Anomalous Heating Ion Traps

Short answer: Anomalous heating is the unexpected rise in motional energy of a trapped ion held near the electrodes of its trap. The heating rate is typically orders of magnitude larger than simple thermal-noise estimates predict, and its origin is not fully understood. Experiments from 2006 to 2018 show the rate falls when electrodes are cooled, grows steeply as the ion gets closer to the surface, and can rise over months of operation, which points to surface effects. It matters for trapped-ion quantum computing because the ion's motion is used to carry out gates.

What the effect is

A 2018 Physical Review Letters paper describes it plainly. Cold ions trapped near conductive surfaces experience heating of their oscillatory motion. Typically the rate is orders of magnitude larger than expected from electric field fluctuations due to the thermal motion of electrons in the conductors. The effect is known as anomalous heating and, the authors say, is not fully understood. A 2011 New Journal of Physics paper adds that work in nanomechanics, nanoelectronics, superconducting quantum electronics, ion trap quantum computing and weak-force measurement is impeded by excessive electric field noise from nearby surfaces. Single trapped ions are extremely sensitive sensors of that noise, and experiments near metallic surfaces reveal noise several orders of magnitude stronger than estimates based on Johnson noise suggest.

Temperature

A 2006 paper in Physical Review Letters measured anomalous heating of an atomic ion in the lowest quantum levels of an rf trap with moveable electrodes. The authors measured how the heating scales with electrode proximity, and report that when the electrodes were cooled from 300 to 150 K the heating rate dropped by an order of magnitude. They say this provides direct evidence that anomalous heating stems from microscopic noisy potentials on the electrodes that are thermally driven, and that the observations are relevant to decoherence in trapped-ion quantum information schemes and perhaps other charge-based systems.

Distance from the surface

The 2018 paper measures how the heating rate depends on ion-electrode separation in a trap of simple planar geometry. They determine the heating rate by imaging the resonance fluorescence of a single ytterbium ion after a variable heating time and deducing temperature from the oscillation amplitude. Assuming a power law, they measure an exponent of minus 3.79 with an uncertainty of 0.12, which means the heating rate drops steeply as the ion is held farther from the surface. The paper lists the dependence on separation as one of the open questions in the field.

Contamination and ageing

The 2011 paper reports heating rate measurements in a microfabricated gold-on-sapphire surface-electrode trap with a trapping height of about 240 micrometres, using the Doppler recooling method. The noise spectral density falls within the range reported for room-temperature ion traps. The authors find that during the first months of operation the heating rates increase by about an order of magnitude, with the largest increase in the ion-loading region. They say this is a strong hint that surface contamination plays a major role in excessive heating. They discuss possible links to impurity atoms adsorbed on metal surfaces and to amorphous dielectrics, and in their summary they conjecture the noise comes from locally contaminated surfaces.

What this does not tell you

These papers measure the effect in particular traps and do not provide a complete theory. They do not say how much heating a given quantum computer can tolerate, or that any one fix removes it. Cooling electrodes and keeping surfaces clean are reported as relevant factors, not solutions.

FAQ

What is anomalous heating?

Unexpected heating of a trapped ion's motion caused by noise from nearby electrodes.

Why is it a problem?

It affects decoherence in trapped-ion quantum information schemes, per the 2006 paper.

Does cooling help?

In one experiment, cooling electrodes from 300 to 150 K cut the heating rate by an order of magnitude.

Does distance matter?

Yes. A 2018 measurement found a steep power-law fall with separation, with an exponent of about minus 3.8.

What causes it?

Not fully understood. Evidence points to noisy potentials on electrodes and surface contamination.