Tag: Fermi gas

• A new kind of quantum engine with ultracold atoms

  In conventional ‘macroscopic’ engines like the ones that guzzle fossil fuels to power cars and motorcycles, the fuels are set ablaze to release heat, which is converted to mechanical energy and transferred to the vehicle’s moving parts. In order to perform these functions over and over in a continuous manner, the engine cycles through four repeating steps. There are different kinds of cycles depending on the engine’s design and needs. A common example is the Otto cycle, where the engine’s four steps are: 

  1. Adiabatic compression: The piston compresses the air-fuel mixture, increasing its pressure and temperature without exchanging heat with the surroundings

  2. Constant volume heat addition: At the piston’s top position, a spark plug ignites the fuel-air mixture, rapidly increasing pressure and temperature while the volume remains constant

  3. Adiabatic expansion: The high-pressure gas pushes the piston down, doing work on the piston, which powers the engine

  4. Constant volume heat rejection: At the bottom of the piston stroke, heat is expelled from the gas at constant volume as the engine prepares to clear the exhaust gases

  So the engine goes 1-2-3-4-1-2-3-4 and so on. This is useful. If you plot the pressure and volume of the fuel-air mixture in the engine on two axes of a graph, you’ll see that at the end of the ‘constant volume heat rejection’ step (no. 4), the mixture is in the same state as it is at the start of the adiabatic compression step (no. 1). The work that the engine does on the vehicle is equal to the difference between the work done during the expansion and compression steps. Engines are designed to meet the cyclical requirement while increasing the amount of work it does for a given fuel and vehicle design.

  It’s easy to understand the value of machines like this. They’re the reason we have vehicles that we can drive in different ways using our hands, legs, and our senses and in relative comfort. As long as we refill the fuel tank once in a while, engines can repeatedly perform mechanical work using their fuel combustion cycles. It’s understandable then why scientists have been trying to build quantum engines. While conventional engines use classical physics to operate, quantum engines are machines that use the ideas of quantum physics. For now, however, these machines are futuristic because scientists have found that they don’t understand the working principles of quantum engines well enough. University of Kaiserslautern-Landau professor Artur Widera told me the following in September 2023 after he and his team published a paper reporting that they had developed a new kind of quantum engine:

  Just observing the development and miniaturisation of engines from macroscopic scales to biological machines and further potentially to single- or few-atom engines, it becomes clear that for few particles close to the quantum regime, thermodynamics as we use in classical life will not be sufficient to understand processes or devices. In fact, quantum thermodynamics is just emerging, and some aspects of how to describe the thermodynamical aspects of quantum processes are even theoretically not fully understood.

  This said, recent advances in ultracold atomic physics have allowed physicists to control substances called quantum gases in the so-called low-dimensional regimes, laying the ground for them to realise and study quantum engines. Two recent studies exemplify this progress: the study by Widera et al. in 2023 and a new theoretical study reported in Physical Review E. Both studies have explored engines based on ultracold quantum gases but  have approached the concept of quantum energy conversion from complementary perspectives.

  The Physical Review E work investigated a ‘quantum thermochemical engine’ operating with a trapped one-dimensional (1D) Bose gas in the quasicondensate regime as the working fluid — just like the fuel-air mixture in in the internal combustion engine of a petrol-powered car. A Bose gas is a quantum system that consists of subatomic particles called bosons. The ‘1D’ simply means they are limited to moving back and forth on a straight line, i.e. a single spatial dimension. This restriction dramatically changes the bosons’ physical and quantum properties.

  According to the paper’s single author, University of Queensland theoretical physicist Vijit Nautiyal, the resulting engine can operate on an Otto cycle where the compression and expansion steps — which dictate the work the engine can do — are implemented by tuning how strongly the bosons interact, instead of changing the volume as in a classical engine. In order to do this, the quantum engine needs to exchange not heat with its surroundings but particles. That is, the particles flow from a hot reservoir to the working boson gas, allowing the engine to perform net work.

  

  Nautiyal’s study focused on the engine’s performance in two regimes: one where the strength of interaction between bosons was suddenly quenched in order to maximise the engine’s power at the cost of its efficiency, and another where the quantum engine operates at maximum efficiency but produces negligible power. Nautiyal has reported doing this using advanced numerical simulations.

  The simulations showed that if the engine only used heat but didn’t absorb particles from the hot reservoir, it couldn’t really produce useful energy at a finite temperatures. This was because of complicated quantum effects and uneven density in the boson gas. But when the engine was allowed to gain or lose particles from/to the reservoir, it got the extra energy it needed to work properly. Surprisingly, this particle exchange allowed the engine operate very efficiently, even when it ran fast. Usually, engines have to choose between going fast and losing efficiency or go slow and being more efficient. The particle exchange allowed Nautiyal’s quantum thermochemical engine avoid that trade-off. Letting more particles flow in and out also made the engine produce more energy and be even more efficient.

  Finally, unlike regular engines where higher temperature usually means better efficiency, increasing the temperature of the quantum thermochemical engine too much actually lowered its efficiency, speaking to the important role chemical work played in this engine design.

  In contrast, the 2023 experimental study — which I wrote about in The Hindu — realised a quantum engine that, instead of relying on conventional heating and cooling with thermal reservoirs, operated by cycling a gas of particles between two quantum states, a Bose-Einstein condensate and a Fermi gas. The process was driven by adiabatic changes (i.e. changes that happen while keeping the entropy fixed) that converted the fundamental difference in total energy distribution arising from the two states into usable work. The experiment demonstrated that this energy difference, called the Pauli energy, constituted a significant resource for thermodynamic cycles.

  The theoretical 2025 paper and the experimental 2023 work are intimately connected as complementary explorations of quantum engine operation using ultracold atomic gases. Both have taken advantage of the unique quantum effects accessible in such systems while focusing on distinct energy resources and operational principles.

  The 2025 work emphasised the role of chemical work arising from particle exchange in a one-dimensional Bose gas, exploring the balance of efficiency and power in finite-time quantum thermochemical engines. It also provided detailed computational frameworks to understand and optimise these engines. Likewise, the 2023 experiment physically realised a related but conceptually different mechanism: the movement of lithium atoms between two states and converting their Pauli energy to work. This approach highlighted how the fundamental differences between the two states could be a direct energy source, rather than conventional heat baths, and one operating with little to no production of entropy.

  Together, these studies broaden the scope of quantum engines beyond traditional heat-based cycles by demonstrating the usefulness of intrinsically quantum energy forms such as chemical work and Pauli energy. Such microscopic ‘machines’ also herald a new class of engines that harness the fundamental laws of quantum physics to convert energy between different forms more efficiently than the best conventional engines can manage with classical physics.

  Physics World asked Nautiyal about the potential applications of his work:

  … 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.

  2025.08.07

• Is mathematics real?

  I didn’t think to think about the realism of mathematics until I got to high school, and encountered quantum mechanics.

  Mathematics was at first just another subject, before becoming a tool with which to think intelligently about money and, later, with advanced statistical concepts in the picture, to understand the properties of groups of objects that couldn’t be deduced from those of individual ones. But by this time, mathematics – taken here to mean the systematic manipulation of numbers according to a fixed and rigid system of rules – seemed to be a world unto its own, separated cleanly from our physical reality akin to the way “a map is not the territory”.

  Put another and limited way, mathematics seemed to me to be a post facto system of rationalisation that people used to understand forces and outcomes whose physical forms weren’t available for direct observation (through one, some or all of the human senses). For example, (a + b)² = a² + b² + 2ab. To what does this translate in the real world? Perhaps I had 10 rupees in one pocket and 20 rupees in the other, and 29 other people turn up with the same combination of funds in their pockets. We could use this formula to quickly calculate the total amount of money there is in all of our pockets. But other than finding application of this sort, I didn’t think the formulae could have any other purpose – and that, certainly, knowing the formula wouldn’t allow us to predict anything new about the world (ergo post facto).

  I was constantly on the cusp of concluding mathematics was made up, a contrivance fashioned to fit our observations, and not real. But in high school, I came upon a form of mathematics-based reasoning that suggested I should think about it differently, if only for the sake of my own productivity. In class XI, my physics teacher at school introduced Wolfgang Pauli’s exclusion principle.

  The principle itself is simple, at least at the outset. Every particle has a fixed set of quantum numbers. An electron in an atom, for example, has four quantum numbers. Each quantum number can take a range of discrete values. A particular combination of the numbers is called a quantum state (i.e. the combination confers the particle with some possibilities and impossibilities). The principle is that no two particles in the same system can occupy the same quantum state.

  Now, it is Pauli’s principle – a logical relationship between various facts – that animates the idea, and not any mathematical rule or prescription. At the same time, the principle itself is arrived at by solving mathematical problems. Why do electrons in atoms have four quantum numbers? Because historically we started off with one, because we perceived the need for one, and over time we added a second, then a third and finally a fourth – all based on experiments in which the electrons behaved in a certain way, but because direct physical observation was out of the question we invented mathematical relationships between the particles’ parameters in different contexts and ascribed meaning to them.

  It was still ‘only’ empirical: scientists tried different things and those that worked stuck. There may be another way to make sense of the particles’ behaviour with, say, five dim sum (🥟) numbers, and reorganise the rest of quantum mechanics to fit in this paradigm. Even then, only the mathematical features of the topic will have changed – the physical features, or more broadly the specific ways in which particles are real, will have not. But this view of mine changed when I read about experiments that proved Pauli’s principle was real. A mathematical system we set up eventually led to the creation of a fixed set (not more, not less) of quantum numbers, and which Wolfgang Pauli eventually combined into a common principle. If scientists had proved that the principle was true and therefore real, could the mathematics undergirding the principle be true and real as well?

  Not all fundamental particles obey Pauli’s exclusion principle. The four quantum numbers of an electron in an atom are: principal (n), azimuthal (l), magnetic (m_l) and spin (s). Of these, the spin quantum number can take two kinds of values: half-integer (1/2, 3/2, …) and integer (0, 1, 2, …). Particles with half-integer spin are called fermions, and the rules describing their behaviour are defined by Fermi-Dirac statistics. They obey Pauli’s exclusion principle. Particles with integer spin are called bosons, and the rules describing their behaviour are defined by Bose-Einstein statistics. They don’t obey Pauli’s exclusion principle.

  When some kinds of heavy stars can no longer continue fusion reactions outside their core, they collapse into a neutron star – an ultra-dense ball of neutrons. Neutrons are fermionic particles – they have half-integer spin – which means they obey Pauli’s exclusion principle, and can’t occupy common quantum states. So the neutrons in a neutron star are tightly packed against each other. Their combined mass generates gravity that tries to pull them even closer together – but at the same time Pauli’s exclusion principle forces them to stay apart and remain stuck in their existing quantum states, creating a counter-force called neutron degeneracy pressure.

  We wouldn’t have neutron stars, or electronic goods or even heavy elements in the periodic table, if Pauli’s exclusion principle didn’t exist.

  Most recently, three separate groups of scientists described a new physical manifestation of the principle, called Pauli blocking. Most atoms are fermions (as a whole); each group first created a gas of such atoms and cooled them to a very low temperature – to ensure that in each gaseous system, all of the lowest available quantum states were occupied. (The higher a particle’s quantum state, the more energy it has.)

  A group at JILA, in Colorado, used strontium-87 atoms. A group from the University of Otago, New Zealand, used potassium-40 atoms. And a group from MIT used lithium-6 atoms. (The last one includes Wolfgang Ketterle, whose work I have discussed before).

  Usually, when a photon and an electron collide, the photon is scattered off into a different direction while the atom absorbs some of the photon’s energy and recoils. The absorbed energy forces the atom into a higher quantum state, with a different combination of the quantum numbers than the one it had before the collision. In an ultra-cold fermionic gas in which the particles have occupied the lowest available quantum states, and are packed tightly together as if in a solid, there is no room for any atom to absorb a small amount of energy imparted by a photon because all of the ‘nearby’ quantum states are taken. So the atoms allow the photons to sail right through, and the gas appears to be transparent.

  This barrier, in the form of the atoms being ‘blocked’ from scattering the photons, is called Pauli blocking. And in the three experiments, its effects were directly observable, without their validity having to be mediated through the use of mathematics.

  My views in high school and through college being what they were, I don’t have any serious position on the matter of whether mathematics is real. In fact, my reasoning could have been flawed in ways that I’m yet to realise but which a philosopher who has seriously studied this question may consider trivial. (Update, December 10, 2024: More than three years later, I can think of one. Both the theoretical description of X and the experimental verification of X — where X is any phenomenon grounded in the exclusion principle, e.g. neutron degeneracy pressure, Pauli blocking, etc. — are founded on a mathematical description of a physical reality, i.e. neither activity/event directly accesses the physical condition of X but deals only with the way we’ve chosen to describe such activity/event mathematically, and thus it’s no surprise that the experimental verification of X holds up the mathematical description of X.)

  This said, having to work my way through different concepts in high-energy, astroparticle and condensed-matter physics (as a science communicator) has forced me to accept not anything about mathematics as much as the importance we place on the distinction between something being real versus non-real, and the consequences of that on what mathematics is and isn’t allowed to tell us about the real world. Ultimately, dwelling on the distinction and its consequences distracted from what I found to be the most worthwhile part of discovery: the discovery itself. Even this post was motivated by an article in Physics World about the three experiments, whose second paragraph (and in fact most of whose second paragraphs) focused on potential, far-in-the-future applications of cold fermionic gases displaying Pauli blocking. I don’t care, and I think that from time to time, no one should.

  2021.11.28