Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators

Abstract

The out-of-time-ordered correlators (OTOC) have been established as a fundamental concept for quantifying quantum information scrambling and diagnosing quantum chaotic behavior. Recently, it was theoretically proposed that the OTOC can be used as an order parameter to dynamically detect both equilibrium quantum phase transitions (EQPTs) and dynamical quantum phase transitions (DQPTs) in one-dimensional many-body systems. Here we report the first experimental observation of EQPTs and DQPTs in a quantum spin chain via quench dynamics of OTOC on a nuclear magnetic resonance quantum simulator. We observe that the quench dynamics of both the order parameter and the two-body correlation function cannot detect the DQPTs, but the OTOC can unambiguously detect the DQPTs. Moreover, we demonstrate that the long-time average value of the OTOC in quantum quench signals the equilibrium quantum critical point and ordered quantum phases, thus one can measure the EQPTs from the non-equilibrium quantum quench dynamics. Our experiment paves a way for experimentally investigating DQPTs through OTOCs and for studying the EQPTs through the non-equilibrium quantum quench dynamics with quantum simulators.

Quantum Information Scrambling in Quantum Many-body Scarred Systems

“…The persistent and synchronized oscillations of the OTOC and Holevo information inside the light cone are attributed to the "local" rather than "global" thermalization and robustness of scarred eigenstates against local perturbations, which are argued in [65] and need future in-depth analytical studies. Experiment proposals.-Recent experimental progress has enabled the measurements of information scrambling dynamics in well-controlled synthetic quantum systems, including nuclear magnetic resonance (NMR) systems [72,73], trapped ions [74][75][76][77] and superconducting qubits [78][79][80][81]. The PXP model can be naturally realized with the Rydberg-atom platform [60,82,83], governed by the following Hamiltonian:…”

Out-of-time-order correlations and Floquet dynamical quantum phase transition

“…Recently, out-of-time-order correlation (OTOC) has gained much attention in the physics community across many different fields, due to its feasibility in experiments [1][2][3][4][5][6][7][8] and also its richness in theoretical physics [9][10][11][12][13][14][14][15][16][17][18][19][20][21][22][23][24][25]. Recent progress in the experimental detection of quantum correlations and in quantum control techniques applied to systems as photons, molecules, and atoms, made it possible to direct observation of an OTOC in nuclear magnetic resonance quantum simulator [6,8] and trapped ions quantum magnets [5].…”

Dynamical Quantum Phase Transitions in the 1D Nonintegrable Spin‐1/2 Transverse Field XZZ Model

“…[ 13,14 ] In analog to some approaches such as the Kibble–Zurek mechanism [ 15 ] and measurement quench, [ 16,17 ] in recent years, the theory of dynamical quantum phase transition (DQPT) manifested with nonanalytic behaviors of the rate function in the time domain, that is, the logarithm function of the Loschmidt echo (LE), has attracted tremendous attention. [ 20–29 ]…”

“…[13,14] In analog to some approaches such as the Kibble-Zurek mechanism [15] and measurement quench, [16,17] in recent years, the theory of dynamical quantum phase transition (DQPT) manifested with nonanalytic behaviors of the rate function in the time domain, that is, the logarithm function of the Loschmidt echo (LE), has attracted tremendous attention. [20][21][22][23][24][25][26][27][28][29] DQPT is established by borrowing the idea from equilibrium statistical mechanics. The phase transitions in a thermodynamic system are marked by the nonanalyticities in the free energy DOI: 10.1002/andp.202000542 density which can be obtained by analyzing the zeros of the partition function where they appeared by cutting the real axis in a complex temperature plane proposed by Fisher [30] or in a complex magnetic plane proposed by Lee-Yang.…”

“…The first direct observation of a DQPT was reported in 2017 [22] where its robust against modifications of microscopic details of the underlying Hamiltonian was indicated. DQPT also has observed in dynamical vortices in momentum space, [23] trapped ions with up to 53 qubits, [24] superconducting qubit simulation, [25] a spinor condensate with correspondence in an excited state phase diagram, [26] out-of-time-order correlations, [27,28] and a topological nanomechanical system. [29] From theoretical point of view, DQPT has studied the various aspects of integrable and nonintegrable systems.…”