Strongly Correlated Bosons on a Dynamical Lattice

Exploring Quantum Phases of Dipolar Gases through Quasicrystalline Confinement

The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our findings reveal that weak quasicrystalline lattices can induce a variety of modulated phases, merging the inherent solid pattern with a quasiperiodic decoration induced by the external potential. As the lattice becomes stronger, we observe a superquasicrystal phase and a Bose glass phase. Our results, supported by a detailed discussion on experimental feasibility using dysprosium atoms and quasicrystalline optical lattice potentials, open a new avenue in the exploration of long-range interacting quantum systems in aperiodic environments. We provide a solid foundation for future experimental investigations, potentially confirming our theoretical predictions and contributing profoundly to the field of quantum gases in complex external potentials.

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

Tuning Long-Range Fermion-Mediated Interactions in Cold-Atom Quantum Simulators

Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Fermionic atoms in ultracold atomic mixtures can act as mediators, giving rise to long-range Ruderman-Kittel-Kasuya-Yosida-type interactions characterized by the dimensionality and density of the fermionic gas. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow one to further control the range and shape of the mediated interactions, extending the existing quantum simulation toolbox. In particular, we include an additional optical lattice for the fermionic mediator, as well as anisotropic traps to change its dimensionality in a continuous manner. This allows us to interpolate between power-law and exponential decays, introducing an effective cutoff for the interaction range, as well as to tune the relative interaction strengths at different distances. Finally, we show how our approach allows one to investigate frustrated regimes that were not previously accessible, where symmetry-protected topological phases as well as chiral spin liquids emerge.

Spin-Holstein Models in Trapped-Ion Systems

In this work, we highlight how trapped-ion quantum systems can be used to study generalized Holstein models, and benchmark expensive numerical calculations. We study a particular spin-Holstein model that can be implemented with arrays of ions confined by individual microtraps, and that is closely related to the Holstein model of condensed matter physics, used to describe electron-phonon interactions. In contrast to earlier proposals, we focus on simulating many-electron systems and inspect the competition between charge-density wave order, fermion pairing, and phase separation. In our numerical study, we employ a combination of complementary approaches, based on non-Gaussian variational ansatz states and matrix product states, respectively. We demonstrate that this hybrid approach outperforms standard density-matrix renormalization group calculations.

Cold atoms meet lattice gauge theory

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more 'accessible' and easier to manipulate for experimentalists, but this 'substitution' also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or [Formula: see text] Bose-Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz-Hubbard ladder, or Gross-Neveu-Wilson and Wilson-Hubbard models. This article is not a general review of the rapidly growing field-it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue 'Quantum technologies in particle physics'.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

An optical lattice with sound

Quantized sound waves-phonons-govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (for example, by binding electrons into superconducting Cooper pairs)^1-3. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff⁴. Optical-lattice realizations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose-Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallization that supports phonons via short-range, photon-mediated atom-atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions⁵ to exotic 'fractonic' topological defects⁶ in the quantum regime.

Dynamical Solitons and Boson Fractionalization in Cold-Atom Topological Insulators

We study the Z_{2} Bose-Hubbard model, a chain of interacting bosons the tunneling of which is dressed by a dynamical Z_{2} field. The interplay between spontaneous symmetry breaking (SSB) and topological symmetry protection gives rise to interesting fractional topological phenomena when the system is doped to certain incommensurate fillings. In particular, we hereby show how topological defects in the Z_{2} field can appear in the ground state, connecting different SSB sectors. These defects are dynamical and can travel through the lattice carrying both a topological charge and a fractional particle number. In the hardcore limit, this phenomenon can be understood through a bulk-defect correspondence. Using a pumping argument, we show that it survives also for finite interactions, demonstrating how boson fractionalization induced by topological defects can occur in strongly correlated bosonic systems. Our results indicate the possibility of observing this phenomenon, which appears for fermionic matter in solid-state and high-energy physics, using ultracold atomic systems.

Photon-Mediated Peierls Transition of a 1D Gas in a Multimode Optical Cavity

The Peierls instability toward a charge density wave is a canonical example of phonon-driven strongly correlated physics and is intimately related to topological quantum matter and exotic superconductivity. We propose a method for realizing an analogous photon-mediated Peierls transition, using a system of one-dimensional tubes of interacting Bose or Fermi atoms trapped inside a multimode confocal cavity. Pumping the cavity transversely engineers a cavity-mediated metal-to-insulator transition in the atomic system. For strongly interacting bosons in the Tonks-Girardeau limit, this transition can be understood (through fermionization) as being the Peierls instability. We extend the calculation to finite values of the interaction strength and derive analytic expressions for both the cavity field and mass gap. They display nontrivial power law dependence on the dimensionless matter-light coupling.

Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model

We excite the vacuum of a relativistic theory of bosons coupled to a U(1) gauge field in 1+1 dimensions (bosonic Schwinger model) out of equilibrium by creating a spatially separated particle-antiparticle pair connected by a string of electric field. During the evolution, we observe a strong confinement of bosons witnessed by the bending of their light cone, reminiscent of what has been observed for the Ising model [Nat. Phys. 13, 246 (2017)NPAHAX1745-247310.1038/nphys3934]. As a consequence, for the timescales we are able to simulate, the system evades thermalization and generates exotic asymptotic states. These states are made of two disjoint regions, an external deconfined region that seems to thermalize, and an inner core that reveals an area-law saturation of the entanglement entropy.

Many-body topological invariants from randomized measurements in synthetic quantum matter

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

Coupling ultracold matter to dynamical gauge fields in optical lattices: From flux attachment to ℤ2 lattice gauge theories

From the standard model of particle physics to strongly correlated electrons, various physical settings are formulated in terms of matter coupled to gauge fields. Quantum simulations based on ultracold atoms in optical lattices provide a promising avenue to study these complex systems and unravel the underlying many-body physics. Here, we demonstrate how quantized dynamical gauge fields can be created in mixtures of ultracold atoms in optical lattices, using a combination of coherent lattice modulation with strong interactions. Specifically, we propose implementation of ℤ2 lattice gauge theories coupled to matter, reminiscent of theories previously introduced in high-temperature superconductivity. We discuss a range of settings from zero-dimensional toy models to ladders featuring transitions in the gauge sector to extended two-dimensional systems. Mastering lattice gauge theories in optical lattices constitutes a new route toward the realization of strongly correlated systems, with properties dictated by an interplay of dynamical matter and gauge fields.

Topological Quantum Transition Driven by Charge-Phonon Coupling in the Haldane Chern Insulator

In condensed matter physics many features can be understood in terms of their topological properties. Here we report evidence of a topological quantum transition driven by the charge-phonon coupling in the spinless Haldane model on a honeycomb lattice, a well-known prototypical model of the Chern insulator. Starting from parameters describing the topological phase in the bare Haldane model, we show that increasing the strength of the charge lattice coupling drives the system towards a trivial insulator. The average number of fermions in the Dirac point, characterized by the lowest gap, exhibits a finite discontinuity at the transition point and can be used as a direct indicator of the topological quantum transition. Numerical simulations show, also, that the renormalized phonon propagator exhibits a two peak structure across the quantum transition, whereas, in the absence of the mass term in the bare Haldane model, there is indication of a complete softening of the effective vibrational mode, signaling a charge density wave instability.

Intertwined topological phases induced by emergent symmetry protection

The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges from a set of configurations enforced by another broken symmetry. This mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.