Quantum technologies and the prospect of advanced, next-generation electronic devices have been maturing at an increasingly rapid pace. Both research groups and governments around the world are investing more attention in this domain.

India for example mooted its National Quantum Mission in 2023 with a decade-long outlay of Rs 6,000 crore. One of the Mission’s goals, in the words of IISER Pune physics professor Umakant Rapol, is “to engineer and utilise the delicate quantum features of photons and subatomic particles to build advanced sensors” for applications in “healthcare, security, and environmental monitoring”.

On the science front, as these technologies become better understood, scientists have been paying increasingly more attention to managing and controlling heat in them. These technologies often rely on quantum physical phenomena that appear only at extremely low temperatures and are so fragile that even a small amount of stray heat can destabilise them. In these settings, scientists have found that traditional methods of handling heat — mainly by controlling the vibrations of atoms in the devices’ materials — become ineffective.

Instead, scientists have identified a promising alternative: energy transfer through photons, the particles of light. And in this paradigm, instead of simply moving heat from one place to another, scientists have been trying to control and amplify it, much like how transistors and amplifiers handle electrical signals in everyday electronics.

Playing with fire

Central to this effort is the concept of a thermal transistor. This device resembles an electrical transistor but works with heat instead of electrical current. Electrical transistors amplify or switch currents, allowing the complex logic and computation required to power modern computers. Creating similar thermal devices would represent a major advance, especially for technologies that require very precise temperature control. This is particularly true in the sub-kelvin temperature range where many quantum processors and sensors operate.

Energy transport at such cryogenic temperatures differs significantly from normal conditions. Below roughly 1 kelvin, atomic vibrations no longer carry most of the heat. Instead, electromagnetic fluctuations — ripples of energy carried by photons — dominate the conduction of heat. Scientists channel these photons through specially designed, lossless wires made of superconducting materials. They keep these wires below their superconducting critical temperatures, allowing only photons to transfer energy between the reservoirs. This arrangement enables careful and precise control of heat flow.

One crucial phenomenon that allows scientists to manipulate heat in this way is negative differential thermal conductance (NDTC). NDTC defies common intuition. Normally, decreasing the temperature difference between two bodies reduces the amount of heat they exchange. This is why a glass of water at 50º C in a room at 25º C will cool faster than a glass of water at 30º C. In NDTC, however, reducing the temperature difference between two connected reservoirs can actually increase the heat flow between them.

NDTC arises from a detailed relationship between temperature and the properties of the material that makes up the reservoirs. When physicists harness NDTC, they can amplify heat signals in a manner similar to how negative electrical resistance powers electrical amplifiers.

A ‘circuit’ for heat

In a new study, researchers from Italy have designed and theoretically modelled a new kind of ‘thermal transistor’ that they have said can actively control and amplify how heat flows at extremely low temperatures for quantum technology applications. Their findings were published recently in the journal Physical Review Applied.

To explore NDTC experimentally, the researchers studied reservoirs made of a disordered semiconductor material that exhibited a transport mechanism called variable range hopping (VRH). An example is neutron-transmutation-doped germanium. In VRH materials, the electrical resistance at low temperatures depends very strongly, sometimes exponentially, on temperature.

This attribute makes them ideal to tune their impedance, a property that controls the material’s resistance to energy flow, simply by adjusting temperature. That is, how well two reservoirs made of VRH materials exchange heat can be controlled by tuning the impedance of the materials, which in turn can be controlled by tuning their temperature.

In the new study, the researchers reported that impedance matching played a key role. When the reservoirs’ impedances matched perfectly (when their temperatures became equal), the efficiency with which they transferred photonic heat reached a peak. As the materials’ temperatures diverged, heat flow dropped. In fact, the researchers wrote that there was a temperature range, especially as the colder reservoir’s temperature rose to approach that of the warmer one, within which the heat flow increased even as the temperature difference shrank. This effect forms the core of NDTC.

The research team, associated with the NEST initiative at the Istituto Nanoscienze-CNR and Scuola Normale Superiore, both in Pisa in Italy, have proposed a device they call the photonic heat amplifier. They built it using two VRH reservoirs connected by superconducting, lossless wires. One reservoir was kept at a higher temperature and served as the source of heat energy. The other reservoir, called the central island, received heat by exchanging photons with the warmer reservoir.

The central island was also connected to two additional metallic reservoirs named the “gate” and the “drain”. These points operated with the same purpose as the control and output terminals in an electrical transistor. The drain stayed cold, allowing the amplified heat signal to exit the system from this point. By adjusting the gate temperature, the team could modulate and even amplify the flow of heat between the source and the drain (see image below).

To understand and predict the amplifier’s behaviour, the researchers developed mathematical models for all forms of heat transfer within the device. These included photonic currents between VRH reservoirs, electron tunnelling through the gate and drain contacts, and energy lost as vibrations through the device’s substrate.

(Tunnelling is a quantum mechanical phenomenon where an electron has a small chance of floating through a thin barrier instead of going around it.)

Raring to go

By carefully selecting the device parameters — including the characteristic temperature of the VRH material, the source temperature, resistances at the gate and drain contacts, the volume of the central island, and geometric factors — the researchers said they could tailor the device for different amplification purposes.

They reported two main operating modes. The first was called ‘current modulation amplifier’. In this configuration, the device amplified small variations in thermal input at the gate. In this mode, small oscillations in the gate heat current produced much larger oscillations, up to 15-times greater, in the photon current between the source and the central island and in the drain current, according to the paper. This amplification was efficient down to 20 millikelvin, matching the ultracold conditions required in quantum technologies. The output range of heat current was similarly broad, showing the device’s suitability to amplify heat signals.

The second mode was called ‘temperature modulation amplifier’. Here, slight changes of only a few millikelvin in the gate temperature, the team wrote, caused the output temperature in the central island to swing by as large as 3.3 times the changes in the input. The device could also handle input temperature ranges over 100 millikelvin. This performance reportedly matched or surpassed other temperature amplifiers already reported in the scientific literature. The researchers also noted that this mode could be used to pre-amplify signals in bolometric detectors used in astronomy telescopes.

An important ability relevant for practical use is the relaxation time, i.e. how soon after operating once the device returned to its original state, ready for the next run. The amplifier in both configurations showed relaxation times between microseconds and milliseconds. According to the researchers, this speed resulted from the device’s low thermal mass and efficient heat channels. Such a fast response could make it suitable to detect and amplify thermal signals in real time.

The researchers wrote that the amplifier also maintained good linearity and low distortion across various inputs. In other words, the output heat signal changed proportionally to the input heat signal and the device didn’t add unwanted changes, noise or artifacts to the input signal. Its noise-equivalent power values were also found to rival the best available solid-state thermometers, indicating low noise levels.

Approaching the limits

For these promising results, realising this device involves some significant practical challenges. For instance, NDTC depends heavily on precise impedance matching. Real materials inevitably have imperfections, including those due to imperfect fabrication and environmental fluctuations. Such deviations could lower the device’s heat transfer efficiency and reduce the operational range of NDTC.

The system also banked on lossless superconducting wires being kept well below their critical temperatures. Achieving and maintaining these ultralow temperatures requires sophisticated and expensive refrigeration infrastructure, which adds to the experimental complexity.

Fabrication also demands very precise doping and finely tuned resistances for the gate and drain terminals. Scaling production to create many devices or arrays poses major technical difficulties. Integrating numerous photonic heat amplifiers into larger thermal circuits risks unwanted thermal crosstalk and signal degradation, a risk compounded by the extremely small heat currents involved.

Furthermore, the fully photonic design offers benefits such as electrical isolation and long-distance thermal connections. However, it also approaches fundamental physical limits. Thermal conductance caps the maximum possible heat flow through photonic channels. This limitation could restrict how much power the device is able to handle in some applications.

Then again, many of these challenges are typical of cutting-edge research in quantum devices, and highlight the need for detailed experimental work to realise and integrate photonic heat amplifiers into operational quantum systems.

If they are successfully realised for practical applications, photonic heat amplifiers could transform how scientists manage heat in quantum computing and nanotechnologies that operate near absolute zero. They could pave the way for on-chip heat control, computers to autonomously stabilise the temperature, and perform thermal logic operations. Redirecting or harvesting waste heat could also improve the efficiency and significantly reduce noise — a critical barrier in ultra-sensitive quantum devices like quantum computers.

Featured image credit: Lucas K./Unsplash.

In the last two or three years, groups of scientists from around the world have made several claims that they had discovered a room-temperature superconductor. Many of these claims concerned high-pressure superconductors — materials that superconduct electricity at room temperature but only if they are placed under extreme pressure (a million atmospheres’ worth). Yet other scientists had challenged these claims on many grounds, but one in particular was whether these materials really exhibited the Meissner effect.

Room-temperature superconductors are often called the ‘holy grail’ of materials science. I abhor clichés but in this case the idiom fits perfectly. If such a material is invented or discovered, it could revolutionise many industries. To quote at length from an article by electrical engineer Massoud Pedram in The Conversation:

Room-temperature superconductors would enable ultra high-speed digital interconnects for next-generation computers and low-latency broadband wireless communications. They would also enable high-resolution imaging techniques and emerging sensors for biomedical and security applications, materials and structure analyses, and deep-space radio astrophysics.

Room-temperature superconductors would mean MRIs could become much less expensive to operate because they would not require liquid helium coolant, which is expensive and in short supply. Electrical power grids would be at least 20% more power efficient than today’s grids, resulting in billions of dollars saved per year, according to my estimates. Maglev trains could operate over longer distances at lower costs. Computers would run faster with orders of magnitude lower power consumption. And quantum computers could be built with many more qubits, enabling them to solve problems that are far beyond the reach of today’s most powerful supercomputers.

However, this surfeit of economic opportunities could also lure scientists into not thoroughly double-checking their results, cherry-picking from their data or jumping to conclusions if they believe they have found a room-temperature superconductor. Many papers written by scientists claiming they had found a room-temperature superconductor have in fact been published in and subsequently retracted from peer-reviewed journals with prestigious reputations, including Nature and Science, after independent experts found the papers to contain flawed data. Whatever the reasons for these mistakes, independent scrutiny of such reports has become very important.

If a material is a superconductor, it needs to meet two conditions*. The first of course is that it needs conduct a direct electric current with zero resistance. Second, the material should display the Meissner effect. Place a magnet over a superconducting material. Then, gradually cool the material to lower and lower temperatures, until you cross the critical temperature. Just as you cross this threshold, the magnet will start to float above the material. You’ve just physically observed the Meissner effect. It happens because when the material transitions to its superconducting state, it will expel all magnetic fields within its bulk to its surface. This results in any magnets already sitting nearby to be pushed away. In fact, the Meissner effect is considered to be the hallmark sign of a superconductor because it’s difficult to fake.

The problem with acquiring evidence of the Meissner effect is the setup in which many of these materials become superconductors. In order to apply the tens to hundreds of gigapascals (GPa) of pressure, a small sample of the material — a few grams or less — is placed between a pair of high-quality diamond crystals and squeezed. This diamond anvil cell apparatus leaves no room for a conventional magnetic field sensor to be placed inside the cell. Measuring the magnetic properties of the sample is also complicated because of the fields from other sources in the apparatus, which will have to be accurately measured and then subtracted from the final data.

To tackle this problem, some scientists have of late suggested measuring the sample’s magnetic properties using the only entity that can still enter and leave the diamond anvil cell: light.

In technical terms, such a technique is called optical magnetometry. Magnetometry in general is any technique that converts some physical signal into data about a magnetic field. In this case the signal is in the form of light, thus the ‘optical’ prefix. To deploy optical magnetometry in the context of verifying whether a material is a high-pressure superconductor, scientists have suggested using nitrogen vacancy (NV) centres.

Say you have a good crystal of diamond with you. The crystal consists of carbon atoms bound to each other in sets of four in the shape of a pyramid. Millions of copies of such pyramids together make up the diamond. Now, say you substitute one of the carbon atoms in the gem with a nitrogen atom and also knock out an adjacent carbon atom. Physicists have found that this vacancy in the lattice, called an NV centre, has interesting, useful properties. For example, an NV centre can fluoresce, i.e. absorb light of a higher frequency and emit light of a lower frequency.

Because each NV centre is surrounded by three carbon atoms and one nitrogen atom, the vacancy hosts six electrons, two of which are unpaired. All electrons have a property called quantum spin. The quantum spin is the constitutive entity of magnetism the same way the electric charge is the constitutive entity of electricity. For example, if a block of iron is to be turned into a magnet, the spins of all the electrons inside have to be made point in the same direction. Each spin can point in one of two directions, which for a magnet are called ‘north’ and ‘south’. Planet earth has a magnetic north and a magnetic south because the spins of the trillions upon trillions of electrons in its core have come to point in roughly the same direction.

The alignment of the spins of different electrons also affects what energy they have. For example, in the right conditions, an atom with two electrons will have more energy if the electrons’ spins are aligned (↑↑) than when the electrons’ spins are anti-aligned (↑↓). This fundamental attribute of the electrons in the NV centres allows the centres to operate as a super-sensitive detector of magnetic fields — and which is what scientists from institutions around France have reported doing in a June 30 paper in Physical Review Applied.

The scientists implanted a layer of 10,000 to 100,000 NV centres a few nanometres under the surface of one of the diamond anvils. These centres had electrons with energies precisely 2.87 GHz apart.** When the centres were then exposed to microwave laser of some frequency, every NV centre could absorb green laser light and re-emit red light.

As the diamond anvils squeezed the sample past 4 GPa, the pressure at which it would have become a superconductor, the sample displayed the Meissner effect, expelling magnetic fields from within its bulk to the surface. As a result, the NV centres were exposed to a magnetic field in their midst that wasn’t there before. This field affected the electrons’ collective spin and thus their energy levels, which in turn caused the red light being emitted from the centres to dim.

The researchers could easily track the levels and patterns of dimming in the NV centres with a microscopy, and based on that were able to ascertain whether the sample had displayed the Meissner effect. As Physical Review Letters associate editor Martin Rodriguez-Vega wrote in Physics magazine: “A statistical analysis of the [optical] dataset revealed information about the magnetic-field strength and orientation across the sample. Mapping these quantities produced a visualisation of the Meissner effect and revealed the existence of defects in the superconductor.”

Because the NV centres were less than 1 micrometre away from the sample, they were extremely sensitive to changes in the magnetic field. In fact the researchers reported that the various centres were able to reveal the critical temperature for different parts of the sample separately than for the sample as a whole — a resolution not possible with conventional techniques. The pristine diamond matrix also conferred the electrons’ spins inside the NV centres with a long lifetime. And because there were so many NV centres, the researchers were able to ‘scan’ them with the microwave laser en masse instead of having to maintain focus on a single point on the diamond anvil, when looking for evidence of changes in the sample’s magnetic field. Finally, while the sample in the study became superconducting at a critical temperature of around 140 K, the centres were stable to under 4 K.

Another major advantage of the technique is that it can be used with type II superconductors as well. Type I superconductors are materials that transition to their superconducting state in a single step, under the critical temperature. Type II superconductors transition to their superconducting states in more than one step and display a combination of flux-pinning and the Meissner effect. From my piece in The Hindu in August 2023: “When a flux-pinned superconductor is taken away from a particular part of the magnetic field and put back in, it will snap back to its original relative position.” This happens because type II materials, while they don’t expel magnetic fields from within their bulk, also prevent the fields from moving around inside. Thus the magnetic field lines are pinned in place.

Because of the spatial distribution of the NV centres and their sensitivity, they can reveal flux-pinning in the sample by ‘sensing’ the magnetic fields at different distances.

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* The material can make a stronger case for itself if it displays two more properties. (i) The heat energy required to raise the material’s electrons by 1º C has to change drastically at the critical temperature, which is the temperature below which the material becomes a superconductor. (ii) The material’s electrons shouldn’t be able to have certain energy readings. (That is, a map of the energies of all the electrons should show some gaps.) These properties are however considered optional.

** While 2.87 GHz is a frequency figure, recall Planck’s equation from high school: E = hv. Energy is equal to frequency times Planck’s constant, h. Since h is a constant (6.62 × 10^-34 m²kg/s), energy figures are frequently denoted in terms of frequency in physics. An interested party can calculate the energy by themselves.