The first step in the coherent control of a photoinduced binary reaction is bond making or photoassociation. We have recently demonstrated coherent control of bond making in multi-photon femtosecond photoassociation of hot magnesium atoms, using line
arly chirped pulses [Levin et al., arXiv:1411.1542]. The detected yield of photoassociated magnesium dimers was enhanced by positively chirped pulses which is explained theoretically by a combination of purification and chirp-dependent Raman transitions. The yield could be further enhanced by pulse optimization resulting in pulses with an effective linear chirp and a sub-pulse structure, where the latter allows for exploiting vibrational coherences. Here, we systematically explore the efficiency of phase-shaped pulses for the coherent control of bond making, employing a parametrization of the spectral phases in the form of cosine functions. We find up to an order of magnitude enhancement of the yield compared to the unshaped transform-limited pulse. The highly performing pulses all display an overall temporally increasing instantaneous frequency and are composed of several overlapping sub-pulses. The time delay between the first two sub-pulses almost perfectly fits the vibrational frequency of the generated intermediate wavepacket.These findings are in agreement with chirp-dependent Raman transitions and exploitation of vibrational dynamics as underlying control mechanisms.
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler,
creating a maximally-entangled state out of some initial product state. For two quantum information platforms of current interest, nitrogen vacancy centers in diamond and superconducting Josephson junctions, we show that an arbitrary perfect entangler can be reached faster and with higher fidelity than specific two-qubit gates or local equivalence classes of two-qubit gates. Our results are obtained with two independent optimization approaches, underlining the crucial role of the optimization target.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here
, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally-entangled state out of some initial product state. The functional depends on easily-computable local invariants and uniquely determines when a gate evolves into a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.
Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive a
n optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.
