Decelerating and bunching molecules with pulsed traveling optical lattices
Guangjiong Dong, Weiping Lu, and P. F. Barker
Department of Physics, School of Engineering Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
Received 9 May 2003; published 23 January 2004
We investigate the deceleration and bunching of cold molecules in a pulsed supersonic jet using a far-off-
resonant optical lattice traveling with a constant velocity. Using an analytical treatment, we show that by
choosing the lattice velocity equal to half the supersonic beam velocity and by optimizing the pulse duration,
a significant fraction ( 33%) of translationally cold 1K CO molecules from a supersonic molecular beam
can be decelerated to zero velocity, and simultaneously bunched in velocity space. Due to the large difference
of polarizability to mass ratio between the buffer gas and the CO molecules in the pulsed jet, the buffer gas can
be precluded from the fraction of stationary molecules by choosing a suitable pulse duration. Furthermore, we
find that spatial bunching within the optical lattice is induced and the position of the bunch within the lattice
can be chosen by varying the lattice velocity.
DOI: 10.1103/PhysRevA.69.013409 PACS numbers: 32.80.Lg, 42.50.Vk, 47.60.+i
I. INTRODUCTION
In recent years, there has been strong interest in extending
the well-established techniques developed for cooling and
trapping of atoms to molecules 1. The creation of cold
stationary molecules offers the capability of ultrahigh-
resolution molecular-beam spectroscopy 2, ultracold chem-
istry 3,4 and collisions 5–8 as well as the possibility of a
molecular Bose-Einstein condensation 9,10. However, the
well-developed laser cooling methods for atomic species are
not applicable to the cooling of molecules because of the
complex molecular energy structure leading to a lack of
closed cycling transitions 11.
Over the last few years, four approaches have been dem-
onstrated for creating cold molecules. The first is to use pho-
toassociation of ultracold alkali-metal atoms 12. The for-
mation of ultracold molecules arises from the deexcitation of
excited molecules created by photoassociating colliding at-
oms into the molecules 13–19. The created molecules are
translationally cold typically, 1 mK). However, they are
not vibrationally cold as they are distributed over a larger
number of vibrational states. Recently two-step photoasso-
ciation 20 and stimulated Raman photoassociation 21
have been performed to generate state-selected molecules. A
second technique uses buffer-gas cooling combined with
magnetic trapping 22. Here paramagnetic molecules such
as CaH are cooled down to temperatures in the 100 mK
range by collision with a cryogenic helium gas, while con-
fined in a magnetic trap. Essential to the success of the tech-
nique is that the spin-relaxation cross section must be much
smaller than the elastic collision cross section 22. A third
technique is to use a supersonic expansion to produce a high
density ( 10
12
cm
-3
) of translationally cold molecules
( 1 K) 23 coupled with time-varying electric fields to
slow the beam 24–29. In this scheme any polar molecule
entering an electric field gains Stark energy while losing its
kinetic energy. After the electric field is switched off, mol-
ecules do not gain the lost kinetic energy, and are therefore
decelerated. In these experiments, an array of electric-field
stages are switched on and off alternatively to create a trav-
eling potential well. The switching time is gradually in-
creased to lower the velocity of the traveling potential well.
In this way, deceleration of an ensemble of molecules, such
as NH
3
and CO, was demonstrated in recent experiments
24–29. A fourth technique uses a supersonic nozzle
mounted at a tip of a high-speed rotor, where the flow veloc-
ity of gas emerging from the nozzle was canceled by the
rotor velocity in the opposite direction 30,31. The veloci-
ties of molecular beams of Xe or O
2
seeded in Xe have been
slowed to a few tens of meters per second with this tech-
nique. Other approaches have been proposed for decelerating
molecules in a molecular beam. Friedrich studied slowing of
supersonically cooled atoms and molecules by time-varying
nonresonant induced dipole forces 32. In this approach, the
molecules are scooped at right angles by a nonresonant laser
beam steered by a scanner and decelerated on a circular path
by gradually reducing the beam’s angular speed. More re-
cently, analogous to the Stark decelerator, Barker et al. have
proposed a microlinear decelerator decelerating optical lat-
tice that could be used to decelerate a fraction of any mo-
lecular beam to zero velocity 33. The microlinear decelera-
tor is created by two counterpropagating far-off-resonant
optical fields, one of which has a linear frequency chirp.
Furthermore, molecules can be trapped and transported by
the optical lattice when the direction of the acceleration of
the optical lattice is opposite to that of beam velocity. In this
scheme, polar and even heavy nonpolar molecules such as I
2
can be slowed to be nearly stationary by the optical lattice
with intensities in the range of 10
10
W cm
-2
33.
Recently, bunching for storage of cold molecules and
other applications has been pursued with time-varying elec-
tric fields 34. Velocity bunching is a dynamic localization
of molecules within the lattice at a particular velocity with a
delocalization in phase space required to maintain phase-
space density. This process has been demonstrated to create
an ensemble of molecules with a longitudinal temperature
width of 250 K 34, which could be used to increase the
phase contrast in molecular-beam diffraction studies. Spatial
bunching, which is a localization of molecules at a particular
phase, has been demonstrated to be highly desirable for trap-
ping and storing cold molecules. For example, it can be uti-
lized to optimize the number of molecules loaded from the
PHYSICAL REVIEW A 69, 013409 2004
1050-2947/2004/691/01340910/$22.50 ©2004 The American Physical Society 69 013409-1