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We address the Bose polaron problem of a mobile impurity interacting strongly with a host Bose-Einstein condensate (BEC) through a Feshbach resonance. On the repulsive side at strong couplings, theoretical approaches predict two distinct polaron branches corresponding to attractive and repulsive polarons, but it remains unclear how the two are related. This is partly due to the challenges resulting from a competition of strongly attractive (destabilizing) impurity-boson interactions with weakly repulsive (stabilizing) boson-boson interactions, whose interplay is difficult to describe with contemporary theoretical methods. Here we develop a powerful variational framework that combines Gaussian correlations among impurity-boson scattering states, including up to an infinite number of bosonic excitations, with exact non-Gaussian correlations among bosons occupying an impurity-boson bound state. This variational scheme enables a full treatment of strong nonlinearities arising in the Feshbach molecule on the repulsive side of the resonance. Within this framework, we demonstrate that the interplay of impurity-induced instability and stabilization by repulsive boson-boson interactions results in a discrete set of metastable many-body bound states at intermediate energies between the attractive and repulsive polaron branches. These states exhibit strong quantum statistical characteristics in the form of non-Gaussian quantum correlations, requiring non-perturbative beyond mean-field treatments for their characterization. Furthermore, these many-body bound states have sizable molecular spectral weights, accessible via molecular spectroscopy techniques. This work provides a unified theory of attractive and repulsive Bose polarons on the repulsive side of the Feshbach resonance., Comment: Submission to SciPost

Magnetic monopoles play a central role in various areas of fundamental physics, ranging from electromagnetism to topological states of matter. While their observation is elusive in high-energy physics, monopole sources of artificial gauge fields have been recently identified in synthetic matter. String theory, a potentially unifying framework that encompasses quantum mechanics, promotes the conventional \emph{vector} gauge fields of electrodynamics to \emph{tensor} gauge fields, and predicts the existence of more exotic \emph{tensor monopoles} in 4D space. Here we report on the characterization of a tensor monopole synthesized in a 4D parameter space by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we characterize the tensor monopole by measuring its quantized topological charge and its emanating Kalb-Ramond field. By introducing a fictitious external field that breaks chiral symmetry, we further observe an intriguing transition in the spectrum, characterized by spectral rings protected by mirror symmetries. Our work represents the first detection of tensor monopoles in a solid-state system and opens up the possibility of emulating exotic topological structures inspired by string theory., Comment: main: 15 pages, 3 figures + SI: 23 pages, 28 figures

We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator in which photons interact through the Kerr nonlinearity. In presence of a phase defect between the modes, a nonlinear attractor develops, which confers a synthetic M\"obius topology to the modal structure of the system. That topology is associated with an inherently protected exchange symmetry between the modes, enabling the realization of spontaneous symmetry breaking in ideal, bias-free, conditions without any fine tuning of parameters. The dynamic manifests itself by a periodic alternation of the modes from one resonator roundtrip to the next reminiscent of period-doubling. This extends to a range of localized structures in the form of domain walls, bright solitons, and breathers, which have all been observed with remarkable long term stability. A rigorous testing of the randomness of the symmetry-broken state selection statistics has also confirmed the robustness of the exchange symmetry in our experiment. Our results and conclusions are supported by an effective Hamiltonian model explaining the symmetry protection in our system. The model also shows that our work has relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. Our work could also be beneficial to the implementation of coherent Ising machines., Comment: 14 pages, 5 figures

Optical box traps for cold atoms offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activate energy-selective chiral edge currents, but also, to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly-correlated and topological phases., Comment: 15 pages, 11 figures including Supplementary material

This work explores the possibility of creating and controlling unconventional nonlinearities by periodic driving, in a broad class of systems described by the nonlinear Schr\"odinger equation (NLSE). By means of a parent quantum many-body description, we demonstrate that such driven systems are well captured by an effective NLSE with emergent nonlinearities, which can be finely controlled by tuning the driving sequence. We first consider a general class of two-mode nonlinear systems - relevant to optical Kerr cavities, waveguides and Bose-Einstein condensates - where we find an emergent four-wave mixing nonlinearity, which originates from pair-hopping processes in the parent quantum picture. Tuning this drive-induced nonlinearity is shown to modify the phase-space topology, which can be detected through relative population and phase measurements. We then couple individual (two-mode) dimers in view of designing extended lattice models with unconventional nonlinearities and controllable pair-hopping processes. Following this general dimerization construction, we obtain an effective lattice model with drive-induced interactions, whose ground-state exhibits orbital order, chiral currents and emergent magnetic fluxes through the spontaneous breaking of time-reversal symmetry. We analyze these intriguing properties both in the weakly-interacting (mean-field) regime, captured by the effective NLSE, and in the strongly-correlated quantum regime. Our general approach opens a route for the engineering of unconventional optical nonlinearities in photonic devices and controllable drive-induced interactions in ultracold quantum matter., Comment: 32 pages, 20 figures, including Appendices. Extended version of arXiv:2203.05554

Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic $\nu=1/2$ Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of $\sigma_\text{H}/\sigma_0= 0.6(2)$ via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.

The application of a mechanical strain to a 2D material can create pseudo-magnetic fields and lead to a quantized valley Hall effect. However, measuring valley-resolved effects remains a challenging task due to their inherent fragility and dependence on the sample's proper design. Additionally, non-local transport probes based on multiterminal devices have often proven to be inadequate in yielding conclusive evidence of the valley Hall signal. Here, we introduce an alternative way of detecting the quantized valley Hall effect, which entirely relies on local density measurements, performed deep in the bulk of the sample. The resulting quantized signal is a genuine Fermi sea response, independent of the edge physics, and reflects the underlying valley Hall effect through the Widom-St\v{r}eda formula. Specifically, our approach is based on measuring the variation of the particle density, locally in the bulk, upon varying the strength of the applied strain. This approach to the quantized valley Hall effect is particularly well suited for experiments based on synthetic lattices, where the particle density (or integrated density of states) can be spatially resolved., Comment: 17 pages, 12 figures

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems., Comment: 6 pages, 4 figures + 13 pages (SI), comments are welcome

Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases., Comment: 14 pages, including 10 figures, appendix and references. Improved version submitted to the journal

The engineering of synthetic dimensions allows for the construction of fictitious lattice structures by coupling the discrete degrees of freedom of a physical system, such as the quantized modes of an electromagnetic cavity or the internal states of an atom. This method enables the study of static and dynamical Bloch band properties in the absence of a real periodic lattice structure. So far, the vast majority of implementations have focused on linear and conservative processes, with the potentially rich physics and opportunities offered by nonlinearities and dissipation remaining largely unexplored. Here, we theoretically and experimentally investigate the complex interplay between Bloch band transport, nonlinearity, and dissipation, exploring how a synthetic dimension realised in the frequency space of a coherently-driven optical resonator influences the dynamics of nonlinear waves of the system. In particular, we observe and study nonlinear dissipative Bloch oscillations occurring along the synthetic frequency dimension, sustained by localized dissipative structures (solitons) that persist endlessly in the resonator. The unique properties of the dissipative soliton states can extend the effective size of the synthetic dimension far beyond that achieved in the linear regime, as well as enable long-lived Bloch oscillations and high-resolution probing of the underlying band structure. Besides representing the first experimental study of the interplay between Bloch oscillations and dissipative solitons, our work establishes Kerr resonators as an ideal platform for the study of nonlinear dynamics in long-scale synthetic dimensions, with promising applications in topological photonics.

Synthetic dimensions provide a powerful approach for simulating condensed matter physics in cold atoms and photonics, whereby a set of discrete degrees of freedom are coupled together and re-interpreted as lattice sites along an artificial spatial dimension. However, atomic experimental realisations have been limited so far by the number of artificial lattice sites that can be feasibly coupled along the synthetic dimension. Here, we experimentally realise for the first time a very long and controllable synthetic dimension of atomic harmonic trap states. To create this, we couple trap states by dynamically modulating the trapping potential of the atomic cloud with patterned light. By controlling the detuning between the frequency of the driving potential and the trapping frequency, we implement a controllable force in the synthetic dimension. This induces Bloch oscillations in which atoms move periodically up and down tens of atomic trap states. We experimentally observe the key characteristics of this behaviour in the real space dynamics of the cloud, and verify our observations with numerical simulations and semiclassical theory. This experiment provides an intuitive approach for the manipulation and control of highly-excited trap states, and sets the stage for the future exploration of topological physics in higher dimensions.

Artificial magnetic fields and spin-orbit couplings have been recently generated in ultracold gases in view of realizing topological states of matter and frustrated magnetism in a highly-controllable environment. Despite being dynamically tunable, such artificial gauge fields are genuinely classical and exhibit no back-action from the neutral particles. Here we go beyond this paradigm, and demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices. Specifically, we propose a protocol by which atoms of one species carry a magnetic flux felt by another species, hence realizing an instance of flux-attachment. This is obtained by combining coherent lattice modulation techniques with strong Hubbard interactions. We demonstrate how this setting can be arranged so as to implement lattice models displaying a local Z2 gauge symmetry, both in one and two dimensions. We also provide a detailed analysis of a ladder toy model, which features a global Z2 symmetry, and reveal the phase transitions that occur both in the matter and gauge sectors. Mastering flux-attachment in optical lattices envisages a new route towards the realization of strongly-correlated systems with properties dictated by an interplay of dynamical matter and gauge fields., 11 pages, 6 figures, 11 pages supplements

We consider a spin-1/2 fermionic ladder with spin-orbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize the symmetry-protected topological phase of this ladder through the identification of fractionalized edge modes and non-trivial spin winding numbers. We propose an experimental scheme to engineer such a ladder system with cold atoms in optical lattices, and we present two protocols that can be used to extract the topological signatures from density and momentum-distribution measurements. We then consider the presence of interactions and discuss the effects of a contact on-site repulsion on the topological phase. We find that such interactions could enhance the extension of the topological phase in certain parameters regimes., 27 pages, 10 figures, 1 appendix

Recent technological advances in integrated photonics have spurred on the study of topological phenomena in engineered bosonic systems. Indeed, the controllability of silicon ring-resonator arrays has opened up new perspectives for building lattices for photons with topologically nontrivial bands and integrating them into photonic devices for practical applications. Here, we push these developments even further by exploiting the different modes of a silicon ring resonator as an extra dimension for photons. Tunneling along this synthetic dimension is implemented via an external time-dependent modulation that allows for the generation of engineered gauge fields. We show how this approach can be used to generate a variety of exciting topological phenomena in integrated photonics, ranging from a topologically-robust optical isolator in a spatially one-dimensional (1D) ring-resonator chain to a driven-dissipative analog of the 4D quantum Hall effect in a spatially 3D resonator lattice. Our proposal paves the way towards the use of topological effects in the design of novel photonic lattices supporting many frequency channels and displaying higher connectivities., Comment: 18 pages, 7 figures

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators., 24 pages, 6 figures