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.

I have access to the premium version of ChatGPT, and every day I ask it a few questions about concepts in physics that I’d like to know more about. Yesterday, for example, I learnt the difference between quenching and annealing…

Is there an opposite phenomenon for quenching?

Yes! The opposite of quenching would be processes that allow gradual relaxation, equilibration, or annealing rather than rapid freezing. Some terms that describe this include:

Annealing (Thermal and Simulated) — In metallurgy and physics, annealing is the process of slow cooling a material so it can reach a more ordered, lower-energy state.

In simulated annealing (used in optimization and machine learning), a system is gradually "cooled" to allow it to find a global minimum rather than getting trapped in local minima (which can happen in quenching).

Slow Equilibration / Adiabatic Processes — Unlike quenching, which often leads to metastable states, slow thermalization allows the system to reach true equilibrium.

Adiabatic processes in quantum mechanics and condensed matter physics allow the system to evolve slowly so that it remains in a well-defined state.

Supercooling vs. Slow Nucleation — When liquids are rapidly cooled (quenched), they might bypass crystallization and form a glass. In contrast, if cooling is slow, proper nucleation occurs, leading to a well-ordered crystal.

Self-Organization & Aging in Complex Systems — Some complex systems exhibit aging (e.g., glasses, biological systems) where they slowly evolve toward an ordered or more stable configuration over time, in contrast to being frozen in a quenched state.

… and later about the Weierstrass function.

Please explain the Weierstrass function to me.

The Weierstrass function is a famous example of a continuous but nowhere differentiable function. It is defined as:

[ W(x) = \sum_{n=0}^{\infty} aⁿ \cos(bⁿ \pi x) ]

where:

• ( 0 < a < 1 ) (controls decay)
• ( b ) is an odd integer ( > 1 ) (controls frequency)
• The product ( ab > 1 + \frac{3\pi}{2} ) ensures nowhere differentiability.

Key Properties

Continuous Everywhere — Despite its wild oscillations, ( W(x) ) is continuous for all ( x ).

Nowhere Differentiable — No well-defined slope exists at any point, making it an early example of a function that is continuous yet "rough" at all scales.

Self-Similarity (Fractal-like Behavior) — Since it is constructed as an infinite sum of cosine waves with exponentially increasing frequencies, it exhibits self-similarity: small-scale structures resemble larger-scale patterns.

Role in Mathematics — This function was introduced by Karl Weierstrass in the 19th century as a counterexample to the assumption that "continuous functions are differentiable almost everywhere."

I have found using ChatGPT in this way to be a valuable learning tool, and I imagine there are already people out there who are repackaging instances of ChatGPT to be autonomous ‘teachers’ for students looking to learn something.

One of my jobs at The Hindu is to get explanatory articles for concepts in (pure) science. I recently attempted one on amplifiers, which required me to explain the working of a NPN bipolar junction transistor, a device I’d until then been happy to leave behind in my high school classroom. I turned to ChatGPT, asking for a visualisation of the transistor, and it obliged. I’m a visual learner and having access to the tool made a big difference.

How does an NPN bipolar junction transistor work? Please explain with a visualisation.

An NPN bipolar junction transistor (BJT) is a type of transistor that consists of three layers of semiconductor material: two n-type layers (emitter and collector) separated by a p-type layer (base). It is commonly used for switching and amplification.

How an NPN Transistor Works

Structure & Terminals:

Emitter (E): Heavily doped n-type region that emits electrons.

Base (B): Thin, lightly doped p-type region.

Collector (C): Moderately doped n-type region that collects electrons.

Operation Principles:

When a small current is applied to the base-emitter junction (forward-biased), it allows a larger current to flow from the emitter to the collector.

The base-emitter junction acts as a diode, allowing electrons to flow into the base.

Most electrons injected from the emitter into the base are swept into the collector due to the voltage difference.

Visualization

      Collector (C)
           |
           |
      |----|----|
      |    N    |   <-- Collector (N-type)
      |----|----|
           |
      |----|----|
      |    P    |   <-- Base (P-type, thin and lightly doped)
      |----|----|
           |
      |----|----|
      |    N    |   <-- Emitter (N-type, heavily doped)
      |----|----|
           |
           |
      Emitter (E)

Current Flow:

Electrons flow from Emitter (E) to Collector (C).

A small Base (B) current controls a much larger Collector (C) current.

Voltage Conditions:

V_BE (Base-Emitter voltage) > 0.7V (Forward biased)

V_CE (Collector-Emitter voltage) > V_BE (Reverse biased)

Electron Flow:

→ Represents electron flow.

I_B (Base Current) is small but controls I_C (Collector Current), which is large.

( +V_C ) | | [C] ← Electrons | | | [B] → Small Base Current (I_B) | | | [E] → Large Electron Flow (I_E) | ( GND )

Working Mechanism:

The Base-Emitter junction is forward-biased, allowing electrons to move from Emitter to Base.

Most electrons are swept into the Collector due to the reverse-biased Collector-Base junction.

A small Base current (I_B) controls a large Collector current (I_C), amplifying the input signal.

I have a background in engineering plus more than a decade’s experience in spotting yellow/red flags in scientific papers, and I imagine anyone with these skills will have an easier time navigating ChatGPT’s answers. For anyone else that lacks these skills, all we need is a guarantee from OpenAI that the tool doesn’t hallucinate or that it hallucinates in specific contexts, and definitely not above a certain rate.