6533b7d8fe1ef96bd12695fe

RESEARCH PRODUCT

Optimal control and shortcuts to adiabaticity techniques in linear and non-linear systems : from ion cyclotron resonance to nuclear magnetic resonance

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The goal of our research is to develop efficient and robust control protocols for classical and quantum systems. To this end, we have applied optimal control theory (OCT) and shortcuts to adiabaticity (STA) with inverse engineering and motion planning approaches in three different examples, which are RC (Resistor Capacitor) circuits, Fourier Transform-Ion Cyclotron Resonance (FT-ICR), and Nuclear Magnetic Resonance (NMR). Some of our results are not limited to these systems but are rather general. We apply OCT and STA with an inverse engineering approach to control the time-evolution of the charge on a capacitor. We show that OCT is a member of the family of STA solutions. In order to control an ensemble of spins and apply it in NMR, we harness the method of mapping spins to springs. We give a more illustrative explanation to this method, hence it becomes clear why this works both under OCT and STA control pulses. The mutual advantages and drawbacks of OCT and STA are discussed. By using the rotating wave approximation (RWA), we show that the control pulses developed for an ensemble of springs are applicable in FT-ICR. In a first step, we have designed robust pulses without any constraint on the amplitude of the pulse following the framework of OCT. Moreover, in a second step, adapting the grape algorithm we have taken into account an important experimental limitation, which is the constraint on the amplitude of the pulse. The OCT and STA control pulses have been compared with standard adiabatic and Stored Waveform Inverse Fourier Transform (SWIFT) pulses. To the best of our knowledge, this is the first time Optimal Control Theory has been applied in Fourier Transform-Ion Cyclotron Resonance.