Real-Time Calibration of a Feedback Trap

Gavrilov, Momčilo

doi:10.1007/978-3-319-63694-8_3

Cited by 3 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It may be noted that the confinement protocol by a sudden quench of resetting profiles introduced above is amenable to experimental realization. Using microscopic particles trapped with optical tweezers [55,59] or feedback traps [58,62,63], it is now possible to measure and control the position of a Brownian particle with subnanometric precision. Recent experimental setups allow to exert random forces to trapped particles, with a user-defined statistics for the random force [52,53,55,64].…”

Section: Shortcuts To Confinementmentioning

confidence: 99%

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

Roldán¹,

Gupta²

2017

Phys. Rev. E

View full text Add to dashboard Cite

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

show abstract

Section: Shortcuts To Confinementmentioning

confidence: 99%

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

Roldán¹,

Gupta²

2017

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Our classical one-bit memory consists of an overdamped silica bead of diameter 1.5 µm trapped in a virtual time-dependent double-well potential imposed by a feedback (or ABEL) trap [29][30][31][32][33]. A feedback trap periodically measures particle position and, after each measurement, applies a force imposed by the potential U (x, y, t) [31,[33][34][35]. Feedback traps have been used to measure properties of particles and molecules [30,[36][37][38][39][40][41][42] and to explore fundamental questions in the nonequilibrium statistical mechanics of small systems [8, 29-32, 35, 43].Since there is no physical potential that traps potentials.…”

mentioning

confidence: 99%

Erasure Without Work in an Asymmetric, Double-Well Potential

Gavrilov¹

2017

Experiments on the Thermodynamics of Information Processing

Self Cite

View full text Add to dashboard Cite

According to Landauer's principle, erasing a memory requires an average work of at least kT ln 2 per bit. Recent experiments have confirmed this prediction for a one-bit memory represented by a symmetric double-well potential. Here, we present an experimental study of erasure for a memory encoded in an asymmetric double-well potential. Using a feedback trap, we find that the average work to erase can be less than kT ln 2. Surprisingly, erasure protocols that differ subtly give measurably different values for the asymptotic work, a result we explain by showing that one protocol is symmetric with the respect to time reversal, while the other is not. The differences between the protocols help clarify the distinctions between thermodynamic and logical reversibility.Introduction. Landauer's principle states that erasing a one-bit memory requires an average work of at least kT ln 2 [1, 2], with the lower bound achieved in the quasistatic limit. It plays a key role in sharpening our understanding of the second law of thermodynamics and of the interplay between information and thermodynamics, an issue first raised Maxwell [3], developed in important contributions by Szilard [4] and Bennett [5] but also subject to a long, sometimes confused discussion [6]. Recent experiments have confirmed Landauer's prediction in simple systems: in a one-bit memory represented by a symmetric double-well potential [7, 8], in memory encoded by nanomagnetic bits [9, 10], and even in quantum bits [11]. These successes have helped to create an extended version of stochastic thermodynamics [12, 13] that views information as another kind of thermodynamic resource, on the same footing as heat, chemical energy, and other sources of work [14]. This new way of looking at thermodynamics has led to experimental realizations of information engines ("Maxwell demons") [15][16][17][18].Despite its success in simple situations, Landauer's principle remains untested in more complex cases, such as systems where the symmetry between states is broken. This case, briefly mentioned but not pursued in Landauer's original paper [1], was followed up in later theoretical work [2,[19][20][21][22][23][24][25]. In addition, erasure in asymmetric states can be interpreted as situations where the initial system is out of global thermodynamic equilibrium. Since nonequilibrium settings are ubiquitous in biological systems, it is important to establish basic scenarios in simpler settings to understand more clearly, for example, why common biological systems may not be able to reach ultimate thermodynamic limits [26].Here, we explore the broken-symmetry case experimentally by studying erasure in a memory represented by an asymmetric, double-well potential. While we find broad agreement with the main predictions of theoretical work,

show abstract

“…Hence, despite the partial success of the optical tweezers in the study of the stochastic and information thermodynamics, its application is still limited when the generation of the mathematically-driven time-varying arbitrary shaped potential is required.Recently, Cohen et al developed a feedback-based technique called anti-Brownian electrokinetic (ABEL) trap by applying the feedback force in the form of electrophoretic force, which enables trapping of a nano-sized object in solution [15,16]. The ABEL trap can also create the arbitrarily-shaped potential [17,18] and has been used to study the dynamics of a Brownian particle in a double-well potential [19][20][21]. However, the design and the implementation of the ABEL trap are quite complicated.…”

mentioning

confidence: 99%

Optical tweezers as a mathematically driven spatio-temporal potential generator

Albay¹,

Paneru²,

Pak³

et al. 2018

Opt. Express

View full text Add to dashboard Cite

The ability to create and manipulate the spatio-temporal potentials is essential in the diverse fields of science and technology. Here, we introduce an optical feedback trap system based on a high precision position detection and an ultrafast feedback control of a Brownian particle in the optical tweezers to generate spatio-temporal virtual potentials of the desired shape in a controlled manner. As an application, we study nonequilibrium fluctuation dynamics of the particle in a time-varying virtual harmonic potential and validate the Crooks fluctuation theorem in highly nonequilibrium condition. IntroductionFor the past three decades, there has been significant progress in the field of stochastic and information thermodynamics, where general laws such as fluctuation theorems and Jarzynski relations applicable to nonequilibrium phenomena have been discovered [1][2][3]. Many of these nonequilibrium relations are validated experimentally, thanks to the development of new technologies, which facilitates trapping and manipulation of Brownian particles, such as optical tweezers (OT). The OT has been a powerful tool for trapping and controlling Brownian particles in fluid [4,5]. It can trap and locate an object with subnanometer resolution and is capable of probing piconewton forces. As a result, it has been successfully used as an experimental tool in the diverse fields of science and engineering [6,7]. It has been used in biophysical experiments for the purpose of the position and force spectroscopy [8,9]. The OT has also been used in the field of nonequilibrium and information thermodynamics to demonstrate the validity of various fundamental relations [10][11][12][13]. For example, varying laser intensity with controlled artificial thermal noise allows one to demonstrate the Brownian nano-heat engine [10]. Placing two traps close enough can create a double-well potential to study Kramers' transition rate [12], stochastic resonance [11], and Landauer's principle of information erasure [14]. However, these prior studies could not modulate the barrier height and the tilt of the double-well potential in a controlled manner. Hence, despite the partial success of the optical tweezers in the study of the stochastic and information thermodynamics, its application is still limited when the generation of the mathematically-driven time-varying arbitrary shaped potential is required.Recently, Cohen et al. developed a feedback-based technique called anti-Brownian electrokinetic (ABEL) trap by applying the feedback force in the form of electrophoretic force, which enables trapping of a nano-sized object in solution [15,16]. The ABEL trap can also create the arbitrarily-shaped potential [17,18] and has been used to study the dynamics of a Brownian particle in a double-well potential [19][20][21]. However, the design and the implementation of the ABEL trap are quite complicated. In particular, ABEL trap requires micro-fabricated 2D flow channel that introduces complicated boundary effect between the trapped particle and the wall of...

show abstract

Real-Time Calibration of a Feedback Trap

Cited by 3 publications

References 24 publications

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

Erasure Without Work in an Asymmetric, Double-Well Potential

Optical tweezers as a mathematically driven spatio-temporal potential generator

Contact Info

Product

Resources

About