The light-pulse horizon

“According to the general theory of relativity, space without aether is unthinkable; for in such space there (not only) would be no propagation of light … But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time.” Albert Einstein, 1920.

Aether, the pure air breathed by gods, is not much in fashion in laboratories today. Physicists speak instead of the vacuum, in the context of quantum physics, and quantum vacuum fluctuations that fill space that is free from real matter. How light slips through these fluctuations was first studied in the 1930s by Werner Heisenberg, H Euler, W Kockel and Victor Weisskopf, and later by Julian Schwinger. Their work revealed the first “effective” interaction – the new and unexpected scattering of light on light, and of light on the background electromagnetic field. This interaction originates in quantum vacuum fluctuations into electron–positron pairs and makes the electric field unstable to pair production. Thus any macroscopic electric field is metastable because in principle, it can decay into particles.

The critical field strength for this instability, E₀, arises when a potential of V₀ = 2mc²/e = 1 MV (where m is the electron’s mass and e its charge) occurs over the electron’s Compton wavelength – that is, when E₀ = 1.3  ×  10¹⁸ V/m. This leads to vacuum decay into pairs at timescales of less than attoseconds (10^–18 s). The back-reaction of the particles that are produced screens the field source, giving an effective upper limit to the strength of the electric field. However, as the applied external field decreases in strength, its lifespan increases rapidly: for a field strength of E = 5 × 10¹⁶ V/m, the lifespan is similar to the age of the universe so that, for all practical purposes, present-day field configurations are stable.

The Compton wavelength of an electron is one three-millionth of a typical optical wavelength, so vacuum fluctuations do not greatly obstruct the propagation of light. Moreover, as Schwinger showed, a coherent ideal plane light-wave cannot scatter from itself (or be influenced by itself) no matter what the field intensity is. This is the only known form of light to which the vacuum is exactly transparent within the realm of quantum electrodynamics. For non-ideal plane waves, space–time translation-invariance symmetry and quantum coherence only partially protect the propagation of light pulses.

A laser pulse of several kilojoules and just a few wavelengths long is all but a plane wave. Such a pulse pushes apart virtual electrons and positrons, in the near future up to an energy of many giga-electron-volts. If the virtual vacuum waves were to decohere, the light pulse would materialize into pairs. However, by quantum “magic” the deeply perturbed vacuum is restored after the pulse has passed. Thus a single pulse, even though it is not a plane wave, will at present-day intensities slip through the vacuum. Colliding light pulses provide a greater opportunity to interact with the vacuum structure because the magnetic field can be compensated and/or the electric wave-number doubled, thereby enhancing the light–vacuum interaction. Two superposed pulses do not so much interact with each other, but interact together with the fluctuations in the vacuum.

High-intensity pulsed lasers also offer a radical approach to accelerating real particles to high energies. The electromagnetic fields of the laser pulses can be huge: current off-the-shelf, high-power lasers can deliver electric fields as great as 10 GeV/μm (10⁴ TeV/m). Metal will typically break down at fields of less than 100 MeV/m – a natural limit and the current standard for accelerator designs based on RF technology. The much higher fields available using lasers promise ultracompact accelerator technology, although the difficulties should not be underestimated. The shorter wavelengths involved imply far better control and precision than with RF acceleration. What helps to push laser technology ahead is the greater intensity of light that is available in comparison with RF. For this reason, laser-pulse technology is the most significant ingredient of laser acceleration, and great progress can now be achieved on timescales of a year.

This was not always so. Until the mid-1980s, efficient ultrashort pulse-amplification that would preserve the beam quality seemed to be unattainable, considering the damage caused to optical devices. A solution emerged in 1985 with the concept of chirped pulse amplification (CPA), in which a short pulse at an energy level as low as nanojoules is stretched by a large factor in time using dispersive elements, such as a pair of diffraction gratings (figure 1). This is possible because of the large number of Fourier frequencies that form the ultrashort pulse. Each frequency takes a different route and hence a different time to traverse the dispersive element.

Once the pulse has been stretched, the red part of the spectrum is ahead, followed by the blue. The stretching factor can be as large as 10⁶ yet the operation does not significantly change the total pulse energy. Consequently the pulse intensity drops by the same ratio, i.e. 10⁶, implying that the long pulse can be amplified safely, preserving the beam quality and laser components. This concept works so well that in modern CPA systems the pulse is stretched by a factor of 10⁶, amplified by 10¹², then compressed by a factor of 10⁶ back to its initial time structure. A nano- to microjoule primary pulse turns into a pulse of up to kilojoules comprising nearly 10²² photons of (sub)micron wavelength. In a nutshell, this pulse is a table-top particle accelerator. The interaction with matter of light pulses containing joules or even kilojoules of energy (compared with the less than microjoules of the most powerful particle accelerators) generates intense bursts of radiation (figure 2).

Accelerating gradients

Nevertheless, laser particle acceleration has had its ups and downs. As the Woodward–Lawson theorem states, direct plane-wave laser acceleration of particles is not possible – you lose what you win in a perfect wave. However, if the intense pulse is so short that it “resonates” with the innate matter(plasma)-oscillations, a huge accelerating gradient is possible. The energy imparted to the particle in each acceleration step can be directly derived from the wave amplitude of the pulse. The short-pulsed nature of the laser is also of great interest in this acceleration method, as is the possibility of using circularly polarized light.

Particle-acceleration schemes use lasers to generate wake waves in plasma in the relativistic regime for electrons in the optical field. Enrico Fermi once contemplated a 1 PeV (10⁹ MeV) accelerator girdling the Earth; laser acceleration may allow us to reach this energy on the scale of 1 km by employing a subpicosecond 15 MJ laser. The route to this goal would test ultrahigh-gradient acceleration theory at 10 TeV, which could be achievable with a laser of 15 kJ and a 50 fs pulse. Such an intense laser pulse is not yet available, but the proposed European Light Infrastructure (ELI) should offer an opportunity to explore this domain. The peak power of ELI will be in the exawatt (10¹⁸ W) region – that is, 100,000 times the power of the global electricity grid – albeit only over several femtoseconds.

Are there other ways to go from the laser pulse to an intense particle beam? If beam quality is not of great concern, it is possible to exploit the action of the pulse on a foil that is only a fraction of the wavelength thick. At the Trident Laser Facility at Los Alamos National Laboratory, Manuel Hegelich and his team shoot a high-contrast (no preceding light) pulse onto a thin, carbon-diamond nanofoil. Such a pulse is not reflected by the “pre-plasma” formed on the foil but propagates through the foil, where it picks up electrons. The cloud of relativistic, wave-riding electrons generates longitudinal electrical fields, which cause carbon ions to follow electrons, creating two “beams”. At ELI such a pulse–foil interaction could provide a source of high-energy relativistic heavy ions, because the pulse intensity that could be achieved would permit direct acceleration of ions in a relativistic regime (figure 3).

The plasma cloud emerging from the foil could form gamma-ray beams suitable for photonuclear physics. Einstein observed that a relativistic “flying mirror” (in this case the plasma) would “square” the relativistic Doppler effect, leading to a boost of photon energy, ω = 4γ²ω₀, where ω₀ is the original energy and γ the Lorentz factor (figure 4). This effect has been demonstrated, both by using the laser wakefield created on the surface of a solid and by using a relativistically moving plasma of thin foil propelled by the laser beam, from which another laser beam is reflected. It should soon lead to compact coherent X-ray and even gamma-ray light sources. Dietrich Habs and colleagues at the Munich-Centre for Advanced Photonics are pursuing an initial design effort. The gamma rays produced in this way are not only of high energy but also compressed by a factor 1/γ² into an ultrashort pulse. The coherent pulse contains increased electromagnetic fields, so the technology leads to ultrahigh electrical-field strengths where the decay of the vacuum becomes observable.

It appears that coherent reflection of a femtosecond pulse is possible from a flying mirror of dense plasma with γ=10,000 – that is, from an electron cloud moving with an energy of 5 GeV. The resulting 400 MeV photon pulse would also be compressed from femtoseconds to 10^–23 s. Such a pulse could, in principle, be focused into a femtometre-scale volume, the size of a nucleon. On such a small distance scale, 10 kJ would be enough to reach temperatures in the 150 GeV range, which should allow the study of the melting of the vacuum structure of the Higgs field and the electroweak phase transition. Clearly this is on the far horizon, but there are other distance/temperature scales of interest on the journey there. Such a system would allow studies of electromagnetic plasma at megaelectron-volt temperatures and exploration of the quark–gluon plasma on a space–time scale at least 1000 times as great as can currently be achieved. This would be truly recreating a macroscopic domain of the early universe in the laboratory.

Another fundamentally important aspect of the science possible with the extremely high fields in lasers concerns the immense acceleration, a, that electrons experience in the electromagnetic field of the pulses (e.g. up to a = 10³⁰ cm/s² for an electron in ELI). According to the equivalence principle, this corresponds to an equivalent external gravitation. The effect for the accelerated electron is that the distance, d = c²/a, to this event horizon becomes as short as the electron’s Compton wavelength, in which limit experiments can probe the behaviour of quantum particles in the realm of strong gravity. Work is under way to demonstrate Unruh radiation, a cousin of Hawking radiation. (Hawking radiation is thermal radiation in strong gravity, while Unruh radiation arises in the presence of strong acceleration.) Such experiments would allow the study of the extent and validity of the special and general theories of relativity, as well as test the equivalence principle in the quantum regime.

To conclude, high-intensity pulsed lasers, and in particular the proposed ELI facility, offer a novel approach to particle acceleration and widen the range of fundamental physics questions that can be studied (Mourou et al. 2006). Light pulses will be able to produce synchronized high-energy radiation and pulses of elementary particles with extremely short time structures – below the level of attoseconds. These unique characteristics, which are unattainable by any other means, could be combined to offer a new paradigm for the exploration of the structure of the vacuum and fundamental interactions. Ultra-intense light pulses will also address original fundamental questions, such as how light can propagate in a vacuum and how the vacuum can define the speed of light. By extension it will also touch on the question of how the vacuum can define the mass of all elementary particles. The unique features of ELI – its high field-strength, high energy, ultrashort time structure and impeccable synchronization – herald the entry of pulsed high-intensity lasers into high-energy physics. This is a new scientific tool with a discovery potential akin to what lay on the horizon of conventional accelerator technology in the mid-20th century.