Historical research guide · 1011 · 2018
Attosecond coherent control of free-electron wave functions using semi-infinite light fields
Giovanni Maria Vanacore · Ivan Madan · Gabriele Berruto · K. Wang · Enrico Pomarico · Raymond J. Lamb · Damien McGrouther · Ido Kaminer · Brett Barwick · F. Javier García de Abajo · Fabrizio Carbone
In one minute
A free electron flying through open space cannot simply swallow a photon — energy and momentum do not both balance, so the exchange is forbidden. Giovanni Maria Vanacore, Ivan Madan and their colleagues at Lausanne, Glasgow, the Technion, Ripon College and Barcelona get around that by cutting the light in half. They bounce a laser pulse off a silver mirror thin enough for 200-kiloelectronvolt electrons to pass straight through, so the light exists on one side of the mirror and not the other. That abrupt edge relaxes the bookkeeping, and the electron starts trading whole photons with the beam — more efficiently, they report, than it would with a resonant nanostructure. They then send two mutually phase-locked pulses in, stepping the delay between them by 500 attoseconds at a time, and watch the electron’s energy ladder fill and empty in step with the optical cycle. That is coherent control of a single free electron’s wave function on the attosecond scale, and their theory says X-ray pulses would push the same scheme into zeptoseconds.
Connection
Chapter 10 is about what the structure of a field can do to a particle when no classical force is doing the work, and this is that argument at its sharpest: a mirror edge, not a force, is what lets light and a free electron exchange quanta. Chapter 5 cares because the electron here behaves as a coherent ladder of states that can be driven up and down by phase alone. And the authors close on chapter 12’s territory — a scheme for reaching inside a nucleus with timed electron and X-ray pulses, with energy-related applications named.
From the source
Direct photon absorption or emission by a free-space electron is forbidden by energy-momentum mismatch. Sending the electrons through a light beam that is abruptly interrupted at a mirror creates a semi-infinite field, in which the light wave extends only over half-space; the energy-momentum conservation constraint is then relaxed and electron-photon interaction can take place — with an efficiency exceeding that produced by a resonant plasmonic nanostructure.Introduction, final paragraphs; Results, Free-electron interaction with a semi-infinite light field; Figure 1b
The strength of the interaction is one complex number, an integral of the optical field along the electron path weighted by the electron’s own phase, and the fraction of electrons emerging in the sideband that has exchanged a given net number of photons is the square of the Bessel function of twice its magnitude. Written out for a mirror, that number is finite and depends explicitly on the field amplitude and the tilting geometry.Results, Equations 1, 2 and 3
Energy and transverse momentum are exchanged together and in quanta. Operating the microscope in high-dispersion diffraction mode, the authors see the electron beam streak along one momentum axis when the mirror is tilted, and mapping the beam in the joint momentum-energy plane shows the streak lying along a line whose slope is the transferred transverse momentum divided by the photon energy: for every photon absorption or emission event, the electron gains or loses one quantum of energy and one quantum of transverse momentum.Results, Quantized energy-momentum exchange in electron-photon coupling; Figure 3e to 3g
Two mutually phase-locked light pulses, delayed against one another in steps of 500 attoseconds, drive the electron population coherently up and down its ladder of states spaced by the photon energy. The sideband intensities oscillate with a period of about 2.6 femtoseconds — exactly one optical cycle — and the ninth and fourteenth sidebands oscillate with a well-defined relative phase shift of about pi, which is the signature of a coherent redistribution rather than a simple change in illumination intensity.Results, Attosecond coherent control of an electron wave function; Figure 4a to 4c and Figure 5
The same scheme is designed for X-rays. A mirror of 30 cobalt layers 1.6 nanometres thick spaced by 1-nanometre gold, 78 nanometres in total, stays transparent to 200-kiloelectronvolt electrons while reflecting about 35 percent of 777-electronvolt light at 45 degrees. Simulated with two 100-femtosecond X-ray pulses of the kind free-electron lasers already deliver, the calculation puts sidebands at plus and minus 777 electronvolts, modulated with the 5.3-attosecond X-ray cycle at a rate of about one percent per 511 zeptoseconds — and at a 300-kilohertz repetition rate that is about three electrons per second in a single detector channel, measurable with existing direct-detection cameras.Results, Zeptosecond coherent control of an electron wave function; Figure 7a to 7d
What to watch: the authors propose using this timing control to reach the nucleus. Nuclear excitation by electron capture has been demonstrated experimentally, and they suggest synchronising the carrier of a tuned X-ray pulse with zeptosecond electron pulses to add and remove electrons from an atom in a push-pull fashion while watching the gamma-ray emission change. Their stated motive is that pressure, magnetic field and chemical environment have little or no effect on decay rates — this would be an external parameter that does, with potential implications from fundamental physics to energy-related applications.Results, External control of nuclear excitations; Figure 7e
The way in
https://doi.org/10.1038/s41467-018-05021-xHow to cite it
Giovanni Maria Vanacore, Ivan Madan, Gabriele Berruto, K. Wang, Enrico Pomarico, Raymond J. Lamb, Damien McGrouther, Ido Kaminer, Brett Barwick, F. Javier García de Abajo, Fabrizio Carbone (2018) Attosecond coherent control of free-electron wave functions using semi-infinite light fields doi:10.1038/s41467-018-05021-x