Discussion of the adiabatic hypothesis in control schemes using exceptional points

Abstract

We present calculations for the action of laser pulses on vibrational transfer within the H2+ and Na2 molecules in the presence of dissipation due to photodissociation of the molecule. The laser fields perform closed loops surrounding exceptional points in the laser parameter plane of intensity and wavelength. In principle the process should produce controlled vibrational transfers due to an adiabatic flip of the dressed eigenstates. We directly solve the Schrödinger equation with the complete time-dependent field instead of using the adiabatic Floquet formalism which initially suggested the design of the laser pulses. Results given by wavepacket propagations disagree with predictions obtained using the adiabatic hypothesis. Thus we show that there are large non-adiabatic exchanges and that the dissipative character of the dynamics renders the adiabatic flip very difficult to obtain. Using much longer durations than expected from previous studies, the adiabatic flip is only obtained for the Na2 molecule and with strong dissociation.

15 pages, 7 figures

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• State Flip at Exceptional Points in Atomic Spectra
• Pontryagin-Optimal Control of a non-Hermitian Qubit
• Exotic states in the strong field control of H${}_2^{+}$ dissociation dynamics: From exceptional points to zero-width resonances
• Controlling vibrational cooling with Zero-Width Resonances: An adiabatic Floquet approach
• Almost quantum adiabatic dynamics and generalized time dependent wave operators
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
• Global integration of the Schrödinger equation: a short iterative scheme within the wave operator formalism using discrete Fourier transforms
• Noise-Canceling Quantum Feedback: non-Hermitian Dynamics with Applications to State Preparation and Magic State Distillation