The world, say many experts, is on the verge of a second quantum revolution. The most talked-about of such technologies is the quantum computer, a device in theory so powerful that it could crack the codes underlying internet security in just a few minutes. But full-scale quantum computers are still potentially decades away. In contrast, devices that exploit quantum phenomena to encrypt codes, rather than break them, are starting to appear on the market.
Yet many scientists believe that quantum will enjoy its first real commercial success in sensing. That’s because sensing can take advantage of the very characteristic that makes building a quantum computer so difficult: the extraordinary sensitivity of quantum states to the environment. Quantum sensors could be transformative, enabling autonomous vehicles that can “see” around corners, underwater navigation systems, early-warning systems for volcanic activity and earthquakes, and portable scanners that monitor a person’s brain activity during daily life.
One of the Quantum sensors, that has attracted considerable attention in the fields of modern science and technology is the quantum thermometer at the nanoscale because conventional thermometry is not applicable when spatial resolution decreases to the submicron scale. A challenging job is how to accurately measure temperature at the nanoscale, which would pave the way towards many groundbreaking applications in quantum science, bioscience, and material science.
The urgent need for temperature measurement at the nanoscale motivated the development of precise quantum thermometric techniques. In the past decade, researchers have developed quantum thermometers that can measure millikelvin temperature variations across nanoscale regions. They have built these thermometers out of single quantum dots—tiny islands of semiconductor within a larger solid—or with impurities in diamond nanocrystals. The thermometers have, for example, measured the temperatures of semiconductor electrons and the thermal variations inside a living cell.
In 2013, for example, Mikhail Lukin of Harvard University and colleagues used a tiny diamond (just 100 nm in diameter) to measure the temperature within a living cell at a spatial resolution of 200 nm (see “Nanodiamond thermometer takes temperature of biological cells“). Other researchers have shown that quantum dots – tiny pieces of semiconductor – can be used to measure the temperature of electrons in samples cooled below 1 K.
In recent years, various quantum systems have been investigated and demonstrated to be possibly used as thermometers. For example, a
single quantum dot as a thermometer can be used to accurately estimate the temperature of fermionic and bosonic reservoirs. The smallest
possible thermometer, namely, a single qubit, can distinguish two different temperatures of a bosonic bath.
The Coulomb blockade thermometer is also an important part of thermometry and has been studied for several decades. It is based on the properties of the Coulomb blockade in tunnel junctions and the electronic temperature can be extracted from the current–voltage characteristics. Recent progress suggests that the unknown temperature of a sample can be estimated by putting it in thermal contact with an individual quantum probe, which can minimize the undesired disturbance on the sample. In this thermometry approach, a hot thermal reservoir and a cold sample are coupled to the machine to form a quantum refrigerator, which allows for simultaneously cooling the
sample and determining its temperature in the case of the refrigerator reaching the Carnot efficiency.
How precise can a thermometer be? In January 2020, Jukka Pekkola, Bayan Karimi and colleagues at the University of Aalto, Finland, and Lund University in Sweden found the answer by building a nanoscale device that can detect fundamental fluctuations in the electron temperature of a sample. The noise level in their thermometer is so low that they could detect the energy change due to the emission of a single microwave photon – all without disturbing the system. Being able to spot such tiny temperature changes could enable advances in fundamental physics, and this “quantum calorimeter” might also be used to make non-invasive measurements of quantum systems such as qubits in superconducting quantum computers.
In most cases, the technique involves first letting the thermometer equilibrate at the sample temperature and then making precise measurements of its spectrum or detecting its temperature-dependent fluorescence. This experimental work has raised questions about the ultimate precision of these thermometers and what sort of object makes the ideal nanoscale thermometer. In 2015, Anna Sanpera and her colleagues at Barcelona State University in Spain and Gerardo Adesso of the University of Nottingham in the UK reported to have used a new theoretical approach that combines mathematical tools from quantum mechanics and thermodynamics.
“At the end of the day, what we have to measure to estimate temperature is closely related to the energy of the thermometer,” says Barcelona team member Luis Correa. The team shows that the most sensitive nanoscale thermometer has the largest heat capacity, which means that small changes in environmental temperature have a large effect on its energy.
By maximizing heat capacity mathematically, the team derives an expression for the maximum sensitivity of a nanoscale thermometer. This sensitivity depends on the thermometer’s energy level configuration and the number of available quantum states. For example, the nanodiamond thermometer that has been used in experiments has a single ground state and two excited states with the same energy. The team finds that the most precise thermometer is a system with two energy levels, like the nanodiamond, but where the upper energy has not two states, but a large number of them.
However, the researchers find a trade-off between a thermometer’s precision and the range of temperatures at which it can operate. Increasing the number of excited states increases precision, but it also narrows the temperature range over which the thermometer operates with maximum efficiency. The team suggests that an experimenter could first use a thermometer with a low precision but a wide temperature range to roughly determine the sample temperature. Then successively more precise probes could be used at different locations—say, in a circuit or a cell—to map smaller temperature variations across different regions of the sample.
In reality, it may not be possible for a thermometer to fully equilibrate with the sample because, for example, the temperature fluctuates in time. In this case, the researchers find that a two level thermometer that starts out very cold and therefore in its ground state (or close to it) before contacting the sample gives the best precision. With a limited amount of time, they also show that the probe should be checked as often as possible, with repeated cycles of cooling and reconnection with the sample. Correa says this work will help researchers learn where they can improve their experiments. Improved precision in temperature measurements could shed light on problems such as the dissipation of heat in nanoscale circuits and the thermal processes inside cells.
Nanodiamond quantum thermometer measures the temperature of worms
Going down to the submicron-scale temperature range, as in this new work, should provide detailed information on cellular and molecular activities. This could be important for clinical applications such as imaging brain sub-tissue structures, visualizing tumour heterogeneity and mapping adipocytes, to cite just three examples. It is, however, no easy task to reduce the size of biocompatible thermometers down to this small scale. Recent years have the seen the emergence of light-emitting nanothermometers – such as thermoresponsive molecular probes and nanoparticles – that could overcome this technical limitation. Most devices made thus far, however, are not robust enough for long-term use and can only monitor temperature changes over relatively long periods (hours). They are also not completely biocompatible.
The nanodiamond quantum thermometers employed in the new study are promising in many respects. The probes are made of nanodiamond, which naturally contains defects, known as NV centres. These occur when two adjacent carbon atoms in a diamond lattice are replaced with a nitrogen atom and an empty lattice site. The nitrogen has an extra electron that remains unpaired and so behaves as an isolated spin. This spin can be “up” or “down” or in a superposition of the two. Its state can be probed by illuminating the diamond with laser light and recording the intensity and frequencies of the emitted fluorescence.
NVs in nanodiamonds are ideal as biological probes because they are non-toxic, photostable, have surfaces that can be functionalized and can be easily inserted into living cells. They are also isolated from their surroundings, which means that their quantum behaviour is not immediately affected by surrounding thermal fluctuations, and can detect the very weak magnetic fields that come from nearby electronic or nuclear spins. They can thus be used as highly-sensitive magnetic resonance probes capable of monitoring local spin changes in a material over distances of a few tens of nanometres. And, in contrast to conventional magnetic resonance imaging (MRI) techniques in biology, in which millions of spins are required to produce a measurable signal, the NV defects can detect individual target spins with nanoscale spatial precision.
In their experiments, Masazumi Fujiwara of Osaka City University in Japan and colleagues functionalized the surfaces of the nanodiamonds with polymer structures and injected them into C. elegans nematode worms (one of the most popular animal models in biology). The sensor began by reading the base “healthy” temperature of the creatures as a frequency shift of the optically detected magnetic resonance of the NV defect centres.
Since the nanodiamonds move much more quickly inside a worm than in cultured cells, the researchers developed a fast particle-tracking algorithm. They also included an error-correction filter that takes into account the worm’s body structure, which can cause substantial fluctuations in the intensity of the fluorescent light emitted and can create temperature-measurement artefacts.
Next, the team, who report their work in Science Advances, induced an artificial “fever” in the worms by stimulating their mitochondria with a chemical. Their sensor successfully recorded this temperature increase with a precision of around ±0.22°C. “It was fascinating to see quantum technology work so well in live animals and I never imagined that the temperatures of tiny worms less than 1 mm in size could deviate from the norm and develop into a fever,” says Fujiwara. “Our results are an important milestone that will guide the future direction of quantum sensing as it shows how it contributes to biology.”
Coulomb coupled Quantum dot thermometer
In Nov 2018, Yanchao Zhang from Xiamen University proposed Coulomb-coupled quantum-dot thermometer can not only determine that the temperature of a sample is higher or lower than that of the reference heat reservoir in the measure environment but also precisely measure the temperature of the sample. The model of a Coulomb-coupled quantum-dot thermometer is illustrated in Fig. A tunneled quantum dot (denoted by QDB) couples two separate electronic reservoirs with temperatures TL and TR.
A second quantum dot QDS is capacitively coupled to QDB. Two quantum dots interact only though the long-range Coulomb force such that
they can only exchange energy U but no particles. The Coulomb-coupled quantum dots as a probe is tunneled to couple to a sample, which is an electronic reservoir with the temperature TS to be measured.
The whole setup, apart from the sample, is referred to as a thermometer. The heat flow into the reservoir is denoted by J , and the charge current, in the thermometer, from the left reservoir to the right reservoir is denoted by I . The voltage bias Delta V is applied to the right
reservoir and used to regulate the charge current.
“Through the regulation of the positive or negative voltage bias in the thermometer, we are able to judge whether the temperature of the sample is higher or lower than that of the reference heat reservoir in the measure environment and to determine the precise temperature of the sample by using a particularly simple temperature-voltage bias relationship in the reversible condition. One outstanding characteristic of the thermometer is that when the sample is at low temperatures, a small temperature change will lead to a large voltage bias change. It means that the proposed thermometer has a high sensitivity when low-temperature samples are measured.”
Researchers develop novel thermometer to accelerate quantum computer development, reported in March 2021
Researchers at Chalmers University of Technology, Gothenburg, Sweden, have developed a novel type of thermometer that can simply and quickly measure temperatures during quantum calculations with extremely high accuracy. The breakthrough provides a benchmarking tool for quantum computing of great value — and opens up for experiments in the exciting field of quantum thermodynamics.
A key component in quantum computers are coaxial cables and waveguides — structures which guide waveforms, and act as the vital connection between the quantum processor, and the classical electronics which control it. Microwave pulses travel along the waveguides to the quantum processor, and are cooled down to extremely low temperatures along the way. The waveguide also attenuates and filters the pulses, enabling the extremely sensitive quantum computer to work with stable quantum states.
In order to have maximum control over this mechanism, the researchers need to be sure that these waveguides are not carrying noise due to thermal motion of electrons on top of the pulses that they send. In other words, they have to measure the temperature of the electromagnetic fields at the cold end of the microwave waveguides, the point where the controlling pulses are delivered to the computer’s qubits. Working at the lowest possible temperature minimises the risk of introducing errors in the qubits.
Until now, researchers have only been able to measure this temperature indirectly, with relatively large delay. Now, with the Chalmers researchers’ novel thermometer, very low temperatures can be measured directly at the receiving end of the waveguide — very accurately and with extremely high time resolution. “Our thermometer is a superconducting circuit, directly connected to the end of the waveguide being measured. It is relatively simple — and probably the world’s fastest and most sensitive thermometer for this particular purpose at the millikelvin scale,” says Simone Gasparinetti, Assistant Professor at the Quantum Technology Laboratory, Chalmers University of Technology
The researchers at the Wallenberg Centre for Quantum Technology, WACQT, have the goal to build a quantum computer — based on superconducting circuits — with at least 100 well-functioning qubits, performing correct calculations by 2030. It requires a processor working temperature close to absolute zero, ideally down to 10 millikelvin. The new thermometer gives the researchers an important tool for measuring how good their systems are and what shortcomings exist — a necessary step to be able to refine the technology and achieve their goal.
“A certain temperature corresponds to a given number of thermal photons, and that number decreases exponentially with temperature. If we succeed in lowering the temperature at the end where the waveguide meets the qubit to 10 millikelvin, the risk of errors in our qubits is reduced drastically,” says Per Delsing, Professor at the Department of Microtechnology and Nanoscience, Chalmers University of Technology, and leader of WACQT. Accurate temperature measurement is also necessary for suppliers who need to be able to guarantee the quality of their components, for example cables that are used to handle signals down to quantum states.
Quantum mechanical phenomena such as superposition, entanglement and decoherence mean a revolution not only for future computing but potentially also in thermodynamics. It may well be that the thermodynamic laws somehow change when working down at the nanoscale, in a way that could one day be exploited to produce more powerful engines, faster-charging batteries, and more. “For 15-20 years, people have studied how the laws of thermodynamics might be modified by quantum phenomena, but the search for a genuine quantum advantage in thermodynamics is still open,” says Simone Gasparinetti, who recently started his own research group and plans to contribute to this search with a novel range of experiments.
The new thermometer can, for example, measure the scattering of thermal microwaves from a circuit acting as a quantum heat engine or refrigerator. “Standard thermometers were fundamental for developing classical thermodynamics. We hope that maybe, in the future, our thermometer will be regarded as pivotal for developing quantum thermodynamics,” says Marco Scigliuzzo, doctoral student at the Department of Microtechnology and Nanoscience, Chalmers University of Technology.
The novel thermometer concept relies on the interplay between coherent and incoherent scattering from a quantum emitter driven at resonance. The emitter is strongly coupled to the end of the waveguide being tested. Thermal photons in the waveguide lead to a measurable drop in the coherently scattered signal, which is recorded continuously. In this way, the number of photons in the propagating mode of the microwave waveguides can be read — this corresponds to a temperature. The Chalmers researchers’ implementation, which uses a superconducting circuit operated at gigahertz frequencies, offers simplicity, large bandwidth, high sensitivity, and negligible power dissipation.
quantum entanglement enables quantum thermometer to measure the coldest temperatures in the universe
Physicists from Trinity College Dublin have proposed a thermometer based on quantum entanglement that can accurately measure temperatures a billion times colder than those in outer space. These ultra-cold temperatures arise in clouds of atoms, known as Fermi gases, which are created by scientists to study how matter behaves in extreme quantum states.
The work was led by the QuSys team at Trinity with postdoctoral fellows, Dr Mark Mitchison, Dr Giacomo Guarnieri and Professor John Goold, in collaboration with Professor Steve Campbell (UCD) and Dr Thomas Fogarty and Professor Thomas Busch working at OIST, Okinawa, Japan. Discussing the proposal, Professor Goold, head of Trinity’s QuSys group, explains what an ultra-cold gas is. He said:
“The standard way in which a physicist thinks about a gas is to use a theory known as statistical mechanics. This theory was invented by giants of physics such as Maxwell and Boltzmann in the 19th century. These guys revived an old idea from the Greek philosophers that macroscopic phenomena, such as pressure and temperature, could be understood in terms of the microscopic motion of atoms. We need to remember that at the time, the idea that matter was made of atoms was revolutionary.”
“At the dawn of the 20th century, another theory came to fruition. This is quantum mechanics and it may be the most important and accurate theory we have in physics. A famous prediction of quantum mechanics is that single atoms acquire wave-like features, which means that below a critical temperature they can combine with other atoms into a single macroscopic wave with exotic properties. This prediction led to a century-long experimental quest to reach the critical temperature. Success was finally achieved in the 90s with the creation of the first ultra-cold gases, cooled with lasers (Nobel Prize 1997) and trapped with strong magnetic fields — a feat which won the Nobel Prize in 2001.”
“Ultra-cold gases like these are now routinely created in labs worldwide and they have many uses, ranging from testing fundamental physics theories to detecting gravitational waves. But their temperatures are mind-bogglingly low at nanokelvin and below! Just to give you an idea, one kelvin is -271.15 degrees Celsius. These gases are a billion times colder than that — the coldest places in the universe and they are created right here on Earth.” So what exactly is a Fermi gas?
“All particles in the universe, including atoms, come in one of two types called ‘bosons’ and ‘fermions’. A Fermi gas comprises fermions, named after the physicist Enrico Fermi. At very low temperatures, bosons and fermions behave completely differently. While bosons like to clump together, fermions do the opposite. They are the ultimate social distancers! This property actually makes their temperature tricky to measure.”
Dr Mark Mitchison, the first author of the paper, explains: “Traditionally, the temperature of an ultra-cold gas is inferred from its density: at lower temperatures the atoms do not have enough energy to spread far apart, making the gas denser. But fermions always keep far apart, even at ultra-low temperatures, so at some point the density of a Fermi gas tells you nothing about temperature.”
“Instead, we proposed using a different kind of atom as a probe. Let’s say that you have an ultra-cold gas made of lithium atoms. You now take a different atom, say potassium, and dunk it into the gas. Collisions with the surrounding atoms change the state of your potassium probe and this allows you to infer temperature. Technically speaking, our proposal involves creating a quantum superposition: a weird state where the probe atom simultaneously does and doesn’t interact with the gas. We showed that this superposition changes over time in a way that is very sensitive to temperature.”
Dr Giacomo Guarnieri gives the following analogy: “A thermometer is just a system whose physical properties change with temperature in a predictable way. For example, you can take the temperature of your body by measuring the expansion of mercury in a glass tube. Our thermometer works in an analogous way, but instead of mercury we measure the state of single atoms that are entangled (or correlated) with a quantum gas.”
Professor Steve Campbell, UCD, remarks:
“This isn’t just a far-flung idea — what we are proposing here can actually be implemented using technology available in modern atomic physics labs. That such fundamental physics can be tested is really amazing. Among the various emerging quantum technologies, quantum sensors like our thermometer are likely to make the most immediate impact, so it is a timely work and it was highlighted by the editors of Physical Review Letters for that reason.”
Professor Goold adds:
“In fact one of the reasons that this paper was highlighted was precisely because we performed calculations and numerical simulations with a particular focus on an experiment that was performed in Austria and published a few years ago in Science. Here the Fermi gas is a dilute gas of trapped Lithium atoms which were in contact with Potassium impurities. The experimentalists are able to control the quantum state with radio frequency pulses and measure out information on the gas. These are operations that are routinely used in other quantum technologies.”
“The timescales that are accessible are simply amazing and would be unprecedented in traditional condensed matter physics experiments. We are excited that our idea to use these impurities as a quantum thermometer with exquisite precision could be implemented and tested with existing technology.”
Professor Goold and his QuSys research group is supported by Science Foundation Ireland. He is the recipient of a Royal Society University Research Fellowship and a European Research Council Starting Grant. He has recently been elected as Fellow of the Young Academy of Europe.
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