Quantum optimal control for atom interferometry

Jack Saywell^1,2, Nikolaos Dedes^1,3, Max Carey^1,2, Joel Abraham¹,  Brynle Barrett⁴, Ilya Kuprov^1,5, Tim Freegarde^1*

Jack Saywell^1,2, Nikolaos Dedes^1,3, Max Carey^1,2, Joel Abraham¹,  Brynle Barrett⁴, Ilya Kuprov^1,5, Tim Freegarde¹

1. School of Physics & Astronomy, University of Southampton, SO17 1BJ, UK 
2. Now at Aquark Technologies, Eastleigh SO50 4SR, UK 
3. Now at Thales RTSI, Reading RG2 6GF, UK 
4. Department of Physics, University of New Brunswick, E3B 5A3, Canada 
5. Weizmann Institute of Science, Rehovot 7610001, Israel

                   *   tim.freegarde@soton.ac.uk 

In atom interferometry-based sensing and measurement, quantum states are prepared and manipulated by laser pulses that act as the mirrors and beamsplitters of the matterwave interferometer. These pulses define the interferometer geometry, which in turn determines the measurement sensitivity. 

If different atoms see different laser intensities at different points within the laser beam, or different frequencies because of their different velocities, the effects of the laser pulses will also differ. This causes variations in state transfer efficiency, superposition phase and phase dispersion, reducing the overall signal-to-noise ratio and scale-factor stability. In general, it is difficult and costly to reduce these variations by further cooling, velocity selection, beam shaping or filtering. 

Quantum optimal control allows a spread of quantum state trajectories to be ‘refocused’ in an analogue of aberration-correcting optics by modulating the pulse phase and/or amplitude according to computationally-designed modulation patterns. Pulses and pulse sequences can be optimised for a range of performance objectives and interferometer geometries, including tracking the differing velocities during Large Momentum Transfer. 

We shall describe here the principles and techniques of quantum optimal control, with computational simulations and experimental verifications, the importance of pulse design for a well-defined measurement scale factor, the concept of the apparent pulse origin, different choices of fidelity function, and some curious features that emerge from the computational optimizations. 

Binary-phase field amplitude (-ve =  phase) during, and superposition phases (various detunings) after, a pulse optimised for scale factor stability, and Bloch sphere trajectories during the pulse.