Ultrafast Phase Control: Quantum Coherence in Helium Atoms, and Entangled States in Hydrogen Molecules, Modified by Attosecond Delays

Coherence arises when a quantum system is excited into a superposition of states. Entanglement additionally requires a spatial separation of the quantum system into (at least) two parts, each of which can be separately measured, and the measurement of one will have consequences on the other part.

Atoms&molecules naturally exhibit quantum correlated ground and excited states. If these correlated states are coherently excited and then the system splits into (at least) two spatially separated entities, they can quickly turn into building blocks (e.g. quantum bits) of quantum-technological applications operating at the ultimate speed limit of the electromagnetic interaction: the time-scale of electronic motion.

Here, I will discuss some of our recent experiments that address these questions, focusing on two systems: Helium atoms and hydrogen molecules.

In transient-absorption measurements on Helium, we introduced a mechanism to manipulate phase shifts of coherently excited quantum states on few-fsec to asec time scales. Even complex (multi-level) systems can be controlled and their dynamics reconstructed. At the highest intensities, the lifetime of coherence is reduced due to mechanisms such as ionization and dephasing caused by complex coupling to other states.

For H₂ in a reaction microscope, we measure both spatially separating photoproducts (a free electron and a proton) in coincidence after interaction with a two-color field, composed of an XUV asec-pulse train and an NIR laser pulse. Depending on the asec timing between the two fields, we observe substantial changes in the emission direction of the proton with respect to the electron.

The experimental observation can be explained by the quantum interference of externally controllable dissociation pathways. The wavefunction of the two electrons can be described as a Bell-type state |1,2> + exp(-i*phi) |2,1>, where the phase phi can be modified by the sub-femtosecond time-delay between the attosecond pulse train and the laser field.

Our results show that it is possible to manipulate relative quantum phases of coherent and entangled states in fundamental atomic and molecular systems on femtosecond-to-attosecond time scales, which may, after much further development, form the basis of future optically programmable molecular-scale quantum processors.