The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction.
The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction.
Department of Physics, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston, MA 02125(Dated: May 22, 2015)Progress in quantum simulation has fostered the research on far-from-equilibrium dynamics. TheKibble-Zurek mechanism is the paradigmatic framework to account for the non adiabatic criticaldynamics of a system driven across a phase transition in a nite time. Its study in the quantumregime is hindered by the requisite of ground state cooling. We report the experimental quantumsimulation of critical dynamics in the transverse- eld Ising model by a set of non-equilibrium pro-cesses in the pseudo-momentum space, that can be probed with high accuracy using a single trappedion. Our results support the validity of the Kibble-Zurek mechanism in the quantum regime andadvance the quantum simulation of critical systems far-away from equilibrium.I. INTRODUCTION
Abstract The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.
We analyze the quantum phase transitions taking place in a one-dimensional transverse-field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in nonequilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferromagnetic and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a nonequilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here, it is found that the predicted nonequilibrium universal behavior, i.e., the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.
The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.
The trapped-ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions.In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena, such as quantum phase transition, localization, thermalization, and information propagation.For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters.Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism.By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite-size effect.For ferromagnetic interaction, our experimental result agrees with the previous numerical prediction.As for the antiferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.
The Kibble-Zurek mechanism is central to the nonequilibrium dynamics and topological structure that occur during phase transitions, which may be manifested as the cosmological strings of the early universe or vortex lines in a superfluid. In recent years, there has been broad interest in performing quantum simulations using different well-controlled physical setups, whose full controllability allows access to regimes that may be difficult to explore. Here, we demonstrate a proof-of-principle quantum simulation of the Kibble-Zurek mechanism in the quantum Ising model as it undergoes a quenched phase transition. We used an electron charge qubit in a double quantum dot as the simulator. We engineered the qubit under Landau-Zener dynamics and successfully reproduced the Kibble-Zurek-like dependence of the topological defect density on the quench time. The high level of tunability of two-level semiconductor systems and the intriguing analogy between the two phenomena (the Kibble-Zurek mechanism and Landau-Zener transition) offer a platform on which to gain new insight into the dynamics of various phase transitions.