Papers

It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the otherwise missing ground state (GS) in a 3D gas of bosonic particles, carrying an electric dipole moment, which are pulled to the central electric charge, with repulsive contact interactions between the particles. In the mean-field approximation, the repulsive interactions are represented by the cubic term in the respective Gross-Pitaevskii (GP) equation. In addition to the GS, excited states with angular momentum are briefly considered too. Another topic considered in the article is 1D and 2D bound states in the linear Schroedinger and GP equations with the repulsive potential, which demonstrates a singularity at r –> infinity. A very recent result is that such a potential, growing faster than the negative harmonic-oscillator potential, produces a full spectrum of counter-intuitive normalizable (localized) bound states. The article puts forward perspectives for further studies of linear and nonlinear bound states existing under the action of the potentials with the singularity at r –> 0 or r –> infinity.

We investigate nonlinear Drude weights (NLDWs) in the one-dimensional repulsive Hubbard model at zero temperature by combining exact Bethe-ansatz calculations with low-energy effective field theory. At quarter filling, we first derive the strong-coupling expansion of the NLDWs and confirm it numerically over a wide range of interaction strength. We then compare the numerical results with the prediction of the Tomonaga-Luttinger liquid (TLL) description including irrelevant perturbations. While band-curvature corrections yield finite contributions to higher-order NLDWs, the Umklapp interaction predicts divergent NLDWs when the order $n$ of the Drude weight exceeds a threshold determined by the TLL parameter. In contrast, finite-size scaling of the exact Bethe-ansatz results indicates that all calculated NLDWs remain finite in the thermodynamic limit, revealing a discrepancy between the exact results and the predictions of the low-energy effective field theory. At half filling, we analyze the finite-size scaling of the NLDWs across the Mott metal-insulator transition. We derive their asymptotic behavior in the insulating phase and propose a hyperscaling ansatz for NLDWs near the critical point, which is verified numerically. Our results clarify the interaction dependence and critical scaling of nonlinear transport coefficients in the one-dimensional Hubbard model and highlight limitations of the conventional low-energy effective description for higher-order transport.

We investigate dynamics of a linear chain of Rydberg atoms driven by a constrained four-body interaction, where two neighboring atoms are excited simultaneously from the electronic ground state $|0\rangle$ to Rydberg state $|1\rangle$ only when their closest neighbors are in $|0\rangle$ state. By employing an ansatz for the many-body ground state, the low-energy Hamiltonian is given by a tridiagonal form. The many-body ground state energy, which scales linearly with the chain length $L$, is obtained analytically in the thermodynamic limit and agrees with the one of the exact diagonalization. Our model supports quantum many-body scar eigenstates that are nearly equally spaced energetically. The scar states overlap strongly with the basis state $|\mathbf{0}\rangle=|0\cdots 0\rangle$. We show that the overlap distribution is tilted by the state-dependent four-body interaction. This leads to non-ergodic dynamics, evidenced by the revival of the initial state. The four-body constrained model can be realized with Rydberg atoms in a Peierls array with alternating bond lengths, where atoms on the shorter and longer bonds experience Rydberg blockade and antiblockade, respectively. Our study provides a pathway to explore constrained non-ergodic dynamics with four-body interactions by combining the Rydberg blockade and antiblockade.

Hard-core dipoles in triangular ladders are an excellent platform for the study of the interplay between frustration and long-range interactions, well described by a modified version of the celebrated $J_1$–$J_2$ model. Interestingly, as shown in [Phys. Rev. Lett. 109, 227203 (2012)], such a model presents, for particular exactly-solvable conditions, a peculiar phase known as an anyon condensate. We show that balanced anyon condensates are robust against deviations from the exactly-solvable conditions, and discuss the requirements for dipolar orientation and ladder geometry, to realize anyon condensates of dipoles in triangular ladders, whose anyonic nature may be easily revealed by time-of-flight measurements. Moreover, the ground-state physics in the vicinity of the exactly-solvable point is very rich, including a phase transition from anyon condensates into chiral superfluids, and self-bound Mott insulators, bond-order insulators, and chiral liquids.

Two-dimensional quantum gas microscopy provides an unparalleled tool to study quantum many-body systems using ultracold atoms. For the SU(2) Fermi Hubbard model (FHM), access to spin-resolved projective measurements has been vital for quantifying correlation functions and mapping out the phase diagram. Recent progress in quantum gas microscopy for experiments with ultracold alkaline-earth atoms, which are well described by the SU(N) FHM and are predicted to host exotic ground-state phases, calls for the development of theory-free numerical techniques to extract physical information from their projective measurements. To that end, we evaluate the multiscale structural complexity of snapshots of an SU(3) FHM in the square lattice at $1/3$-filling. We employ mean-field theory to generate spin-resolved density distributions and compute their structural complexity using rectangular coarse-graining windows. We demonstrate that these complexities are linked to relevant physical observables such as the entanglement entropy, and are extremely sensitive for locating phase boundaries. The results presented here validate the structural complexity as an efficient and reliable tool for analyzing the outputs of SU(N) quantum gas microscopes, offering a theory-free property, immediately accessible to experiments.

The Dicke model is a paradigmatic setting for collective light-matter physics and the superradiant phase transition. Yet extracting the critical exponents is challenging at experimentally accessible mesoscopic sizes, due to the slow divergence of the correlation time under all-to-all coupling and a photon-loss-driven crossover to a distinct dissipative universality class. Here, we perform a large-$N$ analysis that identifies distinct coherent and dissipative fixed points for the closed and open Dicke models. We then develop a unified mesoscopic scaling framework that incorporates the leading irrelevant correction and, going beyond static and spectral probes, brings ramping dynamics under the same scaling description. It recovers the corresponding exponents, verifies Kibble-Zurek scaling, and clarifies how finite size, dissipation, and speed compete in the ramping dynamics. Our work thus establishes a unified framework for resolving static and dynamical critical scaling in closed and open quantum systems, with broader applicability to mesoscopic systems with long-range interactions.

We derive a channel-resolved Lee-Huang-Yang correction and construct an extended GrossPitaevskii model for one-dimensional polar spin-1 quantum droplets. The fluctuation contribution separates into density and spin channels, which supports self-bound droplets even when the spinindependent mean-field interaction is repulsive. Stationary solutions exhibit a continuous crossover from soliton-like to flat-top droplets, accompanied by saturation of the chemical potential and peak density as the particle number increases. Within the parameter range examined here, linear Bogoliubov analysis together with weak-perturbation dynamics supports the stability of both droplet types. A quadratic-Zeeman quench reveals a finite-size crossover in breathing dynamics and distinct nonequilibrium roles of the density and spin fluctuation channels. Representative head-on collisions further show that the finite-size crossover modulates phase-sensitive nonlinear scattering, with in-phase impact producing coalescence-like central retention and out-of-phase impact favoring quasi-elastic separation. The analysis clarifies how density and spin fluctuations shape equilibrium structure and nonequilibrium response in low-dimensional polar spinor droplets.

Bose-Einstein condensates have been used successfully as quantum simulators for early-universe particle production. Here we extend this analogy to the interacting theory. To this end, we compute the leading interaction terms expected in a general experimental setup that determine the 3-point correlations. We apply them to cosmologically motivated expanding model universes, but also periodically oscillating ones. While expanding scale factors do not necessarily lead to easily observable signatures due to experimental constraints on the realizable scale factor, periodically driven ones produce resonant correlators that grow linearly over time and lend themselves well to experimental detection. One direct application of this analysis is the experimental study of late-time infrared divergencies often discussed in the context of massless scalars in de Sitter space.

The recent creation of a Bose-Einstein condensate (BEC) of dipolar molecules has opened a new frontier for many-body quantum systems in which dipolar interactions can drive novel self-organization phenomena. Here, we observe electrostriction in a molecular BEC, an elliptical deformation driven by anisotropic dipolar interactions. We use double microwave dressing, involving $\sigma$- and $\pi$-polarized fields, to control non-axially symmetric dipolar interactions. We compare the experimental observations of electrostriction to a model based on an extended Gross-Pitaevskii equation and find excellent agreement in the regime of weak to moderate interactions. Using electrostriction, we demonstrate that the molecular BEC can be torqued by dynamically changing the orientation of the elliptical $\sigma$ microwave field. This provides a route to setting molecular quantum gases into rotation, opening opportunities to probe vorticity, superfluidity, and supersolidity in strongly dipolar matter.

Programmable arrays of ultracold atoms are a leading platform for quantum computation and simulation, enabling state-of-the-art implementations of quantum error correction, and analog simulations of Hubbard models that address open problems in condensed matter physics. In these systems, all local control is mediated through precisely shaped optical fields, and so the challenge of managing many-body quantum states becomes an exercise in optical design. In particular, one wishes for fast, flexible control with low disorder and heating, and access to large arrays with many atoms. An ideal optical system therefore must generate arbitrary patterns with high spatial resolution and low disorder, and alter these patterns on a timescale that is faster than the relevant atomic dynamics. Here, we present an optical system that is comparable to previous approaches in scale, while advancing all other axes. We demonstrate arbitrary pattern generation with $10^{-3}$ intensity resolution, a frame rate of $>84$ MFPS (megaframes per second), and a spatial resolution of $83 \times 52$ beam waists (with $11 \times 52$ waists accessible via a single $40$ GHz electro-optic modulator). These capabilities unlock a new class of experiments. We develop and numerically validate a scheme for fully programmable Hubbard models, with time-dependent control over local chemical potentials, tunneling amplitudes, on-site interactions, and patterns of artificial magnetic flux. The same architecture performs fast, arbitrary permutations of tweezers in 2D, decoupling optical constraints from the design of high-rate error-correcting codes.

We study one- and two-magnon dynamics in a spin-$1/2$ XX chain coupled to a tunable Bose-Hubbard bath. The XX Hamiltonian transports the magnons, while the bath dresses their motion and mediates an effective attraction. A single magnon forms a mobile polaron whose retarded bosonic cloud reduces its velocity below the static Lang-Firsov prediction and generates magnon-boson entanglement. In the weak-dressing, off-resonant mobile regime, the residual velocity deficit and entanglement are governed by the excitation weight of the cloud, as captured by perturbation theory and tensor network-based real-time simulations. Transport therefore provides a model-calibrated proxy for entanglement without joint-state reconstruction. When two clouds overlap, the bath mediates a finite-range attraction, yielding finite-size evidence for a compact two-magnon bound state and a transient post-scattering signature. On-site bath interactions suppress local boson number fluctuations and stiffen the bath response, reducing entanglement and weakening ground-state binding. Bath deformability thus emerges as a common control parameter for magnon transport, entanglement, and bath-mediated pairing.

We implement a moving boundary condition in a 1D quantum liquid to study nonlinear wave breaking and its regularization by dispersion. Programmable optical potentials allow us to compress a weakly interacting ultra-cold Bose gas trapped on an atomchip at tunable speeds of up to three times the speed of sound and we subsequently measure the quasi-in-situ density distribution to extract the shock wave edge dynamics. We resolve both leading and trailing edge velocities and observe a shock wave width that increases linearly in time, which are distinguishing features of dispersive shock waves, consistent with asymptotic predictions using Whitham's method. Quantitative agreement is found with finite temperature non-polynomial Schrödinger equation simulations, taking into account the imaging process and the finite height of the piston potential. Our results constitute a controlled, quantitative test of dispersive shock dynamics in a 1D quantum fluid and demonstrate that the coarse-grained dispersive-shock phenomenology remains robust even as the microscopic dynamics depart from the strictly integrable 1D regime.

Bose-Einstein condensates of photons in dye filled microcavities are known to feature many properties of the ideal bose gas at thermal equilibrium. Nevertheless, the finite photon life time renders them driven dissipative systems where losses are balanced by continuous driving by a pump laser. We show here with simulations based on a classical field model that their driven-dissipative nature causes their first order coherence to feature Kardar-Parisi-Zhang (KPZ) scaling, a phenomenon well known in the related condensates of exciton-polaritons. Remarkably, we find that the KPZ scaling even occurs in a regime with large density fluctuations. We discuss the modification of the scaling by the occupation of excited states and how to recover the universal scaling behavior by spectral filtering.

We investigate universal quantum corrections to two-body correlations in a zero-temperature binary Bose mixture using the Cornwall-Jackiw-Tomboulis two-particle-irreducible effective action formalism. In the weak interspecies-coupling regime, a saddle-point treatment based on Hubbard-Stratonovich transformations can be combined with a two-loop expansion and a gapless Hartree-Fock correction, thereby preserving the Goldstone theorem and reducing the coupled two-component problem to two analytically solvable single-component theories. Within this framework, we derive the ground-state energy density as a low-density expansion in the gas parameter, together with the quantum depletion and chemical potentials. The results exhibit a simple mapping to the single-component case: the universal quantum corrections of the mixture are obtained by evaluating the known single-component series at an effective scattering length $a_{\sigma\sigma}-a_{12}$ for each species, where $a_{\sigma\sigma}$ and $a_{12}$ are the intra- and interspecies $s$-wave scattering lengths. This reproduces Petrov's equation of state at one-loop order in the weak-coupling limit and yields beyond-Lee-Huang-Yang corrections at two-loop order. We also analyze the role of mass imbalance, which enters the energy density through the exact rescaling factor $(1+m_{1}/m_{2})/2$.

We investigate the nonequilibrium dynamics of strongly interacting bosons in a finite bichromatic Mott lattice following a sudden quench of the secondary lattice amplitude. The coefficient entropies and second Rényi entropy exhibit pronounced growth toward their Gaussian Orthogonal Ensemble (GOE) predictions from random-matrix theory, consistent with GOE-like statistical spreading in the employed multiconfigurational representation. In striking contrast, experimentally accessible observables, including the momentum distribution, fragmentation, and Glauber correlation functions, remain nearly unchanged throughout the evolution. For the sampled strong quenches, the coefficient entropies, second Rényi entropy, and the $N$-body coefficient spreading collapse onto a common relaxation trajectory that becomes largely independent of the perturbation strength. Our results reveal an emergent hidden ergodic relaxation beneath the persistent local Mott-like order. An effective embedded random-matrix model captures the qualitative crossover from restricted to extensive Hilbert-space spreading, providing an interpretive framework for the observed relaxation dynamics.

A long-standing obstacle in quantum turbulence has been the difficulty of sustaining robust statistical steady states, preventing unambiguous identification of universal vortex organization and kinetic scaling. We construct such a steady state in two-dimensional holographic superfluid turbulence by continuous Landau-instability driving, sustaining ${\sim}2500$ vortices free from transient artifacts. The topological charge structure factor $S_c(k)$ reveals Class I disordered hyperuniformity with $S_c(k)\propto k^{\alpha>1}$ as $k\to0$, where $k$ is the wavenumber. This constitutes the strongest long-range order of its kind and its first observation in a strongly driven, far-from-equilibrium quantum fluid with topological defects as the organizing principle, establishing a novel non-equilibrium vortex phase. Exploiting this platform, we resolve the scaling controversy: the apparent $k^{-5/3}$ signature in the kinetic energy spectrum is a narrow crossover between the $k^{-1}$ single-vortex and $k^{-3}$ core regimes, not a genuine Kolmogorov inertial range. The real-space second-order structure function provides decisive evidence via $S_2(r)\propto \ln r$ where $r$ is the spatial separation, with no $r^{2/3}$ Kolmogorov scaling, ruling out a true inertial cascade. These findings reveal that strongly coupled quantum turbulence lacks an inverse cascade due to the absence of macroscopic Onsager clusters, demonstrating energy transport fundamentally distinct from weakly coupled superfluids.

Hydrodynamization refers to the remarkably rapid process in relativistic heavy-ion collisions by which hydrodynamic descriptions become applicable. Following the observation of analogous behavior in ultracold one-dimensional (1D) Bose gases, hydrodynamization has been conjectured to be a universal dynamical phenomenon in quantum systems following high-energy quenches. Theoretical studies in this cold-atom setting have so far been restricted to quenches from ground states. Here we study how nonzero temperatures affect hydrodynamization. Specifically, using a homogeneous 1D gas of hard-core bosons, we explore how the initial temperature affects the timescales associated with hydrodynamization and prethermalization following a Bragg-pulse quench. We find that while the hydrodynamization coherence time remains unchanged, increasing temperature shortens both the damping time of the hydrodynamization oscillations and the prethermalization time. We argue that this is mainly the result of the broadening of the initial rapidity distribution, and introduce a nonzero-temperature dephasing time defined in terms of the extent of the rapidity distribution.

The evolution of quantum field expectation values from an initial non-equilibrium quantum state can be followed numerically using the Truncated Wigner technique. It can track non-perturbative quantum phenomena, such as false vacuum decay, in real time with promising results. Nevertheless, it is an approximate method subject to quantum loop corrections. The extension of Truncated Wigner into a fully fledged effective field equation approach is discussed here, including corrections from higher loops and higher momenta.

A nuclear Fermi liquid exhibits competing pairing instabilities in different spin, isospin, and orbital channels. In a Fermi-surface renormalization group (RG) treatment, the channel that develops a pole first is determined not only by its tree-level attraction but also by its one-loop RG coefficient. We illustrate this mechanism in a minimal $S/P$-wave model. A spherical Fermi surface establishes the reference competition between the lowest even- and odd-parity interactions. Axial deformation changes the relevant Fermi-surface integrals and lifts the degeneracy between longitudinal and transverse $P$-wave components. In isospin-asymmetric matter, neutron–proton Fermi-momentum splitting restricts the simultaneous low-energy contribution of the two species and can terminate the $np$ running at finite threshold scales. Our calculations are intended as controlled one-loop RG illustrations rather than as quantitative nuclear-matter calculations. We show how the Fermi-surface geometry and composition can change the ordering of competing pairing instabilities.

We study the quantum dynamics of two interacting anyons in the Anyon-Hubbard model on a four-site plaquette, a system that is exactly mappable to a Bose-Hubbard model. We reveal that static Aharonov-Bohm (AB) caging, induced by only specific statistical phases, emerges in the strongly interacting limit but breaks down under weak interparticle interactions. To address this, we demonstrate that statistical-factor-induced AB caging can be dynamically restored via Floquet engineering. This dynamical mechanism, governed by the synthetic Floquet flux and the anyonic statistical phase, extends the caging effect into the weakly interacting regime across the full spectrum of statistical phases. Furthermore, we show that the external drive enables the selective caging of anyons, providing an efficient approach for manipulating anyons and identifying statistical phases.

A fundamental quantity characterizing Fermi gases with zero-range interactions is the three-body contact $C_3$, which determines several observables including the number of nearby triplets of fermions and the three-body loss rate in cold atom experiments, as shown in a companion article. Here, we compute $C_3$ to leading order in the non-degenerate limit for the homogeneous gas with negative or infinite scattering length $a$. At $a=\infty$, using a wavefunction approach, we obtain the analytical expression of $C_3$, which has a remarkably slow $1/T^{0.22728}$ dependence on the temperature $T$. In the Feynman diagram technique, which we use for $a<0$, the correct three-body short-distance correlations emerge only after a non-trivial cancellation between leading order two-body and three-body correlations, and the resulting power-law scaling comes from the large-wavevector tail of the 3-body T-matrix, which we derive inspired by the analytical solution of the three-body problem at the unitary limit.

Motivated by recent numerical studies where various $SU(2)$ Chern-Simons-matter theories emerge, we analytically study topological phases and quantum criticality in two-dimensional systems described by such theories. First, we classify $SU(2)_k$ topological orders in all lattice spin systems with a $p4\times SO(3)$ symmetry, where $k$ is an arbitrary nonzero integer. We find that for each odd $k$, the topological order can emerge in systems with an arbitrary Lieb-Schultz-Mattis (LSM) anomaly, and the symmetry cannot permute anyons. If the system has a nontrivial (respectively, trivial) LSM anomaly, then there is exactly one (respectively, nine) symmetry-enriched topological (SET) phases. On the other hand, $SU(2)_k$ topological order with any even $k$ can only emerge in systems with a trivial LSM anomaly. If $k\notin\{6, 10, 14, \cdots\}$, the symmetry cannot permute anyons, and there are 16 SET phases. If $k\in\{6, 10, 14, \cdots\}$, there are 4 different ways how the symmetry can permute anyons, and there are 64 SET phases. Next, we analyze the $SU(2)_k$ Chern-Simons theories coupled to $N_f$ flavors of gapless matter fields that can be either bosonic or fermionic. For both types of theories, we consider a joint large-$N_f$ and large-$k$ limit with $N_f/k$ fixed, and compute the scaling dimensions of the bilinear operators of the bosons or fermions to the order of $1/N_f$. These results sharpen our understanding of these emergent exotic topological phases and quantum criticality, and provide useful guidance to explore them further.

We investigate a single mobile impurity in a two-dimensional hard-core Bose–Hubbard bath at low and intermediate fillings and determine how polaronic dressing evolves with bath filling for impurity–bath couplings ranging from weak to strong and ultimately to the two-component hard-core limit. Using large-scale, sign-problem-free worm-algorithm quantum Monte Carlo simulations, we extract momentum-space quasiparticle properties from the impurity Green's function and resolve the accompanying real-space bath rearrangement from an imaginary-time-averaged impurity-centered correlator. We also vary the impurity hopping $t_{\rm imp}$ to assess how reduced mobility modifies dressing in the strong-coupling regime. For the fillings accessible at each coupling, the impurity remains a dressed quasiparticle whose ground-state energy, effective mass, and residue vary smoothly with filling $n_{\rm b}$. In real space, increasing $n_{\rm b}$ strengthens the short-range depletion while shifting the dominant response toward the impurity. In the two-component hard-core limit $U_{\rm ib}/t_{\rm b}\!\to\!\infty$, the large-distance recovery of the cumulative density deformation exhibits only weak filling dependence over the range considered here, whereas short-range core indicators continue to evolve. Our results quantitatively characterize strongly dressed polarons in a correlated, compressible lattice bath and resolve how filling and impurity mobility modify the near-core response and spatial extent of the dressing cloud.

We uncover a mechanism for far-from-equilibrium topological phase transitions, via a one-dimensional compact phase model evolving deterministically from random initial conditions. It rests on topology and symmetry rather than on phenomenological postulates: phase compactness permits vortices, and a homogeneous fixed point suppresses their nucleation, with the fixed point itself implied by phase-shift symmetry. The competition between vortex-induced disordering and relaxation toward homogeneity drives a continuous nonequilibrium transition, whose universality class we identify as directed percolation (DP). We demonstrate this by constructing the corresponding effective field theory and numerically confirming DP critical scaling through dynamical-scaling analysis.

A supersolid combines density order with phase coherence, and doped lattice solids ask whether added defects can become coherent without melting the ordered background. We study a soft-core Bose-Hubbard model with isotropic hopping and an engineered non-axisymmetric dipolar interaction, \(V_{ij}=V_2(x_{ij}^2-y_{ij}^2)/r_{ij}^5+W_6/r_{ij}^6\), where the sign-changing \(d_{x^2-y^2}\) component selects a fixed \((q,0)\) stripe channel and the \(W_6/r^6\) core stabilizes the short-distance attractive branch. Using sign-problem-free quantum Monte Carlo method with worm algorithm, we find that the half-filled stripe parent responds asymmetrically to doping: the hole side forms locked commensurate stripe solids with vanishing superfluid stiffness, whereas the particle side forms a stripe supersolid with finite compressibility \(\kappa>0\), finite superfluid stiffness \(\rho_s>0\), and enhanced double occupancy \(D\). Keeping the same off-site kernel while increasing \(U/t\) toward the hard-core limit shows that the particle-side supersolid disappears once doublon-like defects are projected out. Thus the engineered dipolar kernel selects the fixed \((q,0)\) stripe channel, while onsite softness selects the phase-coherent defect sector.

We describe turbulent hydrodynamics of superfluids in two spatial dimensions via the dynamics of point-like vortices coupled to an emergent 2+1 dimensional $U(1)$ gauge field. The cascade of superfluid kinetic energy is equivalently described by a cascade of dual electric field energies. We study superfluid turbulence using the equations of motion of the dual gauge theory in the presence of a drive and dissipation. In the limit that the vortices are point-like, the dual equations of motion directly yield the hydrodynamical equations of the superfluid. We obtain a turbulent cascade consistent with Kolmogorov's scaling law for two dimensional fluid turbulence. We observe clustering of like-signed vortices and compute the kinetic energy flux to show that the turbulent regime exhibits an inverse energy cascade.

We consider two two-dimensional (2D) electronic systems in the presence of a perpendicular homogeneous electric field that generates a Rashba spin-orbit interaction (RSOI): a system of non-interacting electrons in a 2D conductor, modeled using the 2D Schrödinger equation (SE), and a single-layer graphene system, modeled using a 2D Dirac equation (DE) for massless fermions. In both cases the RSOI is expressed via an $SU(2)$ Rashba vector potential ${\bf A}_{R}$. We demonstrate that ${\bf A}_{R}$ cannot be eliminated from either the 2D SE or the 2D DE via a gauge transformation. Nevertheless, for a plane wave solution, an $SU(2)$ matrix exists that eliminates ${\bf A}_{R}$ from the resulting 1D SE. This unitary matrix is an Aharonov-Casher (AC) phase factor, and facilitates the calculation of the AC phase in the Schrödinger scheme. The plane wave solution for the DE contains two components of ${\bf A}_{R}$: $A_{R, k}$ in the direction of the wave vector ${\bf k}$, and $A_{R, n}$ normal to ${\bf k}$. The latter generates an effective electron mass that cannot be eliminated from the DE. The former generates an AC phase that can be eliminated by a time-dependent unitary transformation. Thus, the Dirac AC phase is time-dependent, i.e., it is a dynamical phase. This is in contradistinction to the Schrödinger AC phase which is geometrical.

We introduce a framework to classify quantum phases, phase transitions, and non-equilibrium dynamics of interfaces separating ordered bulk domains in 2D quantum magnets - equivalently, confining strings in dual lattice gauge theories - based on effective 1D Hamiltonians governing geometric fluctuations. Building on a "holographic" approach from [Phys. Rev. Lett. 129, 120601 (2022)], here reinterpreted as an exact bosonization, we uncover a rich quantum phase structure, with a variety of stiff and rough interface phases described by gapped and gapless 1D ground states, respectively, all distinguishable through the statistics of 2D wave-function snapshots. Our framework allows us to predict distinct spatiotemporal scaling laws for non-equilibrium curvature-driven interface dynamics across parameter space, which can be readily probed in existing experiments. We finally show that our approach enables the unprecedented experimental opportunity of directly measuring charge full counting statistics and symmetry-resolved properties of an encoded 1D system, as we explicitly demonstrate by numerically simulating a neutral-atom array experiment.

The non-equilibrium properties of open quantum systems are determined by the microscopic laws governing energy exchange with their environment. In particular, an enhancement of the performance of quantum heat engines has been predicted by speeding up the dynamics through control of the system–bath interaction. However, direct microscopic control of heat transfer between the machine and the reservoir has remained elusive so far. Here, we experimentally demonstrate such control in a quantum Otto engine realized with ultracold Cs-133 atoms coupled to an atomic reservoir of ultracold Rb-87 atoms. Heat exchange between the two is mediated by inelastic s-wave collisions whose energy-dependent scattering cross sections lead to an asymmetric equilibration dynamics in the isochoric heating and cooling strokes. By tuning the kinetic temperature of the atomic reservoir, we modify the associated microscopic scattering rates, and thereby the heat transfer law, giving control over the time allocation within the engine cycle through control over the microscopic, multi-exponential relaxation dynamics. This enables power output optimization at fixed efficiency. Our results establish microscopic control of system-reservoir interactions as a tool for manipulating heat flow at the nanoscale and engineering the finite-time performance of quantum thermal machines.

Unconventional photon blockade (UPB) provides an attractive route for generating antibunched light through quantum interference without requiring strong nonlinear coupling. In conventional Markovian systems, irreversible dissipation progressively destroys the phase coherence, even limiting the achievable single-photon purity. Here we propose a scheme for imposing non-Markovian effects on a microwave cavity where a Er$^{3+}$:Y$_2$SiO$_5$ crystal loaded into a hybrid optical-microwave system. Based on the time-convolutionless non-Markovian framework, we derive the time-dependent non-Markovian decay rate and the renormalized microwave drive in the weak-coupling regime. We show that the second-order correlation function is significantly suppressed, even to the order of $10^{-7}$, since the backflow of environmental information enhances photon blocking. In addition, this structured reservoir engineering not only provides an additional degree of freedom, but also further optimizes the blockade via optical detuning. Importantly, the delayed second-order correlation exhibits a broadened antibunching profile, thereby relaxing the timing requirements for single-photon synchronization. Our results demonstrate that environmental non-Markovianity can be transformed from a source of decoherence into a controllable quantum resource, opening new opportunities for high-purity single-photon generation.