Making use of the simple fact that all separable complex Hilbert spaces of given dimension are isomorphic, we show that there are just six basic ways to define generalized coordinate operators in quantum mechanics. In each case, a canonically conjugate generalized momentum operator can be defined, but it may not be self-adjoint. Even in those cases, we show there is always either a self-adjoint extension of the operator or a Neumark extension of the Hilbert space that produces a self-adjoint momentum operator. In one of the six cases, both extensions work, thus leading to seven basic pairs of coordinate and momentum operators. We also show why there are more ways of defining basic coordinate and momentum measurements. A special role is reserved for measurements that simultaneously but imperfectly measure both.

We develop a unified field-theoretical description of the Bose-Hubbard model that captures low-energy dynamics across the insulator-to-superfluid transition. We show that commonly used cumulant expansions about the Mott ground state fail in the superfluid phase not only quantitatively but also fundamentally, because they impose an incorrect canonical structure. Expanding instead about the appropriate mean-field saddle point, we derive an effective action in which the dynamics of fluctuations are governed by a Berry-phase term, giving rise to an emergent magnetic field in the associated oscillator description. This field encodes particle-hole symmetry breaking in both the Mott-insulator phase and the superfluid, and vanishes at the point where a pure Goldstone mode emerges. The resulting effective hydrodynamic theory admits a speed of sound that approaches the Bogoliubov limit in the weakly interacting regime, demonstrating consistency across the entire phase diagram, from the Mott-insulator to the deep superfluid regime. While the total density remains continuous within mean-field theory, we find that quantum fluctuations generate a discontinuous contribution at the quantum phase transition, which vanishes at the tip of the Mott lobe.

Driven nonlinear oscillators constitute a universal paradigm for understanding synchronization, frequency pulling, and frequency comb formation in nonequilibrium systems. Here, we realize such an emergent nonlinear oscillator in strongly interacting cesium Rydberg vapor, where coherent optical excitation, dissipation, and long-range interactions give rise to a driven-dissipative time-crystal phase with intrinsic oscillation frequencies. Applying a radio-frequency (rf) field allows controlled tuning of the intrinsic oscillation frequency. Under rf heterodyne conditions, we observe intermodulations, frequency pulling, and, at strong drive, the emergence of a comblike spectrum in the atomic coherence. We qualitatively capture these observations using a four-level mean-field model and demonstrate a classical analog with a driven Van der Pol oscillator. Our results establish interacting Rydberg ensembles as a tunable platform for exploring nonequilibrium time-crystalline order, nonlinear synchronization, and frequency comb generation in many-body atomic systems.

Antiferromagnetic (AFM) films play a crucial role in advanced spintronic devices by regulating adjacent ferromagnetic (FM) layers via interfacial exchange coupling. However, the impact of antiferromagnets on magnetic dynamics of FM films under ultrashort laser pulses remains largely unknown. Using ultrafast extreme ultraviolet high-harmonic pulses for element-specific magnetization probing, we investigate the femtosecond laser-induced magnetic dynamics in an ultrathin FM Co film with paramagnetic (PM) Cu capping versus AFM Mn capping. Surprisingly, we observe notably shorter demagnetization time for Co in the AFM Mn/FM Co system, approaching the excitation laser pulse duration. During the femtosecond demagnetization process of Co, Mn magnetization arises immediately, indicating a dominant photon-driven interfacial spin-transfer process consistent with optically induced intersite spin transfer (OISTR). Experimental results, supported by time-dependent density functional theory, reveal an increased OISTR magnitude at the Mn/Co interface by a factor of about 1.8 compared to the Cu/Co interface. Furthermore, the photon-driven interfacial contribution saturates at $\sim 1$ nm, consistent with the short-range nature of OISTR. Remarkably, by utilizing AFM Mn as the adjacent material and adjusting its thickness, OISTR can contribute to $\sim 45\%$ of the demagnetization in ultrathin FM films. The combination of OISTR with ultrathin materials paves the way for next-generation petahertz optospintronics.

Several types of active agents self-propel by spinning around their propulsion axis, thus behaving as active screws. Examples include cytoskeletal filaments in gliding assays, magnetically driven colloidal helices, and microorganisms such as the bacterium Myxococcus xanthus. Here, we develop a model for spinning self-propelled rods on a substrate, and we coarse grain it to derive the corresponding hydrodynamic equations. If the rods propel purely along their axis, they form an active nematic at high density and activity. However, spinning rods can also roll sideways as they move. We find that this transverse motion turns the system into a chiral active nematic. Thus, we identify a mechanism whereby individual chirality can give rise to collective local chiral flows. Finally, we analyze experiments on M. xanthus colonies to show that they exhibit chiral flows around topological defects, with a chiral activity about an order of magnitude weaker than the achiral one. Our work reveals the collective behavior of active screws, which is relevant to colonies of social bacteria and groups of unicellular parasites.

We demonstrate robust programmable state preparation in small Vertical Cavity Surface Emitting Laser (VCSEL) arrays with optical feedback using transient optical injection in the form of Gaussian pulses. In Lang-Kobayashi-type models of delay-coupled two- and three-laser arrays, multistability gives rise to coexisting synchronized and symmetry-broken equilibrium branches. We show that short injection pulses applied to one or more lasers can steer the system from free-running operation to any stable equilibrium branch in the absence of noise by appropriate choice of pulse detuning and amplitude, after which the selected state persists without continued forcing. With correlated noise, injection steering remains effective, but branches with small basins of attraction are effectively destabilized by noise. These results validate pulsed injection as a practical mechanism for attractor selection in multistable VCSEL arrays and point to a feasible route toward experimental realization of programmable collective-state control.

We study the equilibrium and nonequilibrium formation of four-particle complexes in a balanced two-species Bose-Hubbard model with repulsive intraspecies and attractive interspecies interactions. Using exact diagonalization, we characterize the transition from weakly to strongly correlated dimer and tetramer states along the one- to two-dimensional crossover in coupled-chain geometries by combining local correlation signatures with global diagnostics such as the binding energy and interspecies entanglement entropy. We show that transverse connectivity between chains qualitatively reshapes the phase diagram, substantially enlarging the tetramer region and, in particular, stabilizing weakly bound tetramers when compared to the one-dimensional chains. By tuning the interchain hopping, we identify a transition from a degenerate manifold of spatially separated dimers to a localized tetramer ground state, driven by the lifting of one-dimensional configurational degeneracies and an associated kinetic-energy gain. By extending our analysis to larger complexes of six and eight particles, we reveal that these binding mechanisms are robust and suggest a general pathway for the formation of higher-order complexes. Finally, we demonstrate interaction and geometric quench protocols to dynamically prepare these complexes with high fidelity. Our results provide a microscopic framework for engineering and probing few-body bosonic bound states in tunable lattice geometries.

We investigate the spectral and topological properties of an atomic chain of red phosphorus. We reveal the separation of flat-band states from the rest of the system and calculate its energy bands analytically. The topological properties of the system are established through the evaluation of the Berry (Zak) phase of the energy bands, revealing nontrivial topology. The Berry phase depends on the relative strength of the hopping parameters and exhibits dual energy-dependent topological phase transitions. Remarkably, the emergence of inert band edges provides a direct spectral signature of these transitions, acting as energy-resolved indicators of the redistribution of topological charge between bands. The existence of the associated edge states is proved numerically for finite lattices. The theoretical predictions, particularly the band structure and the existence of edge states, are further confirmed by numerical simulations of red phosphorus through a phononic lattice in the form of a highly structured aluminum plate.

We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (QED) using density matrices. The approach is based on collision quantum optics, where the many-body state of the waveguide is represented using discrete time bins, which are then efficiently encoded using an MPS chain. Our method is a generalization of previous MPS methods, and we demonstrate how one can efficiently extend the method to density matrices, allowing for the inclusion of various loss processes in the form of Lindblad terms in the Liouvillian superoperator responsible for the relevant dissipation dynamics. As an application of the theory, we study various waveguide QED systems and the influence of emitter pure dephasing (which is one of the most important processes in real systems) on the light-matter interactions, including a two-level system (TLS) in a semi-infinite waveguide with time-delayed feedback, two spatially separated TLSs with finite delays, and finally the scattering of few-photon Fock pulses on a TLS. In addition to emitter pure dephasing, we also show how to include off-chip radiative decay, and show how it differs qualitatively from pure dephasing.

Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for traditional regimes, they are now hitting their limitations for highly open cavities and extended systems, as encountered in cavity experiments with molecules and solid-state systems. Here, we present a method that significantly extends the conceptual underpinning of these discrete-mode models, promoting them to a systematic treatment. We develop an ansatz which allows to quantize the resonator's resonances with position-resolved discrete modes, thus naturally incorporating losses in the formalism. Such a construction effectively unifies key ideas from pseudomodes and quantized quasinormal modes theory. We further present a criterion for construction of the ansatz parameters at every point in space and semianalytically benchmark the resulting solution for a paradigmatic one-dimensional example resonator.

The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct unitary implementation of the $T$ gate using the cubic phase gate has been shown to have a logical error floor unless the GKP codestate has a biased-noise profile. In this work, we propose a method for on-demand noise biasing based on a standard GKP error-correction circuit. This on-demand biasing circuit can be used to bias the GKP codestate before a $T$ gate and return it to a nonbiased state afterward. With the on-demand biasing circuit, we prove that the logical error rate of the $T$ gate can be made arbitrarily small as the quality of the GKP codestates increases. We complement our proof with a numerical investigation of the cubic phase gate subject to a phenomenological noise model, showing that the $T$ gate can achieve average gate fidelities above $99\%$, with 12 dB of GKP squeezing without the use of postselection. Moreover, we develop a formalism for finding optimal unitary representations of logical diagonal gates in higher levels of the Clifford hierarchy that is based on a framework of “polynomial phase stabilizers” whose exponents are polynomial functions of one of the quadrature operators. This formalism naturally extends to multiqubit logical gates and even to number-phase bosonic codes, providing a powerful algebraic tool for analyzing non-Clifford gates in bosonic quantum codes.

We present a first-principles $S$-matrix framework for multiphoton ionization driven by arbitrary quantum states of light, retaining the full spatial structure of the light fields. Within this framework, we show that the utilization of momentum-entangled photon pairs emitted by ultrathin nonlinear crystals can enhance resonant two-photon ionization cross sections by more than two orders of magnitude relative to an uncorrelated reference state. The enhancement stems from the broad distribution of the transverse momentum and is captured only by a nonparaxial treatment, while strongly underestimated in the paraxial approximation. Atom-specific estimates for resonant two-photon ionization in sodium indicate that the predicted effect should be observable with currently available photon-pair sources.

We present a model for a topological quasicrystalline system that is suitable for realization in cold atom experiments. We define the model in terms of complex momentum-space couplings that break time-reversal symmetry (TRS) and detail how it may be experimentally realized using two-photon Raman couplings. In the weak-potential limit, we study the model analytically by calculating the band structure over a “quasi-Brillouin zone” (QBZ). We find symmetry-protected Dirac cones, which are gapped by a TRS-breaking term, resulting in a Chern number $\mathcal{C}=1$. This provides a direct analogy to the Haldane model, but now in a quasicrystalline setting. We also infer the number of states below the topological gap from the QBZ area. We verify our analysis with numerical calculations of periodic approximants to our system, constructing a phase diagram in parameter space that shows a topological region extending beyond the weak-potential regime. We also find examples of narrow Chern bands with the potential for hosting strongly correlated physics. Our work raises questions about the nature of localization and strongly correlated states in Chern bands in quasiperiodic systems.

Since the dawn of the space age, observations of energetic particles in planetary radiation belts have been interpreted within a diffusive transport framework, even though the dominant processes that populate and deplete these belts—such as injections and moon-driven absorption—produce particle distributions that are highly structured and spatially localized. This exposes a fundamental question: How can coherent phase-space structures evolving under collisionless dynamics give rise to observational signatures that appear consistent with diffusion-based transport? Here, we show that diffusionlike behavior inferred from radiation belt observations can arise solely from an observational phase-mixing effect, independent of stochastic wave-particle transport. As orbiting spacecraft sweep across neighboring drift shells while trapped particles undergo electromagnetic drifts, measurements inevitably sample regions with slightly different drift frequencies. This converts spatially localized drift-phase structures into rapidly decorrelating temporal signals, making them observationally indistinguishable from those produced by stochastic wave-particle processes. We derive the associated correlation function analytically and show that the effective lifetime of these structures is only a few drift periods. Consequently, even highly localized injections rapidly lose coherence, preventing spacecraft from resolving fine-scale structure in the distribution function. These results show that collisionless dynamics can produce observational signatures that mimic diffusive transport on timescales shorter than those expected from radial transport, limiting the inference of particle acceleration processes and leading to biased transport rates and inaccurate long-term flux predictions. This calls for a reassessment of diffusion-based interpretations inferred from sparse in situ measurements of radiation belts at Earth, across the solar system, and in the recently discovered radiation belts of ultracool brown dwarfs.

Precision measurements of molecules offer an unparalleled paradigm to probe physics beyond the standard model. The rich internal structure within these molecules makes them exquisite sensors for detecting fundamental symmetry violations, local position invariance, and dark matter. While trapping and control of diatomic and a few very simple polyatomic molecules have been experimentally demonstrated, leveraging the complex rovibrational structure of more general polyatomics demands the development of robust and efficient quantum control algorithms. In this study, we present reinforcement-learning quantum-logic spectroscopy (RL-QLS), a general, reinforcement-learning-designed quantum-logic approach to prepare molecular ions in single, pure quantum states. The reinforcement-learning agent optimizes the pulse sequence, each followed by a projective measurement, and probabilistically manipulates the collapse of the quantum system to a single state. The performance of the RL-QLS control algorithm is numerically demonstrated for the polyatomic molecule ${\mathrm{H}}_3{\mathrm{O}}^{+}$ with 130 thermally populated eigenstates and degenerate transitions within inversion doublets, as well as for ${\mathrm{CaH}}^{+}$ under the disturbance of environmental thermal radiation. We expect that the developed theoretical framework can be readily implemented for quantum control of polyatomic molecular ions with densely populated structures, thereby facilitating experimental tests of fundamental theories.

Generating strongly entangled states within multiparticle systems stands as a pivotal endeavor in quantum physics. It not only serves as a cornerstone for delving into the intrinsic properties of quantum mechanics but also provides indispensable quantum resources vital for the development of emerging quantum technologies that transcend classical capabilities. Here, we propose a method to manipulate the magnon-photon, magnon-phonon, and photon-phonon robust entanglement, and the tripartite entanglement involving magnon, photon, and phonon modes, within a hybrid cavity magnomechanical system, leveraging the interference effects induced by two counterpropagating pump lasers. We find that it becomes feasible to exert effective control over all three different types of bipartite quantum entanglement and the tripartite quantum entanglement by properly adjusting the phase difference between the two pump lasers. Moreover, this approach not only enhances these entanglements but also bolsters their resilience against thermal noise emanating from the surrounding environment. The outcomes of our research reveal a readily implementable technique for the manipulation and preservation of quantum entanglement. This technique is of paramount importance in numerous real-world applications that hinge on purely quantum resources, including noise-resistant quantum computing and high-precision quantum measurements.

There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here, we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light) qubits and on the stationary (matter) qubits. The idea is to combine the benefits of encoded one-way and two-way schemes where effective channel transmission and loss scaling are enhanced by means of photon loss codes and encoded quantum memories, respectively, while sacrificing some of their advantages, such as high clock rates, independent of classical communication times (one-way), and potentially large segment lengths (two-way). More specifically, we illustrate, propose, and analyze such a quantum repeater using the bosonic Gottesman-Kitaev-Preskill (GKP) code, which naturally enables encoding and QEC of qudits, protecting them against transmission and memory loss, the latter, for instance, occurring on collective spin modes of atomic ensembles. While the encoded one-way and two-way schemes on their own either require very high repeater link coupling efficiencies and GKP squeezing or allow for experimentally more feasible, small values of these parameters, respectively, we find that there are intermediate parameter regimes where the combined repeater protocol is superior.

Nonequilibrium systems maintain spatiotemporal order through energy dissipation and entropy production. Here, we demonstrate this principle by engineering a quantum limit cycle that emerges from the interplay between a first-order absorbing-state phase transition and feedback mechanism coupling order and control parameters. The quantum limit cycle manifests dynamical correlations driven by multiplicative quantum noise and periodic traverses through tipping points, which act as a robust early-warning signal for state transitions. This periodic crossing results in the enhanced dynamical susceptibility and transient rise of long-range correlations near each tipping event and their subsequent disappearance away from it. These critical transitions are accompanied by a sharp increase in the energy dissipation rate, leading to a stepwise accumulation of dynamical entropy production over time. Our results provide a way for realizing dynamical fluctuations and long-range correlations in strongly interacting driven-dissipative open quantum systems.

Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin glass models provide a natural framework to explore this connection, as their energy landscapes are governed by competing interactions and constrained topologies. We investigate the nonexponential relaxation behavior of spin glasses on network architectures relevant to quantum annealing hardware—such as finite size Chimera, Pegasus, and Zephyr graphs—where embedding constraints and finite connectivity strongly modulate the distribution of barriers and metastable states. This slow relaxation arises from the combined effects of frustration and disorder, which persist even beyond the conventional spin glass transition. Within the Fortuin-Kasteleyn-Coniglio-Klein cluster formalism, the appearance of unfrustrated cluster regions gives rise to multiple relaxation scales, as distinct domains follow different dynamical pathways across a rugged energy landscape. This framework enables a broader characterization of spin glass energy landscapes and provides physical insight into how topological constraints, frustration, and disorder jointly govern relaxation dynamics in complex networks relevant to quantum annealing architectures.