Elmer as a replacement for Ansys HFSS in superconducting quantum circuits

[ttshaw]

I work in a university group researching superconducting quantum circuits, which is one of the frontrunner technologies in quantum computing. We essentially make microwave structures out of patterned aluminum, which superconducts at low temperatures, deposited on silicon or sapphire chips. We also need nonlinearity for a variety of processes, and create it through superconductor-insulator-superconductor junctions, or Josephson junctions (JJs), which are basically nonlinear inductors: L(I)=L_0+L_1I+L_2I^2+... . These chips are then put into various designs of metal cavities.

There's a popular workflow for designing these devices and extracting important parameters from their Hamiltonians.
1. Come up with a geometry of deposited metal, cavity geometry, and Josephson junction L_0.
2. Enter that design into Ansys HFSS, with the Josephson junction abstracted as a rectangle that fits where the JJ would go with a surface-impedance
boundary condition appropriate for an inductor with inductance L_0
3. Do an eigenmode simulation for some small number of modes
4. In python, grab the E and H fields in each cell of the mesh and calculate how much of the mode's energy is contained in the JJ

See Chapter 4, Section 1 if you're interested in the math.

My question is, how feasible would it be to do this in Elmer instead of HFSS? Where does each of these tasks fall between "there's a GUI option to do that" and "you'd have to rewrite chunks of the FEM engine?"
1. Add a 2D rectangle to represent the JJ with boundary conditions to represent a lumped-element inductor (or parallel LC)
2. Eigenmode simulation for specified number of modes above a given frequency
3. Either export E and H fields and permittivity for each field, or calculate in Elmer the energy participation ratio mentioned in step 4 above

I've been looking around and haven't yet seen an example of anyone doing an electromagnetics eigenmode simulation in Elmer, so that's the part I'm most concerned about. If you know of any examples I can look at I'd appreciate a link. I also saw somewhere that Elmer couldn't handle high-frequency simulations, but that same resource shared an example of a 1GHz waveguide simulation. So I don't know exactly how high frequency they meant; we usually work at less than 10GHz.

[raback]

Hi

Most transient models can also solve eigenmode problems. These are consistency tests for EM waves with two different formulations:

Code: Select all

elmeruser@elmer-VirtualBox:~/Source/elmerfem/fem/tests$ grep -i 'eigen anal' -r | grep wave
EMWaveBoxHexasEigen/emwave.sif:  Eigen Analysis = True
mgdyn_wave_eigen/case.sif:  vtu: eigen analysis = logical True

Now the challenge is not the equation itself but the fact that linear systems arising from electromagnetic wave equation tend to be challenging to solve. When using direct methods you hit the wall rather quickly and for iterative methods the equation is notoriously difficult to precondition.

Certainly interesting topic!

-Peter