We study the relationship between quantum synchronization and the thermodynamic performance of a four-level near-degenerate extension of the Scovil–Schulz-DuBois thermal maser. We show how the existence of interacting coherences can potentially modify the relationship between synchronization and the coherent power output of such a maser. In particular, the cooperation and competition between interacting coherences cause the coherent heat and efficiency to be bounded by the synchronization measure in addition to the well-studied power synchronization bound. Overall, our results highlight the role of quantum synchronization in the working of a thermal machine.

In parameter estimation, the saturation of the quantum Cramér-Rao bound (QCRB) requests one to perform projective measurements on the eigenvectors of the symmetric logarithmic derivative (SLD). However, it maybe infeasible to saturate the QCRB in composite systems on account of the technological difficulties. In practice, it is necessary to perform sequential measurements on different subsystems to obtain a precise estimation. In this paper, we derive the expression of Fisher information (FI) for a sequential measurements scheme in composite systems with $N$ interacting subsystems. The result shows that the more subsystems used, the higher FI obtained due to the nonnegative property of FI. We illustrate the optimal measurements for different conditional density matrices in every subsystems are nonidentical, which depends on the previous outcomes. In addition, utilizing the convexity property of the quantum FI, we prove that the optimal projective measurements on the eigenvectors of the SLD of the subsystem reduced density matrix can be regarded as a trade off of the nonidentical optimal measurements of the conditional density matrices in every subsystems. In addition, importantly, we show the measurement sequence of the subsystem should be considered in the optimization to obtain a precise estimation for the sequential measurements scheme. Finally, we apply the theory to a nuclear spins control model where we concern the estimation of nuclear Larmor frequency. We should point out that the precision obtained by the sequential measurements scheme is no better than the theoretical result in the global system limited by the QCRB but more realistic, and better than the local measurements in one of the subsystems.

Global estimation strategies allow one to extract information on a phase or a set of phases without any prior knowledge, which is required for local estimation strategies. We devise a global multiphase protocol based on Holevo's estimation theory and apply it to the case of digital estimation, i.e., we estimate the phases in terms of the mutual information between them and the corresponding estimators. We test the protocol in two particular cases, i.e., the single-phase and the double-phase estimation. In the single-phase scenario, the protocol encompasses two specific known optimal strategies. We extend them to the simultaneous estimation of two phases and evaluate their performance. Then we retrieve the ultimate digital bound on precision when a generic number of phases is simultaneously estimated. This bound is again expressed in terms of mutual information and is general for any digital multiphase estimation protocol. We show that in the multiphase strategy there is only a constant quantum advantage with respect to a sequence of independent single-phase estimations. This extends a recent similar result, which settled a controversy on the search for the multiphase enhancement.

We present a comprehensive investigation of electron capture ratios spanning a broad range of atomic numbers. The study employs a self-consistent computational method that incorporates electron screening, electron correlations, overlap, and exchange corrections, as well as shake-up and shake-off atomic effects. The electronic wave functions are computed with the Dirac-Hartree-Fock-Slater method, chosen following a systematic comparison of binding energies, atomic relaxation energies, and Coulomb amplitudes against other existing methods and experimental data. A key feature in our calculations is the use of an energy balance employing atomic masses, which avoids approximating the electron total binding energy and allows a more precise determination of the neutrino energy. This leads to better agreement of our predictions for capture ratios in comparison with the experimental ones, especially for low-energy transitions. We expand the assessment of electron capture observable uncertainties by incorporating atomic relaxation energy uncertainties, in contrast to previous studies focusing only on $Q$ value and nuclear level energies. Detailed results are presented for nuclei of practical interest in both nuclear medicine and exotic physics searches involving liquid xenon detectors (${}^{67}\mathrm{Ga}, {}^{111}\mathrm{In}, {}^{123}\mathrm{I}, {}^{125}\mathrm{I}$, and ${}^{125}\mathrm{Xe}$). Our study can be relevant for astrophysical, nuclear, and medical applications.

A full density-matrix simulation is performed for optical deflection of a barium monofluoride (${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$) beam using the bichromatic force, which employs pairs of counterpropagating laser beams that are offset in frequency. We show that the force is sufficient to separate BaF molecules from the other products generated in a helium-buffer-gas-cooled ablation source. For our simulations, the density-matrix and force equations are numerically integrated during the entire time that the molecules pass through a laser beam to ensure that effects of the evolution of the Doppler shift and of the optical intensity and phase at the position of the molecule are properly included. The results of this paper are compared to those of a deflection scheme [A. Marsman, D. Heinrich, M. Horbatsch, and E. A. Hessels, Phys. Rev. A 107, 032811 (2023)] which uses $\pi$ pulses to drive frequency-resolved transitions. This paper is part of an effort by the ${\mathrm{EDM}}^3$ collaboration to measure the electric dipole moment of the electron using BaF molecules embedded in a cryogenic argon solid. Separation of BaF molecules will aid in producing a sufficiently pure solid.

Benchmark variational calculations of the lowest eight Rydberg ${}^2{P}^o$ states of the singly ionized carbon atom (stable isotopes ${}^{12}\mathrm{C}^{+}, {}^{13}\mathrm{C}^{+}$, and ${}^{14}\mathrm{C}^{+}$, as well as the infinite nuclear mass ion ${}^{\infty }{\mathrm{C}}^{+}$) are reported and the fine structure of the energy levels is determined. The nonrelativistic wave functions of this six-particle, five-electron system are approximated using an expansion in terms of up to 16 000 all-particle explicitly correlated Gaussians, the nonlinear variational parameters of which are extensively optimized using a procedure that employs the analytic energy gradient. These highly accurate wave functions are used to compute the fine-structure splittings including the corrections due to the electron magnetic moment anomaly. The results obtained in this paper are considerably more accurate than the data from the previous theoretical calculations and from the available experimental measurements. The present data can be useful in guiding future accurate spectroscopic measurements of C ii.

We have developed and demonstrated a scheme to achieve rotationally closed photon cycling in polyatomic molecules with complex hyperfine structure and sensitivity to hadronic symmetry violation, specifically, ${}^{171}\mathrm{YbOH}$ and ${}^{173}\mathrm{YbOH}$. We calculate branching ratios for spontaneous decay into the different hyperfine levels and identify repumping schemes. We demonstrate our scheme by cycling photons in a molecular beam and verify that we have achieved rotationally closed cycling by measuring optical pumping into unaddressed vibrational states. Our work makes progress along the path toward utilizing photon cycling for state preparation, readout, and laser cooling in precision measurements of polyatomic molecules with complex hyperfine structure.

We study the molecular state in a two-body system where one of the atoms is subject to a Rashba-type spin-orbit coupling and is spin-dependent loss, while interacting spin selectively with the other atom. The short-time conditional dynamics of the two-body system is effectively governed by a non-Hermitian Hamiltonian with an imaginary Zeeman field. Remarkably, the interplay of the exceptional ring and the spin-selective interaction results in a stable molecular state with a small decay rate, which can be 2 orders of magnitude smaller than that of the imaginary Zeeman field strength for a large-mass-ratio case. The stability of molecular state can be reflected by the imaginary part of molecular energy and the momentum distribution of the molecular wave function. We also demonstrate how mass imbalance further stabilizes the molecule. Our results illustrate the interesting consequence of spectral singularity on the few-body level, which may be readily observable in current cold-atom experiments.

We analyze the entanglement properties of deterministic path-entangled photonic states generated by coupling the emission of a quantum-dot biexciton cascade to a chiral nanophotonic waveguide, as implemented by Østfeldt et al. [PRX Quantum 3, 020363 (2022)]. We model the degree of entanglement through the concurrence of the two-photon entangled state in the presence of realistic experimental imperfections. The model accounts for imperfect chiral emitter-photon interactions in the waveguide and the asymmetric coupling of the exciton levels introduced by fine-structure splitting along with time jitter in the detection of photons. The analysis shows that the approach offers a promising platform for deterministically generating entanglement in integrated nanophotonic systems in the presence of realistic experimental imperfections.

Ultralong-range Rydberg molecules (ULRMs) are highly imbalanced bound systems formed via the low-energy scattering of a Rydberg electron with a ground-state atom. We investigate for ${}^{23}\mathrm{Na}$ the $d$ state and the energetically close-by trilobite state, exhibiting avoided crossings that lead to the breakdown of the adiabatic Born-Oppenheimer (BO) approximation. We develop a coupled-channel approach to explore the nonadiabatic interaction effects between these electronic states. The resulting spectrum exhibits stark differences in comparison to the BO spectra, such as the existence of above-threshold resonant states without any adiabatic counterparts, and a significant rearrangement of the spectral structure as well as the localization of the eigenstates. Our study motivates the use of ${}^{23}\mathrm{Na}$ ULRMs, as a probe to explore vibronic interaction effects on exaggerated timescales and length scales.

Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes was introduced [Jäger et al., Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically eliminated, and one can effectively describe the dynamics of the quantum systems. Here, we demonstrate that this effective master equation can also be used to describe cooling in systems with light-matter interactions. We provide two examples: sideband cooling of an optomechanical oscillator in the unresolved as well as resolved sideband regime and cooling of an interacting quantum system, the transverse-field Ising model. We compare our effective description with a full numerical simulation of the composite formed by the quantum system plus bosonic mode and find excellent agreement. In addition, we present how the effective master equation can be extended to the case of nonvanishing mean thermal occupations of the bosonic mode. We use this approach to calculate modifications of the linewidth and frequency for a two-level system coupled to a dissipative thermal bosonic mode. Here, we highlight that our approach allows for a massive reduction of the underlying Liouville-space dimension.

Broadband energy-time entanglement can be used to enhance the rate of two-photon absorption (TPA) by combining a precise two-photon resonance with a very short coincidence time. Because of this short coincidence time, broadband TPA is not sensitive to the spectrum of intermediate levels, making it the optimal choice when the intermediate transitions are entirely virtual. In the case of distinct intermediate resonances, it is possible to enhance TPA by introducing a phase dispersion that matches the intermediate resonances. Here, we consider the effects of a phase flip in the single photon spectrum, where the phases of all frequencies above a certain frequency are shifted by half a wavelength relative to the frequencies below this frequency. The frequency at which the phase is flipped can then be scanned to reveal the position of intermediate resonances. We find that a resonant phase flip maximizes the contributions of the asymmetric imaginary part of the dispersion that characterizes a typical resonance, resulting in a considerable enhancement of the TPA rate. Due to the bosonic symmetry of TPA, the enhancement is strongest when the resonance occurs when the frequency difference of the two photons is much higher than the linewidth of the resonance. Our results indicate that broadband entangled TPA with spectral phase flips may be suitable for phase-sensitive spectroscopy at the lower end of the spectrum where direct photon detection is difficult.

The nonlocal set has received wide attention over recent years. Shortly before, Li and Wang arXiv:2202.09034 proposed the concept of a locally stable set: The only possible orthogonality preserving measurement on each subsystem is trivial. Locally stable sets present stronger nonlocality than those sets that are just locally indistinguishable. In this work, we focus on the constructions of locally stable sets in multipartite quantum systems. First, two lemmas are put forward to prove that an orthogonality-preserving local measurement must be trivial. Then we present the constructions of locally stable sets with minimum cardinality in bipartite quantum systems ${\mathbb{C}}^d\otimes {\mathbb{C}}^d(d\ge 3)$ and ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}(3\le d_1\le d_2)$. Moreover, for the multipartite quantum systems ${\left({\mathbb{C}}^d\right)}^{\otimes n}(d\ge 2)$ and ${\otimes }_{i=1}^n{\mathbb{C}}^{d_i}(3\le d_1\le d_2\le \cdots \le d_n)$, we also obtain $d+1$ and $d_n+1$ locally stable orthogonal states, respectively. Fortunately, our constructions reach the lower bound of the cardinality on the locally stable sets, which provides a positive and complete answer to an open problem raised in arXiv:2202.09034.

In this work, we propose an efficient and accurate computational method to evaluate the many-potential $\alpha {\left(Z\alpha \right)}^{n\ge 3}$ vacuum polarization density of hydrogen-like atoms within the finite-basis approximation of the Dirac equation. To prove the performance of our computational method, we choose to work with the one-electron ${}_{92}{}^{238}\mathrm{U}$ atom. In summary, we find that compliance with charge conjugation symmetry is a priori required to obtain physical results that are in line with our knowledge of the analytical problem. We also note that the final numerical results are found to be in excellent agreement with previous formal analytical (and numerical) evaluations that are limited to a few simple nuclear distribution models. Our technique can be efficiently implemented and evaluated in codes that solve the radial Dirac equation in the finite basis set framework and allows the use of arbitrary (radial) nuclear charge distribution. The obtained numerical results of the nonperturbative vacuum polarization density automatically account for the extended nuclear size effect. This method is hence of special importance for atomic Dirac problems whose analytical Green's functions expressions are not at hand or have relatively complicated analytical forms. Furthermore, we propose a vacuum polarization density formula that forces compliance with charge conjugation symmetry and can be used in cases where the relativistic basis violates this symmetry, as is the case in most relativistic basis set programs. In addition, we have shown that vector components of the vacuum polarization four-current vanish in the case where the Dirac Hamiltonian is symmetric under time-reversal symmetry.

In the atom-interferometric test of the weak equivalence principle (WEP) with multicomponent atomic gases, the difference in the center-of-mass positions between different components, as well as the difference in the center-of-mass velocities, leads to systematic uncertainties. An effective way to reduce these systematic uncertainties is to suppress such differences at the preparation stage of atomic sources. In this work, we propose an efficient strategy for preparing two-component gases with a perfectly spatial overlap of the center-of-mass positions and that of the velocities, according to a scheme of the time-optimized atomic lensing mechanism. The key of the time-optimized atomic lensing lies in a two-step quench process of the trap frequency, which is accessible in free-fall experiments by appropriately manipulating the trapping frequency and the center position of the trap. By taking a dual-species rubidium atomic gas as an example, our calculations indicate that the differences in the center-of-mass positions and velocities between ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ atoms are simultaneously eliminated, which provides an optimized starting point to test the WEP. An estimation of the systematic uncertainties is also presented. Our method can serve as a potential protocol for the preparation of atom sources in tests of the WEP with multicomponent atomic gases.

Control of the external degree of freedom of trapped molecular ions is essential for their promising applications to spectroscopy, precision measurements of fundamental constants, and quantum information technology. Here, we demonstrate near ground-state cooling of the axial motional modes of a calcium mono-oxide ion via sympathetic sideband cooling with a cotrapped calcium ion. We also show that the phonon state of the axial out-of-phase mode of the ion chain is maintained while the mode frequency is adiabatically ramped up and/or down. The adiabatic ramping of the motional mode frequency is a prerequisite for searching for the proposed molecular dipole-phonon interaction [W. C. Campbell and E. R. Hudson, Phys. Rev. Lett. 125, 120501 (2020); M. Mills et al., Phys. Chem. Chem. Phys. 22, 24964 (2020)].

The nonlinear dynamics of large ion clouds ($N\ge 256$ ions) trapped in radio-frequency (rf) traps and coupled to laser cooling give rise to a bistable behavior of the temperature. Numerical simulations of the free evolution of a large three-dimensional spherical cloud is used to characterize how the oscillating field amplitude and the ion number control the rf-heating rate and the switching between the two stable states. We show that the heating rate does not significantly depend on the ion number but strongly depends on the oscillating field. This exhibits the major role played by the density of the ensemble. The competition between the radio-frequency heating and the laser cooling is also discussed. They are used to design scenarios to take advantage of the threshold effect to detect and quantify perturbations by an intruder.

Experimental demonstrations of entangled quantum images produced through parametric down conversion have so far been confined to studying two-photon correlations. Here we show that multiphoton correlations between quantum images are accessible experimentally and exhibit many new features including being sensitive to the phase of the biphoton wave function. As a concrete example, we consider a modification of existing quantum imaging experiments in which the charge-coupled device cameras are moved out of focus, provide detailed analytical predictions for the resulting four-photon interferences, and support these by numerical simulations. The proposed experiment can also be interpreted as entanglement swapping: Bob's photons are initially unentangled, but the joint detection of Alice's photons projects Bob's photons onto an entangled state. The general approach proposed here can be extended to other quantum optics experiments involving high-dimensional entanglement.