Memory erasure using time-multiplexed potentials

Abstract

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 realized by time multiplexed potentials are utilized to experimentally realize erasure with work close to the Landauer's bound. We quantify the work done on the system with respect to the duty-ratio of time multiplexing, which also provides a handle to approach 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 insights into transport at the micro scale. PACS numbers: 05.40.-a, 05.70.LnThe Landauer's principle, pioneered by Rolf Landauer in 1961, provides a critical link between information theory and thermodynamics of physical systems [1]. It states that there is no process where the work done to erase one bit of information is less than k b T ln 2 (Landauer's bound), when the prior probability of the bit being in any of the two states is equal [2]. Here, k b is the Boltzmann constant and T is the temperature of the heat bath.Numerous analyses have established the Landauer's bound through different approaches [3][4][5][6][7]. The experimental study of Landauer's bound has only recently be- In this article, we study the stochastic energetics of transport realized by time multiplexing of a finite width harmonic potential to effectively realize a bi-stable potential. Here a single laser in an optical tweezer setup, is multiplexed at two locations with varying dwell times to create a series of potentials (symmetric as well as asymmetric bi-stable potentials), that effectuates the erasure process. Moreover, experimental variables to realize reversible erasure are identified and utilized for approaching the Landauer's bound. A Langevin framework for a Brownian particle under the influence of a time multiplexed laser is developed and is shown to obey quantitative trends observed in experiments. We use our method of shaping the potential, by changing the dwell time of multiplexing of the laser, to erase one bit of information. The ease of implementation and the high-resolution accounting of energetics enabled by photodiode based measurements are other advantages of the method reported. We resort to Sekimoto's stochastic energetics [12][13][14][15] framework to quantify the work done on the system in the erasure process. The underlying principles developed in this article are applicable toward the study of transport achieved by time multiplexing of a single potential, and are not restricted to realizations based on optical traps.Experiment and Simulation Model for one-bit Memory: A Brownian particle in a double well potential is used to model a one-bit memory. The memory is designated the state 'zero' if the particle is in the left well, and the state 'one' if it is in the right well. We realize a Brownian particle in a harmonic potential of finite width experimentally, by using a custom built op...

Realizing Information Erasure in Finite Time

“…The bead effectively experiences a stable trap in either location. The dynamics of the bead is governed by the overdamped Langevin equation if it is under the influence of the laser trap at L (see (5) below) or −L (see (6) below), otherwise it undergoes a random walk, where the particle dynamics is described by (7). Thus the dynamics is given by,…”

“…The above mentioned protocol with d > 0.7 results in erasures with more than 95% accuracy. For further details about the erasure protocol please refer to [6].…”

“…gives a unit speed "displacement interpolation" of of f 0 an f 1 along a Wasserstein geodesic. As depicted in the figure below the protocol of [6] is suboptimal for regimes with duty ratio > .75. We hypothesize that a protocol that encourages the bead's distribution to mimic that transportation depicted in figure 10, can reduce heat dissipation.…”

“…The scale of the energy specified by the Landauer's bound necessitates the use of nano scale systems with pico-Newton force resolution. Landauer [4], [5], [6], [7] only after significant scientific advances in nanotechnology and nano scale probing.…”

Error Bounds on a Mixed Entropy Inequality

“…The estimates on the entropy, h(X + Z), of the sum, X + Z, are employed to estimate the capacity of a channel with X as the input and X + Z as the output. The special case of a Gaussian Z and Bernoulli X was relevant to the modeling of an experimental testing of Landauer's bound [11,12], and will be the focus of section 3. In Section 4 we will approach the general log-concave case.…”