Attosecond STM: Filming an Electron Mid-Jump

10⁰ sour world

The film nobody could shoot

Electrons are both the smallest and the fastest actors in chemistry — and that combination has kept them off camera.

Every chemical bond that forms, every current that flows, every solar cell that absorbs a photon — the action is carried by electrons. But an electron isn't a little ball. It's a wave packet: a small cloud of quantum probability, typically the size of an atom, that moves and reshapes itself in attoseconds.

To film something, your camera has to beat it in both dimensions at once: a fine enough sensor to resolve where it is, and a fast enough shutter to freeze when. For electrons that means ångström resolution (10⁻¹⁰ m) and attosecond resolution (10⁻¹⁸ s) — simultaneously. Physicists call this the space-time limit. Microscopes that see atoms are far too slow; laser techniques that see attoseconds average over millions of atoms. Until this paper, no instrument had both.

Heisenberg's uncertainty principle makes the problem worse in a beautiful way: the more tightly you pin an electron down in space, the broader the spread of speeds it carries — so a compact electron cloud starts smearing itself out within attoseconds of being confined. Watching one demands entering its own reference frame of size and speed.

10⁻¹⁸ sthe attosecond

How short is an attosecond?

A guided descent through twelve orders of magnitude — tap the stops, or let it run.

Here's the vertigo-inducing comparison: one attosecond is to one second roughly what one second is to twice the age of the universe. The electron bursts in this paper last 988 of them.

κ ≈ 1quantum regime

Tunnelling: the quantum escape act

The star phenomenon of this paper, running live below — a real Schrödinger-equation simulation, computed in your browser.

Put a wall in front of a ball and the ball bounces back. Put an energy barrier in front of an electron and something stranger happens: because the electron is a wave of probability, a faint tail of that wave leaks through the barrier. Sometimes — with small but real probability — the electron simply materializes on the far side. That's quantum tunnelling. It's how this microscope senses atoms, and it's the event this paper clocks with attosecond precision.

The animation below solves the same equation the authors used for Figure 1 of the paper (the time-dependent Schrödinger equation — they used the Crank–Nicolson method; your browser is running a split-operator version). A wave packet (the glowing cloud) sits next to a barrier (the pale wall). An oscillating light field periodically tilts the landscape — exactly the paper's mechanism — and with each tilt, part of the cloud spills through.

live simulation · Schrödinger equation

Light-field strength 0.9×

Purple cloud: electron probability |ψ|². Pale wall: the energy barrier. Red curve: the oscillating light field tilting the potential. Set the field to zero and the leak almost stops — turn it up and watch the cloud pour through with every cycle.

The paper operates at a special crossover called κ ≈ 1 (the Keldysh parameter). At κ ≫ 1 electrons absorb photons and hop over the barrier; at κ ≪ 1 the field tilts the barrier so hard they slide through it. At κ ≈ 1 both happen at once: the electron grabs a photon or two, rises to a puffier, more extended state facing a thinner barrier — and the field shoves it across. This hybrid, "photon-assisted lightwave tunnelling," is the paper's central physics.

10⁻¹⁰ mthe ångström

A microscope that feels atoms

The scanning tunnelling microscope: half of the marriage this paper performs.

A scanning tunnelling microscope (STM) doesn't use lenses. It drags a metal needle — sharpened until its tip is a single atom — across a surface at a distance of a few ångströms. Electrons tunnel across the vacuum gap between tip and surface, forming a tiny current. That current is fantastically sensitive to distance: it grows roughly tenfold for every ångström the tip approaches. Track the current while scanning, and atomic bumps appear like braille under a fingertip.

The catch: an STM is atomically sharp in space but hopelessly slow in time — its current amplifier hears nothing faster than about a millisecond. Ultrafast laser physics has the opposite problem: attosecond shutters, but focused light can never be squeezed smaller than roughly half its wavelength — about a micrometre, ten thousand atoms wide. This paper welds the two together: the light doesn't need to be small, because it merely powers the junction — the single sharp atom of the tip does the pointing. The light field itself becomes an ultrafast voltage: its oscillating electric field biases the junction for one half-swing at a time.

~5 Kjunction temperature (−268 °C)

<2·10⁻¹⁰ mbarvacuum — quieter than deep space

80 MHzlaser shots per second

4.3 µmfocal spot on a single-atom tip

10⁻¹⁵ sthe femtosecond

Sculpting a single beat of light

The experiment's control panel, rebuilt for you: two lasers, one delay knob, one phase switch.

Ordinary laser pulses contain many wiggles of the light field. The Regensburg team needed the opposite: a waveform with essentially one dominant crest — a single beat — so that tunnelling fires once, not ten times. They built it by overlapping two infrared pulses of different colours (centred at 164 THz and 249 THz) and tuning two knobs, which you now hold:

τ (tau) — the delay between the two pulses. φ_CE — the carrier-envelope phase, which decides where the crests sit under the pulse envelope: at φ_CE = 0 the strongest crest points one way; at φ_CE = π it flips upside down — and with it, the direction electrons are pushed.

interactive · waveform synthesis

Delay τ 0.0 fs Phase φ_CE

Top: the two pulses (purple 164 THz, orange 249 THz). Bottom: their sum — the waveform that actually hits the junction. At τ = 0 they fuse into a single-cycle transient of 5.2 fs; the marker tracks its strongest crest. Drag τ and watch the waveform breathe; flip φ_CE and the crest inverts. The animation sweeps τ on its own until you take the slider.

A subtlety that makes the whole experiment trustworthy: the two colours share no frequencies, so they cannot interfere — the average power arriving at the junction stays perfectly flat while τ changes. Any current that does wiggle with the waveform must therefore come from genuine sub-cycle physics, not from heating. This artifact-proofing is one of the paper's quiet innovations.

917 Hzthe secret handshake

Hearing one electron in a storm

The attosecond signal is a whisper buried in noise. The trick to extracting it is beautifully simple.

Here's the problem: the currents that carry the attosecond information are a small ripple on top of a much larger, noisy background — thermal drifts, ordinary DC tunnelling, amplifier hiss. The team's solution: flip the phase switch φ_CE between 0 and π, 917 times per second. Each flip reverses the push on the electrons. Only the genuinely light-driven part of the current flips along in perfect rhythm; every source of noise ignores the beat. A "lock-in" amplifier then listens for exactly that rhythm — like picking out a friend in a roaring crowd because they're clapping to a beat only you two know.

animation · lock-in detection

Top: the raw measured current — noise plus a hidden component. The badge shows the phase flipping 0 ↔ π (slowed down about 400× so you can see it). Bottom: what survives when you keep only the part that dances to the flip — the attosecond current, I_CEO.

988 asthe flash

What they caught

A current that switches on and off again in under a femtosecond.

With the waveform sculpted and the lock-in listening, a clean, stable signal emerged — and its shape told the story. As the delay τ was scanned, the current I_CEO showed structure changing on sub-femtosecond scales, and its strength grew steeply — nonlinearly — with pulse energy, the fingerprint of field-driven tunnelling. The team's quantum simulations, run atom-by-atom, reproduced the measured curves and revealed the current pulse itself:

reconstruction · the tunnelling burst

The single-cycle light field (red) swings the junction; charge crosses in one burst (glowing spike): 988 attoseconds wide at half maximum — the simulated transient behind the measured signal (paper, Fig. 3a). One dominant crest → one burst. That is the "shutter" of this camera.

Four pulse energies were tested — 171, 93, 55 and 36 picojoules — and the signal scaled up steeply while keeping its shape, exactly as sub-cycle tunnelling should. Even the phase of the current carried physics: it advanced in step-like jumps as τ scanned across the waveform's crest changes.

10⁻⁶ a.u.the theory movie

The supercomputer's slow-motion replay

311 atoms, full quantum mechanics: how an electron cloud actually crosses the gap.

To see what the measurement couldn't show directly, the team simulated the whole junction with time-dependent density functional theory: a pyramid of 55 atoms for the tip, a 256-atom slab for the surface, every electron treated quantum mechanically while the light wave washes over. The replay below is a stylized re-creation of those four published snapshots (paper, Fig. 3b) — watch the charge cloud shake, swell, and finally bridge the vacuum gap:

re-creation · TD-DFT charge dynamics

Δρ — the change in electron density — between tip (top) and surface (bottom) as the field swings. At −24 fs: faint stirrings. Around −2 fs to +0.5 fs: a violent shake-up as the field alternates. At +2.0 fs: the cloud spans the gap — the electron is crossing. Times auto-loop; the red trace shows where the light field is in its swing.

The simulations settled a key question: the electrons don't just slide through the ground-state barrier. They first absorb one or two photons, rising into excited states that physically bulge further out from tip and surface — and face a thinner, lower barrier. This is why the crossover regime matters: the photon absorption and the field-push happen within the same half-cycle of light.

8.7 Åthe packet's size

Measuring the electron's reach

Pull the tip back, watch the attosecond current die away — the decay length is the wave packet's size.

Because the tip can be positioned with sub-ångström precision, the team could do something unprecedented: measure the spatial extent of the tunnelling wave packet itself. Retract the tip step by step and record how fast the attosecond current fades:

measurement · vertical decay

Everyday (DC) tunnelling current dies with a decay length of ~1 Å — the tightest curve. The attosecond current at high pulse energy stretches to 8.7 Å: the light-driven electrons occupy visibly fatter, excited-state wavefunctions. Turn the pulse energy down and the packet tightens below 5 Å — the electron cloud is tunable.

Read that again: they didn't infer the wave packet's size from a model — they dragged a needle through it and measured where it ends. Confinement: under 1 femtosecond in time, a few ångströms in space. That is the space-time limit, reached.

32×32the portrait

Photographing one atom with attosecond flashes

The proof that it all works: a picture of a single copper atom, taken with sub-femtosecond electron bursts.

For the finale, the team dropped single copper atoms onto the silver surface, parked the tip above one, switched off the ordinary imaging current — and rastered across it recording only the attosecond current, pixel by pixel, 32 × 32. The animation below rebuilds that scan:

re-creation · attosecond-current image

Left: the scan assembling line by line — each pixel is the attosecond tunnelling current at that position (stylized; the paper's real map is Fig. 4b). Right: the height profile through the atom's centre. The copper adatom appears with the same atomic sharpness as a conventional STM image — attosecond time resolution costs no spatial resolution.

An image of a single atom, drawn by electrons that each existed as a travelling wave for less than a millionth of a billionth of a second. That sentence is the paper.

t → ∞what's next

Why this matters

A camera for the quantum world's fastest, smallest events.

Chemistry is electrons rearranging. Until now, science could watch atoms move (femtosecond chemistry earned a Nobel Prize in 1999) and could clock electrons in gases (attosecond physics earned one in 2023) — but never both at once, at a chosen single atom. Attosecond lightwave STM opens exactly that: filming a chemical bond as it forms or breaks, watching charge slosh through a single molecule, probing the quantum behaviour of tomorrow's smallest transistors — one atom, one electron, one attosecond at a time.

The authors list what they want to point the camera at next: exotic states of atoms held in intense light, signatures of quantum chaos, barriers that turn momentarily transparent, and the spatio-temporal choreography of bonds being made and broken.