content_image/387305.jpg
ing nuclear polarizations s$_{L}$ and s$_{R}$ have different time dependence, generating an asymmetry between the dots, s$_{L}$ ̸ = s$_{R}$ . As we shall see, such asymmetry is dramati- cally reflected in the time-dependence of electric current. 

In this work we focus on the effects in nuclear po- larization dynamics due to the shot-noise arising from the discreteness of carriers passing through the system. Electrons are injected into the system one-by-one, with random spin orientations. While transiting through the dots, each such electron may exchange its spin with the nuclear subsystem. Crucially, these stochastic spin-flip processes comprise an intrinsic source of broadband noise that couples to nuclear dynamics. The intensity of this noise, which is proportional to the DC current, remains nonzero even when the average rates of up and down spin-flips are equal: S ∝ (Γ$_{+}$ + Γ − ). The resulting DNP fluctuations are relatively slow due to the large number of nuclear spins in the dots, N ≈ 10 $^{6}$, which requires many electrons to be transmitted through the system before DNP can change substantially. 

Another important aspect of the double dot system is the complex relationship between the system’s inter- nal variables and measurable quantities, i.e. between the nuclear polarization and electric current. Due to the res- onant energy dependence of transition rates, current is sensitive to the alignment of energy levels via a number of external and internal variables (gate voltages, magnetic field, Overhauser fields in each dot, etc). Changes in the hyperfine spin flip rates feed back into DNP dynamics, giving rise to a variety of interesting nonlinear phenom- ena occurring on long time scales, exemplified in Fig.1b,c. Numerical simulations based on this microscopic model, which is described in detail below, demonstrate how the complex long timescale dynamics arise from the stochas- tic nature of electron transport. 

In particular, we find that the high frequency noise can drive intermittency in electric current resembling the multi-scale switching behavior observed in experiments, which will be discussed below. In dynamical systems, intermittency refers to the alternation of phases of ap- parently regular and chaotic dynamics $^{15}$. Such behavior arises in many physical systems. For example, fluores- cence intermittency, or blinking, is commonly observed in the optical repsonse of various nanoscale systems, such as large molecules or quantum dots, where it signals com- petition between the radiative and non-radiative relax- ation pathways $^{16}$. In our system, a commonly observed type of behavior is slow build-up followed by intermittent switching between “quiet” and highly fluctuating current states, illustrated in Fig.1b,c and Fig.2a,b. 

Throughout this paper, simulation results are com- pared to data from the measurements described in Ref.7. Figure 2a shows typical experimental current traces ob- served in the regime of moderate magnetic field ( B = 200 mT) and with a gate voltage setting where the elec- trostatic energy makes lowest two singlet states, one with one electron in each dot and the other with both elec- trons in the right dot, nearly degenerate (i.e. near zero 

<img src='content_image/387305.jpg'>

“detuning”). In this case, these “(1 , 1)” and “(0 , 2)” sin- glet states are strongly hybridized by the tunnel cou- pling between the dots (see Fig.3a). The traces were taken after a long waiting period which allowed the sys- tem to relax to equilibrium. Current displays dynamics on a very long time scale, with a smooth transient “slow build-up” period lasting several tens of seconds followed by a “steady-state” featuring intermittent large ampli- tude fluctuations with a correlation time on the scale of seconds (blue trace). The fluctuations can be abruptly suppressed by a relatively small change of detuning (red trace). Similar behavior was observed during slow sweeps of magnetic field (shown in Fig.4). 

Similar-looking fluctuations were reported by Reilly et al. as ‘blinking’ of the Overhauser field measured in a double-dot which was repeatedly pulsed through a singlet-triplet level-crossing $^{8}$. There, long timescale noise correlations were attributed to nuclear spin diffusion re- sulting from the dipole-dipole interaction. In contrast, below we describe a mechanism where diffusion of the net nuclear polarization is not driven by the conventional dipole-dipole mediated spin flips, but rather is driven by shot noise in the current passing through the system. 

The rest of the paper is organized as follows. In Sec- tion I we describe the physical mechanism of shot-noise- induced multiscale intermittent fluctuations of current. Then in Section II we present the mathematical descrip- tion of our model for describing the time dependence of nuclear polarization and current in spin-blockaded dou- ble quantum dots. In Section III we present the results of simulations based on the model described in Sec.II, and compare with experimental data. Finally, our con- clusions are summarized in Section IV. 

