Various methods have been explored to prepare the spin-adapted ground state—the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, nonvariational methods incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. Such additional terms would require a quartic number of gates in terms of the number $n_{\text{spin}}$ of spins when naively implemented. To circumvent this computationally intensive scaling, this paper proposes a nonvariational procedure to obtain the spin-adapted ground states that requires only quadratic scaling. The proposed method consists of two stages: the first stage is to prepare a spin-magnitude adapted state and the second stage is postprocessing for the desired $S_z$. By separating into two stages, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O\left(n_{\text{spin}}^4\right)$ to $O\left(n_{\text{spin}}^2\right)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness.

We propose a general class of open fermionic models where quadratic Liouvillians governing the dissipative dynamics feature analytically characterized higher-order exceptional points (EPs). Invoking the formalism of third quantization, we show that, among the multiple EPs of Liouvillian, an EP with its order approaching the system size arises as the dominant modes of the system at long times, leading to a gapless Liouvillian spectrum. By introducing perturbations, in the form of many-body quantum-jump processes, these higher-order EPs break down, leading to finite Liouvillian gaps with fractional power-law scalings. While the power-law scaling is a signature of the higher-order EP, its explicit form is sensitively dependent on the many-body perturbation. Finally, we discuss the long-time dynamics which can serve as detectable signals for the higher-order Liouvillian EPs.

We employ an all-particle multireference Fock-space relativistic coupled-cluster theory to compute the ionization potential, excitation energy, transition rate, and hyperfine structure constants associated with the $7s^2{}^1{S}_0\to 7s7p{}^3{P}_1$ and $7s^2{}^1{S}_0\to 7s7p{}^1{P}_1$ transitions in nobelium (No). Using our state-of-the-art calculations in conjunction with available experimental data [S. Raeder et al., Phys. Rev. Lett. 120, 232503 (2018)], we extract the values of nuclear magnetic dipole ($\mu$) and electric quadrupole ($Q$) moments for ${}^{253}\mathrm{No}$. Further, information on nuclear deformation in even-mass isotopes is extracted from the isotope shift calculations. Moreover, we employ a perturbed relativistic coupled-cluster theory to compute the ground-state electric dipole polarizability of No. In addition, to assess the accuracy of our calculations, we compute the ionization potential and dipole polarizability of lighter homolog ytterbium (Yb). To account for strong relativistic and quantum electrodynamical (QED) effects in No, we incorporate the corrections from Breit interaction, vacuum polarization, and self-energy in our calculations. The contributions from triple excitations in coupled cluster is accounted perturbatively. Our calculations reveal a significant contribution of $\approx 10\%$ from the perturbative triples to the transition rate of the $7s^2{}^1{S}_0\to 7s7p{}^3{P}_1$ transition. The largest cumulative contribution from $\mathrm{Breit}+\mathrm{QED}$ is observed to be $\approx 4\%$, to the magnetic dipole hyperfine structure constant of the $7s7p{}^1{P}_1$ state. Our study provides a comprehensive understanding of atomic and nuclear properties of nobelium with valuable insights into the electron-correlation and relativistic effects in superheavy elements.

The three-level $5S_{1/2}\text{−}5P_{3/2}\text{−}5D_{5/2}$ cascade transition of ${}^{87}\mathrm{Rb}$ is widely used as a reference for optical frequency standards based on two-photon spectroscopy, implemented with either single-color excitation at 778 nm or two-color excitation at 780 and 776 nm. Although primarily exploited as a clock transition, its relatively large scattering rate enables significant radiation pressure. Here we theoretically investigate two-color laser cooling based on this optical clock transition. Using a semiclassical model, we calculate the radiation force, damping and diffusion coefficients, and equilibrium temperatures as a function of laser detunings and intensities. We show that sub-Doppler temperatures, below the Doppler limit of the $5S_{1/2}\text{−}5D_{5/2}$ transition, can be achieved with a weak probe field at 780 nm and a strong coupling field at 776 nm. We further demonstrate that, under appropriate cooling conditions, the ac Stark shift of the clock transition can be strongly reduced or canceled through suitable choices of laser detunings and power ratios. These results suggest a route toward incorporating laser cooling directly into two-color rubidium optical clocks using the same interrogation lasers, potentially improving stability while minimizing experimental complexity.

By introducing spatially varying profiles of pairing interaction or spin polarization to quasi-one-dimensional two-component atomic Fermi gases confined in box potentials, we analyze the ground-state structures and properties when multiple phases coexist in real space by implementing the Bogoliubov–de Gennes equation suitable for describing inhomogeneous fermion systems. While the BCS, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO), and normal phases occupy different regions on the phase diagram when the parameters are uniform, a spatial change of pairing strength or spin polarization can drive the system from the FFLO phase to a normal gas or from a BCS superfluid to the FFLO phase in real space. The FFLO phase exhibits its signature modulating order parameter at the FFLO momentum due to population imbalance, and the pair correlation penetrates the polarized normal phase and exhibits proximity effects. Meanwhile, the BCS phase tends to repel population imbalance and maintain a plateau of pairing. Interestingly, a buffer FFLO phase emerges when the spatial change attempts to join the BCS and normal phase in the presence of spin polarization. By analyzing the pairing correlations, interfacial properties, and momentum-space spectra of the inhomogeneous structures, relevant length and momentum scales and their interplay are characterized. We also briefly discuss implications of inhomogeneous multiphase atomic Fermi gases with population imbalance.

We have realized an interferometer using a thermal cloud of magnetically trapped rubidium-87 atoms on a chip. The interferometer resembles a Ramsey interferometer with a state selective spatial splitting of the two internal states as proposed by [M. Ammar et al., Phys. Rev. A 91, 053623 (2015)]. The splitting is effected by microwave fields from two on-chip waveguides while the atoms remain magnetically trapped. The inferred maximum separation is $1.2\pm 0.1\mu \mathrm{m}$. We observe interference fringes with a contrast around 8% limited by the velocity difference of the two interferometer states when we close the interferometer. We develop a model describing this contrast decay.

Recent experiments have probed the stability of ring superfluids in the presence of Josephson barriers or Gaussian impurities. Here we present a theoretical analysis that extends beyond the regimes explored so far. We study the onset of dynamical instabilities in a ring superfluid, addressing both tunneling and hydrodynamic regimes. The stability of the system is controlled by the effective rotation frequency $\omega$, given by the difference between the initial quantized circulation and the frequency of barrier rotation. The instability occurs when $\omega$ overcomes a critical value ${\omega }_c$. We show that ${\omega }_c$ increases approximately linearly with the number of barriers, with a slope set by the barrier height and width. When the system is quenched into the dynamically unstable regime, it emits multiple solitons, which can switch or even reverse the direction of circulation. The stabilization mechanism is robust against imperfections of the potential and does not require a perfectly periodic array of barriers. In particular, we find that adding a disordered speckle potential to an ordered array of barriers can further increase ${\omega }_c$; disorder can therefore make a ring superfluid more resilient to dynamical instabilities.

Based on the multiband strong-field approximation model, we perform a pathway-resolved analysis of high-order harmonic generation in bulk MgO crystals under monochromatic infrared laser and combined pulses. The results show that under the driving of monochromatic infrared pulse, due to the large energy gap between the second conduction band and the valence band of MgO crystal, it is difficult for electrons in the valence band to directly transition to the second conduction band, so the transition pathway with strong harmonic radiation intensity is the pathway containing electrons first transitioning from the valence band to the first conduction band. After adding the ultraviolet high-frequency field, the probability of electron direct transition to the second conduction band is significantly enhanced, and the harmonic radiation intensity of the transition pathway containing electrons first transitioning from the valence band to the second conduction band is significantly improved. In addition, compared with the monochromatic case, we observed a large energy range of harmonic enhancement under the combined pulse drive. Through further analysis, we reveal the main transition pathway sources of the harmonic enhancement region. By adjusting the time delay between the combined pulses and the wavelength of the high-frequency field, both the enhancement region and the spectral peak structure can be effectively controlled. This study demonstrates a pathway-resolved control strategy for harmonic enhancement and highlight its potential for probing and manipulating ultrafast electron dynamics in solids.

Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available scattering channels. Diffraction gratings and metagratings overcome this limitation by supporting multiple propagating diffraction orders, thus providing additional degrees of freedom for controlling wave propagation. However, when several diffraction channels are present, it becomes nontrivial to predict how spatial symmetries combined with reciprocity affect the overall scattering response. For this purpose we develop a formalism to determine the scattering symmetries of diffraction gratings supporting multiple diffraction orders. The approach is based on constructing a global scattering matrix that connects all incident and scattered diffraction channels and on introducing matrix representations of spatial symmetry operations acting on the field amplitudes. From these representations we derive an invariance condition that directly constrains the subscattering matrices associated with each pair of diffraction orders. This provides a rigorous approach for computing the grating scattering coefficients imposed by symmetry and reciprocity. We illustrate the application of this approach via several examples and show how metagratings may be used to achieve, for instance, angle-asymmetric transmission and extrinsic chiral effects.

Photon sources based on spontaneous parametric down-conversion (SPDC) are central to experimental quantum optics and quantum technologies. Their performance is commonly quantified by three metrics: pair-collection probability, heralding efficiency, and spectral purity. In bulk-crystal SPDC, these metrics are known to be mutually constrained, yet the physical origin of the resulting tradeoffs is often obscured. We show that these tradeoffs originate from the frequency-dependent population of discrete spatial modes in the SPDC emission. By performing a Laguerre-Gauss mode decomposition at each frequency component, we show how spectral-spatial nonseparability impacts collection probability, heralding efficiency and purity. We apply this framework to two widely used quasi-phase-matching configurations, collinear degenerate type-0 and type-II SPDC in periodically poled bulk crystals, and quantify how different phase-matching functions shape the spectral-spatial mode structure. In particular, for type-II SPDC we compare standard periodically poled and aperiodically poled Gaussian phase matching. We experimentally validate some of our theoretical results using spatial- and spectral-projection measurements. This spectral-spatial mode analysis provides a quantitative and predictive framework for understanding and engineering bulk-crystal photon sources, enabling systematic multiparameter optimization beyond qualitative design guidelines.

If we could shrink the ground-state wave function of a hydrogen atom to a size $R$, at fixed electron mass and charge, the singlet hyperfine attraction in a spin singlet state would scale as $1/R^3$—faster than the increase in kinetic energy—raising the question of why the hyperfine interaction does not lead to collapse of hydrogen or similarly, positronium. We resolve this issue within the framework of the full Dirac equation for the hydrogen atom ground state, employing a minimax variational calculation. The result is that in a variational state of size $R$, the magnetic moment of the electron assumes its usual value, $e\hslash /2mc$, when $R$ minimizes the total energy. However, for $R<\hslash /mc$ there is no energy minimum, and the effective electron magnetic moment becomes essentially $eR/2$, softening the hyperfine interaction compared with the zero-point energy. When the Dirac variational calculation is extended to Coulombic atoms with two oppositely charge pointlike fermions of arbitrary masses, e.g., positronium or muonium, the effective magnetic moment of both particles are similarly suppressed in small atomic configurations, leading to stability against collapse, while in hydrogen, the finite size of the proton is enough to ensure stability. This same framework is, in addition, applicable for treating diquarks as relativistic Coulombic systems in the presence of color electric and magnetic interactions.

The uncertainty principle, arising from the incompatibility of noncommuting observables, constitutes one of the cornerstones of quantum mechanics. While uncertainty relations involving pairs of observables have been extensively investigated, experimentally accessible tight uncertainty relations for multiple observables in bipartite systems remain largely unexplored. Here, we experimentally investigate tight triple uncertainty relations in two-qubit systems using two physically motivated constructions of angular-momentum operators. On a photonic quantum platform, we formulate and verify both product-form and additive-form triple uncertainty relations associated with the operators $\vec{J}={\vec{S}}_1\times {\vec{S}}_2$ and $\vec{K}={\vec{S}}_1\otimes \mathbb{1}+\mathbb{1}\otimes {\vec{S}}_2$. We experimentally observe saturation of the tight bound with high fidelity and verify the universal constant $2/\sqrt{3}$ for the investigated classes of triple uncertainty relations. Furthermore, we construct optimized uncertainty functions whose maximal values exhibit a monotonic correspondence with entanglement concurrence for Bell-type and Werner-state families. Our results establish an experimentally accessible framework for studying multiobservable uncertainty relations in bipartite quantum systems and provide additional insight into the interplay between measurement incompatibility and quantum entanglement.

In the field of quantum information science, feedback control has become an important method for preparing and manipulating nonclassical beams. Here we theoretically propose an active nonlinear feedback control system utilizing two four-wave-mixing processes ${\text{FWM}}_1$ and ${\text{FWM}}_2$ with spatially structured pumping, where the second four-wave-mixing process ${\text{FWM}}_2$ acts as an active nonlinear controller. After considering practical losses, the input-output relation of the system is derived. The effects of the feedback strength, the phase of the feedback loop, and the gain of the ${\text{FWM}}_1$ on the relative intensity-difference squeezing (IDS) of the nonlinear feedback control system are investigated theoretically. Remarkably, we find that even when the ${\text{FWM}}_1$ operates at a significantly low level of pump power, the degree of the IDS across all six output fields of the system is enhanced for a certain range of intensity gain and phase. Moreover, there exists an optimal intensity gain and phase to maximize the IDS. In addition, we analyze the entanglement properties of the system by applying the partial transpose criterion and find that the intensity gain and phase can tailor the entanglement structure of the hexapartite state. Our results highlight a promising strategy for improving the fidelity of quantum communication and for enhancing the measurement precision in quantum metrology.

The temperature sensitivity of a probe in equilibrium can be gauged by its thermal quantum Fisher information (QFI). It is known that probes exhibiting degeneracy in their energy-level structure can achieve larger sensitivities, while probes with a more uniform spectrum may remain sensitive over a broader temperature range. Here, we study the thermometric performance of a multilevel quantum Rabi model in which two well-separated atomic manifolds of near-degenerate levels couple to a single cavity mode. We generalize the standard quantum Rabi treatment in the adiabatic regime to find an approximate closed-form expression for the thermal QFI. We then characterize two complementary limits. On the one hand, a large dark-state manifold (dark-manifold saturation) produces a robust peak in thermal sensitivity due to bright-dark population transfer. Such increase in sensitivity is further maximized at an intermediate light-matter coupling strength. Maximizing instead the number of bright states (bright-manifold saturation) generates a broadband thermal response that becomes increasingly stable under random light-matter couplings as the number of levels is increased. The rich spectral structure of our cavity-QED model thus makes it a versatile and sensitive equilibrium thermometer over a broad range of temperatures.

Continuous-variable quantum key distribution (CV-QKD) over free-space channels offers more flexibility for secure key exchange between authenticated parties than fiber-based CV-QKD in practical scenarios. However, traditional CV-QKD systems use 1550-nm optical signals as the quantum source, which are susceptible to atmospheric conditions, thereby limiting their practical deployment. Additionally, the intrinsic imperfections of practical detectors result in potential security loopholes that eavesdroppers may exploit in real-world attack scenarios. To address these issues, we propose a microwave-enabled continuous-variable measurement-device-independent QKD (CV-MDI-QKD) protocol that uses microwave two-mode squeezed states generated by traveling-wave parametric amplifiers operated in a cryogenic environment as quantum sources. This enables robust free-space operation under dynamically varying atmospheric conditions and further enhances the practical security of CV-QKD systems. Numerical simulations illustrate that the proposed microwave CV-MDI-QKD system operates stably at room temperature and exhibits improved robustness against adverse weather and variations in both symmetric ($L_{\mathrm{BC}}=L_{\mathrm{AC}}$) and asymmetric ($L_{\mathrm{BC}}=0$) cases, compared to the 1550-nm scheme. The proposed microwave system exhibits a high secret key rate at suitably short distances.

The $W$ state, a canonical representative of multipartite quantum entanglement, plays a crucial role in quantum information science due to its robust entanglement properties. Quantum uncertainty relations, on the other hand, form a fundamental cornerstone of quantum mechanics. This work introduces an alternative approach to identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations. Using a specific set of noncommuting observables, we formulate an uncertainty-based criterion for identifying $W$ states and rigorously demonstrate its generality in distinguishing them from other tripartite entangled states, such as the Greenberger-Horne-Zeilinger state. Our approach bypasses the need for full quantum state tomography, requiring only the verification of a set of uncertainty inequalities for efficient $W$-state identification. This work provides a theoretical tool for identifying multipartite entangled states and highlights the significant role of quantum uncertainty relations in entanglement characterization.

In this work, we establish a structural correspondence between quantum states and matroid theory. This connection demonstrates that key properties of quantum states, including entanglement and measurement, can be characterized in purely combinatorial terms via matroids, despite the apparent conceptual distance between these two fields. Using this framework, we show that a matroid-supported state is genuinely entangled when its underlying matroid is connected. Moreover, a uniform superposition over all bases of a matroid is genuinely entangled if and only if the matroid is connected. We also demonstrate that a local measurement in the $Z$ basis on such a state yields another matroid-supported state, whose underlying matroid is a minor of the original one. Inspired by matroid duality, we further propose a notion of quantum state duality, uncovering a deep structural symmetry in state transformations.

We develop a control framework for broadband population transfer in ensembles of $n$-level quantum systems with time-dependent energy levels and time-varying dispersion across ensemble members. Ensemble inhomogeneity is modeled through time-varying dispersion functions that capture Hamiltonian variations across the ensemble. The control field is chosen so that the $n$-level dynamics reduces to an effective retained subspace for the target transition that is dynamically decoupled from the rest of the space in the reduced description. By careful phase design, ensemble dispersion appears only as a global phase in the final state, thereby ensuring uniform population transfer across all ensemble members. We apply the proposed control framework to quadrupolar nuclei under magic-angle spinning, where rotor motion naturally generates both explicit time dependence of the nominal energy levels and time-dependent dispersion across crystallites. Numerical simulations in this setting demonstrate uniform broadband population transfer and illustrate the framework in a physically meaningful multilevel ensemble system with explicitly time-varying inhomogeneity.

Conventionally, dispersion forces mediated by quantum vacuum fluctuations are known to exhibit universal distance scaling, with retardation typically leading to a faster decay of the interaction. Here, we show that this expectation fails for intrinsically discrete systems. Using the microscopic scattering approach, we study the Casimir-Polder interaction between two atomic arrays and uncover an unconventional distance scaling in which the force crosses over from a faster decay at short separations to a slower decay in the retarded regime. This behavior originates from the discrete lattice structure and can be consistently understood within the scattering picture. Extending our analysis to Rydberg atomic arrays, we predict an even stronger deviation from conventional scaling and propose an experimentally feasible scheme for direct measurement. Our results provide a platform for exploring dispersion forces beyond the continuum limit.