Project title: Theoretical Control of Trapped Ions
Supervisor: Dr Florian Mintert and Professor Richard Thompson
I have independently found an algorithm for evolving a two-level ion trapped in a harmonic potential cooled to the quantum ground state into any arbitrary target superposition, up to a relative phase difference between the elements. This is done using discrete time-independent pulses of the carrier, first red and first blue sidebands of the internal transition, allowing it to be carried out within the Lamb--Dicke regime without any kind of special pulse-shaping equipment often used in optimal control. On the way to deriving the algorithm, I have investigated some methods and pitfalls in numerical optimisation of pulse sequences, including the limits of double-precision numerics for certain target functions.
I am now working on the optimisation of pulse sequences using time-varying amplitudes of the same transition frequencies to minimise the effects of heating and other decoherence effects to achieve optimal sequences for creating arbitrary motional superpositions. I am also working on creating higher fidelity quantum gates in trapped ions using the Floquet method for pulse shaping. Both of these aims build on work that has previously been done in the controlled quantum dynamics group here at Imperial College London. The Floquet method has found real success in the field of optimal control of quantum systems, allowing for smoothly varying control pulses to be found, rather than the discretised solutions with small time-steps found by algorithms such as GRAPE.
Part of my role also involves working closely with the experimental ion trapping group, helping to identify areas of theoretical interest to investigate, and finding solutions to problems that arise when trying to experimentally implement the protocols that the theorists find. I will assist in the setup of new equipment coming into the lab under a new grant, and play a minor role in the building of a new linear rf trap to complement the existing Penning trap. My immediate work with the group is to attempt to experimentally realise the discrete time pulse sequences that I have previously found to form arbitrary motional states in a single trapped ion.