Few-photon coherent control schemes are often analyzed in the frequency domain, which
provides the opportunity to understand the control over the transition in terms
of interference effects between different channels. Complementary
information can be gained by comparing the time evolution of the laser field with
the response of the quantum system.
The Figure shows (a) the electric
field of a particular dark pulse and (b) the time-dependent probability of the
(dark) two-photon transition
from the 1s to the 2s state in hydrogen atom. Although the transition probability
at the end of the pulse is zero (as expected for a dark pulse), at intermediate times the
population in the excited 2s state is nonzero. As a result,
the system can be further excited or ionized from the 2s state during the pulse,
as can be seen from the time-dependent ionization probability (panel c).
Similar analysis in the case of a molecule shows how these control schemes fail for
transitions to dissociative states due to the coupling of electronic and nuclear motion.
In contrast, for a molecular bound state the control is given via the time delay and
the carrier-envelope phase different between two consecutive pulses in the train.
Modern applications of quantum mechanics such as quantum information technology or
steering molecular reactions require a precise control over the internal state of
a molecule. Manipulation of the quantum state is still a great challenge, in particular
for nonpolar molecules, in which the rovibrational states cannot be coupled by light
directly. We propose a new control scheme (see Figure), in which a high control efficiency is achieved
with a single laser pulse operating at infrared wavelengths. Our theoretical analysis,
confirmed by the results of numerical simulations for the hydrogen molecular ion,
shows that electron population can be
transfered from one internal state to the other through intermediate excited
electronic states via multiphoton transitions. We find that the scheme is applicable
for nonpolar molecules and even for intermediate repulsive electronic states.
The advent of attosecond
laser pulses has paved the way to steer electrons in
a molecular bond using control techniques known from femtosecond chemistry.
This has been demonstrated in numerical simulations for the
dissociating hydrogen molecular ion interacting with two time-delayed
laser pulses.
The first attosecond pulse initiates
the dissociation process.
While the distance between the protons increases, the
internuclear Coulomb barrier acts as an ultrafast shutter and traps
the electron with equal probability
at either one of the two nuclei (upper panel). By applying a
second ultrashort pulse during
the shutter time the electron is driven by the oscillating electric
field and located with high probability at one of the nuclei (lower
panel).
References:
F. He et al. Phys. Rev. Lett. 99, 083002 (2007)F. He and A. Becker, J. Phys. B 41, 074017 (2008)
F. He et al. J. Phys. B 41, 081003 (2008)