A natural extension of cooling atoms to the ultralow temperature regime is
the production of ultracold molecules. Beside being more complex objects, with
a lot of internal states (e.g., vibrational and rotational levels), ultracold
molecules could be used to investigate quantum mechanical effects in chemical reactions,
the effect of anysotropic interactions (e.g., long-range dipole-dipole forces)
in degenerate quantum gases, fundamental physics (e.g., in high-precision
measurements for the permanent electric dipole of the electron), or the
implementation of quantum information processing gates, to name a few.
There are several ways to obtain ultracold molecules.
Our group investigate their formation using a photon to bind
two atoms. This process, called photoassociation (PA), is illustrated
in the figure beside: a pair of ground state atoms approach each
other along a potential curve (blue curve) with relative kinetic
energy ϵ, and absorb a photon from a laser L
detuned from a bound level v'. The pair is photoassociated into
an excited electronic curve (red), which decays radiatively back
into the ground electronic state (blue). A fraction of this decay
will populate bound levels v with a branching ratio r. The resulting
molecule basically has the same kinetic energy as the ultracold
atoms, hence this process leads to the formation of ultracold molecules.
We study several variations of this method, using a one-photon excitation
followed by radiative decay (as above), or using two-photon excitations
(Raman scattering). The most likely populated ultracold molecular states
using this approach are the upper bound levels. This is due to small
branching ratios (or Franck-Condon factors reflecting the poor overlap
between excited and ground state wave functions). To improve
the formation of deeply bound molecules, we proposed to take advantage
of the enhancement of scattering events in the vicinity of a Feshbach
resonance. A Feshbach resonance occurs when the energy in the entrance
channel coincides with that of a bound level in a closed channel
(see left panel in figure beside). Coupling between the two potential
curves (e.g., due to hyperfine and Zeeman interactions) will mix the wave
functions, and lead to a large enhancement of scattering amplitudes
(see also
Ultracold scattering and chemical reactions for more details about
Feshbach resonances). In FOPA, which stands for Feshbach Optimized Photo-Association,
we take advantage of the increase of the initial scattering wave function
at short range to obtain much large photoassociation rates into deeply
bound molecular levels. The figure's right panel sketch the idea:
the open channel (blue) wave function usually reach extended states in the
target molecular curve (red). In FOPA, by tuning the magnetic field
appropriately, the open (blue) wave function is strongly coupled to the
resonant closed channel (green) wave function, which amplifies the probability
of being at short range and the PA rate into a more deeply bound target
level (red).
We applied this idea to a few cases, such as the excitation of a pair
of 7Li into the
13Σg+
excited molecular state. In this system, a Feshbach resonance exists
at magnetic field B ~ 736 G in the
entrance channel corresponding to both 7Li
atoms being in the state |f,m⟩=|1,1⟩. The figure (a) beside shows
the expected results: without B-field, the PA-rate
Kv' into a bound level v' is the largest
for upper levels v', and decreases rapidly for more deeply bound levels,
showing an oscillatory behavior reminescent of the wave nature of the
bound levels.
For B nearing the resonance at 735 G, we find large variations in
Kv'. First, a sharp increase occurs
at the resonance for all target levels v', which corresponds to the enhanced
overlap between the entrance channel wave function and the target state.
This increase over the off-resonance PA-rate can be many-orders of magnitude,
basically reaching the unitarity limit which corresponds to the maximum
rate possible (i.e. all pairs of atoms form a molecule). We also notice
the presence of a sharp minimum a bitaway from the resonance. This is due
to "destructive interference" where the mixture of open and closed channels
lead to a nodal structure in the entrance channel that has a very small
overlap with the target state.
The exact position of this minimum is very sensitive to the exact
nodal structure of the wave functions, and thus can preceed or follow
the resonance. The figure (b) beside shows a contour plot of the
PA-rate for a restricted range of target levels. The maximum is basically
always at the resonantce position (736 G), except for level v=63, for
which the "destructive interference" coincides with it. The position of
the minimum, on the other hand, follows a "croissant shape" trajectory,
moving to fields higher than 736 G for v < 63. This sensitivity of the
minimum position could actually be used as a high-precision spectroscopic
tool, since its location is really sensitive to the position of the target
levels.
Our group has proposed using FOPA to probe the potential variation of
fundamental constants, such as the proton/electron mass ratio. By
performing PA measurement near the minimum, which is very sensitive to
small difference in the relative position of bound states, one could
detect a small shift in the mass ratio that would be amplified by
the sharp variation in the PA-rate. As opposed to the maximum PA-rate
at the resonance which exhibits saturation effects, the minimum would
give a cleaner measurement.
We also explored other methods to produce ultracold molecules.
For example, we looked at a pump-dump scheme near a Feshbach resonance,
that marries both FOPA and a time-dependent treatment to excite
pairs of atoms into a wave packets (near a Feshbach resonance) that
will then be dumped into a deeply bound level at the appropriate time
(usually in the 50 picosecond time frame). Another time-dependent
approach is based on STIRAP (STImulated Rapid Adiabatic Passage) using
a multistep chain of levels, again using a Feshbach molecule as a
starting point. We obtain a very efficient transfer into deeply
bound ground state molecules: such approach was used by the experimental
group in Innsbruck. We are continuing to explore ways to obtain
large amount of ultracold molecules, including larger molecules such as
tetramers made by the PA of two diatomic molecules.