Research · Computational physics

Ultrafast electron dynamics

A simulation lab for the fastest motion in chemistry: electrons moving through a molecule in the first femtoseconds after a laser pulse strikes it. Built to run on graphics cards and to be differentiable from end to end, so that the pulse itself can be designed to steer where the charge goes.

Discuss a collaboration What it measures

DisciplineComputational physics

IssuePublic extract

AccessBy collaboration

The question

Charge moves before atoms do.

When an ultrashort pulse pulls an electron out of a molecule, the positive charge it leaves behind does not sit still. It can travel from one end of the molecule to the other within a few femtoseconds, long before any nucleus has moved. That motion decides where a molecule will break and what it will become. Seeing it, predicting it and steering it is one of the open problems of ultrafast science, and it is first a simulation problem of unusual difficulty.

Faster than chemistry

The electrons move on attosecond timescales, so the simulation has to resolve a field that changes many times within a single femtosecond, for as long as the motion lasts.

Electrons that leave

Some of the electron density escapes the molecule entirely. The calculation has to follow it into open space and still account for what it leaves behind.

Steerable by light

Because the motion starts from a pulse, a well-shaped pulse can push it one way or another. Finding that shape is an optimization problem on top of the physics.

The physics engine

Many electrons, open space and a field that changes faster than chemistry, in one calculation.

E-1

Many-electron states from first principles

The molecule's electronic states and the couplings between them are computed from first principles and kept in graphics-card memory, rather than handed between separate programs through files.

E-2

The space around the molecule

An electron that leaves is followed on a spatial grid that is fine near the nuclei and coarse far away, coupled to the bound states, so that ionization belongs to the same calculation as the motion it starts.

E-3

Open boundaries in a finite box

Absorbing edges remove outgoing density smoothly, so that a finite domain behaves like open space and nothing reflects back into the molecule.

E-4

Time steps that conserve probability

High-order time-steppers built so that every step preserves the total probability, at the time resolution the field demands rather than the one that is convenient.

E-5

Coherence made explicit

The state is evolved as a density matrix, so the coherence that drives charge migration, and its loss, are quantities the model carries rather than assumptions it makes.

E-6

Laser fields as code

Single pulses and trains of pulses, with ramps, delays and polarization in three dimensions. The electric field is derived consistently from its potential, and every parameter can be learned.

What it measures

The quantities an experiment records, computed from the same state.

FIG. 1Illustration of charge migration. A short pulse (top left) removes an electron; the positive charge left behind moves back and forth across the molecule, shown in snapshots and as the charge on each of its three heavy atoms over time. A later, weaker pulse (top right) probes it. Drawn from a toy model for illustration.

O-1

The dipole over time

How the molecule's charge distribution responds to the field, moment by moment: the signal that radiates and that experiments detect.

O-2

Charge density in three dimensions

The change in electron density on a three-dimensional grid around the molecule, at every step of the simulation.

O-3

Charge on each atom

A smooth partition of space assigns density to each atom without hard boundaries, so that charge on individual atoms can be followed through time.

O-4

Absorption spectra

Pump-probe absorption spectra computed from the dipole response, as a function of the delay between the pulses: the measurement used to watch charge migration in the laboratory.

O-5

Movies and dashboards

Synchronized movies of density evolving against the field, and multi-panel dashboards that put geometry, density, atomic charges and the field on one timeline.

Steering with light

Design the pulse by asking what it should do.

FIG. 2Every stage is written in one differentiable framework, so the gradient of an objective measured at the end flows back through the time evolution to the parameters of the pulse.

C-1

Differentiable from field to observable

Fields, time evolution and observables are written in one framework with automatic differentiation, so the effect of every pulse parameter on the result is computed, not guessed.

C-2

Objectives that mean something

Reach a chosen target state, maximize how much is ionized, or localize the charge on a chosen atom at a chosen moment.

C-3

Gradients over long simulations

Long, finely resolved pulses are practical to optimize only when the memory a gradient needs does not grow with the length of the simulation. That constraint shapes how the solver is built.

C-4

Learned controllers

On top of the gradients, learned controllers that propose pulses and improve them, so that a design can be refined without starting from scratch each time.

Learned surrogates

Models that learn the physics, held to the physics.

The full calculation stays the reference that any learned model has to agree with.

S-1

Compressed dynamics

Large density matrices compressed into a small learned representation and evolved in continuous time by a learned model that keeps the structure of the physics, then expanded back for measurement.

S-2

Geometry-aware networks

Networks that respect the rotations and translations of three-dimensional space, used to predict the operators of a molecule from its geometry.

S-3

Fast enough to search

A surrogate that is accurate enough can stand in for the full calculation inside a search over many pulses or many molecules, with the full calculation used to confirm the result.

Engineering

One framework, from the molecule to the spectrum.

G-1

Graphics-card native

Every stage runs as tensor operations on one or several graphics cards, from loading the molecule's states to rendering the result.

G-2

Exact cases first

A one-dimensional hydrogen-like atom, whose states are known exactly, is the first test of every piece before a molecule is attempted.

G-3

Modern rebuild of established methods

Methods long proven in research code, rebuilt in one modern framework, with every claimed equivalence checked against the original, line by line.

G-4

Headless pipelines

Runs from the command line on a workstation or a cluster and writes its results, spectra and movies without supervision.

Connections

The same ideas, elsewhere in our work.

X-1

By collaboration.

Every engagement begins with a conversation and is scoped before work begins.

Research collaboration

Groups in ultrafast and attosecond science with a problem to simulate or a pulse to design.

Subject: Research

Custom simulation

Electron dynamics, spectra or pulse design for a specific system.

Subject: Build

Partnerships

Computing and instrument partners.

Subject: Partnership

Investment

Briefings and a demonstration, under confidentiality.

Subject: Funding

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