulsive to attractive. By solving the associated Gross-Pitaevskii equation for a rotating system, our initial approach concentrates on stabilizing a collapsing condensate with attractive $s$-wave two-body interactions by employing sufficiently large repulsive DDIs. Subsequently, the same procedure was applied after reversing the signs of both interactions to evaluate the sensitivity of vortex formation to such an interchange of interactions. As a reference to guide our investigation, valid for generic dipolar atomic species, we have assumed a condensate with the strong dipolar dysprosium isotope, ${}^{164}\mathrm{Dy}$. The correlation of the results with other dipolar BEC systems was exemplified by considering rotating BECs with two other isotopes, namely ${}^{168}\mathrm{Er}$ and ${}^{52}\mathrm{Cr}$. For a purely dipolar condensate (no contact interactions) under fixed rotation, we show how the number of visible vortices increases as the DDI becomes more repulsive, accomplished by tuning the orientation of the dipoles through a characteristic angle parameter.

Hermite-Gaussian (HG) beams are standard modes delivered by continuous or pulsed lasers systems, and pulse-front tilt is one of the most common, detrimental or beneficial, spatiotemporal couplings affecting ultrashort pulses. Combining them, we show that focusing a pulsed HG beam with a tilt generates an elliptical spatiotemporal optical vortex (STOV), or a chain of them. The elliptical STOVs differ from standard STOVs in an additional spatial chirp that is manifested as a wave front temporal rotation, and results in an enhanced transverse orbital angular momentum. The longitudinal field is significantly larger than that of normal STOVs, and may also take the form of an elliptical STOV. Our concept greatly simplifies previous arrangements for the generation of STOVs, whose additional features make them attractive for improving their applications in electron trapping and acceleration, or as driving fields for the generation of higher-order harmonics and other interactions with matter.

In this paper, employing the metric-adjusted skew information, we bring up a family of decompositions of the total uncertainty as quantified by the variance into the quantum uncertainty and classical uncertainty. Based on the decompositions of uncertainty, we further establish a family of complete complementarity relations for predictability, interference, and correlation in multipath interferometers. Explicitly, we show that the predictability can be quantified by the (reverse) total uncertainty, the interference can be quantified by the quantum uncertainty, while the correlation can be quantified by the classical uncertainty. The family of complementarity relations established in this paper generalize previous characterizations of interference in multipath interferometers via the quantum Fisher information [Y. Sun et al., Phys. Rev. A 108, 062416 (2023)]. As an illustration, we calculate the relevant quantities for some extremal quantum states, and also give explicitly the complementarity relations in two-path interferometers, which demonstrate the validity of the quantifiers. We compare our results with two related complementarity relations established recently and highlight the main differences. The results obtained in this work reveal the close connections between uncertainty and complementarity.

The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and error rates can vary greatly between different qubits and at different points in the circuit. Nevertheless, it would be useful to distill all this complicated behavior down to a single parameter: an effective error rate for a simple uniform error model. Here we show that this can be done by means of the average detector likelihood, which quantifies the rate at which error detection events occur. We show that this parameter is predictive of the overall code performance for two variants of the surface code: Floquet codes and the 3-CX surface code. This is then used to define an effective error rate at which simulations for a simple uniform noise model result in the same average detector likelihood, as well as a good prediction of the logical error rate.

We discuss a quantum logic spectroscopy technique that uses the geometric phase gate interaction to implement quantum nondemolition (QND) measurements, distinguishing between two subspaces within a hyperfine manifold of a trapped ion. We then discuss how to use these binary subspace measurements for efficient, high-fidelity state preparation and measurement (SPAM) as well as nondestructive leakage detection. We show how to use (classical) error-correction methods to suppress SPAM error, at least to the extent the binary subspace measurements maintain QND purity. Suppressing SPAM error through redundant operations, rather than precise field engineering, could reduce some of the engineering complexity associated with building larger trapped-ion quantum computers.

Quantum approximate optimization algorithm (QAOA) is one of the fundamental variational quantum algorithms, while a version of QAOA that includes counterdiabatic driving, termed digitized counterdiabatic QAOA (DC-QAOA), is generally considered to outperform QAOA for all system sizes when the circuit depth for the two algorithms are held equal. Nevertheless, DC-QAOA introduces more cnot gates per layer, so the overall circuit complexity is a tradeoff between the number of cnot gates per layer and the circuit depth and must be carefully assessed. In this paper, we conduct a comprehensive comparison of DC-QAOA and QAOA on maxcut problem with the total number of cnot gates held equal, and we focus on one implementation of counterdiabatic terms using nested commutators in DC-QAOA, termed as DC-QAOA(NC). We have found that DC-QAOA(NC) reduces the overall circuit complexity as compared to QAOA only for sufficiently large problems, and for maxcut problem the number of qubits must exceed 16 for DC-QAOA(NC) to outperform QAOA. Additionally, we benchmark DC-QAOA(NC) against QAOA on the Sherrington-Kirkpatrick model under realistic noise conditions, finding that DC-QAOA(NC) exhibits significantly improved robustness compared to QAOA, maintaining higher fidelity as the problem size scales. Notably, in a direct comparison between one-layer DC-QAOA(NC) and three-layer QAOA where both use the same number of cnot gates, we identify an exponential performance advantage for DC-QAOA(NC), further signifying its suitability for large-scale quantum optimization tasks. We have further shown that this advantage can be understood from the effective dimensions introduced by the counterdiabatic driving terms. Moreover, based on our finding that the optimal parameters generated by DC-QAOA(NC) strongly concentrate in the parameter space, we have devised an instance-sequential training method for DC-QAOA(NC) circuits, which, compared to traditional methods, offers performance improvement while using even fewer quantum resources. Our findings provide a more comprehensive understanding of the advantages of DC-QAOA circuits and an efficient training method based on their generalizability.

Cavity optomechanics, which investigates the interaction of electromagnetic fields with mechanical resonators via radiation pressure, offers an intriguing perspective on how quantum mechanical concepts materialize at macroscopic scales. Here, we present a novel approach to investigate the photonic spin Hall effect (SHE) in a multilayered system, by introducing $\mathrm{\Lambda }\text{−}\mathrm{type}$ three-level coherent atomic medium inside a mirror and dielectric slab, causing an optomechanical effect on light incidence. Unlike typical photonic SHE systems that rely on fixed material setup, we demonstrate that photon-phonon coupling in an optomechanical cavity permits dynamic manipulation of the spin-orbit interaction of light. We employ the transfer matrix approach for computing the ratio of reflection coefficients for the TM and TE components, illustrating the manipulation of the transverse shift of reflected light from positive to negative near the Brewster angle. Further, we demonstrate that manipulating important variables such as photon-phonon, atom-photon coupling strengths, and atomic Rabi frequency can impact both the magnitude and angular position of the photonic SHE. This optomechanical interaction has significant advantages over conventional approaches because it allows for real-time tuning of the SHE, increasing its potential for applications in optical sensing, spintronic devices, and quantum information processing. Our findings pave the way for further research into dynamically controlled photonic spin-dependent effects, offering a diverse platform to advance light manipulation.

Time-dependent terms in Hamiltonians and equations of motion are rather important for a quantum-mechanical description of particles with arbitrary spins in nonstationary fields. We use the Foldy-Wouthuysen representation which allows one to obtain the Schrödinger picture of relativistic quantum mechanics. We determine exact nonexponential and exponential operators of the Foldy-Wouthuysen transformation for arbitrary-spin particles in the nonstationary case. Some fundamental properties of these operators and the Foldy-Wouthuysen Hamiltonian are also identified.

The quantum trajectory sensing problem seeks quantum sensor states which enable the trajectories of incident particles to be distinguished using a single measurement. For an $n$-qubit sensor state to unambiguously discriminate a set of trajectories with a single projective measurement, all post-trajectory output states must be mutually orthogonal; therefore, the $2^n$ state coefficients must satisfy a system of constraints which is typically very large. Given that this system is generally challenging to solve directly, we introduce a group-theoretic framework which simplifies the criteria for sensor states and exponentially reduces the number of equations and variables involved when the trajectories obey certain symmetries. These simplified criteria yield general families of trajectory sensor states and provide bounds on the particle-sensor interaction strength required for perfect one-shot trajectory discrimination. Furthermore, we establish a link between trajectory sensing and quantum error correction, recognizing their common motivation to identify perturbations using projective measurements. Our sensor states in fact form quantum codes, and conversely, a number of familiar stabilizer codes (such as toric codes) also provide trajectory sensing capabilities. This connection enables noise-resilient trajectory sensing through the concatenation of sensor states with quantum error-correcting codes.