Observation of a Dynamical Quantum Phase Transition by a Superconducting Qubit Simulation

Abstract

A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum state return amplitude, analogous to nonanalyticity of the free energy density at the critical temperature in macroscopic systems. A variety of many-body systems can be represented in momentum space as a spin-1/2 state evolving on the Bloch sphere, where each momentum mode is decoupled and thus can be simulated independently by a single qubit. Here, we report the observation of a dynamical quantum phase transition in a superconducting qubit simulation of the quantum quench dynamics of many-body systems. We take the Ising model with a transverse field as an example for demonstration. In our experiment, the spin state, which is initially polarized longitudinally, evolves based on a Hamiltonian with adjustable parameters depending on the momentum and strength of the transverse magnetic field. The time evolving quantum state is read out by state tomography. Evidence of dynamical quantum phase transitions, such as paths of time evolution states on the Bloch sphere, non-analytic behavior of the dynamical free energy and the emergence of Skyrmion lattice in momentum-time space, is observed. The experimental data agrees well with theoretical and numerical calculations. The experiment demonstrates for the first time explicitly the topological invariant, both topologically trivial and non-trivial, for dynamical quantum phase transitions. Our results show that the quantum phase transitions of this class of many-body systems can be simulated successfully with a single qubit by varying certain control parameters over the corresponding momentum range. * schen@iphy.ac.cn † dzheng@iphy.ac.cn ‡ hfan@iphy.ac.cn curring at critical temperature. The DQPT is intimately related to quantum phase transitions in many-body systems [20][21][22][24][25][26][27][28][29][30][31][32][33][34][35][36].Recently, experimental explorations of DQPT have been performed in ion-trap systems [3,5] and cold atom systems [4,6] with dozens of individual addressable qubits or a cloud of fermionic atoms. Our experiment follows the DQPT simulation approach by emulating a corresponding two-band model separately for each momentum mode with a single qubit. By ranging over the Brillouin zone of momentum space, the results are equivalent to that of simulating manybody systems in space. The finite size effect can be observed for a finite number of momenta implemented experimentally. Our experimental system consists of superconducting Xmon qubits, which is one of the most promising platforms for quantum simulation and quantum computation [37][38][39][40][41]. We provide concrete evidence that the DQPT is successfully simulated. In particular, we demonstrate experimentally the topological invariant in DQPT, which was studied recently in Refs. [24,33], and have obtained quantitatively the dynamical free energy and Skyrmion lattice.

Measuring a dynamical topological order parameter in quantum walks

“…Note added: During the preparation of the manuscript, four other experimental works have been made public which address measurements of PGP or dynamical quantum phase transitions [47][48][49][50]. Here, based on our directly obtained DOTP, we give a dynamical classification of the quenched QW, establish the relation between the temporal behavior of DTOP and the underlying quasi-equilibrium picture, and further reveal a intriguing connection between the non-analytic of the DTOP and DQPT.…”

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

“…Among many other intriguing applications (see Ref. [19] for a review), DQPTs have become an important diagnostic tool for identifying topological insula- tor phases [27,28] in systems far from equilibrium, as has been demonstrated in recent experiments on various physical platforms, ranging from ultracold atomic gases [18], over superconducting qubit systems [29], and quantum walks in photonic systems [30,31], to nanomechanical settings [32]. The underlying conceptual insight is that changes in the topological properties over a quench generically imply the occurrence of DQPTs [14,15].…”

Simulating Dynamic Quantum Phase Transitions in Photonic Quantum Walks

“…Besides conventional continuous phase transitions that are signaled by symmetry breaking, topological phase transitions, characterized by the change of topology in their ground-state wavefunctions, have attracted much attention since the discovery of quantum Hall effects [2,3]. Recent experimental progress has further led to the exciting possibility of creating novel quantum phases of matter in dynamical processes [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and thus raised the challenging question on the understanding of emergent phases and phase transitions in non-equilibrium dynamics.…”

“…Proposed as temporal analogues to continuous phase transitions, dynamical quantum phase transitions (DQPTs) are associated with non-analyticities in the time evolution of physical observables [19][20][21], and have been experimentally observed in various systems [15][16][17][18]. DQPT occurs as a consequence of the emergence of dynamic Fisher zeros [22,23], where the Loschmidt amplitude G(t) = ψ(0)|ψ(t) vanishes at critical times and the corresponding rate function g(t) = −1/N ln |G(t)| 2 becomes non-analytical [21].…”