Complementarity relations impose constraints on different aspects of quantum states. We study the complementarity relation within a multipath interferometer that includes detectors and quantum memory. We consider mixed states as the input states. We establish a duality relation between the visibility and the path distinguishability. Based on this duality, two triality relations are derived, one related to visibility, path distinguishability, and mixedness and the other related to visibility, path distinguishability, and entanglement. Therefore, the role of entanglement in multipath interferometer is characterized quantitatively. These complementarity relations are all complete for the two-path interferometer.

We utilize the time-dependent wave-packet propagation method to simulate the complete fragmentation dynamics of ${\mathrm{H}}_2$ molecules subjected to the two-color field. The study focuses on elucidating the influence of the carrier-envelope phase (CEP) difference between the two laser beams on key dynamical properties, including the alignment of neutral molecules, ionization probability, dissociation probability, proton angular distribution, and kinetic energy release (KER). Our study shows that two-color fields can simultaneously provide coherent and incoherent modulations of molecular dynamics. For neutral molecular alignment, two-color modulation proves ineffective as it depends quadratically on intensity rather than wave properties. However, strong-field ionization's inherent nonlinearity enables coherent control through intensity-dependent angular distributions and ionization probabilities. Examining ${\mathrm{H}}_2^{+}$ fragmentation dynamics, we observe coexisting first-, second-, and third-order processes under two-color irradiation. First-order transitions exhibit incoherent modulation via laser component competition, altering vibrational distributions and KER spectra phase independently. The second-order ${\omega }_2-{\omega }_1$ process repopulates bound states but minimally affects fragmentation. Crucially, at high intensities, the dominant third-order ${\omega }_2-{\omega }_1+{\omega }_1$ process enables phase-dependent coherent control through reexcitation of second-order-created bound states, revealing fundamental insights into multiorder process interplay in strong-field molecular dynamics.

We explore the excitation spectra of cold ${}^{87}\mathrm{Rb}$ atoms to the $55D_{3/2}$ Rydberg state in the presence of microwave (MW) radiation as a function of MW frequency. The spectra reveal several features around the transition frequencies between adjacent Rydberg states. We argue that some of these features are indicative of variations in the Rydberg excitation probability while others result from the removal of atoms from the cold cloud as a consequence of a MW-induced strong dipole-dipole interatomic force. Our claim is supported by experimental observations and theoretical modeling.

There is a severe impediment in Stern-Gerlach interferometry with a spin-embedded nanoparticle. This is because particle rotation creates a significant mismatch of the wave function of angular degrees of freedom during the creation and recombination of the spatial superposition, resulting in an inferior visibility contrast. We show that imparting angular momentum along the direction of a defect, such as the nitrogen-vacancy (NV) center, during the Stern-Gerlach interferometry provides excellent gyroscopic quantum stability to a nanodiamond, which opens up a way to maintain significant visibility in the quantum interference. The spin contrast improves by many folds for a wide-ranging value of the initial angular momentum, e.g., ${10}^3\text{–}{10}^6$ Hz for a mass of order ${10}^{-14}\text{–}{10}^{-17}$ -kg nanodiamond. Our scheme is independent of the material and is pertinent to any nanoparticle that can be used to create massive and large spatial superpositions with an embedded spin defect.

Nanoscale lasers that generate short pulses at high repetition rates have exciting applications in various fields. However, creating short pulses as well as broad frequency combs in nanoscale lasers is complex and remains a relatively unexplored area. Research has focused on materials with two or more types of resonantly coupled dyes for applications in energy harvesting, biocentered uses, and expanding the tuning range of lasers. We propose that a gain medium composed of two types of coupled dye molecules can produce the saturable gain and absorption necessary for short-pulse generation. We present a mathematical model for this proposed two-dye gain material and integrate it with a finite-difference time-domain method. This developed model is used to assess the effectiveness of the two-dye material for pulse shortening in miniature lasers and to explore the role of a simple one-dimensional photonic cavity in pulsed laser operation. Additionally, we investigate various possible modes of laser operation by varying key design parameters of the dye molecules and the cavity. The findings indicate that the proposed laser can emit a train of short pulses and frequency combs with appropriate tuning of both the laser medium and the cavity. When the parameters of the material and cavity are optimally adjusted, the two-dye gain-medium-based laser is capable of emitting subpicosecond pulses at repetition rates in the hundreds of gigahertz.

We consider a two-dimensional (2D) atomic array coupled to different photonic environments, focusing on the half-filled excitation subspace, where strong photon interactions can give rise to complex many-body states. In particular, we demonstrate that the least radiant state in this sector is well described by a coherent superposition of all possible quantum dimer coverings: a resonating valence bond liquid state. We discuss possible strategies to probe this exotic state, along with their limitations and challenges. Finally, we show that such a quantum dimer covering can also emerge as the ground state of the coherent Hamiltonian describing a 2D atomic array coupled to a photonic band-gap material.

This comment critically examines the paper “Hermitian stochastic methodology for x-ray superfluorescence” by Chuchurka, Sukharnikov, and Rohringer [Phys. Rev. A 109, 063705 (2024)]. The paper proposes a Hermitian framework based on the positive-$P$ stochastic equations (PPSEs), claimed to be derived “from first principles,” through a redefinition of physical variables without a clear rationale. However, because the original PPSEs cannot satisfy Hermiticity under any stochastic-diffusion-gauge transformation, the framework necessarily employs representations beyond this gauge freedom, thereby contradicting the original PPSEs and their ensemble-average predictions. The resulting equations have close structural similarities with the previously established Hermitian formalism of stochastic Maxwell-Bloch equations [arXiv:2305.04653 and Phys. Rev. A 110, 023724 (2024)].

This Reply addresses the Comment by Park, Kim, and Lindberg on our article, “Hermitian stochastic methodology for x-ray superfluorescence” [Phys. Rev. A 109, 063705 (2024)]. The Comment presents criticism, primarily claiming that our derivations involve “a redefinition of physical variables without a clear rationale.” Additionally, it asserts that our methodology closely resembles the stochastic Maxwell-Bloch equations (SMBEs) introduced by Park et al. We disagree with these observations. In this Reply, we further elaborate on the rationale behind our derivations, building on the explanation already provided in the original article. Furthermore, we demonstrate that the “redefinition of physical variables” is an example of stochastic gauge freedom, a well-established concept in methodologies based on positive-$P$ stochastic equations (PPSEs), which underscores the consistency of our derivations with the PPSE formalism. Additionally, we highlight the fundamental differences between our methodology and the SMBEs.

Quantum metrology employs quantum properties to enhance the precision of physical parameters, in order to characterize quantum states as well as channels. Frequency and temperature estimations are of fundamental importance for these tasks and have been extensively studied in quantum sensing strategies. Among the quantum features that can be exploited in quantum metrology, those related to non-Hermitian systems have received much attention in recent times. Here, we consider a paradigmatic non-Hermitian system, the quantum Swanson oscillator, as a probe system in order to investigate how the non-Hermitian contribution affects the frequency and temperature estimation. We use the quantum Fisher information to compute the main results. Furthermore, to perform a fair comparison, we define a gain function which is the ratio between the quantum Fisher information with the non-Hermitian contribution and the quantum Fisher information when this term becomes Hermitian. In addition, the quantum Fisher information is discussed in terms of the energetic cost to include the non-Hermitian contribution. Dissipative effects are also considered by interacting different probe systems with a Markovian thermal reservoir. Given that we obtain the Hermitian counterpart of the Hamiltonian by applying the Dyson map, we also study the estimation of the parameters characterizing this mapping. Our results indicate that the non-Hermitian contribution in the Swanson quantum oscillator can contribute to enhancing the frequency and temperature estimation.

We propose a new formalism of the adiabatic perturbation theory that is invariant under the unitary transformations. A strict distinction is made between the Hamiltonian operator and the instantaneous energy operator. The state of the system is expanded in terms of the eigenstates of the instantaneous energy operator. The expansion coefficients, which represent the transition amplitudes among instantaneous energy eigenstates, are invariant under the unitary transformations. A perturbative series, whose zeroth-order term is the adiabatic approximation invariant under the unitary transformations, is generated up to second order for the state of the system. A diagrammatic representation of the perturbative series is developed. The first-order nonadiabatic correction yields two first-order adiabatic conditions, of which the first one is the unitary-invariant version of the traditional adiabatic condition. A simple physical interpretation is given for it in terms of the physical power operator. The second-order nonadiabatic correction yields two second-order adiabatic conditions. The second first-order condition and the first second-order condition are the unitary-invariant versions of the supplemented conditions derived by Tong et al. [Phys. Rev. Lett. 98, 150402 (2007)]. The second second-order adiabatic condition provides an additional condition setting the bound on the total evolution time.

Quantum Fisher information, which serves as a powerful tool for quantifying the sensitivity of quantum states to parameter variations, has profound implications for quantum metrology. In this work, we establish a general framework for characterizing both the wave and particle features in multipath interferometers using the quantum Fisher information. Furthermore, we derive a complete complementarity relation involving the interference (wave feature), the predictability (particle feature), and the quantum $f$ entropies. As an illustration, we calculate the relevant quantities for the two-path interferometers. Compared with two related characterizations about the complementarity relations, we emphasize that the quantum Fisher information serves as the unified figure of merit for both wave and particle properties. This work builds the connections between the quantum Fisher information and the foundational complementarity principles, offering a fresh and unified perspective for the wave-particle duality in multipath interferometers.

Recently, the synchronization of coupled quantum oscillators has attracted a great deal of interest. Synchronization requires driven constituents, and in such systems, the coupling can be designed to be nonreciprocal. Nonreciprocally coupled oscillators exhibit a rich variety of behavior including active traveling-wave-type states. In this work, we study the interplay of three competing synchronization mechanisms in a setup of two nonreciprocally coupled quantum van der Pol oscillators. One of the oscillators is driven externally, which induces phase locking. A dissipative interaction leads to antiphase locking, whereas a coherent interaction nurtures bistable phase locking and active states. We approximate the phase diagram of the quantum case by evaluating the synchronization measure of a perturbation expansion of the steady state. Effective unidirectional interactions lead to synchronization blockades between the undriven oscillator and the external drive as well as between both oscillators. Furthermore, we study the phase diagrams of two and three oscillators in the mean-field limit and find highly nontrivial active states.

Quantum computers represent a significant threat to the security of current public-key cryptographic systems. Postquantum cryptographic schemes, which are conjectured to be resistant to quantum attacks, are being actively developed. Among these, lattice-based cryptography has emerged as a prominent candidate, relying on the computational hardness of problems such as the shortest vector problem (SVP) for its security. In this paper, we propose a quantum approach that translates lattice enumeration into a quantum computing framework, which utilizes amplitude amplification to speed up the search process and pruning constraints to reduce unnecessary search space. This approach significantly lowers time complexity and improves performance, especially when solving the SVP in two variations of lattice enumeration. The effectiveness and efficiency of our approach are validated through small-scale simulations, which demonstrate notable speed improvements.

Solid-state quantum emitters, such as quantum dots, color centers, rare-earth dopants, and organic molecules, offer qubit systems that integrate well with chip-scale photonic and electronic devices. To fully harness their potential for quantum applications requires the generation of entanglement between two remote qubits with high fidelity and efficiency. In this article, we compare the performance of three common photon-mediated entanglement schemes under realistic noise for solid-state quantum emitters, including optical dephasing and spectral diffusion. We identify the optimal scheme across different noise regimes and calculate the measurement parameters needed to achieve the highest entanglement fidelity at a given rate. Additionally, we explore the effects of temporal and spectral filtering in enhancing entanglement fidelity. Our findings provide practical guidelines for selecting optimal entanglement schemes and outline the measurement strategies for achieving better entanglement fidelity.

We continue our investigation of multipartite open quantum systems comprising layers of structure using the atom-field-medium interactions as a familiarly important example. Same as in Paper I [J.-T. Hsiang and B. L. Hu, Phys. Rev. A 110, 062807 (2024)] we consider a system of $N$ harmonic oscillators, modeling the internal degrees of freedom (idf) of $N$ neutral atoms interacting with a scalar quantum field altered by the presence of a dielectric medium. Different from Paper I, which uses the graded influence action formalism, here, taking advantage of the Gaussian nature of our extended system's interactions, we use the quantum Langevin equation method to calculate the time evolution of the covariance matrix elements of the quantum correlation functions of the idfs of the $N$ system atoms in a dielectric-altered quantum field. The covariance matrix is particularly useful for extracting quantum informational properties of a Gaussian system related to quantum correlations, such as quantum entanglement. As an illustration of the method we calculate the entanglement between one system atom and the ambient quantum field outside the dielectric half-space, measured by the purity function and the von Neumann entropy. We highlight one somewhat peculiar feature in our results and one important technical issue: The special feature refers to the nonmonotonic behavior of the purity function when the atom is positioned very close to the dielectric surface. By deriving the Robertson-Schrödinger function and displaying a similar qualitative behavior under these conditions we attribute this novelty to a manifestation of the uncertainty relation. The technical issue refers to the order-reduction scheme to remove the third time derivative term in the Langevin equation for the idfs of the atom. We point out the inconsistencies in the traditional treatments and propose a new consistent scheme of order reduction for Gaussian open systems.

Thorium ions and molecules, recognized for their distinctive nuclear and atomic attributes, are central to numerous trapped-ion experiments globally. Our study introduces an effective, compact source of thorium atomic and molecular ions produced via laser ablation of microgram-scale, salt-based samples. We thoroughly analyze the variety of ion species and charge states generated at varying laser fluences. Utilizing 10 $\mu \text{g}$ of thorium fluoride crystals and laser fluences between 1.00(5) and 6.75(35) J/${\mathrm{cm}}^2$, we produce thorium molecular ions ${{}^{232}\mathrm{ThF}_x}^{n+}$ (with $x=0–3$ and charge states up to $n=3$), including ${\mathrm{ThF}}^{2+}$ and ${\mathrm{ThF}}^{3+}$. These species are particularly relevant for spectroscopy; ${\mathrm{ThF}}^{3+}$ is valuable due to its stable closed-shell configuration, while ${\mathrm{ThF}}^{2+}$, which is isoelectronic to RaF, offers a unique probe for studying nuclear structure and fundamental symmetries due to its simple electronic structure with a single unpaired electron. Density-functional-theory-based calculations of the electric charge distribution aid in understanding the formation of the observed species. Positive charges are found to be mainly located on the thorium atom, which points to an inhibition of immediate Coulomb explosion, thus supporting the existence of the observed ion species. The simplicity of the method and similarities among the actinide elements suggest that our approach will also be applicable to other actinide species.

Alkali-metal hydride cations $X{\mathrm{H}}^{+}$ ($X=\text{Na}$, K, Rb, Cs) are potentially important in interstellar chemistry and early cosmological environments, yet their photodissociation properties remain poorly characterized. We present a systematic study of their photodissociation cross sections based on high-accuracy ab initio electronic structure calculations. The cross sections are computed under the assumption of local thermodynamic equilibrium, covering photon wavelengths from 50 nm up to the dissociation threshold, and include transitions from most rovibrational levels in the ground electronic state $1^2{\mathrm{\Sigma }}^{+}$. Prominent shape resonances are identified near the Lyman $\alpha$ line, significantly modulating the photodissociation behavior. In particular, for ${\mathrm{CsH}}^{+}$, strong contributions from the $2^2\mathrm{\Pi }$ and $4^2{\mathrm{\Sigma }}^{+}$ states are found in the spectral region between the Lyman $\alpha$ line and the Lyman limit. These results provide critical theoretical data for the spectral characterization of alkali-metal hydride cations and offer valuable input for astrophysical modeling of UV-driven processes and early-universe chemistry.