Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

Abstract

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the 'shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit.The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.

The experimental realization of high-fidelity ‘shortcut-to-adiabaticity’ quantum gates in a superconducting Xmon qubit

“…x y z is the vector of Pauli matrices. The amplitude Ω(t), the polar angle θ(t) and the azimuthal angle f(t) are modulated by microwave pulse sequences in our experiment [23,24]. At a given time t, the instantaneous eigenstates, y y ñ ñ + -…”

“…In many artificial systems, the influence of higher excited states cannot be fully ignored so that the two-level qubit has to be re-modeled as a multi-level anharmonic oscillator [1,32]. For example, the Hamiltonian of a three-level anharmonic oscillator in the rotating frame is written as [24]…”

“…where ε(t) and ε 2 (t) are two shifted energies [24,29]. The qubit subspace of ñ ñ {| | } 0 , 1 is decoupled with the second excited state ñ |2 .…”

Experimental demonstration of work fluctuations along a shortcut to adiabaticity with a superconducting Xmon qubit

“…Soon after the theoretical proposal, experimental implementation has been executed in various quantum devices [14][15][16][17][18][19][20][21]. In our recent studies, we have applied the STA protocol in a superconducting qubit for the realization of a Berry phase measurement [19], quantum state transfer [20] and high-fidelity gates [21]. The STA protocol was also used by us to simulate topological phase transition through an experimental construction of the first Brillouin zone [20].…”

Fast adiabatic method for measuring topological Chern number

“…The direct measurement of Berry curvature takes advantage of linear term in the response, and only need to change the parameters slowly, but not necessarily adiabatically. It provides a general means to probe topological properties.In a recent experiment, Wang and his collaborators [13] applied the "shortcut to adiabaticity" (STA) protocol [14,15] to measure the Chern number, and simulated the topological transition of the Su-Schrieffer-Heeger model using a superconducting qubit. In the STA protocol, an additional counterdiabatic Hamiltonian was designed to satisfy that there is no non-adiabatic transitions of the ground state, which speed up the adiabatic evolution of original Hamiltonian and achieve the fast adiabatic state transfer.…”