Memory erasure using time-multiplexed potentials

We study the thermodynamics of a Brownian particle under the influence of a time-multiplexed harmonic potential of finite width. The memory storage mechanism and the erasure protocol based on time-multiplexed potentials are utilized to experimentally realize erasure with work performed close to Landauer's bound. We quantify the work performed on the system with respect to the duty ratio of time multiplexing, which also provides a handle for approaching reversible erasures. A Langevin dynamics based simulation model is developed for the proposed memory bit and the erasure protocol, which guides the experimental realization. The study also provides insight into transport on the microscale.

Figure 1

The potential energy landscape of a bead in a laser trap. The experiments are performed with the bead initially at 500 nm (red curve) and $-500\mathrm{nm}$ (black curve). The position of the bead is measured for 50 s. The potential $U\left(x\right)$ is mostly flat after a certain distance $w$ from the stable equilibrium point. In the Monte Carlo simulations, the bead is initialized randomly between 500 and $-500\mathrm{nm}$. The position trajectory of the bead obtained from 100 Monte Carlo simulations is collected to determine $U\left(x\right)$ from simulations (blue curve).

Figure 2

Double well potential for $L=550\mathrm{nm}$ obtained using Monte Carlo simulations and experiments.

Figure 3

The effect of the duty ratio on the nature of the double well potential. Increasing the duty ratio at $-L$ from 0.75 in (a) to 0.8 in (b), increases the asymmetry of the potential.

Figure 4

(a) A schematic showing the erasure process with a bead initially in the right well. The initial bead position is 1 (right well) with potential energy $V_2$. The duty-ratio $d$ in the left well then is increased, which lifts the bead and takes it to position 2 with energy $V_1$. Thermal fluctuations enable the bead to cross the barrier and reach position 3 with energy $V_3$. Decreasing the duty ratio back to 0.5 lifts the bead to position 4, which has energy $V_2$. The process $1\to 2\to 3\to 4$ is the erasure process. (b) A schematic showing the erasure process with a bead initially in the left well. Here, the process $1\to 2\to 3$ is the erasure process. (c) The signals $r\left(t\right)$ and $l\left(t\right)$ denote the presence or absence status of the laser at $L$ and $-L$, respectively. A value of 1 means present, and 0 means absent. To ensure a duty ratio greater than 0.5, we maintain $d=T_{\mathrm{on}}/T_{\mathrm{cycle}}>0.5$.

Figure 5

Effect of the duty ratio on success proportion $p$. The duty ratio of 0.65 has a success proportion of 0.82, whereas, a duty ratio greater than 0.7 yields a success proportion higher than 0.95.

Figure 6

The blue and red points represent the normalized barrier heights of the right well as a function of $\frac{1}{d-0.5}$, obtained using simulations and experiments, respectively. The green line is the least squares fit to the simulation data points.

Figure 7

The blue and red points represent the normalized stiffnesses of the right well as a function of $\frac{1}{d-0.5}$, obtained using simulations and experiments, respectively. The green line is the least squares fit to the simulation data points.

Figure 8

The blue circles represent the average work performed on the bead obtained using 300 Monte Carlo realizations ($150,0\to 0$ and $150,1\to 0$ transfers) for duty ratios of 0.7, 0.75, 0.8, and 0.85. The vertical lines represent the standard error in the mean for each duty ratio. The black dotted line denotes the Landauer bound of $k_{b}Tln2$. The red dotted line is the fit with the free parameters $A$ and $B$.

Figure 9

The blue circles represent the average work performed on the bead obtained from 100 experiments ($50,0\to 1$ and $50,1\to 1$ transfers) for duty ratios of 0.7, 0.75, 0.8, and 0.85. The vertical lines represent the standard error in the mean for each duty ratio. The black dotted line denotes the Landauer bound of 0.7, 0.75, 0.8, and 0.85. The red dotted line is the fit with the free parameters $A$ and $B$.

Figure 10

The distribution of work performed on the bead obtained from the simulations and experiments for a duty ratio of 0.7. The nature of the distribution is bimodal.