Non-equilibrium critical phenomena in a trapped-ion quantum simulator*

Recent work has predicted that quenched near-integrable systems can exhibit dynamics associated with thermal, quantum, or purely non-equilibrium phase transitions, depending on the initial state [1]. Using a trapped-ion quantum simulator with intrinsic long-range interactions, we investigate collective non-equilibrium properties of critical fluctuations after quantum quenches. In particular, we probe the scaling behavior of fluctuations near the critical point of the ground-state disorder-to-order phase transition, after single and double quenches of the transverse field in a long-range Ising Hamiltonian. With system sizes of up to 50 ions, we show that both the post-quench fluctuation magnitude and dynamics scale with system size with distinct critical exponents, charaterizing the type of phase-transition. Furthermore we demonstrate that the critical exponents after a single and a double quenches are different and correspond to effectively thermal and truly non-equilibrium behavior, respectively. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium context. 

 [1] Paraj Titum and Mohammad F. Maghrebi, Phys. Rev. Lett. 125, 040602 (2020).