All-optical generation of quantum entangled states with strictly constrained ultrafast laser pulses

Abstract

We present a quantum optimal control theory study combined with theoretical analysis to determine a pulsed laser field, capable of generating a maximally entangled state in two trapped two-level atoms. By expanding the time-dependent unitary operator to the first leading term of Magnus expansion, we reexamine the pulse area theorem for the trapped atoms driven by an arbitrarily temporary field. Due to the dipole-dipole interaction blockade, we find that the two trapped atoms described by a three-level ladder system can be reduced into an equivalent two-level model by using narrow-bandwidth pulses, leading to an analytical solution for generating the maximally entangled state. We also solve a highly constrained optimization problem to search for optimal laser pulses with broad bandwidths. A zero pulse-area constraint is employed to remove the dc offset of the optimized laser pulses, and a fixed fluence limitation combined with a constant pulse-area constraint at the resonant frequency of the equivalent two-level system are utilized to restrict the unitary evolution of quantum systems by the first leading term of Magnus expansion. This work provides a potentially useful approach to find all-optical control schemes for generating the maximally entangled state by using ultrafast laser pulses while satisfying multiple strict limitations.