A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theoriesA Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$ gauge theories

Enrico C. Domanti, Dario Zappalà, A. Bermúdez +1 more

Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the non-perturbative mechanisms underlying the confinement of quarks. In this work, considering periodically-driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $\mathbb{Z}_2$ LGT. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms, and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically-modulated real-time dynamics.Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the non-perturbative mechanisms underlying the confinement of quarks. In this work, considering periodically-driven arrays of Rydberg atoms in a tweezer ladder geometry, we devise a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $\mathbb{Z}_2$ LGT. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms, and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically-modulated real-time dynamics.

arXiv:2311.16758Nov 28, 20230 citations

Metastable confinement in Rydberg lattice gauge theories

Yaohua Li, Devendra Singh Bhakuni, Yong-Chun Liu +1 more

Confinement and string breaking are two fundamental phenomena in gauge theories. Signatures of both are currently pursued in quantum-simulator experiments, opening a new angle on strongly interacting dynamics of gauge fields out of equilibrium, complementary to traditional particle-physics settings. In this work, we report the emergence of metastable confinement dynamics in a U(1) lattice gauge theory, originating from the competition between string tension and four-Fermi coupling - a competition that naturally arises in Rydberg atom arrays. We show that the initial string state can be resonantly melted through controlled energy matching, a phenomenon we identify as resonant string breaking. We demonstrate this mechanism for both static and Floquet-driven systems, where periodic modulation generates a spectrum of tunable sideband resonances. Our work provides new insights into the mechanisms of confinement and string breaking driven by long-range interactions and time-dependent fields, which are available in current quantum simulators on a variety of platforms.Confinement and string breaking are two fundamental phenomena in gauge theories. Signatures of both are currently pursued in quantum-simulator experiments, opening a new angle on strongly interacting dynamics of gauge fields out of equilibrium, complementary to traditional particle-physics settings. In this work, we report the emergence of metastable confinement dynamics in a U(1) lattice gauge theory, originating from the competition between string tension and four-Fermi coupling - a competition that naturally arises in Rydberg atom arrays. We show that the initial string state can be resonantly melted through controlled energy matching, a phenomenon we identify as resonant string breaking. We demonstrate this mechanism for both static and Floquet-driven systems, where periodic modulation generates a spectrum of tunable sideband resonances. Our work provides new insights into the mechanisms of confinement and string breaking driven by long-range interactions and time-dependent fields, which are available in current quantum simulators on a variety of platforms.

cond-mat.quant-gasCross-listedarXiv:2602.22890Feb 27, 20260 citations

Quantum simulation of dynamical gauge theories in periodically driven Rydberg atom arrays

Johannes Feldmeier, Nishad Maskara, Nazlı Uğur Köylüoğlu +1 more

Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting frontier in quantum science. Programmable quantum simulators based on neutral atom arrays are a promising approach to achieve this goal, since strong Rydberg blockade interactions can be used to naturally create low energy subspaces that can encode local gauge constraints. However, realizing regimes of LGTs where both matter and gauge fields exhibit significant dynamics requires the presence of tunable multi-body interactions such as those associated with ring exchange, which are challenging to realize directly. Here, we develop a method for generating such interactions based on time-periodic driving. Our approach utilizes controlled deviations from time-reversed trajectories, which are accessible in constrained PXP-type models via the application of frequency modulated global pulses. We show that such driving gives rise to a family of effective Hamiltonians with multi-body interactions whose strength is non-perturbative in their respective operator weight. We apply this approach to a two-dimensional U(1) LGT on the Kagome lattice, where we engineer strong six-body magnetic plaquette terms that are tunable relative to the kinetic energy of matter excitations, demonstrating access to previously unexplored dynamical regimes. Potential generalizations and prospects for experimental implementations are discussed.Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting frontier in quantum science. Programmable quantum simulators based on neutral atom arrays are a promising approach to achieve this goal, since strong Rydberg blockade interactions can be used to naturally create low energy subspaces that can encode local gauge constraints. However, realizing regimes of LGTs where both matter and gauge fields exhibit significant dynamics requires the presence of tunable multi-body interactions such as those associated with ring exchange, which are challenging to realize directly. Here, we develop a method for generating such interactions based on time-periodic driving. Our approach utilizes controlled deviations from time-reversed trajectories, which are accessible in constrained PXP-type models via the application of frequency modulated global pulses. We show that such driving gives rise to a family of effective Hamiltonians with multi-body interactions whose strength is non-perturbative in their respective operator weight. We apply this approach to a two-dimensional U(1) LGT on the Kagome lattice, where we engineer strong six-body magnetic plaquette terms that are tunable relative to the kinetic energy of matter excitations, demonstrating access to previously unexplored dynamical regimes. Potential generalizations and prospects for experimental implementations are discussed.

arXiv:2408.02733Aug 5, 20240 citations

Quantum simulation with gauge fixing: From Ising lattice gauge theory to dynamical flux model

Junsen Wang, Xiangxiang Sun, Wei Zheng

Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local gauge symmetries. And the other is to engineer the projected Hamiltonian in one gauge subsector. In this work, we provide the third way towards the simulation of gauge theories based on . To demonstrate this concept, we fix the gauge of an Ising lattice gauge field coupled with spinless fermions on a ladder geometry. After the gauge fixing, this gauge theory is reduced to a simpler model, in which fermions hop on a ladder with a fluctuating dynamical Z 2 flux. Then we show that this model can be realized via Floquet engineering in ultracold atomic gases. By analytical and numerical studies of this dynamical flux model, we deduce that there is a confinement-to-deconfinement phase transition in the original unfixed gauge theory. This work paves the way to quantum simulate lattice gauge theory using the concept of gauge fixing, relevant both for condensed-matter and high-energy physics.Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local gauge symmetries. And the other is to engineer the projected Hamiltonian in one gauge subsector. In this work, we provide the third way towards the simulation of gauge theories based on . To demonstrate this concept, we fix the gauge of an Ising lattice gauge field coupled with spinless fermions on a ladder geometry. After the gauge fixing, this gauge theory is reduced to a simpler model, in which fermions hop on a ladder with a fluctuating dynamical Z 2 flux. Then we show that this model can be realized via Floquet engineering in ultracold atomic gases. By analytical and numerical studies of this dynamical flux model, we deduce that there is a confinement-to-deconfinement phase transition in the original unfixed gauge theory. This work paves the way to quantum simulate lattice gauge theory using the concept of gauge fixing, relevant both for condensed-matter and high-energy physics.

arXiv:2407.01422Physical Review ResearchMar 25, 20253 citations

Spin Exchange-Enabled Quantum Simulator for Large-Scale Non-Abelian Gauge Theories

Jad C. Halimeh, Lukas Homeier, Annabelle Bohrdt +1 more

A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU ( N ) and U ( N ) LGTs with dynamical matter in d + 1 D , enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2 + 1 D SU ( 2 ) and U ( 2 ) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU ( N ) and U ( N ) LGTs with dynamical matter in d + 1 D , enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2 + 1 D SU ( 2 ) and U ( 2 ) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024

arXiv:2305.06373PRX QuantumSep 30, 202413 citations

Emerging Two-Dimensional Gauge Theories in Rydberg Configurable Arrays

Alessio Celi, Benoît Vermersch, Oscar Viyuela +3 more

Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter.On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize.Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian-a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics.Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade.Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs.We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations.We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.Solving strongly coupled gauge theories in two or three spatial dimensions is of fundamental importance in several areas of physics ranging from high-energy physics to condensed matter.On a lattice, gauge invariance and gauge-invariant (plaquette) interactions involve (at least) four-body interactions that are challenging to realize.Here, we show that Rydberg atoms in configurable arrays realized in current tweezer experiments are the natural platform to realize scalable simulators of the Rokhsar-Kivelson Hamiltonian-a 2D U(1) lattice gauge theory that describes quantum dimer and spin-ice dynamics.Using an electromagnetic duality, we implement the plaquette interactions as Rabi oscillations subject to Rydberg blockade.Remarkably, we show that by controlling the atom arrangement in the array we can engineer anisotropic interactions and generalized blockade conditions for spins built of atom pairs.We describe how to prepare the resonating valence bond and the crystal phases of the Rokhsar-Kivelson Hamiltonian adiabatically and probe them and their quench dynamics by on-site measurements of their quantum correlations.We discuss the potential applications of our Rydberg simulator to lattice gauge theory and exotic spin models.

arXiv:1907.03311Physical Review XJun 16, 2020122 citations

A Floquet-Rydberg quantum simulator for confinement in

\mathbb{Z}_2

gauge theories

\mathbb{Z}_2

LGT. Resorting to an external magnetic field to tune the angular dependence of the Rydberg dipolar interactions, and by a suitable tuning of the driving parameters, we manage to suppress the main gauge-violating terms, and show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques. Depending on the lattice size, we present a thorough numerical test of the validity of this scheme using either exact diagonalization or matrix-product-state algorithms for the periodically-modulated real-time dynamics.