Optical Clock and Ion Trap Simulation

Behavior in your non-uniform field

A DC Stark shift is one line: −(Δα/2)|E|², with the polarizability Δα taken from measurement. Give it one field value and it returns one shift, accurately.

A vacuum chamber has variable field values. Patch charges on viewports, electrode asymmetries, and charged dielectric surfaces vary the field across the millimeters your cloud occupies, so the ensemble carries a distribution of shifts. Variability in the mean moves the clock. Variability in the spread dephases it and broadens the line. At today's target error levels both matter.

Getting from a real field to that distribution is not feasible with analytical solutions. So numerical calculations are needed on field states exported from COMSOL, Ansys, or SIMION.

CliffordClock saves your team development time

A distribution from a single run. Every atom is followed through the field along its own trajectory, whether a thermal Monte Carlo cloud or the motional states of a lattice. Out comes the mean fractional shift, the spread, the dephasing time T₂* that spread implies, and the resulting line shape.
There are no fit parameters. Clifford Clock uses independent published measurements like polarizability as inputs. Demonstrated on NPL's independently measured 1.52 V/m stray field, CliffordClock reproduces published clock shift.
High accuracy validated by two equivalent but different mathematical representations. The textbook approach is used as one method. The other method uses a Clifford algebra. They agree to machine precision on all shipped test cases. But more interestingly, the Clifford algebra approach can also represent rotations, boosts, and the geometry of motion, meaning it has the machinery for designing high accuracy atomic clocks under acceleration or strong magnetic fields.

CliffordClock

An open-source (AGPLv3) accuracy simulator for optical lattice clocks, with trapped-ion support on the roadmap. Compatible with COMSOL's native export or common CSV for defining the chamber geometry and fields. Each atom's clock shift is integrated along its worldline. A one-second interrogation of a hundred atoms runs in seconds to minutes on a laptop CPU.

CliffordClock example output: the field map, the shift each atom accumulates along its worldline, and the line shape the ensemble produces.

Where we are aiming

Transportable and spaceborne clocks. A lab controls its environment. A clock on a ship, an aircraft, or a satellite carries its field environment with it, and the systematic budget has to be predicted, because there is no way to measure it away in flight. The rotor engine exists for the accelerating-frame physics those systems add.
Trap design before fabrication. Evaluate an electrode geometry for its shift and dispersion budget while it is still a CAD file, before the vacuum system is built around it.

Working on a clock?

View on GitHub

velar-mbr/CliffordClock

A Spacetime Algebra simulation tool for optical lattice clocks. Predicts field-gradient shifts, ensemble dispersion, and the resulting line shape from your exported field map. Trapped-ion support on the roadmap.