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John Bechhoefer

Publications and source records attributed to John Bechhoefer.

At least 37 records · Page 2Linked to original sources

Nanoscale virtual potentials using optical tweezers

We combine optical tweezers with feedback to impose arbitrary potentials on a colloidal particle. The feedback trap detects a particle's position, calculates a force based on an imposed "virtual potential," and shifts the trap center to generate the desired force. We create virtual harmonic and double-well potentials to manipulate particles. The harmonic potentials can be chosen to be either weaker or stiffer than the underlying optical trap. Using this flexibility, we create an isotropic trap in three dimensions. Finally, we show that we can create a virtual double-well potential with fixed well separation and adjustable barrier height. These are accomplished at length scales down to 11 nm, a feat that is difficult or impossible to create with standard optical-tweezer techniques such as time sharing, dual beams, or spatial light modulators.

physics.bio-ph↗

From rods to blobs: When geometry is irrelevant for heat diffusion

Thermal systems are an attractive setting for exploring the connections between the lumped-element approximations of elementary circuit theory and the partial-differential field equations of mathematical physics, a topic that has been neglected in physics curricula. In a calculation suitable for an undergraduate course in mathematical physics, we show that the response function between an oscillating heater and temperature probe has a smooth crossover between a low-frequency, "lumped-element" regime where the system behaves as an electrical capacitor and a high-frequency regime dominated by the spatial dependence of the temperature field. Undergraduates can easily (and cheaply) explore these ideas experimentally in a typical advanced laboratory course. Because the characteristic frequencies are low, ($\approx$ 30 s)$^{-1}$, measuring the response frequency by frequency is slow and challenging; to speed up the measurements, we introduce a useful, if underappreciated experimental technique based on a multisine power signal that sums carefully chosen harmonic components with random phases. Strikingly, we find that the simple model of a one-dimensional, finite rod predicts a temperature response in the frequency domain that closely approximates experimental measurements from an irregular, blob-shaped object. The unexpected conclusion is that the frequency response of this irregular thermal system is nearly independent of its geometry, an example of---and justification for---the "spherical cow" approximations so beloved of physicists.

physics.class-ph↗

When memory pays: Discord in hidden Markov models

When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state of the hidden Markov models from the observations in two ways: through naive observations, which take into account only the current observation, and through Bayesian filtering, which takes the history of observations into account. Defining a discord order parameter to distinguish between the different state estimates, we explore hidden Markov models with various numbers of states and symbols and varying transition-matrix symmetry. All behave similarly. We calculate analytically the critical point where keeping a memory of observations starts to pay off. A mapping between hidden Markov models and Ising models gives added insight into the associated phase transitions.

cond-mat.stat-mech↗

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out the first direct test of this mechanism for diffusion in inhomogeneous media.

cond-mat.stat-mech↗

Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form

Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here, for the first time, we measure experimentally this function. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.

cond-mat.stat-mech↗

Erasure without work in an asymmetric, double-well potential

According to Landauer's principle, erasing a memory requires an average work of at least $kT\ln2$ 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 $kT\ln2$. 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.

cond-mat.stat-mech↗

Feedback traps for virtual potentials

Feedback traps are tools for trapping and manipulating single charged objects, such as molecules in solution. An alternative to optical tweezers and other single-molecule techniques, they use feedback to counteract the Brownian motion of a molecule of interest. The trap first acquires information about a molecule's position and then applies an electric feedback force to move the molecule. Since electric forces are stronger than optical forces at small scales, feedback traps are the best way to trap single molecules without "touching" them. Feedback traps can do more than trap molecules: They can also subject a target object to forces that are calculated to be the gradient of a desired potential function U(x). If the feedback loop is fast enough, it creates a virtual potential whose dynamics will be very close to those of a particle in an actual potential U(x). But because the dynamics are entirely a result of the feedback loop--absent the feedback, there is only an object diffusing in a fluid--we are free to specify and then manipulate in time an arbitrary potential U(x,t). Here, we review recent applications of feedback traps to studies on the fundamental connections between information and thermodynamics, a topic where feedback plays an even more-fundamental role. We discuss how recursive maximum likelihood techniques allow continuous calibration, to compensate for drifts in experiments that last for days. We consider ways to estimate work and heat to a precision of 0.03 kT over these long experiments. Finally, we compare work and heat measurements of the costs of information erasure, the Landauer limit of kT ln2 per bit of information erased. We argue that when you want to know the average heat transferred to a bath in a long protocol, you should measure instead the average work and then infer the heat using the first law of thermodynamics.

cond-mat.stat-mech↗

Brownian duet: A novel tale of thermodynamic efficiency

We calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine driven by a duo of time-periodic forces, including its Onsager coefficients, the stochastic work of each force, and the corresponding stochastic entropy production. We verify the relations between different operational regimes, maximum power, maximum efficiency and minimum dissipation, and reproduce the signature features of the stochastic efficiency. All these results are experimentally tested without adjustable parameters on a colloidal system.

cond-mat.stat-mech↗

Arbitrarily slow, non-quasistatic, isothermal transformations

For an overdamped colloidal particle diffusing in a fluid in a controllable, virtual potential, we show that arbitrarily slow transformations, produced by smooth deformations of a double-well potential, need not be reversible. The arbitrarily slow transformations do need to be fast compared to the barrier crossing time, but that time can be extremely long. We consider two types of cyclic, isothermal transformations of a double-well potential. Both start and end in the same equilibrium state, and both use the same basic operations---but in different order. By measuring the work for finite cycle times and extrapolating to infinite times, we found that one transformation required no work, while the other required a finite amount of work, no matter how slowly it was carried out. The difference traces back to the observation that when time is reversed, the two protocols have different outcomes, when carried out arbitrarily slowly. A recently derived formula relating work production to the relative entropy of forward and backward path probabilities predicts the observed work average.

cond-mat.stat-mech↗

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics

The diffusing-diffusivity mechanism proposed by Chubynsky and Slater [PRL 113, 098302, 2014] predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar wall. Because the local effective diffusivity is known, we have been able to carry out the first direct test of this mechanism for diffusion in inhomogeneous media.

physics.bio-ph↗

Hidden Markov models for stochastic thermodynamics

The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to shed light on a recent discussion of phase transitions in the optimized response of an information engine, for which measurement noise serves as a control parameter. The HMM formalism also shows that the value of additional information shows a maximum at intermediate signal-to-noise ratios. Finally, we discuss how systems open to information flow can apparently violate causality; the HMM formalism can quantify the performance gains due to such violations.

cond-mat.stat-mech↗

What is superresolution microscopy?

I explain what is, what is not, and what is only sort of superresolution microscopy. I discuss optical resolution, first in terms of diffraction theory, then in terms of linear systems theory, and finally in terms of techniques that use prior information, nonlinearity, and other tricks to improve performance. The discussion reveals two classes of superresolution: Pseudo superresolution techniques improve images up to the diffraction limit but not much beyond. True superresolution techniques allow substantial, useful improvements beyond the diffraction limit. The two classes are distinguished by their scaling of resolution with photon counts. Understanding the limits to imaging resolution involves concepts that pertain to almost any measurement problem, implying that the framework given here has broad application beyond optics.

physics.optics↗

Split PID control: two sensors can be better than one

The traditional proportional-integral-derivative (PID) algorithm for regulation suffers from a tradeoff: placing the sensor near the sample being regulated ensures that its steady-state temperature matches the desired setpoint. However, the propagation delay (lag) between heater and sample can limit the control bandwidth. Moving the sensor closer to the heater reduces the lag and increases the bandwidth but introduces offsets and drifts into the temperature of the sample. Here, we explore the consequences of using two probes---one near the heater, one near the sample---and assigning the integral term to the sample probe and the other terms to the heater probe. The \textit{split-PID} algorithm can outperform PID control loops based on one sensor.

physics.ins-det↗

Numerical modeling of inhomogeneous DNA replication kinetics

We present a calculation technique for modeling inhomogeneous DNA replication kinetics, where replication factors such as initiation rates or fork speeds can change with both position and time. We can use our model to simulate data sets obtained by molecular combing, a widely used experimental technique for probing replication. We can also infer information about the replication program by fitting our model to experimental data sets and also test the efficacy of planned experiments by fitting our model to simulated data sets. We consider asynchronous data sets and illustrate how a lack of synchrony affects replication profiles. In addition to combing data, our technique is well-adapted to microarray-based studies of replication.

q-bio.QM↗

High-precision test of Landauer's principle in a feedback trap

We confirm Landauer's 1961 hypothesis that reducing the number of possible macroscopic states in a system by a factor of two requires work of at least kT ln 2. Our experiment uses a colloidal particle in a time-dependent, virtual potential created by a feedback trap to implement Landauer's erasure operation. In a control experiment, similar manipulations that do not reduce the number of system states can be done reversibly. Erasing information thus requires work. In individual cycles, the work to erase can be below the Landauer limit, consistent with the Jarzynski equality.

cond-mat.stat-mech↗

Real-time calibration of a feedback trap

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that an extended recursive least-squares (RLS) parameter-estimation algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the extended-RLS algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.

physics.ins-det↗

Virtual potentials for feedback traps

The recently developed feedback trap can be used to create arbitrary virtual potentials, to explore the dynamics of small particles or large molecules in complex situations. Experimentally, feedback traps introduce several finite time scales: there is a delay between the measurement of a particle's position and the feedback response; the feedback response is applied for a finite update time; and a finite camera exposure integrates motion. We show how to incorporate such timing effects into the description of particle motion. For the test case of a virtual quadratic potential, we give the first accurate description of particle dynamics, calculating the power spectrum and variance of fluctuations as a function of feedback gain, testing against simulations. We show that for small feedback gains, the motion approximates that of a particle in an ordinary harmonic potential. Moreover, if the potential is varied in time, for example by varying its stiffness, the work that is calculated approximates that done in an ordinary changing potential. The quality of the approximation is set by the ratio of the update time of the feedback loop to the relaxation time of motion in the virtual potential.

cond-mat.stat-mech↗

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.

physics.class-ph↗