Quantum Fisher information and the associated quantum Cramér-Rao bound (QCRB) are fundamental tools in frequentist quantum metrology, offering both analytical simplicity and practical precision limits for parameter estimation. The QCRB sets a lower bound on the mean square error (MSE) in the idealized limit of infinite measurement trials ($\nu \to \infty$). Here we perform a systematic expansion in powers of $1/\nu$ to refine MSE estimates in realistic, finite-resource scenarios. These corrections reveal differences between measurements that appear equally optimal under the QCRB. They also help to distinguish among multiple optimal state families for estimating an unknown unitary transformation. Additionally, we explore the Bhattacharyya bound and its quantum counterpart, which constrain these corrections. Our results are relevant for preasymptotic metrology, enabling optimized protocols with limited resources without reliance on numerical simulations.

The advent of quantum batteries (QBs) has coincided with the accelerated progress in quantum science and technology. Here, we propose a novel double-cavity QB design, wherein the maximum charging power can be enhanced to $N^{2.5}$ times or even higher, up to $N^3$ times, through the manipulation of atomic distribution, which surpasses the upper limit of $N^2$ reported in previous study. The advantage of this manipulation is pronounced with an increasing number of atoms in the QB. A significant atom number discrepancy between the two cavities results in the simultaneous optimization of charging power and battery capacity, thereby enhancing charging efficiency without compromising energy storage capacity. Additionally, by modulating the number of atoms within each cavity, the QB is theoretically capable of transitioning between “fast charging” and “slow charging” modes. Notably, in an open system environment, the superiority of the QB is even more pronounced, with negligible energy loss at the final steady state relative to the maximum energy storage of an isolated system.

Excluding the very shallow potential minimum of the electronic ground state, all bound electronic states of ${\mathrm{He}}_2$ have Rydberg character. Their potential-energy functions are very similar to the potential-energy functions of the ${\mathrm{He}}_2{}^{+}$ states to which the Rydberg series converge. Photoionization and electron-impact ionization of the metastable $a{}^3{\mathrm{\Sigma }}_u{}^{+}$ state of ${\mathrm{He}}_2$ are thus characterized by diagonal Franck-Condon factors and only provide access to low vibrational levels of the ${\mathrm{He}}_2{}^{+} X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic ground state. For this reason, hardly any experimental information is available on the excited vibrational levels of ${\mathrm{He}}_2{}^{+}$. We report on a measurement, by high-resolution photoelectron spectroscopy, of 17 vibrational levels of the $X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ state of ${}^4{\mathrm{He}}_2{}^{+}$, with vibrational quantum number $v^{+}$ ranging from 3 to 19 and covering more than 95% of the potential well. To access these states, we exploit a hump in the potential-energy function of the $c{}^3{\mathrm{\Sigma }}_g{}^{+}$ state, which has vibrational wave functions extending to large internuclear distance by quantum-mechanical tunneling through the potential barrier. Combining these new results with data available on the lowest ($v^{+}=0–2$) and highest ($v^{+}=22,23$) vibrational levels of ${}^4{\mathrm{He}}_2{}^{+}$, we derive a full map of the rovibrational level structure of ${\mathrm{He}}_2{}^{+}$ and use it to determine, in a least-squares fit, an empirical effective potential-energy function that describes all experimental data within their uncertainties. This potential-energy function is used to calculate the positions of the 409 bound rovibrational levels and the positions and widths of the 74 shape resonances of the $X^{+}{}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic ground state of ${}^4{\mathrm{He}}_2{}^{+}$. The dissociation energy of ${\mathrm{He}}_2{}^{+}$ is determined to be $D_{\mathrm{e}}=19956.10\left(10\right) {\mathrm{cm}}^{-1}[D_0{(}^4{\mathrm{He}}_2{}^{+})=19101.29\left(10\right){\mathrm{cm}}^{-1}]$.

Exploiting quantum interference presents a significant challenge in ultracold inelastic scattering. In this study we propose a method to verify quantum interference within the two-body loss rate that arises from multiple inelastic-scattering channels, where the colliding particles are initially prepared in their individual hyperfine states. Our approach employs a ring-coupling configuration, accomplished by combining external radio-frequency and static electric fields during ultracold atomic collisions. To validate our proposal, we perform close-coupling calculations for ${}^7\mathrm{Li}\text{−}{}^{41}\mathrm{K}$ collisions at the ultracold limit. The results reveal that the interference profile, as manifested in the two-body loss rate, can be verified with optimized external field parameters. Notably, our findings indicate that the two-body loss rate coefficient exhibits a distinct pattern of constructive or destructive interference when crossing a magnetically induced $p$-wave resonance in the incoming channel. These interference patterns become increasingly pronounced as the intensities of the external fields increase. This work presents a potential approach to controlling inelastic-scattering processes in ultracold collisions.

Realizing fractional quantum Hall (FQH) states in ultracold atomic systems remains a major goal despite numerous experimental advances in the last few decades. Recent progress in trap anisotropy control under rapid rotation has renewed interest in ultracold atomic FQH physics, enabling experiments that impart much larger angular momentum per particle and offer in situ imaging with resolution finer than the cyclotron orbit size. In this paper, we present a theoretical investigation of a rapidly rotating anisotropic Bose gas. By projecting the full Hamiltonian, including both kinetic and interaction terms, onto the lowest Landau level, we derive a compact two-parameter model that captures the effects of interaction strength, rotation rate, and anisotropy. Using exact diagonalization and density matrix renormalization group, we obtain a phase diagram that features broken-symmetry phases and topologically ordered quantum Hall states, while also highlighting the distinctive physics arising from the system's edges. Our results demonstrate the potential for future theoretical and experimental exploration of anisotropic quantum fluids, offering a unified framework for weakly interacting Bose condensates, vortex matter, and strongly correlated topological phases.

Quantum batteries (QBs), harnessing quantum systems to transfer and store energy, have garnered substantial attention recently, enabling potentials in enhanced charging capacity, increased charging power, and device miniaturization. However, constrained by the weak interaction between the quantum nodes, the implementations of QB networks exhibit limited charging performance. In this work, we propose an efficient approach to improving charging in multibattery systems by capitalizing on nonreciprocity. By constructing non-Hermitian Aharonov-Bohm triangles to establish unidirectional energy transfer in both cascaded and parallel configurations, we can achieve a significant enhancement of the stored energy in QBs under weak interaction. Remarkably, the nonreciprocal cascaded setups display an exponentially increasing gain in the battery energy as the charging distance lengthens compared to the reciprocal counterparts. Furthermore, we demonstrate that nonreciprocity can also lead to the same enhancement in the charging power of QBs, accelerating the charging processes. Our findings provide a practical pathway for enhancing the charging performance of QBs and exhibit the potentials for constructing efficient QB networks.

We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing time evolutions of the total (system, bath, and interaction) Hamiltonian and intermittent tracing out the environment degrees of freedom. This results in a unified framework where any near-term Hamiltonian simulation algorithm can be incorporated to implement an arbitrary number of such collisions on early fault-tolerant quantum computers: we do not assume access to specialized oracles such as block encodings and minimize the number of ancilla qubits needed. In particular, using the correspondence between Lindbladian evolution and completely positive trace-preserving maps arising out of memoryless collisions, we provide an end-to-end quantum algorithm for simulating Lindbladian dynamics. For a system of $n$-qubits, we exhaustively compare the circuit depth needed to estimate the expectation value of an observable with respect to the reduced state of the system after time $t$ while employing different near-term Hamiltonian simulation techniques, requiring at most $n+2$ qubits in all. We compare the cnot gate counts of the various approaches for estimating the transverse field magnetization of a 10-qubit XX-Heisenberg spin chain under amplitude damping. Finally, we also develop a framework to efficiently simulate an arbitrary number of memory-retaining collisions, i.e., where environments interact, leading to non-Markovian dynamics. Overall, our methods can leverage quantum collision models for both Markovian and non-Markovian dynamics on early fault-tolerant quantum computers, shedding light on the advantages and limitations of simulating open systems dynamics using this framework.

We theoretically propose a method for implementing a Hamiltonian incorporating Heisenberg and Dzyaloshinskii-Moriya (DM) interactions within Rydberg atoms arranged in a two-dimensional square lattice, utilizing Floquet engineering. In our scheme, we use both global and local operations of the spins. The global operations can be realized by applying microwave pulses, and the local operations can be realized by locally addressing atoms with off-resonant lasers, which induce the site-dependent ac-Stark shift. Since our engineered Hamiltonian contains bond-dependent DM interactions, we expect the emergence of quantum skyrmions in the ground state.

The decay of metastable false-vacuum states via bubble nucleation plays a crucial role in many cosmological scenarios. Cold-atom analog experiments will soon provide the first empirical probes of this process, with potentially far-reaching implications for early-universe cosmology and high-energy physics. However, an inevitable difference between these analog systems and the early universe is that the former have a boundary. We show, using a combination of Euclidean calculations and real-time lattice simulations, that these boundaries generically cause rapid bubble nucleation on the edge of the experiment, obscuring the bulk nucleation that is relevant for cosmology. We demonstrate that implementing a high-density trench region at the boundary completely eliminates this problem and recovers the desired cosmological behavior. Our findings are relevant for ongoing efforts to probe vacuum decay in the laboratory, providing a practical solution to a key experimental obstacle.

We present a fully quantum mechanical description of a free ${}^6\mathrm{Li}$ atom scattering from a trapped ${}^{171}\mathrm{Yb}^{+}$ ion in one dimension. By reformulating the system in polar coordinates and employing the adiabatic representation, we extract a set of coupled adiabatic potentials representing the atom interacting with the ion in different trap states. In an approach similar to quantum defect theory, we leverage the vast difference in energy scale between the interaction, the trap, and the scattering energy to encapsulate the short-range atom-ion scattering behavior in a single phase parameter. The presence of trapped ${\left({}^{171}\mathrm{Yb}{}^6\mathrm{Li}\right)}^{+}$ molecular-ion states leads to a series of roughly evenly spaced resonances in the scattering cross section. The predicted distribution of resonances at low collision energies is at odds with the expectation of quantum chaos and the Bohigas-Giannoni-Schmit conjecture.

By numerically solving semiconductor Bloch equations under the three-band model, we investigate the high-order harmonic emission of bulk MgO crystals irradiated by linearly polarized laser pulses. Our results reveal that as the laser wavelength increases, interband polarization dominates over intraband current near the minimum band gap (7.8 eV) in the $\langle 001\rangle$ orientation, with contributions shifting toward lower-energy regions. This shift arises from enhanced electron density accumulation at the Brillouin zone boundary and increased interband harmonics between conduction bands. The findings highlight the critical role of laser wavelength in shaping harmonic contributions and deepen our understanding of high-order harmonic generation in crystalline materials.

We propose a backaction evading scheme for a free mass that combines reservoir engineering with velocity measurement. The underlying principle follows the double-pass-type speed meter, which measures the mirror's velocity using a nonreciprocal interaction. In our method, the nonreciprocal coupling is realized through reservoir engineering, following the recipe proposed by Metelmann and Clerk [Phys. Rev. X 5, 021025 (2015)]. We show that reservoir engineering can reproduce the double-pass speed meter with optimal feedforward, using only reciprocal interactions. The resulting force sensitivity surpasses the standard quantum limit, providing an alternative route to quantum backaction evasion in cavity optomechanical systems.

The topological properties of open quantum lattice systems have attracted much attention, due to their fundamental significance and potential applications. However, experimental demonstrations with large-scale lattice models remain challenging. On top of that, formulations of topology in terms of quantum trajectories require monitoring along with the detection of quantum jumps. This is particularly the case for the dark-state-induced topology that relies on averaging quantum trajectories at their jump times. Here we propose two significant simplifications to ease the experimental burden to demonstrate dark state-induced topological phase transitions: First, we emulate the topology in the phase space of small systems, where the effective size of the system is reflected by the accessible parameter range. Second, we develop a method how to, by augmenting the system with an auxiliary system, access the jump-time-averaged state through standard wall-time averaging, which effectively substitutes the monitoring along with the counting of quantum jumps. While these simplifications are applicable to general lattice systems, we demonstrate them with a one-dimensional Su-Schrieeffer-Heeger model. In this case, the lattice system is emulated by a four-level system, while the jump-time-averaged state up to the second jump is accessed through a three-level auxiliary system.

In quantum information science, Clifford operators and stabilizer codes play a central role for systems of qubits (or qudits). In this paper, we study their analogs for systems composed of Majorana fermions. In this case, a crucial role is played by fermion parity symmetry, which is an unbreakable symmetry present in any system with fundamentally fermionic degrees of freedom. We prove that the subgroup of parity-preserving Majorana Cliffords can be represented by the orthogonal group over the binary field ${\mathbb{F}}_2$, and we show how it can be generated by braiding operators and used to construct any (even-parity) Majorana stabilizer code. We also analyze the frame potential for this so-called p-Clifford group when acting on a fixed-parity sector of the Hilbert space, proving that it is equivalent to the frame potential of the ordinary Clifford group acting on the same sector.

Parametrized quantum circuits (PQCs) are central to variational quantum algorithms (VQAs), yet their performance is hindered by complex loss landscapes that make their trainability challenging. Quantum natural gradient descent, which leverages the geometry of the parametrized space through quantum generalizations of the Fisher information matrix, offers a promising solution but has been largely limited to pure-state scenarios, with only approximate methods available for mixed-state settings. This paper addresses this question, originally posed by Stokes et al., Quantum 4, 269 (2020), by providing exact methods to compute three quantum generalizations of the Fisher information matrix—the Fisher-Bures, Wigner-Yanase, and Kubo-Mori information matrices—for PQCs initialized with thermal states. We prove that these matrix elements can be estimated using quantum algorithms combining the Hadamard test, classical random sampling, and Hamiltonian simulation. By broadening the set of quantum generalizations of Fisher information and realizing their unbiased estimation, our results enable the implementation of quantum natural gradient descent algorithms for mixed-state PQCs, thereby enhancing the flexibility of optimization when using VQAs. Another immediate consequence of our findings is to establish fundamental limitations on the ability to estimate the parameters of a state generated by an unknown PQC, when given sample access to such a state.

In this paper, we extend our recent work on cesium $S$ and $D$ states [P. Shen et al., Phys. Rev. Lett. 133, 233005 (2024)] to the $F$ states. We present absolute frequency measurements of the $|6S_{1/2},F=3\rangle \to n{F}_{5/2,7/2}(n=28–68)$ Rydberg series to measure the spectrum of ${}^{133}\mathrm{Cs}$. Atomic spectra are obtained using a three-photon excitation scheme referenced to an optical frequency comb in a sample of ultracold ${}^{133}\mathrm{Cs}$. By globally fitting the absolute-frequency measurements to the modified Ritz formula, we determine the quantum defects of the $n{F}_{5/2}$ and $n{F}_{7/2}$ series. The ionization potential extracted for both series from the modified Ritz formula agrees with our measurements based on the $S$ and $D$ series. Fine-structure intervals are calculated and parameterized. The wave functions computed for the energies from the quantum defects are used to calculate transition dipole moments. We compare the reduced electric-dipole matrix elements with available benchmarks and find agreement within the precision of those works. The scalar and tensor polarizabilities of the $n{S}_{1/2}$, $n{P}_J$, $n{D}_J$, and $n{F}_J$ series are calculated based on the now more accurate set of wave functions. Moreover, we report the polarizability as a series in powers of the effective principal quantum number and find the main coefficients of the expansion. The results will be useful for calculating properties of ${}^{133}\mathrm{Cs}$ such as collision and decay rates, polarizabilities, and magic wavelengths.

We demonstrate the formation of a novel eigenstate in a strongly dipolar binary ${}^{164}\mathrm{Dy}\text{−}{}^{162}\mathrm{Dy}$ mixture, where the inter- and intraspecies dipolar lengths are larger than the corresponding scattering lengths. When this mixture is confined by a quasi-two-dimensional harmonic trap, the total density exhibits the formation of droplets on a spatially symmetric triangular or square lattice, where each droplet is formed of a single species of atoms; two types of atoms never exist on the same lattice site. The density of any of the species shows a partially filled incomplete lattice; only the total density exhibits a completely full lattice structure. In this theoretical investigation we employ the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction in the intraspecies components alone, meant to stop a collapse of the atoms at high atom density.

Unidirectional light emission is essential for various optoelectronic applications. Moreover, dynamically switching the emission direction while maintaining a stable wavelength is highly desirable. In this work, switchable unidirectional guided resonances are achieved through mode coupling between a grating and a waveguide, enabled by a phase-change material. The emission direction can be dynamically switched from upward to downward without altering the wavelength. Through systematic parameter sweeping, feasible geometric configurations that support this directional switching are identified and analyzed. This study offers valuable insights for advancing dynamic light control in optoelectronic devices.