Dephasing-assisted diffusive dynamics in superconducting quantum circuits

Abstract

Random fluctuations caused by environmental noise can lead to decoherence in quantum systems. Exploring and controlling such dissipative processes is both fundamentally intriguing and essential for harnessing quantum systems to gain practical advantages and deeper insights. In this work, we first demonstrate the diffusive dynamics assisted by controlled dephasing noise in superconducting quantum circuits, contrasting with coherent evolution. We show that dephasing can give distinct dynamical behavior in a superconducting qubit array with quasiperiodic order. Furthermore, by preparing different excitation distributions in the qubit array, we observe that a more localized initial state relaxes to a uniformly distributed mixed state faster with dephasing noise, illustrating another counterintuitive phenomenon called Mpemba-effect-like quantum dynamics, i.e., a far-from-equilibrium state can relax toward the equilibrium faster. These results deepen our understanding of diffusive dynamics at the microscopic level, and demonstrate controlled dissipative processes as a valuable tool for investigating Markovian open quantum systems.

Figures (4)

• Figure 1: Dephasing-assisted transition from ballistic to diffusive transport and accelerated equilibration in a 1D qubit array. (a) Illustration of the density profile for an initial state $\vert \psi_0\rangle$ evolved under Hamiltonian $H$ without (upper panel) and with dephasing noise (lower panel). (b) Schematic for Mpemba-effect-like dynamics, where a far-from-equilibrium state (red line) reaches equilibrium (denoted as blue dashed line) faster than a state closer to equilibrium (yellow line) under certain conditions (here with dephasing noise). (c) The 1D array model used in this experiment to demonstrate the above phenomena, where controlled dephasing is incorporated by randomly modulating the qubit frequencies on each site.
• Figure 2: Diffusive spreading dynamics with dephasing noise. (a) Schematic of the experimental pulse sequence. (b)-(c) Measured population dynamics $n_j$ without (b) and with (c) dephasing noise, illustrating ballistic- and diffusive-like spreading, respectively. (d) The integrated moment $M(t)$ as a function of normalized time $Jt$, which captures the ballistic (b) and diffusive manner of spreading (c) during early dynamics. Dots indicate measured results, while the red (blue) solid line denotes the scaling function of $M\sim t^1$ ($t^{0.5}$).
• Figure 3: Dephasing-assisted dynamics in a quasiperiodic lattice. (a) Schematic for the off-diagonal Aubry-André model with aperiodic coupling strengths, where the controlled dephasing noises are injected into the qubits. (b) Numerical calculation of $M$ versus $\kappa$ with and without dephasing noise for $L=89$ sites. (c)-(f) Measured population dynamics $n_j(t)$ without (c,e) and with (d,f) noise for $L=7$ qubits, showing oscillatory dynamics and diffusive spreading behavior, respectively. (g)-(h) The integrated moment $M$ evaluated from the measured dynamics shown in (c-f), where the solid bars and black frames denote the measured and numerical results. The ratio $\kappa = B/A$ is $0.3$ for (c,d,g), and $0.7$ for (e,f,h).
• Figure 4: Mpemba-effect-like dynamics with dephasing noise. (a)-(b) Measured population dynamics $n_j$ with a dephasing rate $\Gamma/J\approx 3$, where the system is initially prepared in states with density matrices (a) $\rho_1 = \vert 1_0 \rangle \langle 1_0 \vert$, and (b) $\rho_4 = 1/4\sum_{j=0}^{3} \vert 1_j \rangle \langle 1_j \vert$. (c) Measured distance function $D(t)$ from the equilibrium for initial states $\rho_1 = \vert 1_0 \rangle \langle 1_0 \vert$, $\rho_2 = 1/2\sum_{j=2}^{3}\vert 1_j \rangle \langle 1_j \vert$, $\rho_3 = 1/3\sum_{j=1}^{3}\vert 1_j \rangle \langle 1_j \vert$, and $\rho_4 = 1/4\sum_{j=0}^{3}\vert 1_j \rangle \langle 1_j \vert$. Solid lines are numerical simulation results. $\rho_1$, the farthest from the equilibrium state, relaxes faster than the other three mixed states closer to the equilibrium state $\rho_E=1/7\sum_{j} \vert 1_j \rangle \langle 1_j \vert$, illustrating the Mpemba-effect-like dynamics.