Papers

We derive a unified set of scaling equations for Bose-Einstein condensates in time-dependent harmonic traps, connecting the weakly interacting Gaussian regime to the strongly interacting Thomas-Fermi regime. The exact Gross-Pitaevskii ground-state density is taken as a fixed profile in rescaled coordinates, with its dynamics described by three scaling factors corresponding to compression or expansion along the three spatial directions. The resulting equations contain no adjustable parameter, since their coefficients are determined once from the initial state. They recover analytically the Gaussian variational and Thomas-Fermi scaling equations in their respective limits and satisfy an axis-resolved virial theorem. The approach also yields the global phase and the low-lying collective-mode frequencies of the condensate. We benchmark the model against three-dimensional Gross-Pitaevskii simulations and against measured expansion energies. The model remains accurate across all interaction regimes, in strongly anisotropic traps, and along time-dependent sequences including a relatively fast quench, up to the point where the underlying frozen-profile hypothesis, shared by all three scaling approaches, breaks down.

The microscopic origin of the pseudogap phase constitutes a longstanding puzzle related to the emergence of high-temperature superconductivity in cuprate materials. In this work, we develop an effective model for doped antiferromagnets in terms of fluctuating stripes, or string-like domain walls, which obscure the antiferromagnetic order of the spin background. The open ends of such domain walls of the N'eel order are treated as vortices in the resulting lattice gauge theory. We numerically evaluate the phase diagram by classical Monte Carlo simulations, using percolation-based geometric order parameters to diagnose hidden N'eel order. At high temperatures, we identify a BKT-type crossover in which the domain wall ends become deconfined. We interpret this as the $T^*$ crossover from the hidden order regime to the paramagnetic metal above. At low temperatures, we identify stripe instabilities. Predictions of our effective model can be tested in ultracold fermion quantum simulators.

We study weakly interacting bosons on the three-dimensional torus at temperatures proportional to the critical temperature for Bose–Einstein condensation. We show that, as the expected particle number tends to infinity, the grand canonical Gibbs state is asymptotically described by the coherent state quantization of a random field that converges to a novel Bogoliubov random field. Moreover, the point process associated with the Gibbs state can be approximated by a Cox process. These results are based on and extend the approximation of the Gibbs state recently obtained by the first two authors and Nam. Using these approximations, we compute limiting distributions of the number of particles outside the condensate, the joint occupation statistics of finitely many momentum modes, and particle-number fluctuations in macroscopic subsets of the torus, all governed by the Bogoliubov field. We further prove convergence of the empirical measure of the associated point process to the uniform measure and convergence of the microscopic particle-number statistics to the boson point process. The latter result establishes the universality of particle-number statistics on microscopic length scales.

In an open, $U(1)$-symmetric Dicke model with chiral atom-cavity couplings, we show that dissipation drives two limit-cycle phases of opposite chirality in the thermodynamic limit, obtaining exact analytical solutions. These phases are separated by a $U(1)$-broken superradiant state, lending the phase diagram a topological character, and persist under $U(1)$-preserving perturbations, making them candidates for chiral continuous time crystals. In addition to stable normal and inverted steady states, the model also exhibits multistability, where the long-time dynamics is set by the initial state. Our results establish dissipation as a resource for inducing chiral dynamical order in light-matter coupled systems.

Finite-component light-matter systems realize dissipative phase transitions in a single controllable atom-cavity setup, but how atomic dephasing - ubiquitous in real cavity- and circuit-QED devices - affects this criticality remains unknown. We study the anisotropic open Rabi model under cavity decay, spontaneous emission, and atomic dephasing together. We show that when spontaneous emission stabilizes a long-lived metastable superradiant phase, atomic dephasing actively competes with it - eroding its coherence and shortening the lifetime. This direct competition reveals that a dissipation channel's microscopic character, not its strength, controls its nonequilibrium criticality - a distinction directly tunable via independent spontaneous-emission and dephasing rates in circuit-QED and trapped-ion platforms.

Ultracold atomic systems offer a highly controllable platform for investigating quantum state transfer through the precise dynamical manipulation of system parameters. While quantized Thouless pumping has been extensively explored in these systems, adiabatic edge-to-edge transfer of localized quantum states remains largely unexplored. Here, we consider a one-dimensional ultracold atomic gas confined in a bichromatic optical lattice realizing a quasiperiodic Aubry–André–Harper system. We use its edge-localized winding states to implement quantum state transfer between opposite boundaries. Starting from the instantaneous spectral properties of the corresponding tight-binding model, we construct locally adiabatic protocols and extend the approach to higher protocol orders. We then simulate their dynamics under the full continuum bichromatic-lattice Hamiltonian. Our results reveal a tradeoff between edge localization and the minimum spectral gap: strongly localized states require longer transfer times, but can benefit substantially from higher protocol orders. We are also able to capture the main fidelity trends and coherent oscillations over a broad parameter regime using an effective two-level Landau–Zener description. Our results provide practical guidelines for selecting experimentally accessible parameters and tailoring quantum transfer protocols in quasiperiodic ultracold atomic systems.

We investigate condensation and finite-temperature magnetic phase transitions in a coherently (Rabi) coupled Bose gas confined in a three-dimensional harmonic trap. For the noninteracting system, we derive analytical expressions for the critical temperature and condensate fraction using a semiclassical description of the single-particle spectrum and density of states. At fixed particle number, coherent coupling enhances the critical temperature relative to the uncoupled system, and this enhancement decreases with increasing particle number $N$. The finite-size correction, in contrast, lowers the transition temperature, with its effect diminishing for larger $N$. We then incorporate repulsive interactions within the Hartree–Fock–Bogoliubov–Popov framework to investigate the finite-temperature phase diagram in the temperature–Rabi coupling plane. The system undergoes successive transitions from a ferromagnetic to a paramagnetic condensate and, at higher temperature, to a thermal gas. The transition boundaries obtained from the vanishing of the condensate fraction show excellent agreement with the analytical Hartree-Fock predictions. We find that the interactions substantially suppress the variation in the condensation temperature with an increase in the coherent coupling.

In this work, we study finite-time effects in ultracold atomic systems by considering time-dependent modulations with variable waveforms and durations. These two characteristics can be controlled by adjusting only a single parameter. For arbitrarily short pulses, our model recovers the paradigmatic kicked rotor while maintaining the impulse transmitted per period and unit amplitude constant. Furthermore, we demonstrate that finite-time effects have a profound impact on dynamical localization, a result that cannot be captured by the {\delta}-kicked-rotor model. Through a detailed analysis of the effects of different modulation amplitudes, periods, and waveforms, we identify the conditions for which dynamical localization is significantly enhanced. We show that the strength of dynamical localization increases sharply as the system approaches the {\delta}-kicked-rotor limiting case. Moreover, we establish the existence of an optimal value of the period that maximizes dynamical localization for given values of the amplitude and shape parameter.

We study polar molecules where short-range losses are suppressed by a shielding scheme involving a static electric field and an elliptically polarized microwave field. Using perturbation theory, we derive the effective interaction potential and validate it against coupled channel calculations. We identify a parameter regime where two-body losses are strongly suppressed and the extended mean-field description of dilute molecular Bose-Einstein condensates is justified. We calculate the collective excitations and show that intriguingly, supersolidity in quasi-two-dimensional confinement emerges as a stripe phase even at small values of microwave ellipticity.

We study quantum droplets in a symmetric two-component Bose mixture with interspecies $p$-wave interactions and a two-dimensional transverse optical lattice. The lattice drives a crossover from an anisotropic three-dimensional gas to weakly coupled one-dimensional tubes. We calculate the ground-state energy and quantum depletion at the Gaussian level and derive their limiting forms. At $y=g_{12}/g=-0.95$, where the bare mean field is repulsive and no free-space droplet exists, the calculated bulk equation of state supports a self-bound minimum across the crossover: a negative lattice contribution at order $n^{2}$ supplies the attraction in the three-dimensional regime, and attractive fluctuations do so in the quasi-one-dimensional regime, with the intermediate, transdimensional range described quantitatively by neither limit. The interspecies $p$-wave interaction modifies only the spin branch. In the parameter range studied, increasing its strength lowers the equilibrium density across the crossover, consistently with a weakening of the induced binding.

Nonergodic features of chaotic quantum many-body systems are commonly characterized through local observables, fidelity, and entanglement entropy. Here, using global and nonlocal measures of nonstabilizerness (magic), we study quantum many-body scars near infinite temperature in $(1+1)$-dimensional Abelian $\mathbb{Z}_2$ and U$(1)$ lattice gauge theories, both analytically and numerically. We derive an exact closed-form expression for the nonlocal trace distance magic solely from the Schmidt spectrum, reducing the optimization over local unitaries to a finite maximization over stabilizer-compatible Schmidt ranks. We find that scar eigenstates can exhibit extensive global magic despite their anomalously low entanglement, while retaining anomalously large nonlocal magic compared with ergodic states. We further show that constrained Hilbert spaces can generate irreducible nonlocal magic through stabilizer-incompatible Schmidt ranks, even for a flat entanglement spectrum.

Altermagnetism has recently emerged as a distinct collinear magnetic phase exhibiting momentum-dependent spin-splitting despite vanishing net magnetization, as a consequence of inequivalent non-magnetic environments. Lately, it has been proposed that strong electronic correlations may yield spontaneous altermagnetism due to orbital ordering even for equivalent non-magnetic environments. While previous studies have largely focused on the electronic structure, a unified understanding of the collective excitations associated with these two different microscopic mechanisms stabilizing altermagnetism remains absent. Here, we develop an extended Kugel'-Khomskiĭ spin-orbital model on a decorated square lattice that simultaneously incorporates inequivalent non-magnetic environments and correlation-driven orbital ordering within a common theoretical framework. Employing a self-consistent mean-field spin-wave orbital-wave formalism, we demonstrate the emergence of mutually unhybridized but interdependent magnon and orbiton excitations exhibiting characteristic chiral-splitting. We show that the splitting originates from two distinct microscopic contributions: a lattice-dependent term arising from inequivalent non-magnetic environments and an orbital-order-induced exchange-anisotropy term that survives even for equivalent non-magnetic environments. The proposed framework therefore unifies the collective excitations associated with both types of altermagnetism. We further investigate the finite-temperature evolution of the coupled spin-orbital system, revealing the breakdown of spin-wave and orbital-wave approximations through spurious 1st-order transitions, while complementary classical Monte Carlo simulations recover the expected continuous 2nd-order behaviour. Our work establishes a unified microscopic framework for understanding collective magnon and orbiton excitations in altermagnets.

Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.

We map the transport regimes of a wave packet evolving under the one-dimensional discrete nonlinear Schrödinger (Gross-Pitaevskii) equation with a quasiperiodic Aubry-André potential and a static (Stark) field, as a function of self-interaction $g$, field $F$, and quasiperiodic strength $\lambda$, for two initial states (delta and Gaussian). Instead of one expensive long-time simulation per grid point, we run 3600 short simulations, reduce each to eight dynamical features, and cluster parameter space with a Gaussian mixture model. Clustering finds the boundaries between regimes unsupervised; each cluster's name is then assigned by a hand-calibrated rule, and an ablation shows clustering measurably smooths those boundaries rather than merely relabeling them. The five resulting regimes (ballistic, localized, oscillatory-localized, subdiffusive, and self-trapped) are validated against 100 long runs on a lattice eight times larger than the short sweep, so the validation window is longer than the training window even for the fastest-spreading regime. The short-time clusters predict the long-time asymptotic spreading exponent ($\alpha_\infty = 2.01\pm0.07$ ballistic, $0.28\pm0.16$ subdiffusive, consistent with the weak-chaos prediction $\alpha=1/3$) and, independently, a long-time retention $\Pi_0=0.72\pm0.32$ for the self-trapped cluster, whose exponent alone is not diagnostic. The initial-state contrast is striking: the delta state develops a broad self-trapping wedge (onset at $g=3.907\pm0.017$ at $\lambda=0$) that invades the ballistic and localized regions as $g$ grows, while the Gaussian state shows no self-trapping, instead opening a subdiffusive corridor along the Aubry-André critical line that widens with $g$. The scheme yields a full $15\times15$ phase map in minutes per slice, where direct asymptotic simulation ($t\gtrsim10^6$ per point) is prohibitive.

Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order \(10^{-3}E_R\), corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.

Prethermal states–long-lived quasi-equilibrium configurations–occur in a wide range of physical systems that exhibit fast dephasing or reconfiguration followed by slow relaxation towards thermal equilibrium. We experimentally studied the 1D interface between immiscible 2D Bose-Einstein condensates (BECs); following a quench, the interfacial capillary waves (ripplons) quickly relaxed into a long-lived prethermal state characterized by a persistent non-equipartition of energy, evoking the classic Fermi-Pasta-Ulam-Tsingou problem. We directly measured the interface's height profile as it evolved in time, identified the contribution of individual ripplon modes, and find that, though their individual amplitudes are thermally distributed, they are not in thermal equilibrium–high-momentum modes rapidly equilibrated with the bulk phonon modes of the 2D BEC, while lower momentum modes remained at elevated temperatures, forming a long-lived prethermal configuration for the whole system. We attribute this to kinematic isolation: the absence of energy- and momentum-conserving relaxation processes in our system at ultracold temperature.

Ultracold atomic quantum systems offer an unprecedentedly powerful platform for exploring interacting symmetry-protected topological phases. Here, we show that their characteristic control over temperature provides a resource for engineering effective topological regimes with no zero-temperature counterpart. Employing finite-temperature matrix-product-state calculations, we investigate experimentally accessible Hamiltonians - the interacting bosonic Su-Schrieffer-Heeger and spin-1 XXZ chains - that host a topological phase at zero temperature, as well as a fermionic dipolar ladder model whose ground state exhibits no topological order. By tracking complementary topological markers, we identify an intriguing mechanism rooted in the structure of the zero-temperature phase diagrams: in finite-size systems, excitation gaps with different magnitudes define an intermediate-temperature window where the correlations associated with the lower gap are suppressed, while those protected by the larger gap persist. This enables the emergence of effective finite-temperature regimes exhibiting topological features that are either absent or qualitatively different from those at zero temperature. Our results establish a novel route toward exploring effective topological phases in ultracold atomic quantum systems.

The Anderson orthogonality catastrophe (AOC) is a paradigmatic many-body phenomenon in which a local perturbation induces a macroscopic response of a Fermi sea. We probe signatures of the AOC by coherently driving heavy Fermi polarons in an ultracold $^6$Li-$^{133}$Cs mixture. We observe a power-law dependence of the measured Rabi frequency on the drive strength, with exponents consistent with AOC predictions. Finite-temperature simulations quantitatively reproduce the observed scaling, indicating that AOC signatures persist beyond the idealized zero-temperature, infinite-mass limit. The damping of the Rabi oscillations provides access to polaron dephasing and reveals a nonmonotonic drive dependence, qualitatively consistent with current theories. Our results establish coherently driven impurities as a versatile probe of quantum many-body dynamics through local coherent control.

Quantum statistics in low-dimensional systems predicts anyonic particles with fractional exchange statistics which are neither that of bosons nor fermions. While anyons are typically found in two dimensions as excitations of topologically-ordered states of matter, anyon-like exchange statistics has also been discussed in one dimension, for instance, in the context of the anyon-Hubbard model (AHM), the physics of which has recently been observed in experiment [Kwan et al., arXiv:2306.01737; Dhar et al., arXiv:2412.21131; and Bakkali-Hassani et al., arXiv:2602.20421]. The AHM can be formulated in terms of bosons featuring density-dependent Peierls phases, described by a statistical phase angle $\theta$, which controls asymmetric transport and the formation of dynamically bound pairs at finite momentum. Here, we show theoretically that the AHM also hosts exact two-body bound states in the continuum (BICs) for arbitrary $\theta\neq 0$, and genuine three- and four-body bound states. Unlike conventional bound states stabilized by attractive (or repulsive) interactions, which are energetically localized with a large effective mass, these clusters here are bound by a purely kinematic mechanism endowing them with fast chiral transport properties. We provide a simple variational approximation to the three-body bound states and explain their binding mechanism. Moreover, we show that the signatures of three-body bound states in the AHM can be directly probed experimentally from the expansion dynamics starting from three localized particles.

Attractors are effective low-dimensional structures, defined in a chosen set of observables, that trajectories from different initial states approach; hydrodynamic attractors are those on which the late-time evolution is governed by hydrodynamic constitutive relations. Motivated by nuclear collisions and ultracold atomic gases, this chapter distinguishes attractorization (the loss of sensitivity to some directions in the space of initial states) from hydrodynamization (the onset of validity of hydrodynamic constitutive relations). Using mainly conformal, boost-invariant Bjorken flow, we compare Müller-Israel-Stewart-type theories, kinetic theory, holography, and classical Yang-Mills fields. Forward attraction, produced by the decay of non-hydrodynamic modes, is distinguished from pullback attraction, which can select a unique regular solution, and from expansion-driven attraction, which can suppress initial-state sensitivity before microscopic relaxation, with or without a subsequent fluid regime. Divergent gradient expansions and their transseries completions, the state-space picture, and adiabatic hydrodynamization provide complementary descriptions. Applications to nuclear collisions include particle production, transverse energy and flow, the initialization of and linear response around attracting backgrounds, jet quenching, and attractor-informed modifications of hydrodynamic models. For ultracold Fermi gases, we review theoretical proposals for bulk-channel attractors under scattering-length drives and distinguish them from recent measurements of short-time contact and momentum-distribution dynamics.

We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent, eliminating the bare coupling in favor of the physical zero-total-momentum two-body bound-state energy. The resulting cutoff-independent resolvent defines a self-adjoint Hamiltonian in each fixed particle-number sector. We treat the two-body problem explicitly and show, in the norm-resolvent sense, that the nonrelativistic limit reproduces the attractive Lieb–Liniger Hamiltonian. We also formulate a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, it predicts an exponentially increasing binding scale whose exponent is determined by a one-dimensional variational problem.

We report simultaneous sub-Doppler cooling and optical dipole trapping of $^{39}$K-Cs and $^{41}$K-Cs mixtures. Both mixtures are cooled to temperatures $\sim10$ $\mathrm{\mu}$K, achieving performance comparable to that obtained with each species individually. To the best of our knowledge, this constitutes the first realization of a laser-cooled and optically trapped $^{41}$K-Cs mixture. For the $^{39}$K-Cs mixture, we additionally implement parallel spin-resolved Feshbach spectroscopy enabled by Stern-Gerlach separation. For potassium isotopes, we implement sub-Doppler cooling with $D_1$-line gray molasses, while for cesium the entire cooling sequence is implemented using $D_2$ transitions. We spin-polarize the atoms and confine Bose-Bose mixtures in a 1064 nm optical dipole trap. Using the resulting $^{39}$K-Cs samples, we observe 14 heteronuclear Feshbach loss features. Five agree with resonances reported previously, while nine have, to the best of our knowledge, not been observed experimentally before, including $p$-wave features and resonances in additional spin channels. The shorter lifetime of the $^{41}$K-Cs mixture in the optical dipole trap currently hinders systematic Feshbach spectroscopy, which we therefore do not pursue in this work. To characterize this limitation quantitatively, we study the decay dynamics of $^{39}$K-Cs and $^{41}$K-Cs mixtures under comparable temperature and density conditions, revealing a substantially stronger nonexponential loss in the $^{41}$K-Cs mixture. The demonstrated preparation of ultracold $^{41}$K-Cs mixtures provides a starting point for Feshbach-resonance and photoassociation spectroscopy of this previously unexplored isotopologue. Such measurements are essential for identifying suitable pathways for magnetoassociation and coherent optical transfer, and ultimately for the production of ultracold ground-state $^{41}$KCs molecules.

We propose an epsilon-near-zero (ENZ) artificial cavity that can enhance light-matter coupling around the ENZ frequency and theoretically show the possibility of exciton-polariton condensation in the suggested platform. By using a rate equation model based on the driven-dissipative reservoir approach, we calculate the pump threshold for condensation and then compare the suggested platform's advantages/disadvantages with distributed Bragg reflector cavities. We also discuss the validity of the mean field theory within our model.

We study topological band structures and superfluid phases in two-dimensional square-lattice systems with homogeneous SU($N$) non-Abelian gauge fields. Starting from an SU(4) gauge-field model related to the Hofstadter model with flux $\alpha=1/4$, we show that the lowest and highest bands are isolated Chern bands that carry Chern numbers $C=-4$ and give rise to four chiral edge modes in a strip geometry. Remarkably, although the two middle bands touch and form $16$ gapless Dirac cones, their combined Chern number is $C=8$. We then generalize the construction to SU($N$) systems and reveal an even–odd structure of the band topology: when $N$ is odd, all bands are isolated and carry nonzero Chern numbers; when $N$ is even, the two middle bands touch at $N^{2}$ Dirac points, while all other bands remain isolated and topologically nontrivial. We find that the uppermost and lowermost bands become increasingly flat and their Berry curvature becomes more uniform as $N$ increases, providing a promising platform for realizing fractional Chern insulating phases. We further examine the spin-$3/2$ SU(4) model with on-site attractive Hubbard interactions, exploring its superfluid phases at partial filling. We find that the non-Abelian gauge field breaks the hidden SO(5) degeneracy of the quintet pairing and selects distinct nematic superfluid states. For fillings in the middle-band regime, the resulting spectrum can host topologically protected Bogoliubov Fermi surfaces. Our results provide a starting point for exploring both topological band physics and unconventional superfluidity in synthetic SU($N$) cold-atom systems.

During the experimental sequence, a large atom number is important for the creation of high-quality Bose–Einstein condensates. We report an experimental increase of about 15% in magnetic-trap (MT) loading efficiency by optimizing the MT loading process. The loading time is much shorter than the lifetime of the atoms in the MT, which means atom loss during loading due to the finite trap lifetime can be neglected. We obtain an almost pure $^{39}\mathrm{K}$ condensate with $1.2\times10^{5}$ atoms after evaporative cooling in our optical trap.

Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at $2t_h$, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the $1/U$ law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.

Interactions govern the emergence of collective behaviour in classical and quantum many-body systems. While conservative interactions are well known to generate nonlinear phenomena ranging from self-trapping to pattern formation, it remains largely unexplored whether purely dissipative – i.e., non-Hermitian – interactions can give rise to similarly rich dynamics and nontrivial system states. Here, we experimentally realise tuneable non-Hermitian interactions in two coupled condensates of light confined within a dye-filled double-well microcavity. Local coupling to molecular reservoirs generates the effective dissipative photon interactions. We show that the interplay between coherent tunnelling and interactions stabilises limit-cycle oscillations, a hallmark of nonlinear dynamics traditionally associated with Hermitian nonlinearities. By tuning the reservoir coupling, we map out the dynamical phase diagram comprising stable fixed points and limit cycles, thereby demonstrating direct control over the interaction strength. Our experimentally validated model reveals both supercritical and subcritical Hopf bifurcations, giving rise to hysteresis, bistability and excitability. These results validate dissipative interactions as a mechanism for organising collective nonlinear dynamics in driven-dissipative systems and pave the way towards exploring nonequilibrium many-body physics through controlled dissipation.

Chiral $p_x\!\pm\! i p_y$ superfluidity in fermionic polar molecules offers a direct route to topological quantum matter with non-Abelian excitations, yet the parameter regime in which pairing survives strong correlations and competing instabilities has remained unresolved. Here we determine this regime for microwave-shielded polar molecules. Under tight confinement along the \(z\) direction, the microscopic molecular interaction collapses onto a universal quasi-two-dimensional form specified by an interaction length $\sigma$, defined as the position of its attractive minimum, and a single dimensionless coupling. We combine Fermi-hypernetted-chain Euler–Lagrange theory with correlated-basis pairing theory, thereby treating the correlation hole, density response, stability of the homogeneous fluid, and $p$-wave pairing within one framework. The largest pairing gap occurs immediately on the stable side of a long-wavelength spinodal instability at a two-dimensional density $4\times10^{-2}/\sigma^2$. Mapping this universal regime onto microscopic shielding schemes exposes an intrinsic limitation of single-microwave dressing: weakening the attraction to the optimal pairing range simultaneously weakens collisional shielding. Dual-microwave dressing removes this constraint by compensating the long-range attraction while retaining a large repulsive core. Imposing explicit requirements on collisional loss, confinement, and microwave-amplitude stability, we identify the regime of molecular mass and dipole moment favorable for \(p\)-wave superfluidity and determine experimentally realistic microwave and confinement conditions for its realization. These results turn the search for molecular $p$-wave superfluidity into a quantitative optimization problem and define a route toward the topological weak-pairing phase.

Rotating supersolids challenge the conventional notion of superfluid flow: quantized vortices coexist with crystalline order arising from the system's intrinsic density modulation. Drawing on concepts developed in the context of superfluid helium, this seemingly paradoxical state is often described phenomenologically in terms of a dual response, combining superfluid flow with rigid-body-like motion. Here we show that these apparently distinct behaviors emerge from a single microscopic velocity field, globally constrained by irrotationality. By applying a Helmholtz decomposition, we disentangle a divergence-free incompressible component, which carries vortex circulation, from a curl-free compressible component generated by the intrinsic density modulation. In absence of vortices, the response is entirely encoded in the compressible field: the droplets co-rotate with the external drive, while the interstitial fluid develops an oppositely directed counterflow that preserves vanishing circulation. Above the vortex nucleation threshold, the incompressible component carries the usual quantized circulation, whereas the compressible field counteracts the vortex-induced angular momentum, reducing the total jump with respect to an unmodulated condensate. Our results recast supersolid rotation in terms of a flow-counterflow response, providing a microscopic interpretation of the phenomenological rigid/superfluid partitioning.

We propose a cold-atom platform for precision tests of nonlinear and stochastic modifications to the Schrödinger equation, utilizing strongly correlated ultracold $^{133}$Cs in a uniform array of one-dimensional tubes formed by a two-dimensional optical lattice. Objective collapse models can be tested using the metastable super-Tonks-Girardeau gas. Based on a calibration test performed on our existing experimental setup, we project a sensitivity to the Continuous Spontaneous Localization collapse rate of $\lambda_c \simeq 1.8\times10^{-11}\,\mathrm{s^{-1}}$ at a correlation length of $r_c = 10^{-7}\,$m. This would establish a new bound an order of magnitude below the strongest existing constraint that remains robust against a cutoff in the collapse noise spectrum. Additionally, we can test deterministic nonlinear modifications by probing the symmetry-protected breathing mode frequency of the Tonks-Girardeau gas in harmonic traps. Crucial to both measurement schemes is the capability to independently tune the atom number and the linear density. By exploiting the different scaling laws associated with these parameters, we can cleanly distinguish genuine new physics signals from technical systematics.