The engines in everyday devices such as cars, vacuum cleaners and fans rely on a classical understanding of heat, energy and work. In recent years, scientists have designed (and in some cases built) new types of engines that incorporate unique quantum features. In addition to boosting performance, these features allow quantum engines to perform tasks that classical machines cannot.
Vijit Nautiyal from the University of New England, Armidale, New South Wales, Australia has now proposed a new type of quantum engine that exchanges not only heat, but also particles, with thermal reservoirs. The advantage of Nautiyal’s proposed quantum thermochemical engine, as described in Physical Review E, is that it combines near-maximum efficiency with high power output. “It’s equivalent to driving a Ferrari at the running cost of a Toyota,” Nautiyal explains. “You enjoy the thrill of high power while saving on fuel efficiency.”
Classical and quantum engines
Car engines typically operate in a four-stroke (Otto) cycle. In the intake stroke, the piston moves downwards, drawing air and fuel into a cylinder. The compression stroke then causes the piston to move upwards, compressing the mixture and increasing its temperature and pressure adiabatically (that is, without losing or gaining heat). Next comes the expansion stroke, when heat is added in the form of an igniting spark, causing the gas to expand adiabatically and performing work on the piston. Finally, during the exhaust stroke, the piston moves up, expelling the spent exhaust gases out of the cylinder.
Nautiyal’s proposed quantum engine replaces the fuel in a car engine with a weakly interacting one-dimensional Bose-Einstein condensate, or Bose gas, in a harmonic trap. Here, the ignition and exhaust (thermalization) strokes are equivalent to coupling the Bose gas to a surrounding cloud of thermal atoms that serves as a hot or cold reservoir. Because the Bose gas (the working fluid) can exchange both heat and particles with this reservoir, the setup can be considered an open quantum system. During the two work strokes (compression and expansion), the gas is instead treated as an isolated quantum many-body system.
The piston in this quantum engine is the strength of inter-atomic interactions in the gas. To move the piston, Nautiyal’s scheme calls for abruptly increasing this interaction strength during the compression stroke and abruptly decreasing it during the expansion stroke.
Engine operations
When Nautiyal’s system exchanges only heat with the hot and cold reservoirs, it cannot operate as an engine because its beneficial output work is less than the input work. However, if it also exchanges particles with the reservoirs, it operates as a thermochemical engine with output work greater than the input, compensating for any quantum friction experienced during the process.
Like the classical Otto engine cycle, Nautiyal’s quantum engine experiences a trade-off between power and efficiency. In classical engines, operating the cycle at a faster speed increases engine power; however, it also typically decreases efficiency because dissipative effects such as heat and friction increase irreversible losses. Similarly, in quantum engines, driving the system faster during the work stroke produces losses in the form of non-adiabatic energy excitations.
These excitations can be suppressed if the work strokes are performed extremely slowly (a quasi-static quench), leading to maximum efficiency. However, this comes at the cost of null power output due to extremely long driving time. Optimizing this trade-off between power and efficiency is thus one of the main goals of this field of finite-time quantum thermodynamics.
The upper bound on the work and efficiency produced by Nautiyal’s thermochemical engine is set by an adiabatic quantum thermochemical engine operating at zero temperature. Remarkably, this engine can operate at near maximum efficiencies while maintaining high power output even in the sudden quench, out-of-equilibrium regime. This is because instead of increasing efficiency by extending cycle time, one can increase it by boosting the flow of particles from the hot reservoir, which raises the internal energy of the working fluid. The additional energy can then be converted into mechanical work during the expansion stroke.
Asked about possible applications of his quantum engine, Nautiyal referred to “quantum steampunk”. This term, which was coined by the physicist Nicole Yunger Halpern at the US National Institute of Standards and Technology and the University of Maryland, encapsulates the idea that as quantum technologies advance, the field of quantum thermodynamics must also advance in order to make such technologies more efficient. A similar principle, Nautiyal explains, applies to smartphones: “The processor can be made more powerful, but the benefits cannot be appreciated without an efficient battery to meet the increased power demands.” Conducting research on quantum engines and quantum thermodynamics is thus a way to optimize quantum technologies.
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