Heat engines convert thermal energy into mechanical work and generally involve a large number of particles. We report the experimental realization of a single-atom heat engine. An ion is confined in a linear Paul trap with tapered geometry and driven thermally by coupling it alternately to hot and cold reservoirs. The output power of the engine is used to drive a harmonic oscillation. From direct measurements of the ion dynamics, we were able to determine the thermodynamic cycles for various temperature differences of the reservoirs. We then used these cycles to evaluate the power P and efficiency η of the engine, obtaining values up to P = 3.4 × 10(-22)joules per second and η = 0.28%, consistent with analytical estimations. Our results demonstrate that thermal machines can be reduced to the limit of single atoms.

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A single-atom heat engine

Fundamental aspects of steady-state conversion of heat to work at the nanoscale

An optically trapped colloidal particle serves as the first realization of a stochastic thermal engine, extending our understanding of the thermodynamics behind the Carnot cycle to microscopic scales where fluctuations dominate.

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Realization of a micrometre-sized stochastic heat engine

We propose an experimental scheme to realize a nanoheat engine with a single ion. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered laser reservoirs. The quantum efficiency at maximum power is analytically determined in various regimes. Moreover, Monte Carlo simulations of the engine are performed that demonstrate its feasibility and its ability to operate at a maximum efficiency of 30% under realistic conditions.

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Single-ion heat engine at maximum power.

MEMS-based oscillators are an emerging class of highly miniaturized, batch manufacturable timing devices that can rival the electrical performance of well-established quartz-based oscillators. In this review, a description is given of the key properties of a MEMS resonator that determine the overall performance of a MEMS oscillator. Piezoelectric, capacitive and active resonator transduction methods are compared and their impact on oscillator noise and power dissipation is explained. An overview is given of the performance of MEMS resonators and MEMS-based oscillators that have been demonstrated to date. Mechanisms that affect the frequency stability of the resonator, such as temperature-induced frequency drift, are explained and an overview is given of methods that have been demonstrated to improve the frequency stability. The aforementioned performance indicators of MEMS-based oscillators are benchmarked against established quartz and CMOS technologies.

https://iopscience.iop.org/article/10.1088/0960-1317/22/1/013001/pdf

A review of MEMS oscillators for frequency reference and timing applications

Heat engines provide most of our mechanical power and are essential for transportation on the macroscopic scale. However, although significant progress has been made in the miniaturization of electrostatic engines, it has proved difficult to reduce the size of liquid- or gas-driven heat engines below 107 μm3. Here we demonstrate that a crystalline silicon structure operates as a cyclic piezoresistive heat engine when it is driven by a sufficiently high d.c. current. A 0.34 μm3 engine beam draws heat from the d.c. current using the piezoresistive effect and converts it into mechanical work by expansion and contraction at different temperatures. This mechanical power drives a silicon resonator of 1.1×103 μm3 into sustained oscillation. Even below the oscillation threshold the engine beam continues to amplify the resonator’s Brownian motion. When its thermodynamic cycle is inverted, the structure is shown to reduce these thermal fluctuations, therefore operating as a refrigerator. A micrometre-scale device that exploits the piezoresistive characteristics of silicon acts like an engine, converting heat into mechanical work in one mode of operation, and, in another, like a refrigerator, suppressing mechanical fluctuations.

Piezoresistive heat engine and refrigerator

This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators. (Some figures in this article are in colour only in the electronic version)

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Amplitude saturation of MEMS resonators explained by autoparametric resonance

This paper demonstrates a 1.1 GHz MEMS resonator operating in fundamental mode occupying a chip area of only several mum2. To our knowledge this is the smallest and first fundamental mode Si resonator operating above 1 GHz. The resonator is excited by means of an electrostatic force and the mechanical motion is detected using the piezo-resistive properties of Si. The effective impedance at resonance is orders of magnitude lower than the impedance obtained using the more common capacitive or field effect read-out. More importantly, its effective impedance is in principle insensitive to uniform and directional geometric scaling.

Scalable 1.1 GHz fundamental mode piezo-resistive silicon MEMS resonator

A recently found extension of the Nijboer–Zernike approach to optical aberrations allows analytic computation of the intensity point-spread function in the focal region of an optical system. Here, the exit pupil function is expanded as a Zernike series , with a complex coefficient of the single aberration , and the contribution of each of the terms of this series to the complex-amplitude point-spread function U in the focal region has an analytic form. This representation of U, and hence of the intensity point-spread function I=|U|2, is highly efficient since normally a pupil function is already accurately described by a few β's. In this paper, the inverse problem of retrieving the β's from a given intensity I in the focal region is studied. A computation scheme for solving this nonlinear estimation problem, under the assumption of small-to-medium–large aberrations, is proposed. The key step is to linearize the theoretical intensity, comprising the β's as unknowns, by deleting second-order terms, and to o...

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Aberration retrieval from the intensity point-spread function in the focal region using the extended Nijboer–Zernike approach

A MEMS resonator using electrostatic to piezo-resistive transduction is demonstrated to be capable of simultaneous signal filtering and amplification. The mechanical resonance serves as a high Q electrical filter, while the piezo-resistive readout allows for signal amplification. Amplification factors up to 4.6 dB and Q values up to 60,000 are obtained for a 15 MHz resonator.

C. van der Avoort

Papers

Piezoresistive heat engine and refrigerator

Amplitude saturation of MEMS resonators explained by autoparametric resonance

Scalable 1.1 GHz fundamental mode piezo-resistive silicon MEMS resonator

Aberration retrieval from the intensity point-spread function in the focal region using the extended Nijboer–Zernike approach

A piezo-resistive resonant MEMS amplifier