Quantum Physics. Big Ideas.
A curious human using physics to explore reality
Dr. DAMON EXPLAINS
Dr. DAMON EXPLAINS
Watch me talk about trapping electron qubits in solids!
How to trap Electrons in a Crystal!
I conducted my Ph.D research at the CCNY Meriles Lab. My group was attempting to better understand how to trap electrons to use them as qubits.
The goal was to develop “flying qubit” architecture using NV centers and single electrons as a way to facilitate quantum computing.
tl;dr: Although the technology still needs to be developed in order to fulfill our original goal, We found that it’s feasible to trap electrons non-invasively inside a crystal.
Read the case study below for more details!
CASE STUDY 🔬
CASE STUDY 🔬
The Strategy
Quantum computers are a big deal…maybe. The nitrogen vacancy center is an atom-scale qubit in diamond and it’s is a REALLY good qubit - here are the criteria we typically use. The NV is especially good because it can hold onto quantum information at room temperature - 300K - which is usually way too hot in the qubit world. Still, it’s difficult to find a good qubit that can easily transfer information to other qubits. Check out this paper for more background.
One idea for doing this is the “flying qubit” which uses a particle like an electron to coherently transfer spin information between fixed qubits. For this to work the flying qubit needs to go where we want it to go…but its inside a diamond crystal - we need to trap or guide a conduction band electron inside of a solid without actually having to prod it with instruments.
We hypothesized that we could use a Paul Trap, a type of electrodynamic trap, to do this.
What electric field strength and frequency are needed to trap electrons?
This is a simulation of electrons rocketing around in the Paul trap!
Applying Newton’s 2nd Law to an ideal Paul Trap tells us what an electron in a vacuum will do when the trap is turned on…
Luckily, if an electron is very near the conduction band minimum it will behave almost exactly like an electron in free space!
This is called the semiclassical approximation and treats the electron as a wave packet with a spread that is several lattice constants.
This is an ordinary differential equation with a periodic driving term…Maybe I can simulate it!
(I used COMSOL and MATLAB to do most of my simulations 💪)
The Simulations
The dots are electrons and the black hyperbolic curves are the trap electrodes generating the electric field (the red arrows). The color of the particle is proportional to its kinetic energy - blue is slow and red is fast.
Electrons are very light compared to atoms, and atoms are usually the things trapped in Paul Traps, so we needed to see what parameters would be needed for these tiny particles.
We need to make sure our simulation agrees with the theory.
WHAT WE DISCOVERED!
Our simulations work in vacuum but…we still need to solve this equation for electrons in a solid which is difficult because of forces exerted on the electron by the crystal lattice…
We account for (some of) these forces by using an “effective mass” for the electrons called “m star” or m*. The crystal lattice changes the effective mass of the electron depending on the direction the electric field tries to push or pull the electron relative to the crystal! The mass is “anisotropic” because its magnitude depends on the direction of the applied force.
This simulation proved we could trap electrons with a Paul Trap at reasonable microwave frequencies (a few GHz).
One benchmark for this simulation is checking the average particle displacement against the equations of motion for the system.
Here I’ve plotted the average displacement of the electrons relative to the trap center - you can see the “macro-motion” which is the big wiggle the electrons make and the “micro-motion” are the superimposed smaller wiggles!
This shows our simulation agrees with the theory in vacuum, so now we can start modifying it for the crystal.
By understanding the conditions needed for stable trapping we can modify the electrode geometry so even this anisotropic mass doesn’t prevent trapping the electrons inside the crystal! We even simulated it… Cool!
In silicon, for example, the mass of the electron changes by almost 5X depending on the direction the electric field points relative to the crystal lattice! That’s why the electrons in this simulation create an elongated cloud shape - they are “heavier” along the horizontal direction so they’re harder to trap and they tend to move farther from the trap center.