We present a formulation and implementation of exact two-component (X2C) relativistic theory in the generalized pseudospectral representation. When combined with the Hartree-Fock-Slater framework, this approach enables efficient and accurate treatments of scalar-relativistic and spin-orbit effects in atomic electronic structures without the computational overhead of four-component methods. Benchmark calculations across light and heavy elements demonstrate that the our X2C scheme yields substantially more accurate relativistic corrections to core-electron binding energies than perturbational Breit-Pauli treatments while converging more rapidly with respect to basis size. The method provides an improved computational framework for modeling ultrafast x-ray-induced processes in heavy-element systems.

Recent experimental studies by Perreault et al. [J. Phys. Chem. Lett. 13, 10912 (2022)] have cast some doubts on the quality of the available interaction potentials for the He-${\mathrm{H}}_2$ complex. Perreault et al. investigated rotational quenching of HD and ${\mathrm{D}}_2$ prepared in the $v=2$ vibrational level and $j=2$ rotational level using the Stark-induced adiabatic Raman passage techniques. Experiments predicted a strong $l=2$ shape resonance near 1 K in the energy dependence of the $\mathrm{\Delta }j=-2$ rotational quenching rates for both systems, while quantum scattering calculations employing highly accurate interaction potentials predicted an $l=1$ resonance at energies lower than 1 K. To provide more insight into this process, we report here a detailed theoretical study of how the resonant features in the energy dependence of the cross section vary among three isotopologues: He-${\mathrm{H}}_2$, He-${\mathrm{D}}_2$, and He-${\mathrm{T}}_2$. Further, to explore how the resonance position is modified across these systems, we examine He-HX and He-XX collisions in which the mass of X is varied smoothly between the limiting cases of H and T, including realistic systems of HD, HT, and DT. Results are reported for both ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ collisions. Our calculations show that for the entire range of H-atom mass considered in our study, the $l=1$ resonance prevails and no dominant $l=2$ resonance exists, in agreement with previous theoretical studies on He-${\mathrm{H}}_2$, He-HD, and He-${\mathrm{D}}_2$ collisions.

We investigate atomic ionization driven by an attosecond broadband XUV pulse and streaked by a phase-locked IR field. The resulting set of streaking spectrograms, comprising sequences of photoelectron spectra recorded at varying XUV or IR delays is analyzed to retrieve the XUV photoionization phase and the associated atomic time delay. By applying a rainbow-style timing analysis to the full streaking trace, we extract the phase and time delay continuously across a wide range of photoelectron energies. We illustrate the method for ionization of He $1s$, Ar $3p$, and Xe $4d$. In helium, the near-threshold delay is dominated by the Coulomb phase, with an offset introduced by Coulomb-laser coupling in the IR field. In argon and xenon, the retrieved time delays resolve the characteristic features of the Cooper minimum and the giant shape resonance, respectively. These features are canonical examples of strong, correlation- and structure-driven phase variations in photoionization and their associated time-delay signatures. Our results are benchmarked against conventional narrowband streaking and reconstruction of attosecond beating by interference of two-photon transitions, demonstrating that rainbow streaking provides a robust and unified route to broadband phase and time-delay reconstruction.

Hydrogen-like alkali atoms with a single valence electron are the most common objects in quantum optics and, at the same time, serve as essential tools of the field. Under conditions of optical pumping, strong spin-exchange and ultraweak magnetic field [spin-exchange relaxation free (SERF) mode], ensembles of such atoms in the gas phase can demonstrate not only the absence of spin-exchange relaxation, but also nonlinear collective effects. We present experimental evidence that the alignment, i.e., the quadrupole momentum, can not only be preserved under SERF conditions, but also coexist and interact with the orientation, i.e., the dipole momentum. We also show that this interaction leads to bistability: a small change in conditions can cause the medium to transition to a different steady state, an effect characterized by hysteresis. The combination of properties of this effect opens up a wide range of applications as optical keys or memory elements with a storage time of hundreds of seconds in tasks of quantum information and cryptography.

Applying the previously developed systematic thermal (imaginary time) perturbative expansion to the relevant effective field theory, we compute the free energy $F$ of the diluted gas of (nonrelativistic) spin-$1/2$ fermions interacting through a spin-independent repulsive two-body potential as a function of the numbers $N_{+}$ and $N_{-}$ of spin-up and spin-down fermions (i.e., as a function of the system's polarization) and the temperature $T$. We give the complete order ${\left(k_{\mathrm{F}}{a}_0\right)}^3$ ($k_{\mathrm{F}}$ is the Fermi wave vector and $a_0$ is the $s$-wave scattering length characterizing the interaction potential) contribution to $F$. We also extend the computation beyond a fixed order by resumming to all orders in the parameter $k_{\mathrm{F}}{a}_0$ the contributions to $F$ of two infinite sets of Feynman diagrams: the so-called particle-particle rings and the particle-hole rings. We find that including the second one of these two contributions has a dramatic consequence for the transition of the system from the paramagnetic to the ferromagnetic phase (the so-called Stoner phase transition): in this approximation the phase transition simply disappears. This result does not contradict the expectation that a transition to the magnetically ordered state should occur in truly repulsive systems. The $p$-wave and higher scattering lengths, as well as other parameters chacterizing the interaction potential, are in such systems generally of the same order of magnitude as $a_0$ and contributions depending on them should be, therefore, also included in $F$. Our results may, however, have implications for the search of the itinerant ferromagnetism of cold atomic gases in which large $a_0$, much larger than all other parameters, is artificially created by exploiting the physics of the Feshbach resonance.

Four-wave parametric amplification (FWPA) in hybrid quantum systems holds substantial promise for advancing high-performance photonic devices, yet achieving ultrahigh probe-wave gain while preserving tunability remains a key challenge. To address this challenge, we investigate a coupled system consisting of a semiconductor quantum dot (SQD) and a metallic nanoshell (MNS) system, where the MNS comprises a metallic core and a dielectric shell. We utilize nonlinear polarization to analyze the spatial propagation effect and derive an analytical expression for the probe-wave gain $G$ that extends beyond the dipole approximation. Our key findings show that in the strong exciton-plasmon coupling regime, the probe-wave gain $G$ exhibits weak dependence on pump intensity. Importantly, significant parametric amplification is achievable by simply adjusting either the interparticle distance between the SQD and MNS or the dielectric shell thickness of the MNS. Notably, when quasi or perfect collinear phase matching is satisfied, the FWPA-mediated $G$ exhibits an extraordinary tunable range, spanning from $2.0\times {10}^{-5}$ to $1.23\times {10}^{16}$. These findings provide a new pathway for the design of high-performance parametric oscillators and signal amplifiers.

We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, $N$ two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which in the squeezed representation effectively transforms the collective spin operators into a Bogoliubov form. Under large-detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling versatile squeezing schemes including the two-axis twisting (TAT) protocol. In particular, with a phonon-induced auxiliary collective spin term, our protocol exhibits more robust squeezing against dissipation, outperforming the standard TAT protocol. Furthermore, both analysis and numerical simulations show that the maximum squeezing degree asymptotically converges to a constant as $N$ increases, which implies that the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract scaling relations of the optimal squeezing which surpass existing schemes in the literature. Moreover, the optimization can also lead to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.

The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons takes only discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.

We investigate the propagation of an optical vector vortex weakly interacting with a coherently prepared atomic medium (phaseonium) in a three-level $\mathrm{\Lambda }$ configuration. The vector beam consists of vortex pulse pairs with right- and left-circular polarizations, corresponding to opposite spin angular momenta (SAMs) and carrying opposite orbital angular momentum (OAM) charges $\pm l$. We show that during the propagation of the vortex pairs, analytically obtained in the linear regime, the medium inherits the topology of the vortex pair, mapping the OAM onto a spatially structured atomic coherence. This mapping produces $2\left|l\right|$-fold azimuthal transparency structures that reshape the beam intensity from a ring into a petallike pattern. The OAM-structured atomic coherence induces a corresponding optical anisotropy within the medium, which feeds back into the propagating vector beam, resulting in optical spin-orbit coupling manifested as SAM exchange, rotation, and evolution of polarization textures. Depending on the initial ground-state population of the phaseonium, the polarization state evolves between left-circular, linear, and right-circular polarizations.

We introduce the concept of mereological quantum phase transitions (m-QPTs). Our framework is based on a variational family of operator algebras defining generalized tensor product structures (g-TPS), a parameter-dependent Hamiltonian, and a quantum scrambling functional. By minimizing the scrambling functional, one selects a g-TPS, enabling a pullback of the natural information-geometric metric on the g-TPS manifold to the parameter space. The singularities of this induced metric—so-called algebra susceptibility—in the thermodynamic limit characterize the m-QPTs. We illustrate this framework through analytical examples involving quantum coherence and operator entanglement. Moreover, spin-chains numerical simulations show susceptibility sharp responses at an integrability point and strong growth across disorder-induced localization, suggesting critical reorganizations of emergent subsystem structure aligned with those transitions.

We investigate a generalized three-spin-boson model in which three spins interact via an Ising-type coupling and are each coupled to an independent bosonic bath. Using the variational matrix product state method with an optimized boson basis, we compute the ground-state phase diagram and identify three distinct phases: a delocalized phase, a permutationally symmetric localized phase, and a symmetry-broken frustrated phase. The nature of the quantum phase transitions depends strongly on the sign of the spin-spin interaction, with second-order transitions into the delocalized and localized phases, and a first-order transition between the localized and frustrated phases. In the strong-coupling regime, we find that bosonic observables exhibit a universal scaling behavior across different phases, suggesting that the environment remains insensitive to symmetry breaking in the spin sector. We further analyze spin-resolved quantities such as correlation functions, mutual information, and genuine multipartite entanglement to characterize the influence of the bosonic baths, and observe the emergence of an asymmetric correlation pattern among the three spins, reflecting a tendency toward bipartite separability in the frustrated regime.

Quantum reservoir computing (QRC) is a promising quantum machine learning framework for near-term quantum platforms, yet the performance of different QRC architectures under realistic constraints remains largely unexplored. Here we provide a comparative numerical study of single-step (SS) QRC and multistep (MS) QRC architectures implemented on a Rydberg atom array. We demonstrate that while MS QRC performance is highly sensitive to the underlying dynamical phase of matter and decoherence, SS QRC exhibits greater robustness. Using the randomized measurement toolbox to mitigate measurement overhead, we reveal that sampling noise undermines the convergence property required for MS QRC. This leads to a significant reduction in the information processing capacity (IPC) of MS QRC, deteriorating its performance on nonlinear time-series benchmarks. In contrast, SS QRC maintains high IPC and accuracy across both temporal and nontemporal tasks. Our results suggest SS QRC as a preferred candidate for near-term practical applications due to its resilience to system configurations and statistical noise.

Quantum energy teleportation (QET) is a process that leverages quantum entanglement and local operations to transfer energy between two spatially separated locations without physically transporting particles or energy carriers. We construct a QET-based quantum key distribution protocol and analyze its security and robustness to noise in both the classical and the quantum channels. We generalize the construction to an $N$-party information sharing protocol, possessing the feature that dishonest participants can be detected.

Time-continuous quantum measurement allows for the tracking of a quantum system in real time via sequences of short, and individually weak, measurement intervals. Such measurements are necessarily invasive, imparting backaction to the system, and allowing the observer to update their state estimate based on stochastic measurement outcomes. Feedback control then involves real-time interventions by an observer, conditioned on the time-continuous measurement signal that they receive. We consider here diffusive quantum trajectories and focus on the “noise-canceling” subset of feedback protocols that aim to minimize the degree of stochasticity in the dynamics. We derive such a class of feedback operations, showing that under the idealized assumptions of pure states, unit measurement efficiency, and zero time delay in implementing feedback operations, perfectly noise-canceling feedback always exists. We consider the resulting noise-canceled dynamics generated by an effective non-Hermitian Hamiltonian; while non-Hermitian Hamiltonians from continuous monitoring generally describe rare dynamics (accessible by costly postselection), the use of noise-canceling feedback here leads to non-Hermitian dynamics that occur deterministically. We demonstrate this via examples of entangled state preparation and stabilization. We then illustrate the potential for the application of noise cancellation to boost success rates in magic state distillation protocols. We show that adding feedback based on noise cancellation into a time-continuous five-to-one distillation protocol leads to higher probabilities of successful distillation across a range of input errors and increases the threshold on input errors for which the protocol is effective. Our results highlight the efficacy of noise-canceling feedback-aided protocols for quantum state preparation and stabilization tasks.

Determining the best attainable threshold for qudit magic-state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit correcting code for magic-state distillation is captured by its complete weight enumerator. For the qutrit “strange” state—a maximally magic nonstabilizer state—the performance of a code is captured by its simple weight enumerator. This result allows us to carry out an extensive search for high-threshold magic-state distillation routines for the strange state. Our search covers all ${\left[[n,1]\right]}_3$ qutrit stabilizer codes with a complete set of transversal Clifford gates for $n\le 23$, and all ${\left[[n,1]\right]}_3$ stabilizer codes with a transversal $H^2$ gate with $n\le 9$ qudits. For $n=23$, we find over 600 css codes that can distill the qutrit strange state with cubic noise suppression. While none of these codes surpasses the threshold of the 11-qutrit golay code, their existence suggests that, for large codes, the ability to distill the qutrit strange state is somewhat generic.

Magic state distillation is a leading but costly approach to fault-tolerant quantum computation, and it is important to explore all possible ways of minimizing its overhead cost. The number of ancillas required to produce a magic state within a target error rate $\epsilon$ is $O\left[{ln}^{\gamma }\left({\epsilon }^{-1}\right)\right]$ where $\gamma$ is known as the yield parameter. Hastings and Haah derived a family of distillation protocols with sublogarithmic overhead (i.e., $\gamma <1$) based on punctured Reed-Muller codes. Building on work by Campbell et al. and Krishna-Tillich, we generalize the Hastings-Haah construction to qudits of arbitrary prime dimension $p$. Although existing qubit-based constructions achieve sublogarithmic overhead, these advantages only emerge at block sizes that are prohibitively large for practical implementation. In contrast, using an analytically tractable puncturing scheme, we show that the block size required to achieve sublogarithmic overhead decreases drastically as $p$ increases for our qudit construction, with yield parameter approaching $\frac{1}{lnp}$ as $p\to \infty$. We also perform a small computational search for optimal puncture locations, which results in several interesting triorthogonal codes, including a ${\left[[519,106,5]\right]}_5$ code with $\gamma =0.99$. These results demonstrate that qudit-based distillation routines allow sublogarithmic overheads to be realized at much smaller and more physically viable block lengths.

Discovering exoplanets in orbit around distant stars via direct imaging is fundamentally impeded by the combined effect of optical diffraction and photon shot noise under extreme star-planet contrast. Coronagraphs strive to increase the signal-to-noise ratio of exoplanet signatures by optically suppressing light from the host star while preserving light from the exoplanet. However, it is unclear whether direct-imaging coronagraphs constitute an optimal strategy for attaining fundamental limits relevant to exoplanet discovery. In this work, we first review the quantum information limits of exoplanet detection and localization characterized by (1) the quantum Chernoff exponent for symmetric hypothesis testing, (2) the quantum relative entropy for asymmetric hypothesis testing, and (3) the quantum Fisher information matrix for multiparameter estimation. We demonstrate that coronagraphs designed to completely suppress light in the fundamental mode of the telescope, while perfectly transmitting higher-order orthogonal modes, indeed achieve these limits in the regime of high star-planet contrasts. Furthermore, we formulate coronagraphs as quantum channels, thus generalizing the classical framework of coronagraphy to the quantum setting. Using this framework, we compare the information-theoretic performance of leading coronagraph designs against the quantum limits. Our analysis indicates that quantum-optimal coronagraphs offer enhanced information efficiency in the subdiffraction regime compared to leading coronagraph designs and may significantly expand the domain of accessible exoplanets.

Xenon nuclei may be hyperpolarized through collisions with optically pumped rubidium, with the Xe hyperfine coupling (HFC) between the unpaired Rb electron and xenon nucleus transferring spin polarization from the Rb atom to Xe. We model the polarization transfer to ${}^{129}\mathrm{Xe}$ in short binary collisions and long van der Waals (VDW) complexes between gaseous Rb and Xe. The simulations feature molecular dynamics of the Rb-Xe mixture, spin-Hamiltonian parameters extracted from relativistic quantum chemistry, and explicit spin dynamics simulations of the Rb-Xe interaction events on a novel Python code. Oscillation in the VDW bond-length $R$ strongly modulates the Xe HFC, imposing steps in the Xe polarization build-up. The Rb nucleus and the unpaired electron constitute a strongly coupled two-spin system, with practically constant Rb HFC regardless of $R$. Explicit numerical propagation of the time-dependent Schrödinger equation for a simplified model VDW complex reveals that the spin system undergoes two simultaneous Rabi-like oscillations between the initial, fully spin-polarized state of the Rb atom, and two final states after the Xe spin flip, one in each of the two branches of the hyperfine spectrum of the Rb atom. The simulations indicate that incorporating the Rb HFC explicitly results in an overall reduction of the Xe polarization as compared with the simple model, in which the Rb HFC is neglected. Slow oscillations between the Rb spin states constitute an envelope on which the steps in the Xe polarization are superimposed, and this determines the achievable Xe polarization in long-lived VDW events. A simple empirical polarization transfer model based on the lifetime distribution of the VDW events and the Rabi transition probabilities reveals that, in the simulated conditions, a large part of the polarization transfer takes place due to the transition between separate branches of the hyperfine states of the Rb atom. This is due to the fact that maxima of the transition probability can, for this faster oscillation, be reached within the lifetime of the VDW complexes. We expect that these findings will contribute to the understanding of the spin-exchange optical pumping process and aid in its optimization.

We demonstrate the operation of a dual-frequency Paul trap and characterize its performance by storing either electrons or calcium ions while simultaneously applying two quadrupole fields which oscillate at ${\mathrm{\Omega }}_{\text{fast}}=2\pi \times 1.6\mathrm{GHz}$ and ${\mathrm{\Omega }}_{\text{slow}}=2\pi \times 2\mathrm{MHz}$. The particles are loaded and stored in the trap under various conditions, followed by detection employing an electron multiplier tube. We find that tens of electrons or ions can be trapped for up to 10 ms and a small fraction remains trapped even after hundreds of milliseconds with no further signs of loss on this timescale. During dual-frequency operation we find that while the number of trapped electrons rapidly decreases with the increase of the ${\mathrm{\Omega }}_{\text{slow}}$ field amplitude, the number of trapped ions shows no dependence on the ${\mathrm{\Omega }}_{\text{fast}}$ field amplitude, as supported by our extensive numerical simulations. We aim to use a similar trap for synthesizing antihydrogen from antiprotons and positrons. Accordingly, we discuss open challenges such as the cotrapping of oppositely charged species and difficulties related to trap material and manufacturing techniques.