Tag: atomic cooling

When cooling down really means slowing down

Consider this post the latest in a loosely defined series about atomic cooling techniques that I’ve been writing since June 2018.

Atoms can’t run a temperature, but things made up of atoms, like a chair or table, can become hotter or colder. This is because what we observe as the temperature of macroscopic objects is at the smallest level the kinetic energy of the atoms it is made up of. If you were to cool such an object, you’d have to reduce the average kinetic energy of its atoms. Indeed, if you had to cool a small group of atoms trapped in a container as well, you’d simply have to make sure they – all told – slow down.

Over the years, physicists have figured out more and more ingenious ways to cool atoms and molecules this way to ultra-cold temperatures. Such states are of immense practical importance because at very low energy, these particles (an umbrella term) start displaying quantum mechanical effects, which are too subtle to show up at higher temperatures. And different quantum mechanical effects are useful to create exotic things like superconductors, topological insulators and superfluids.

One of the oldest modern cooling techniques is laser-cooling. Here, a laser beam of a certain frequency is fired at an atom moving towards the beam. Electrons in the atom absorb photons in the beam, acquire energy and jump to a higher energy level. A short amount of time later, the electrons lose the energy by emitting a photon and jump back to the lower energy level. But since the photons are absorbed in only one direction but are emitted in arbitrarily different directions, the atom constantly loses momentum in one direction but gains momentum in a variety of directions (by Newton’s third law). The latter largely cancel themselves out, leaving the atom with considerably lower kinetic energy, and therefore cooler than before.

In collisional cooling, an atom is made to lose momentum by colliding not with a laser beam but with other atoms, which are maintained at a very low temperature. This technique works better if the ratio of elastic to inelastic collisions is much greater than 50. In elastic collisions, the total kinetic energy of the system is conserved; in inelastic collisions, the total energy is conserved but not the kinetic energy alone. In effect, collisional cooling works better if almost all collisions – if not all of them – conserve kinetic energy. Since the other atoms are maintained at a low temperature, they have little kinetic energy to begin with. So collisional cooling works by bouncing warmer atoms off of colder ones such that the colder ones take away some of the warmer atoms’ kinetic energy, thus cooling them.

In a new study, a team of scientists from MIT, Harvard University and the University of Waterloo reported that they were able to cool a pool of NaLi diatoms (molecules with only two atoms) this way to a temperature of 220 nK. That’s 220-billionths of a kelvin, about 12-million-times colder than deep space. They achieved this feat by colliding the warmer NaLi diatoms with five-times as many colder Na (sodium) atoms through two cycles of cooling.

Their paper, published online on April 8 (preprint here), indicates that their feat is notable for three reasons.

First, it’s easier to cool particles (atoms, ions, etc.) in which as many electrons as possible are paired to each other. A particle in which all electrons are paired is called a singlet; ones that have one unpaired electron each are called doublets; those with two unpaired electrons – like NaLi diatoms – are called triplets. Doublets and triplets can also absorb and release more of their energy by modifying the spins of individual electrons, which messes with collisional cooling’s need to modify a particle’s kinetic energy alone. The researchers from MIT, Harvard and Waterloo overcame this barrier by applying a ‘bias’ magnetic field across their experiment’s apparatus, forcing all the particles’ spins to align along a common direction.

Second: Usually, when Na and NaLi come in contact, they react and the NaLi molecule breaks down. However, the researchers found that in the so-called spin-polarised state, the Na and NaLi didn’t react with each other, preserving the latter’s integrity.

Third, and perhaps most importantly, this is not the coldest temperature to which we have been able to cool quantum particles, but it still matters because collisional cooling offers unique advantages that makes it attractive for certain applications. Perhaps the most well-known of them is quantum computing. Simply speaking, physicists prefer ultra-cold molecules to atoms to use in quantum computers because physicists can control molecules more precisely than they can the behaviour of atoms. But molecules that have doublet or triplet states or are otherwise reactive can’t be cooled to a few billionths of a kelvin with laser-cooling or other techniques. The new study shows they can, however, be cooled to 220 nK using collisional cooling. The researchers predict that in future, they may be able to cool NaLi molecules even further with better equipment.

Note that the researchers didn’t cool the NaLi atoms from room temperature to 220 nK but from 2 µK. Nonetheless, their achievement remains impressive because there are other well-established techniques to cool atoms and molecules from room temperature to a few micro-kelvin. The lower temperatures are harder to reach.

One of the researchers involved in the current study, Wolfgang Ketterle, is celebrated for his contributions to understanding and engineering ultra-cold systems. He led an effort in 2003 to cool sodium atoms to 0.5 nK – a record. He, Eric Cornell and Carl Wieman won the Nobel Prize for physics two years before that: Cornell, Wieman and their team created the first Bose-Einstein condensate in 1995, and Ketterle created ‘better’ condensates that allowed for closer inspection of their unique properties. A Bose-Einstein condensate is a state of matter in which multiple particles called bosons are ultra-cooled in a container, at which point they occupy the same quantum state – something they don’t do in nature (even as they comply with the laws of nature) – and give rise to strange quantum effects that can be observed without a microscope.

Ketterle’s attempts make for a fascinating tale; I collected some of them plus some anecdotes together for an article in The Wire in 2015, to mark the 90th year since Albert Einstein had predicted their existence, in 1924-1925. A chest-thumper might be cross that I left Satyendra Nath Bose out of this citation. It is deliberate. Bose-Einstein condensates are named for their underlying theory, called Bose-Einstein statistics. But while Bose had the idea for the theory to explain the properties of photons, Einstein generalised it to more particles, and independently predicted the existence of the condensates based on it.

This said, if it is credit we’re hungering for: the history of atomic cooling techniques includes the brilliant but little-known S. Pancharatnam. His work in wave physics laid the foundations of many of the first cooling techniques, and was credited as such by Claude Cohen-Tannoudji in the journal Current Science in 1994. Cohen-Tannoudji would win a piece of the Nobel Prize for physics in 1997 for inventing a technique called Sisyphus cooling – a way to cool atoms by converting more and more of their kinetic energy to potential energy, and then draining the potential energy.

Indeed, the history of atomic cooling techniques is, broadly speaking, a history of physicists uncovering newer, better ways to remove just a little bit more energy from an atom or molecule that’s already lost a lot of its energy. The ultimate prize is absolute zero, the lowest temperature possible, at which the atom retains only the energy it can in its ground state. However, absolute zero is neither practically attainable nor – more importantly – the goal in and of itself in most cases. Instead, the experiments in which physicists have achieved really low temperatures are often pegged to an application, and getting below a particular temperature is the goal.

For example, niobium nitride becomes a superconductor below 16 K (-257º C), so applications using this material prepare to achieve this temperature during operation. For another, as the MIT-Harvard-Waterloo group of researchers write in their paper, “Ultra-cold molecules in the micro- and nano-kelvin regimes are expected to bring powerful capabilities to quantum emulation and quantum computing, owing to their rich internal degrees of freedom compared to atoms, and to facilitate precision measurement and the study of quantum chemistry.”

The imperfection of strontium titanate

When you squeeze some crystals, you distort their lattice of atoms just enough to separate a pair of charged particles and that in turn gives rise to a voltage. Such materials are called piezoelectric crystals. Not all crystals are piezoelectric because the property depends on what the arrangement of atoms in the lattice is.

For example, the atoms of strontium, titanium and oxygen are arranged in a cubic structure to form strontium titanate (SrTiO3) such that each molecule displays a mirror symmetry through its centre. That is, if you placed a mirror passing through the molecule’s centre, the object plus its reflection would show the molecule as it actually is. Such molecules are said to be centrosymmetric, and centrosymmetric crystals aren’t piezoelectric.

In fact, strontium titanate isn’t ferroelectric or pyroelectric either – an external electric field can’t reverse their polarisation nor do they produce a voltage when they’re heated or cooled – for the same reason. Its crystal lattice is just too symmetrical.

The strontium titanate lattice. Oxygen atoms are red, titanium cations are blue and strontium cations are green.

However, scientists haven’t been deterred by this limitation (such as it is) because its perfect symmetry indicates that messing with the symmetry can introduce new properties in the material. There are also natural limits to the lattice itself. A cut and polished diamond looks beautiful because, at its surface, the crystal lattice ends and the air begins – arbitrarily stopping the repetitive pattern of carbon atoms.

An infinite diamond that occupies all points in the universe might look good on paper but it wouldn’t be nearly as resplendent because only the symmetry-breaking at the surface allows light to enter the crystal and bounce around. Similarly, centrosymmetric strontium titanate might be a natural wonder, so to speak, but the centrosymmetry also keeps it from being useful (despite its various unusual properties; e.g. it was the first insulator found to be a superconductor at low temperatures, in 1967).

Tausonite, a naturally occurring mineral form of strontium titanate. Credit: Materialscientist/Wikimedia Commons, CC BY-SA 3.0

So does strontium titanate exhibit pyro- or piezoelectricity on its surface? Surprisingly, while this seems like a fairly straightforward question to ask, it hasn’t been straightforward to answer.

A part of the problem is the definition of a surface. Obviously, the surface of any object refers to the object’s topmost or outermost layer. But when you’re talking about, say, a small electric current originating from the material, it’s difficult to imagine how you could check if the current originated from the bulk of the material or just the surface.

Researchers from the US, Denmark and Israel recently reported resolving this problem using concepts from thermodynamics 101. If the surface of strontium titanate is pyroelectric, the presence of electric currents should co-exist with heat. So if a bit of heat is applied and taken away, the material should begin cooling (or thermalising) and the electric currents should also dissipate. The faster the material cools, the faster the currents dissipate, and the faster the currents dissipate, the lower the depth to which the material is pyroelectric.

In effect, the researchers induced pyroelectricity and then tracked how quickly it vanished to infer how deeply inside the material it existed.

Both the bulk and the surface are composed of the same atoms, but the atomic lattice on the surface also has a bit of surface tension. Materials scientists have already calculated how deeply this tension penetrates the surface of strontium titanate, so the question was also whether the pyroelectric behaviour was contained in this region or went beyond, into the rest of the bulk.

The team sandwiched a slab of strontium titanate between two electrodes, at room temperature. At the crystal-electrode interface, which is a meeting of two surfaces, opposing charged particles on either side gather and neutralise themselves. But when an infrared laser is shined on the ensemble (as shown above), the surface of strontium titanate heats up and develops a voltage, which in turn draws the charges at its surface away from the interface. The charges in the electrode are then left without a partner so they flow through a wire connected to the other electrode and create a current.

The laser is turned off and the strontium titanate’s surface begins to cool. Its voltage drops and allows the charged particles to move away from each other, and some of them move towards the surface to once again neutralise oppositely charged particles from the other side. This process stops the current. So measuring how quickly the current drops off gives away how quickly the voltage vanishes, which gives away how much of the material’s volume developed a voltage due to the pyroelectric effect.

The penetration depth the group measured was in line with the calculations based on surface tension: about 1.2 nm. To be sure the effect didn’t involve the bulk, the researchers repeated the experiment with a thin layer of silica (the major component of sand) on top of the strontium titanate surface, and there was no electric current when the laser was on or off.

In fact, according to a report in Nature, the team also took various precautions to ensure any electric effects originated only from the surface, and due to effects intrinsic to the material itself.

… they checked that the direction of the heat-induced current does not depend on the orientation of the crystal, ruling out a bulk effect; and that the local heating produced by the laser is very small…, which means that the strain gradients induced by thermal expansion are insignificant. Other experiments and data analysis were carried out to exclude the possibility that the induced current is due to molecules … adsorbed to the surface, charges trapped by lattice defects, excitation of free electrons induced by light, or the thermoelectric Seebeck effect (which generates currents in semiconductors that contain temperature gradients).

Now we know strontium titanate is pyroelectric, and piezoelectric, on its surface at room temperature – but this is not all we know. During their experiments (with different samples of the crystal), the researchers spotted something odd:

The pyroelectric coefficient – a measure of the strength of the material’s pyroelectricity – was constant between 193 K and 225 K (–80.15º C to –48.15º C) but dropped sharply above 225 K and vanished above 380 K. The researchers note in their paper, published on September 18, that others have previously reported that the strontium titanate lattice near the surface changes from a cubic to a tetragonal structure at around 150 K, and that a similar transformation could be happening at 225 K.

In other words, the surface pyroelectric effect wasn’t just producing a voltage but could in fact be altering the relative arrangement of atoms itself. What the precise mechanism of action could be we don’t know – nor any other features that might arise in the material as a result. The researchers hope future studies can resolve these questions.

The trouble with laser-cooling anions

For scientists to use lasers to cool an atom, the atom needs to have two energy states. When laser light is shined on an atom moving towards the source of light, one of its electrons absorbs a photon, climbs to a higher energy state and the atom as a whole loses some momentum. A short span of time later, the electron loses the photon in a random direction and drops back to its lower energy state, and the atom’s momentum changes only marginally.

By repeating this series of steps over and over, scientists can use lasers to considerably slow atoms and decrease their temperature as well. For a more detailed description + historical notes (including a short profile of a relatively forgotten Indian scientist who contributed to the development of laser-cooling technologies), read this post.

However, it’s hard to use this technique with most anions – negatively charged ions – because they don’t have a higher energy state per se. Instead, when laser light is shined on the atom, the electron responsible for the excess negative charge absorbs the photon and the atom simply ejects the energised electron.

If the technique is to work, scientists need to find an anion that is bound to its one excess electron (keeping it from being electrically neutral) strongly enough that as the electron acquires more energy, the atom ascends to a higher energy state with it instead of just losing it. Scientists discovered the first such anion in the previous decade – osmium– – and have since added only three more candidates to the list: lanthanum–, cerium– and diatomic carbon (C2–). Lanthanum is and remains the most effective anion coolable with lasers. However, if the results of a study published on November 12 are to be believed, the thorium anion could be the new champion.

Laser-cooling is relatively simpler than most atomic cooling techniques, such as laser-assisted evaporative cooling, and is known to be very effective. Applying it to anions would expand its gamut of applications. There are also techniques like sympathetic cooling, in which one type of laser-cooled anions can cool other types of anions trapped in the same container. This way, for example, physicists think they can produce ultra-cold anti-hydrogen atoms required to study the similarities between matter and antimatter.

The problem with finding a suitable anion is centred on the atom’s electron affinity. It’s the amount of energy an electrically neutral atom gains or loses when it takes on one more electron and becomes an anion. If the atom’s electron affinity is too low, the energy imparted or taken away by the photons could free the electron.

Until recently, theoretical calculations suggested the thorium anion had an electron affinity of around 0.3 eV – too low. However, the new study found based on experiments and calculations that the actual figure could be twice as high, around 0.6 eV, advancing the thorium anion as a new candidate for laser-cooling.

The study’s authors also report other properties that make thorium even more suitable than lanthanum. For example, the atomic nucleus of the sole stable lanthanum isotope has a spin, so as it interacts with the magnetic field produced by the electrons around it, it subtly interferes with the electrons’ energy levels and makes laser-cooling more complicated than it needs to be. Thorium’s only stable isotope has zero nuclear spin, so these complications don’t arise.

There doesn’t seem to be a working proof of the study’s results but it’s only a matter of time before other scientists devise a test because the study itself makes a few concrete predictions. The researchers expect that thorium anions can be cooled with laser light of frequency 2.6 micrometers to a frosty 0.04 microkelvin. They suggest doing this in two steps: first cooling the anions to around 10 kelvin and then cooling a collection of them further by enabling the absorption and emission of about 27,000 photons, tuned to the specified frequency, in a little under three seconds.

Using light to cool sound

Laser light has been used to cool atoms down to near absolute zero. The technique is simple, if versatile. (And includes some history involving a little-known Indian physicist.)

Laser light is shined on an atom that’s made to move towards the source of light. When the atom absorbs a photon, it slows down because of the law of conservation of momentum. The atom then emits the photon from a different direction.

By Newton’s third law, it should then receive a ‘kick’ in the direction opposite to this emission. But because the photons will be emitted in various random directions, their total ‘kick’ will be far smaller than the brakes applied by swallowing photons from just one direction.

By carefully tuning the laser’s frequency and intensity, scientists can ensure that the atom absorbs and emits enough photons to slow down. And when an atom slows down, it simply means – in the language of thermodynamics – that it has cooled down.

This entire process involves a coupling between light and matter, nothing else. The atom absorbs the photons and then spits them out – i.e. the atom interacts with electromagnetic radiation. The resulting drop in temperature is simply the result of the atom losing its kinetic energy. There are no other forms of energy involved.

However, because laser-cooling is such a cool technique, scientists have been curious about whether it could be used to slam the brakes on the kinetic energy of objects other than atoms. In a new study, published November 27, that’s what scientists say they have done (preprint here).

And this time, what they have done might just be cooler: they have used laser to slow down sound waves.

The technique is the same – and equally simple – except for one small change. In the case of atoms, photons mediated the interaction between the laser light and the atom. In the case of sound waves, there is a second mediator: Brillouin scattering.

We know sound in the air is simply a series of blocks of compressed and rarefied air. Another way to describe this is as a wave. The air is less dense in the rarefied parts and more dense in the compressed parts, so the sound is effectively a density wave. When sound passes through a solid, it does so through a similar density wave.

All waves carry some energy (according to the Planck-Einstein relation: E = hv, where h is Planck’s constant and v is the wave’s frequency). For example, the electromagnetic wave carries energy that, at certain frequencies, we call light or heat. The energy carried by a density wave moving through a solid is, at some frequencies, perceived by the human ear as sound.

So when photons from a laser can be used to remove energy from the density wave, it will effectively reduce the energy of the sound waves. We just need to figure out how to create a coupling between the laser photons and the density waves. This isn’t hard because part of the answer is in the language itself.

How do you couple a particle to a wave? You can’t – unless you can describe both of them as waves or both of them as particles. This is possible in physics through the wave-particle duality. You’ll remember from high school that light is both waves and particles. It’s just two different ways to describe the transport of electromagnetic energy.

You can do this with sound as well. It can be described as a density wave or a particle moving through a medium – two ways to describe the transport of acoustic energy. These ‘sound particles’ are called phonons (cf. quasiparticles).

So to cool a sound wave using lasers, you need to couple the laser photons with the phonons. Put another way, one packet of one kind of energy has to transform into a packet of a different kind of energy. The scientists accomplished this by colliding photons and phonons in a waveguide (a fancy term for any medium that’s carrying a wave).

When a photon is scattered off of a phonon, it can either lose some of its energy to the sound particle or gain energy. When the scattering is such that the photon gains energy, the phonon slows down according to the same mechanism at play between photons and an atom – based on the law of conservation of momentum. This interaction is called a Brillouin scattering.

In their experiment, the scientists, from North Arizona University and Yale University, used a silicon waveguide 2.3 cm long and carrying sound waves at 6 GHz. When they shined laser light of frequency close to the infrared part of the EM spectrum, they observed that the waveguide cooled by 30 K due to interactions between the photons and its phonons.

They used other techniques to make sure that this was the case, and that the material didn’t cool in other ways. For example, they measured the duration for which phonons of certain frequencies persisted in the system. For another, the phonons were found to slow down (a.k.a. “cool down” in thermodynamic-speak) only in one direction – the direction in which the laser was incident – and not others.

There are two more ways in which this experiment is interesting.

First, the scientists found that they didn’t have to setup a closed space, typically called an optomechanical cavity, to perform this experiment. Previous experiments involving light-matter coupling have required the use of such cavities to produce amplified effects. In this experiment, the effect was pronounced in an (relatively) open space itself.

Second, the scientists were able to show that they could influence different groups of phonons in the continuum of the solid simply by changing the frequency of laser light being shot at them.

The applications are obvious. Many devices in our lives, from ultra-sensitive instruments studying gravitational waves to machines that are used regularly, carry unnecessary vibrations that interfere with their purposes. The new study suggests that they can all be damped out simply by using lasers tuned to the right frequencies.

Collective spin modes in ultracold atoms

Physicists created a Bose-Einstein condensate of chromium atoms, ensured the atomic spins were each aligned 90º to the condensate’s plane, applied a magnetic field gradient and separated the atoms by a small but relatively significant distance, fired radio pulses at the condensate to get the atoms’ spins to rotate – and then measured the way the atoms were spinning. They found that instead of each atom having its own direction of spin, they all exhibited a collective spin that they tried to maintain!

This is fascinating because such behaviour has previously only been observed in solids in liquids, where atoms are more closely situated, and not in a Bose-Einstein condensate, which is more like a dilute gas. That it has been observed in the latter points to the presence of quantum mechanical phenomena that are reaching across atoms to influence them to behave collectively.

A Bose-Einstein condensate is a group of particles that has been cooled to such a low temperature that each particle behaves like just one kind of particle, the boson. In this state, all of the particles acquire the same quantum numbers and coexist to form a new phase of matter: the condensate.

There are four kinds of quantum numbers for every particle, and each particle can’t have the same set of four numbers as that of another particle in the same system. E.g. all the electrons in an atom have different values for each of these numbers. However, particles called bosons (such as the photon) flout this rule when cooled to a really low temperature, when they form a Bose-Einstein condensate: a system of particles that all have the same four quantum numbers, i.e. occupying the same lowest energy state.

In this state, all the particles in the condensate together behave like a liquid-like fluid while being more similar to a dilute gas. Physically this may sound boring but in quantum mechanics, a Bose-Einstein condensate is known to have unique properties that particles don’t otherwise exhibit.

In the experiment described above, physicists created a Bose-Einstein condensate by cooling approx. 40,000 chromium atoms to 400 nK and then confining them using an optical trap. While atoms aren’t exactly particles, and are instead imagined to be composed of them, the Stern-Gerlach experiment showed in 1922 that atomic-scale systems, including atoms, do exhibit quantum mechanical properties as a whole.

The chromium atoms’ spins – for simplicity’s sake imagined to be the atoms’ individual orientation – were aligned perpendicular to the axis of the rugby-ball-shaped Bose-Einstein condensate. Next, using a technique similar to the Stern-Gerlach experiment, the physicists applied a graded, i.e. uneven, magnetic field along the plane of the condensate. This caused each atom’s spin to become coupled with – or affected by – those of its neighbours such that all the atoms were encouraged to have the same alignment (keeping the condensate in its ground state). The graded magnetic field also caused the atoms to move apart slightly. Finally, radio pulses were fired at the atoms such that they produced a torque that caused the atoms to spin, i.e. change their orientation.

When the spins fall out of alignment, the spin coupling should also fall out of alignment, and the atoms would all become aligned differently. … at least this is what the physicists thought would happen. It didn’t. The atoms were found to be reorienting under the radio pulses’ assault in a spin wave. It was if each atom’s spin was holding the hands of the two spins on either side of it and refusing to let go, causing the atoms to move together.

In this video, looking upon the surface of the liquid is akin to looking upon a sea of atoms in the condensate. Imagine you were looking at the waterbody edge on. The ripples would be the atomic spins bobbing up and down because of the radio pulses, which would be the metaphorical stones thrown in the water. According to the physicists, when the magnetic field’s gradient is smaller, the shape of the bobbing motion – a.k.a. the spin wave – would more look like the graph below:

Graphical representation of a damped oscillation. Source: Quora

This is the first time such a phenomenon has been observed in a Bose-Einstein condensate and more so in a dilute gas. In their effort to understand what could be causing this so-called collective spin mode, the physicists also found some interesting connections. As they write in their preprint paper:

Although complex oscillatory behaviours are obtained when b [the magnetic field gradient] is large, at low gradients we observe a rather simple damped oscillatory behaviour for both the population dynamics and the separation [between atoms], … The amplitude of oscillation also depends on b, and vanishes for b → 0. … These observations indicate that the interaction with magnetic field gradients has excited a collective mode which couples the [condensate’s] spin degrees of freedom to [its] spatial degrees of freedom. (emphasis mine)

Even more interestingly, according to the physicists, the condensate under these specially engineered circumstances behaved like a ferrofluid, a type of fluid that, in the words of Physics World, “becomes strongly magnetised when placed in a magnetic field”. They realised this was the case because they found that they could predict the condensate’s behaviour using the rules of ferrofluid hydrodynamics.

Remembering S. Pancharatnam

Scientists have combined one atom of sodium (Na) and one of caesium (Cs) to form one molecule of NaCs, achieving the most precisely controlled chemical reaction in history. They were able to achieve this using a fascinating bit of technology called a magneto-optical trap. While the trap itself has a sophisticated design, its essential modus operandus is founded on a deceptively simple technique called Doppler cooling.

If a laser is shined on an atom that is moving towards the source of light, then the atom will absorb a photon (due to the Doppler effect). Because of the conservation of momentum, the atom ‘acquires’ the photon’s momentum as well, and its own momentum drops. The laser is tuned such that its frequency imparts the atom with a photon that kicks one electron to a higher energy state. When the electron drops back down to its original state, it emits the photon, and the atom spits it out.

The emitted photon’s recoil gives the atom another momentum ‘kick’ (a la Newton’s third law), but because it happens in a random direction, the atom has been effectively slowed in the direction it was originally moving in. By repeating this process over and over, an atom can be slowed down considerably (from hundreds of metres per second to a few centimetres per second), dragging its kinetic energy down as well in the process.

Since the kinetic energy of a set of atoms defines the temperature of the group, this Doppler cooling can effectively cool atoms down. The technique is most suited for atoms that have a simple electronic structure – where, for example, the electrons don’t have more than two possible states to be in: ground state and one excited state. However, most atoms do exhibit such hyperfine structure, limiting the applications of Doppler cooling. Additionally, there is also a Doppler cooling limit when the technique is applied because the atom’s kinetic energy can’t be lowered below the recoil temperature imparted by the departing photon.

One alternative is called Sisyphus cooling. Instead of constantly removing the kinetic energy of an atom, Sisyphus cooling uses a combination of lasers to create a jagged potential gradient such that an atom in motion is forced to from a region of lower potential to one that is higher.

Imagine this ‘jag’ as a series of mountains. The atom moves up the first mountain, in the process of which its kinetic energy is converted to potential energy. At the summit, an optical pump – a technique similar to Doppler cooling – removes this potential energy, dropping the atom to a state with lower energy than it had before climbing the mountain. And because the atom is still in motion, it begins to climb the second mountain, after which it is left with even lower energy.

Once the atom has crossed a series of mountains, successive conversions of kinetic to potential energy, and successive pump-outs of this potential energy, leave it with very little energy to call its own. In short, it has been cooled to a sub-Doppler temperature. The title of ‘Sisyphus’ is self-explanatory at this point: like the Greek king cursed to roll a boulder uphill only for it to roll back down as he neared the peak, the atom is also forced to climb uphill only for the optical pump to send it back down each time.

Interestingly, Claude Cohen-Tannoudji, the French physicist who devised Sisyphus cooling and won a piece of the physics Nobel Prize in 1997 for it, published a paper in Current Science on the subject in 1994. This issue of Current Science was dedicated to the work of Shivaramakrishnan Pancharatnam, a physicist noted for his work in optics. The foreword, penned by George William Series, with whom Pancharatnam worked from 1964 at St Catherine’s College, Oxford, until he died in 1969, states,

[He] made some outstanding contributions to optics, first, in the fifties, in the area of polarisation and coherence phenomena in the classical regime, and then, in the sixties, in the study of atoms simultaneously interacting with resonant radiation and low frequency magnetic fields. His work in the latter area drew international attention before it was cut short by his early death at the age of thirty-five. … But it is fair to say that his work received renewed attention and acclaim only after the recognition, in the eighties, that he had derived and used the concept of geometric phases in his studies of the interference of polarised light.

Cohen-Tannoudji acknowledges Pancharatnam’s research as part of the foundation on which more advanced cooling/trapping techniques, like the Sisyphus, rest. From his paper,

All Pancharathnam’s works were done at a time where the only light sources available for optical pumping experiments were spectral lamps, excited by DC or microwave discharges and emitting a light with a broad spectral width and a weak intensity. The spectacular development of unable laser sources, which started in the early seventies, stimulated several experimental and theoretical studies. … A new research field, called laser cooling and trapping of atoms, has appeared and is expanding very rapidly. … In this special issue dedicated to the memory of S. Pancharathnam, I would like to briefly describe two examples of recent developments which, I am sure, would have pleased him, because they use concepts which were quite familiar to him.

Pancharatnam’s doctoral adviser was C.V. Raman, at the Raman Research Institute. He is most well known for independently discovering the geometric phase in the study of waves in 1956.

All waves can be described by their phase and amplitude. When the values of both parameters are changed at the same time and in slow-motion, one can observe the wave evolving through different states. In some cases, when the phase and amplitude are cycled through a series of values and brought back to their original, the wave looks different from what it did at the start. The effective shift in phase is calling the geometric phase.

The British physicist Michael Berry was able to provide a generalised description of the geometric phase in 1986, and it has since been commonly known as the Berry phase. He, too, had published an article in that issue of Current Science, in which he acknowledges that he couldn’t properly appreciate the relevance of Pancharatnam’s paper on the geometric phase until he visited Sivaraj Ramaseshan in Bangalore in 1987. Berry’s article concludes thus:

Now, as we remember Pancharatnam’s untimely death in his creative prime, and celebrate his youthful achievements, it is time to look again through all his work. Who knows what further delicious physics this will reveal?

Delicious indeed. Modern science – such as one that can guide two atoms, manoeuvred one by one, step by step, to strike a chemical bond under the watchful gaze of physicists trying to build better quantum computers – stands on the shoulders of many giants. One of them was Pancharatnam.