Active Quantum Particles from Engineered Dissipation

Abstract

We introduce and characterize different models for an active quantum particle where activity arises from engineered dissipation-- specifically, from a suitably coupled nonequilibrium environment. These include a model of a particle moving on a lattice with coherent and dissipative hopping, as well as quantum generalizations of well-studied models of active behavior, such as the active Ornstein-Uhlenbeck process, run-and-tumble dynamics, and the active Brownian particle. Despite the different microscopic mechanisms at play, we show that all these models display key features of active motion. Notably, we observe a crossover from diffusive to active-diffusive behavior at long times, leading to an effective Péclet number, as well as a strong sensitivity to boundary conditions which, in our open quantum system context, arises from the Liouville skin effect. We discuss the role of quantum fluctuations and experimental realizations with superconducting circuits or cold gases, closing with perspectives for many-body effects in quantum active matter.

Figures (3)

• Figure 1: Sketch of the setup. (a) A quantum particle moves in presence of coherent and environment-induced hoppings, with rates $J$ and $\Gamma_{L,R}$. (b) A dissipative quantum particle in a noisy force with finite persistence time. (c) A dissipative quantum particle coupled to a two-level system mimicking an effective spin-orbit coupling.
• Figure 2: Environment-assisted hopping model. (a) Variance of the particle position for $J/\Gamma_+ = 4$ and $\Gamma_-=0$ displaying a crossover from diffusive to ballistic to active-diffusive behavior, the latter regime with enhanced diffusion coefficient $D(J,\Gamma_+)$. The two crossover times are shown with vertical dashed lines. (b) Crossover in the variance for different values of $J/\Gamma_+$. The black dashed lines represent the formula (\ref{['eq:varX-exact-modela']}). (c) Steady-state density profile for open-boundary conditions, for different values of $J/\Gamma_+$ with $\Gamma_- = 0.5$ - the dotted lines represent the analytic expression \ref{['eq:SkinCorr']}. In the three panels $\Gamma_+ = 1$.
• Figure 3: (a)-(b) Dynamics of the mean-squared displacement $\Delta^2(t)$ for the qAOUP. (a) Diffusive-ballistic-diffusive crossover at finite temperature, obtained by changing the active diffusion coefficient $\tilde{D}_a=D_a/4\gamma^2$ at fixed persistence time $\tau$. Numerical Parameters: $\gamma=10^{-5}$, $\beta=1/T=10^{-4}$, $\tau=100$, $D_T=T/2\gamma$. (b) Zero temperature crossover from quantum Brownian motion to active diffusion, tuning the persistence time $\tau$. Numerical Parameters: $\gamma=10^{-3}$, $\beta=1$, $D_a=1$. In both (a)-(b) panels the frequency cut-off is $\omega_c = 10^4$. (c) Dynamics of the particle variance $\hbox{Var}{(\hat{x})}$ for the qABP model for symmetric rates, showing the crossover from diffusive to active diffusive motion, with $D$ given in Eq. (\ref{['eqn:D_qabp']}). The velocities $v_0,v_{\infty}$ of the intermediate and long-time ballistic motion are given in Ref. supplementary_mat. Numerical Parameters: $m=10$, $\lambda, \Gamma_+, \Gamma_d$ = 5, 1, 0.1. Inset: infinite mass limit for different values of the spin-orbit coupling $\lambda$.