How do you study a laser firing for one-quadrillionth of a second?

I’m grateful to Mukund Thattai, at the National Centre for Biological Sciences, Bengaluru, for explaining many of the basic concepts at work in the following article.

An important application of lasers today is in the form of extremely short-lived laser pulses used to illuminate extremely short-lived events that often play out across extremely short distances. The liberal use of ‘extreme’ here is justified: these pulses last for no more than one-quadrillionth of a second each. By the time you blink your eye once, 100 trillion of these pulses could have been fired. Some of the more advanced applications even require pulses that last 1,000-times shorter.

In fact, thanks to advances in laser physics, there are branches of study today called attophysics and femtochemistry that employ such fleeting pulses to reveal hidden phenomena that many of the most powerful detectors may be too slow to catch. The atto- prefix denotes an order of magnitude of -18. That is, one attosecond is 1 x 10-18 seconds and one attometer is 1 x 10-18 metres. To quote from this technical article, “One attosecond compares to one second in the way one second compares to the age of the universe. The timescale is so short that light in vacuum … travels only about 3 nanometers during 1 attosecond.”

One of the more common applications is in the form of the pump-probe technique. An ultra-fast laser pulse is first fired at, say, a group of atoms, which causes the atoms to move in an interesting way. This is the pump. Within fractions of a second, a similarly short ‘probe’ laser is fired at the atoms to discern their positions. By repeating this process many times over, and fine-tuning the delay between the pump and probe shots, researchers can figure out exactly how the atoms responded across very short timescales.

In this application and others like it, the pulses have to be fired at controllable intervals and to deliver very predictable amounts of energy. The devices that generate these pulses often provide these features, but it is often necessary to independently study the pulses and fine-tune them according to different applications’ needs. This post discusses one such way and how physicists improved on it.

As electromagnetic radiation, every laser pulse is composed of an electric field and a magnetic field oscillating perpendicular to each other. Of these, consider the electric field (only because it’s easier to study; thanks to Maxwell’s equations, what we learn about the electric field can be inferred accordingly for the magnetic field as well):

Credit: Peter Baum & Stefan Lochbrunner, LMU München Fakultät für Physik, 2002

The blue line depicts the oscillating electric wave, also called the carrier wave (because it carries the energy). The dotted line around it depicts the wave’s envelope. It’s desirable to have the carrier’s crest and the envelope’s crest coincide – i.e. for the carrier wave to peak at the same point the envelope as a whole peaks. However, trains of laser pulses, generated for various applications, typically drift: the crest of every subsequent carrier wave is slightly more out of step with the envelope’s crest. According to one paper, it arises “due to fluctuations of dispersion, caused by changes in path length, and pump energy experienced by consecutive pulses in a pulse train.” In effect, the researcher can’t know the exact amount of energy contained in each pulse, and how that may affect the target.

The extent to which the carrier wave and the envelope are out of step is expressed in terms of the carrier-envelope offset (CEO) phase, measured in degrees (or radians). Knowing the CEO phase is crucial for experiments that involve ultra-precise measurements because the phase is likely to affect the measurements in question, and needs to be adjusted for. According to the same paper, “Fluctuations in the [CEO phase] translate into variations in the electric field that hamper shot-to-shot reproducibility of the experimental conditions and deteriorate the temporal resolution.”

Ignore all the symbols and notice the carrier wave – especially how its peak within the envelope shifts with every next pulse. The offset between the two peaks is called the carrier-envelope offset phase. Credit: HartmutG/Wikimedia Commons, CC BY-SA 3.0

This is why, in turn, physicists have developed techniques to measure the CEO phase and other properties of propagating waves. One of them is called attosecond streaking. Physicists stick a gas of atoms in a container, fire a laser at it to ionise them and release electrons. The field to be studied is then fired into this gas, so its electric-wave component pushes on these electrons. Specifically, as the electric field’s waves rise and fall, they accelerate the electrons to different extents over time, giving rise to streaks of motion – and the technique’s name. A time-of-flight spectrometer measures this streaking to determine the field’s properties. (The magnetic field also affects the electrons, but it suffices to focus on the electric field for this post.)

This sounds straightforward but the setup is cumbersome: the study needs to be conducted in a vacuum and electron time-of-flight spectrometers are expensive. But while there are other ways to measure the wave properties of extreme fields, attosecond streaking has been one of the most successful (in one instance, it was used to measure the CEO phase at a shot frequency of 400,000 times per second).

As a workaround, physicists from Germany and Canada recently reported in the journal Optica a simpler way, based on one change. Instead of setting up a time-of-flight spectrometer, they propose using the pushed electrons to induce an electric current in electrodes, in such a way that the properties of the current contain information about the CEO phase. This way, researchers can drop both the spectrometer and, because the electrons aren’t being investigated directly, the vacuum chamber.

The researchers used fused silica, a material with a wide band-gap, for the electrodes. The band-gap is the amount of energy a material’s electrons need to be imparted so they can ‘jump’ from the valence band to the conduction band, turning the material into a conductor. The band-gap in metals is zero: if you placed a metallic object in an electric field, it will develop an internal current linearly proportional to the field strength. Semiconductors have a small band-gap, which means some electric fields can give rise to a current while others can’t – a feature that modern electronics exploit very well.

Dielectric materials have a (relatively) large band-gap. When it is exposed to a low electric field, a dielectric won’t conduct electricity but its internal arrangement of positive and negative charges will move slightly, creating a minor internal electric field. But when the field strength crosses a particular threshold, the material will ‘break down’ and become a conductor – like a bolt of lightning piercing the air.

Next, the team circularly polarised the laser pulse to be studied. Polarisation refers to the electric field’s orientation in space, and the effect of circular polarisation is to cause the electric field to rotate. And as the field moves forward, its path traces a spiral, like so:

A circularly polarised electric field. Credit: Dave3457/Wikimedia Commons

The reason for doing this, according to the team’s paper, is that when the circularly polarised laser pulse knocks electrons out of atoms, the electrons’ momentum is “perpendicular to the direction of the maximum electric field”. So as the CEO phase changes, the electrons’ directions of drift also change. The team used an arrangement of three electrodes, connected to each other in two circuits (see diagram below) such that the electrons flowing in different directions induce currents of proportionately different strengths in the two arms. Amplifiers attached to the electrodes then magnify these currents and open them up for further analysis. Since the envelope’s peak, or maximum, can be determined beforehand as well as doesn’t drift over time, the CEO phase can be calculated straightforwardly.

(The experimental setup, shown below, is a bit different: since the team had to check if their method works, they deliberately insert a CEO phase in the pulse and check if the setup picks up on it.)

The two tips of the triangular electrodes are located 60 µm apart, on the same plane, and the horizontal electrode is 90 µm below the plane. The beam moves from the red doodle to the mirror, and then towards the electrodes. The two wedges are used to create the ‘artificial’ CEO phase. Source: https://doi.org/10.1364/OPTICA.7.000035

The team writes towards the end of the paper, “The most important asset of the new technique, besides its striking simplicity, is its potential for single-shot [CEO phase] measurements at much higher repetition rates than achievable with today’s techniques.” It attributes this feat to attosecond streaking being limited by the ability of the time-of-flight spectrometer whereas its setup is limited, in the kHz range, only by the time the amplifiers need to boost the electric signals, and in the “multi-MHz” range by the ability of the volume of gas being struck to respond sufficiently rapidly to the laser pulses. The team also states that its electrode-mediated measurement method renders the setup favourable to radiation of longer wavelengths as well.

Featured image: A collection of lasers of different frequencies in the visible-light range. Credit: 彭嘉傑/Wikimedia Commons, CC BY 2.5 Generic.

A gear-train for particle physics

Clockwork theory has been revived and reformulated by scientists from CERN to solve a difficult problem at the heart of particle physics.

It has come under scrutiny at various times by multiple prominent physicists and thinkers, but it’s not hard to see why, when the idea of ‘grand unification’ first set out, it seemed plausible to so many. The first time it was seriously considered was about four decades ago, shortly after physicists had realised that two of the four fundamental forces of nature were in fact a single unified force if you ramped up the energy at which it acted. (electromagnetic + weak = electroweak). The thought that followed was simply logical: what if, at some extremely high energy (like what was in the Big Bang), all four forces unified into one? This was 1974.

There has been no direct evidence of such grand unification yet. Physicists don’t know how the electroweak force will unify with the strong nuclear force – let alone gravity, a problem that actually birthed one of the most powerful mathematical tools in an attempt to solve it. Nonetheless, they think they know the energy at which such grand unification should occur if it does: the Planck scale, around 1019 GeV. This is about as much energy as is contained in a few litres of petrol, but it’s stupefyingly large when you have to accommodate all of it in a particle that’s 10-15 metres wide.

This is where particle accelerators come in. The most powerful of them, the Large Hadron Collider (LHC), uses powerful magnetic fields to accelerate protons to close to light-speed, when their energy approaches about 7,000 GeV. But the Planck energy is still 10 million billion orders of magnitude higher, which means it’s not something we might ever be able to attain on Earth. Nonetheless, physicists’ theories show that that’s where all of our physical laws should be created, where the commandments by which all that exists does should be written.

… Or is it?

There are many outstanding problems in particle physics, and physicists are desperate for a solution. They have to find something wrong with what they’ve already done, something new or a way to reinterpret what they already know. The clockwork theory is of the third kind – and its reinterpretation begins by asking physicists to dump the idea that new physics is born only at the Planck scale. So, for example, it suggests that the effects of quantum gravity (a quantum-mechanical description of gravity) needn’t necessarily become apparent only at the Planck scale but at a lower energy itself. But even if it then goes on to solve some problems, the theory threatens to present a new one. Consider: If it’s true that new physics isn’t born at the highest energy possible, then wouldn’t the choice of any energy lower than that just be arbitrary? And if nothing else, nature is not arbitrary.

To its credit, clockwork sidesteps this issue by simply not trying to find ‘special’ energies at which ‘important’ things happen. Its basic premise is that the forces of nature are like a set of interlocking gears moving against each other, transmitting energy – rather potential – from one wheel to the next, magnifying or diminishing the way fundamental particles behave in different contexts. Its supporters at CERN and elsewhere think it can be used to explain some annoying gaps between theory and experiment in particle physics, particularly the naturalness problem.

Before the Higgs boson was discovered, physicists predicted based on the properties of other particles and forces that its mass would be very high. But when the boson’s discovery was confirmed at CERN in January 2013, its mass implied that the universe would have to be “the size of a football” – which is clearly not the case. So why is the Higgs boson’s mass so low, so unnaturally low? Scientists have fronted many new theories that try to solve this problem but their solutions often require the existence of other, hitherto undiscovered particles.

Clockwork’s solution is a way in which the Higgs boson’s interaction with gravity – rather gravity’s associated energy – is mediated by a string of effects described in quantum field theory that tamp down the boson’s mass. In technical parlance, the boson’s mass becomes ‘screened’. An explanation for this that’s both physical and accurate is hard to draw up because of various abstractions. So as University of Bruxelles physicist Daniele Teresi suggests, imagine this series: Χ = 0.5 × 0.5 × 0.5 × 0.5 × … × 0.5. Even if each step reduces Χ’s value by only a half, it is already an eighth after three steps; after four, a sixteenth. So the effect can get quickly drastic because it’s exponential.

And the theory provides a mathematical toolbox that allows for all this to be achieved without the addition of new particles. This is advantageous because it makes clockwork relatively more elegant than another theory that seeks to solve the naturalness problem, called supersymmetry, SUSY for short. Physicists like SUSY also because it allows for a large energy hierarchy: a distribution of particles and processes at energies between electroweak unification and grand unification, instead of leaving the region bizarrely devoid of action like the Standard Model does. But then SUSY predicts the existence of 17 new particles, none of which have been detected yet.

Even more, as Matthew McCullough, one of clockwork’s developers, showed at an ongoing conference in Italy, its solutions for a stationary particle in four dimensions exhibit conceptual similarities to Maxwell’s equations for an electromagnetic wave in a conductor. The existence of such analogues is reassuring because it recalls nature’s tendency to be guided by common principles in diverse contexts.

This isn’t to say clockwork theory is it. As physicist Ben Allanach has written, it is a “new toy” and physicists are still playing with it to solve different problems. Just that in the event that it has an answer to the naturalness problem – as well as to the question why dark matter doesn’t decay, e.g. – it is notable. But is this enough: to say that clockwork theory mops up the math cleanly in a bunch of problems? How do we make sure that this is how nature works?

McCullough thinks there’s one way, using the LHC. Very simplistically: clockwork theory induces fluctuations in the probabilities with which pairs of high-energy photons are created at some energies at the LHC. These should be visible as wavy squiggles in a plot with energy on the x-axis and events on the y-axis. If these plots can be obtained and analysed, and the results agree with clockwork’s predictions, then we will have confirmed what McCullough calls an “irreducible prediction of clockwork gravity”, the case of using the theory to solve the naturalness problem.

To recap: No free parameters (i.e. no new particles), conceptual elegance and familiarity, and finally a concrete and unique prediction. No wonder Allanach thinks clockwork theory inhabits fertile ground. On the other hand, SUSY’s prospects have been bleak since at least 2013 (if not earlier) – and it is one of the more favoured theories among physicists to explain physics beyond the Standard Model, physics we haven’t observed yet but generally believe exists. At the same time, and it bears reiterating, clockwork theory will also have to face down a host of challenges before it can be declared a definitive success. Tik tok tik tok tik tok