While real-time simulation of Quantum Chromodynamics remains technologically out of reach, many simplified models for studying elements of QCD phenomenology are being investigated. In this work, we present a simple model, a spin-1 truncation of the Compact Abelian Higgs Model simulated on qutrit sites, in which confinement and string breaking are accessible to current simulation methods. In the low-energy regime of 1+1 dimensional scalar electrodynamics, the heavy modes are integrated out, producing a spin chain effective Hamiltonian in which Gauss' law is automatically satisfied. We study the spectrum of string-like excitations using DMRG methods on the order of 100 sites. We demonstrate that an added, local chemical potential, playing a role analogous to external charges, permits parameter-dependent measurements of physical features of interest like the string tension and effective meson mass. Varying the chemical potential also permits a characterization of string stability not assessed in prior studies of confining lattice models.
While real-time simulation of Quantum Chromodynamics remains technologically out of reach, many simplified models for studying elements of QCD phenomenology are being investigated. In this work, we present a simple model, a spin-1 truncation of the Compact Abelian Higgs Model simulated on qutrit sites, in which confinement and string breaking are accessible to current simulation methods. In the low-energy regime of 1+1 dimensional scalar electrodynamics, the heavy modes are integrated out, producing a spin chain effective Hamiltonian in which Gauss' law is automatically satisfied. We study the spectrum of string-like excitations using DMRG methods on the order of 100 sites. We demonstrate that an added, local chemical potential, playing a role analogous to external charges, permits parameter-dependent measurements of physical features of interest like the string tension and effective meson mass. Varying the chemical potential also permits a characterization of string stability not assessed in prior studies of confining lattice models.
String breaking is a fundamental concept in gauge theories, describing the decay of a flux string connecting two charges through the production of particle-antiparticle pairs. This phenomenon is particularly important in particle physics, notably in quantum chromodynamics, and plays a crucial role in condensed matter physics. However, achieving a theoretical understanding of this nonperturbative effect is challenging, as conventional numerical approaches often fall short and require substantial computational resources. On the experimental side, studying these effects necessitates advanced setups, such as high-energy colliders, which makes direct observation difficult. Here, we report an experimental investigation of the string breaking mechanism in a one-dimensional U(1) lattice gauge theory using an optical lattice quantum simulator. By deterministically preparing initial states of varying lengths with fixed charges at each end, and adiabatically tuning the mass and string tension, we observed in situ microscopic confined phases that exhibit either string or broken-string states. Further analysis reveals that string breaking occurs under a resonance condition, leading to the creation of new particle-antiparticle pairs. These findings offer compelling evidence of string breaking and provide valuable insights into the intricate dynamics of lattice gauge theories. Our work underscores the potential of optical lattices as controllable quantum simulators, enabling the exploration of complex gauge theories and their associated phenomena.
The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms [J. Zhang et al., Phys. Rev. Lett. 121, 223201 (2018)]. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.
To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories, including unexplored regimes of the QCD phase diagram. In this work, using superconducting transmon qutrit processors, we formulate and implement a pulse-based, three-level, hybrid analog-digital simulation protocol of the (1+1) dimensional Abelian Higgs model (AHM) on two sites. Alongside this approach, we experimentally realize a gate-based implementation of the same model. Using the natural mapping of the three-level truncation of the transmon Hilbert space to the spin-1 truncated AHM, we observe real time dynamics of AHM field observables, which are analogous to electric field operators, with both protocols. For the analog-digital protocol, we engineer a Floquet simulation with a combination of local analog drives, driven modification of the natural interaction Hamiltonian of the two transmons, and dynamical decoupling pulses. For the digital protocol, we use a state-of-the-art qutrit processor to implement a Trotterized simulation of the model incorporating advanced error mitigation techniques. We further discuss the scalability of the two approaches, and their potential to be extended to the simulation of other model Hamiltonians. Our experiments demonstrate a viable platform for future studies of spin-1 and SU(3) based gauge theory models on current and near-term transmon qutrit processors.
Abstract The spontaneous formation of particle pairs is one of the most intriguing phenomena in nature. A canonical example is when the potential energy between two elementary particles increases with their separation, as if the particles were confined to one another by a tense string. When the separation exceeds a critical value, new particle pairs can form, which causes the string to break. String-breaking dynamics in quantum chromodynamics, the theory of the strong force, play a fundamental role in high-energy particle collisions and the evolution of matter in the early universe. Simulating the evolution of strings and the formation of composite particles, or hadrons, is a grand challenge of modern physics. Quantum simulators are well suited to study dynamical processes. They are, therefore, expected to provide an edge over conventional methods based on classical computing. However, the experimental capabilities required to simulate the string-breaking phenomenon have not yet been demonstrated, even for simpler prototypical models of the strong force. In this work, we probe, for the first time on a quantum simulator, the spatiotemporally-resolved dynamics of string breaking in a (1+1)-dimensional Z2 lattice gauge theory, a theory that also exhibits confinement of charges. We employ a fully programmable trapped-ion quantum simulator, and emulate the effects of external static charges and strings via site-dependent control of magnetic fields, using a dual array of tightly focused laser beams targeting individual ions. First, we study the effect of confinement on the evolution of isolated charges. We find that these charges freely spread in the absence of string tension, but exhibit localized coherent oscillations as the string tension is increased. Then, we observe and characterize the breaking dynamics of a string initially stretched between two static charges, following an abrupt increase of the string tension. We find that charge pairs appear near the string edges and then spread out into the bulk, thereby identifying a route to dynamical string breaking that is distinct from the conventional Schwinger mechanism. This work, therefore, demonstrates that analog quantum simulators have achieved the control needed to uncover features of string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.
Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation. Simulating the real-time dynamics of such strings, including their breaking, remains a major challenge for classical computations and a promising target for quantum simulations. While recent quantum simulation experiments explored string-breaking dynamics in abelian lattice gauge theories, non-abelian theories are qualitatively distinct because gauge fields themselves carry charge. Here, we report the first quantum simulation of genuine non-abelian string-breaking dynamics in a pure SU(2) lattice gauge theory, where gauge-field self-interactions drive string breaking even in the absence of dynamical matter. Our results are obtained on a trapped-ion quantum computer, using native qudit Hilbert spaces to encode truncated gauge fields on a ladder geometry and implement digital Trotter dynamics. We experimentally study unbreakable and breakable strings generated by fundamental and adjoint static charges, respectively. We locally resolve string oscillations and coherent string breaking through the creation of gluonic excitations driven by non-abelian plaquette interactions. Our work establishes hardware-efficient, problem-tailored qudit simulations as a promising route for accessing non-perturbative dynamics relevant to high-energy physics.
Spontaneous particle-pair formation is a fundamental phenomenon in nature. It can, for example, appear when the potential energy between two particles increases with separation, as if they were connected by a tense string. Beyond a critical separation, new particle pairs can form, causing the string to break. String-breaking dynamics in quantum chromodynamics play a vital role in high-energy particle collisions and early universe evolution. Simulating string evolution and hadron formation is, therefore, a grand challenge in modern physics. Quantum simulators, well-suited for studying dynamics, are expected to outperform classical computing methods. However, the required experimental capabilities to simulate string-breaking dynamics have not yet been demonstrated, even for simpler models of the strong force. We experimentally probe, for the first time, the spatiotemporal dynamics of string-breaking in a (1+1)-dimensional Z2 lattice gauge theory using a fully programmable trapped-ion quantum simulator. We emulate external static charges and strings via site-dependent magnetic-field control enabled by a dual array of tightly focused laser beams targeting individual ions. First, we study how confinement affects isolated charges, finding that they freely spread without string tension but exhibit localized oscillations when tension is increased. Then, we observe and characterize string-breaking dynamics of a string stretched between two static charges after an abrupt increase in string tension. Charge pairs appear near the string edges and spread into the bulk, revealing a route to dynamical string-breaking distinct from the conventional Schwinger mechanism. Our work demonstrates that analog quantum simulators have achieved the necessary control to explore string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.