Nanoscale heat engine exceeds standard efficiency limit

January 27, 2014 by Lisa Zyga, feature

The heat engine’s efficiency at maximum power is shown as a function of the squeezing parameter. The results of the Monte Carlo simulations (black dots) show that the efficiency of the proposed heat engine can be increased by a factor of four when the squeezing parameter is equal to or greater than 0.4. The generalized Carnot limit is the efficiency limit for an engine interacting with a squeezed thermal reservoir. Credit: J. Roßnagel, et al. ©2014 American Physical Society
( —In 2012, a team of physicists from Germany proposed a scheme for realizing a nanoscale heat engine composed of a single ion. Like a macroscale heat engine, the theoretical nanoscale version can convert heat into mechanical work by taking advantage of the temperature difference between two thermal reservoirs. Because the single-ion heat engine is so small, at the time the physicists noted that it had the potential to tap into the quantum regime and experience quantum effects.

Now in a new paper, the physicists, from the Universities of Mainz and Erlangen-Nürnberg in Germany, have theoretically shown that a nanoscale can take advantage of nonthermal effects.

"Our theoretical and numerical findings show that the performance of quantum heat engines may be enhanced by coupling them to engineered nonthermal reservoirs, like squeezed reservoirs," coauthor Eric Lutz, Physics Professor at the University of Erlangen-Nürnberg, told "These results follow from the application of the second law of thermodynamics to a reservoir configuration that is more general than usually considered in textbooks. From a theoretical point of view, they indicate that the second law is less restrictive away from equilibrium."

In their paper, the physicists showed that when the high-temperature thermal reservoir to which the quantum heat engine is attached is "squeezed," the heat engine's efficiency at maximum power dramatically increases and can exceed the standard Carnot limit by a factor of two. Since the power of an engine vanishes at maximum efficiency, the efficiency at maximum power is the quantity of prime interest for practical applications.

As an expression of the second law of thermodynamics, Carnot's result places a fundamental limit on a heat engine's . However, this limit holds only for the particular configuration that involves two thermal reservoirs at different temperatures.

The engine proposed here has only one thermal reservoir, since the reservoir that is squeezed is considered nonthermal. While thermal reservoirs are characterized only by their temperatures, nonthermal reservoirs can be controlled in additional ways, such as by squeezing.

As the physicists explain, squeezing is a quantum optics concept that has been shown to be a useful tool in high-precision spectroscopy, quantum information, quantum cryptography, and other areas. However, the use of squeezed thermal reservoirs in quantum thermodynamics has been largely unexplored until now.

The physicists' simulations showed that this heat engine can be experimentally realized with current technology involving a single ion and laser reservoirs. The simulations revealed that such a heat engine could realistically operate at with an efficiency that is up to four times larger than the efficiency obtained with two thermal reservoirs, and a factor of two above the standard Carnot limit.

In the future, these dramatic improvements in through squeezing could lead to the realization of more efficient nanoengines.

"We succeeded recently to trap ions and plan to verify the predicted results in the lab," Lutz said. "We are currently investigating heat pumps and the options to scale the number of ions up."

Explore further: Can a car engine be built out of a single particle?

More information: J. Roßnagel, et al. "Nanoscale Heat Engine Beyond the Carnot Limit." Physical Review Letters. DOI: 10.1103/PhysRevLett.112.030602

Also available at arXiv:1308.5935 [quant-ph]

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5 / 5 (1) Jan 27, 2014
Are we talking here (if massively parallel configuratioins are considered) about a way to extract useful amounts of energy from very small thermal differentials? Like a stack of matrices of nanotubes in a sandwich configuration with a single ion confined within that acts as the motor between two interleaved plates attached to different theraml reservoirs?

That's probably too far fetched, but it would be awesome to have those types of energy harvesters from (near) ambient conditions - as they'd work most anywhere.
5 / 5 (1) Jan 27, 2014
They do not consider the efficiency to make a squeezed reservoir out of equilibrium, but overall, it will not be above standard Carnot limit.
not rated yet Jan 27, 2014
Carnot cycles are barely Newtonian in orientation, never-mind Einsteinian and never mind Quantum.

Carnot can hold true for 'back of the envelope' calculations for general day to day use of associated engineered systems.

HOWEVER....When things are addressed on the quantum-nano level, it can be seen that the Carnot limits can be exceeded. easily so.

Many intrepid discovered and experimenters have noted these aspects, for many many years.

They make what the pundit of axioms might call 'over unity' devices They are not over unity, they rely upon quantum and nano level analysis (to start) to explain their function.

Hundreds of such systems, all varied... have been built and exhibited over the years.

The greater majority of such systems....operated as stated -and as offered.

There's a near unlimited number of ways to get there--start looking around, and you will find them.

The derision toward such is coming from a controlled and enabled corner, with vast resources.
not rated yet Jan 28, 2014
I absolutely no idea what they mean by "squeezed reservoirs"
although I note they do say "... squeezing is a quantum optics concept that has been shown to be a useful tool in high-precision spectroscopy, quantum information, quantum cryptography, and other areas...."

I tried goggling "squeezed reservoirs" but couldn't get a straight explanation of what it actually is. Can anyone here explain to me what is a "squeezed reservoir" and what is meant by "squeezing" in this context baring in mind I have pretty good understanding of basic physics from my university courses?
not rated yet Feb 02, 2014
Can anyone here explain to me what is a "squeezed reservoir" and what is meant by "squeezing" in this context baring in mind I have pretty good understanding of basic physics from my university courses?

It relates to the uncertainty principle. In this case, if you trap an ion (thus squeezing or diminishing the uncertainty in its position), then there is a corresponding increase in the uncertainty of the ion's momentum.

They do not consider the efficiency to make a squeezed reservoir out of equilibrium...

Sure they do. From the paper: "To achieve comparable values with a thermal bath interaction, while maintaining a maximized power output, an increase of the temperature ratio by 70% would be needed, while having a power output still 35% lower than the engine employing squeezing." (p. 4), "To ensure that an increase in efficiency can only be attributed to the squeezed state…" (p. 3), and "… no work is performed by the squeezing operation." (p. 4).

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