Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Abstract

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

Measurement-induced criticality in extended and long-range unitary circuits

“…The consequences of this competition are manifested in quantities that are not directly captured by the averaged density matrix of the stationary state, such as quantum information measures: by varying the rate or strength of the measurements, the system undergoes a phase transition, whose universality class is related both to the system unitary dynamics and to the measurement protocol used. Differences among these phases are equally well captured by other observables, provided they are non-linear in the wave-function [2,24,[36][37][38][39][40][41][42][43][44]52].…”

“…Recently these hybrid system have been implemented experimentally in trapped-ion hardware [46], where other experimental realizations have been proposed in Ref. [35,42]. Crucially, trapped ions naturally allow to introduce controllable long-range interactions [70], hence with a unitary evolution that in general favours entanglement between arbitrary far spins of the system.…”

Topological order and entanglement dynamics in the measurement-only XZZX quantum code

“…In a quantum circuit, frequent local measurements, which do not commute with the generators of the unitary dynamics induce a phase transition in the dynamics of entanglement [1][2][3]. This phenomenon has been observed in random quantum circuits, where the unitary evolution is generated by Clifford [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] or Haar [1,3,[18][19][20][21][22][23][24][25][26] random gates and in Hamiltonian systems, where the unitary time evolution is continuous [27][28][29][30][31][32][33][34][35][36][37][38][39]. Due to the inherent randomness of the measurement process, the entanglement phase transitions do not manifest on the level of ensemble averaged, local order parameters but only in higher moments, or replicas of the state [11,20,31,<...>…”

Measurement-induced criticality in extended and long-range unitary circuits

“…The consequences of this competition are manifested in quantities that are not directly captured by the averaged density matrix of the stationary state, such as quantum information measures: by varying the rate or strength of the measurements, the system undergoes a phase transition, whose universality class is related both to the system unitary dynamics and to the measurement protocol used. Differences among these phases are equally well captured by other observables, provided they are non-linear in the wavefunction [2,24,[36][37][38][39][40][41][42][43][44]52].…”

“…Recently these hybrid system have been implemented experimentally in trapped-ion hardware [46], where other experimental realizations have been proposed in Ref. [35,42]. Crucially, trapped ions naturally allow to introduce controllable long-range interactions [70], hence with a unitary evolution that in general favours entanglement between arbitrary far spins of the system.…”