Interplay of Noise and Reservoir-induced Decoherence in Persistent Currents

Abstract

Persistent current is a hallmark of quantum phase coherence. We study the fate of the persistent current in a non-equilibrium setting, where a tight-binding ring is subjected to stochastic disorder as well as a fermionic reservoir attached to each site. We evaluate the current using Keldysh technique and find that it exhibits non-monotonic behavior, suggesting two distinct mechanisms of decoherence. While coupling to the reservoirs introduces a coherence length scale given by the inverse of the coupling strength, the other mechanism is more subtle and driven by the ratio of noise strength to reservoir coupling. The interplay of noise and reservoir constitutes a purely non-equilibrium steady state with a flatter distribution function that we effectively describe using classical rate equations. We discuss possibilities of realizing our findings in ultracold-atom experiments.

Figures (4)

• Figure 1: (a) Schematic of the tight-binding ring in the presence of a time-dependent stochastic noise with strength $\gamma$ and identical one-dimensional fermionic reservoirs coupled to each site with coupling strength $\tau_c$. The ring is threaded by a magnetic flux $\phi$ that gives rise to the persistent current in the system. (b) Persistent current in units of $I_0 = ev_F/L$ as a function of flux $\phi/ \phi_0$ for three different sets of parameter values $(\gamma, \Delta) = (0,0.1), (0.001, 0.01), (0.01,0.001)$ in the units of $t$. $\Delta$ is the bath hybridization function defined in the main text. The system size is $L=16$ with $N=8$ electrons.
• Figure 2: (a) Amplitude of the persistent current ($I_{\mathrm{max}}$) plotted as a function of the bath hybridization function $\Delta$, for different values of the noise strength $\gamma$. For non zero $\gamma$, $I_{\mathrm{max}}$ exhibits non-monotonic behavior showing first a growth, then a peak, and finally decay with increasing $\Delta$. We fix $L=16$ and $N=8$, respectively. (b) Two independent and distinct mechanisms for the suppression of the persistent current are revealed, if $I_{\mathrm{max}}$ is plotted as a function of the pair of parameters ($\gamma/\Delta$, $\Delta$), as opposed to ($\gamma$, $\Delta$).
• Figure 3: (a) Plot for $I_{\mathrm{max}}$ as a function of $\Delta$ for different system sizes $L= 8, 16, \ldots,120$ at half-filling in the absence of noise ($\gamma= 0$). The curves show a systematic $L$ dependence and excellent scaling collapse if plotted as a function of $L\Delta$ [inset of (a)], leading to the notion of a coherence length scale $\xi_{\Delta} = 1/\Delta$. (b) $I_{\mathrm{max}}$ as a function of the ratio $\gamma/\Delta$ for different $L = 16, 24,\ldots,120$ at half-filling for fixed $\Delta =0.001$. Except for the peak values, the curves are almost independent of $L$, which becomes clear if each of the curves is normalized by its peak value and plotted for different $L$ [inset of (b)]. (c) The momentum occupation function $n(k)$ for different ratios $\gamma/\Delta = 0.01, 1, \ldots 100$ at a given $\Delta =0.001$. As $\gamma/ \Delta$ increases, $n(k)$ becomes progressively flatter, though the sharp jump at $k_F =\pi/2$ persists indicating the emergence of a pure non-equilibrium state distinct from a high-temperature equilibrium state.
• Figure 4: (a) Ratio of steady-state average occupation above ($n_{>}$) and below ($n_{<}$) the Fermi energy obtained using Keldysh calculation for different $\Delta = 0.1, 0.01, ~\&~ 0.001$ contrasted with the same obtained from the classical rate equations \ref{['rate_eq']}. (b) The difference of steady state average occupation $n_<-n_>$ for the same values of $\Delta$ as (a) contrasted with rate equation calculations.