Observation of string-breaking dynamics in a quantum simulator
Arinjoy De, Alessio Lerose, De Luo, Federica Maria Surace, Alexander Schuckert, Elizabeth R. Bennewitz, Brayden Ware, William Morong, Kate Collins, Zohreh Davoudi, Alexey Vyacheslavovich Gorshkov, Or Katz, Christopher R. Monroe
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 $\mathbb{Z}_2$ 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.
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.
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.
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.
Observation of glueball excitations and string breaking in a 2+1D Z2 lattice gauge theory on a trapped-ion quantum computer
A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a Z2 lattice gauge theory in 2+1D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a 6×5 matter-site square lattice utilizing all 56 available qubits to execute over 1000 entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine 2+1D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to 1+1D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.
Abstract Lattice gauge theories (LGTs) describe a broad range of phenomena in condensed matter and par11 ticle physics. A prominent example is confinement, responsible for bounding quarks inside hadrons such as protons or neutrons [1]. When quark-antiquark pairs are separated, the energy stored in the string of gluon fields connecting them grows linearly with their distance, until there is enough energy to create new pairs from the vacuum and break the string. While such phenomena are ubiquitous in LGTs, simulating the resulting dynamics is a challenging task [2]. Here, we report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator based on neutral atom arrays [3–5]. We show that a (2+1)D LGT with dynamical matter can be efficiently implemented when the atoms are placed on a Kagome geometry [6], with a local U(1) symmetry emerging from the Rydberg blockade [7], while long-range Rydberg interactions naturally give rise to a linear confining potential for a pair of charges, allowing us to tune both their masses as well as the string tension. We experimentally map out the corresponding phase diagram by adiabatically preparing the ground state of the atom array in the presence of defects, and observe substructure of the confined phase, distinguishing regions dominated by fluctuating strings or by broken string con24 figurations. Finally, by harnessing local control over the atomic detuning, we quench string states and observe string breaking dynamics exhibiting a many-body resonance phenomenon. Our work paves a way to explore phenomena in high-energy physics using programmable quantum simulators.
Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called : the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.