Non-degenerate Four-Wave Mixing through Rydberg States in a MOT
Experimental Apparatus
We generate Rydberg atoms in a Rb-87 MOT by means of a cw
780 nm laser and a 960 nm diode laser frequency doubled in a
PPKTP crystal. We deliver up to 20 mW cw of 480 nm light to the
atoms. The Rydberg atoms are de-excited to the 6P3/2 state by 100
mW of light from a 1015 nm cw diode laser. Two photon counters
are used to detect the 422 nm photons from the decay of the 6P3/2
state, the first in the phase-matched direction of four-wave mixed
photons, and the second on a separate port from the other lasers.
J. O. Day, E. Brekke, T. G. Walker
We obtain spectra of the 6P3/2 state by first exciting the atoms to a Rydberg
level via an off-resonant two-photon excitation of the 480 and 780 nm lasers.
Then, while a portion of the MOT atoms are in a Rydberg state, we scan the
frequency of the 1015 nm laser across the Rydberg-6P3/2 resonance. The
isotropic decay of the 6P3/2-5S1/2 is registered on counter 2 and can be
compared to the MOT population signal. We find that the MOT loss rate is
reduced by around a factor of 2, which implies that the atoms excited into the
Rydberg state have a 50/50 chance of being de-excited back into the MOT or
being lost due to fast collisions with other Rydberg atoms.
422 nm photon counts (1/s)
3
25x10
20
Rydberg-Detuned
Four-Wave Mixing
When the 480 nm laser is detuned from the rydberg state, we observe a
frequency separation between the phase-matched photons and those
resulting from an incoherent de-excitation process. We observe nonphase-matched photons when the 1015 nm de-excitation laser is
resonant with the nD-6P3/2 transition. By contrast, we observe phasematched photons only when the sum of the three laser fields (780 nm +
480 nm - 1015 nm) is resonant with the 5S1/2-6P3/2 transition.
Intensity Correlation
Spectroscopy
We observe large transition linewidths in our scans due to drift in the absolute
frequency of our lasers. To avoid this problem, we have developed a method of
measuring the transition linewidth at very short timescales using the correlation
of the collected de-excitation photons. The frequency of the 780 nm excitation
laser is modulated with a triangle ramp as shown below. The time between
successive 420 nm photons is then measured and averaged over long times.
The peaks observed at integer multiples of the ramp period are insensitive to
laser drift at rates slower than the ramping frequency. The result is a practical
means to measure the transition linewidth with good signal to noise while
eliminating long term drift.
Excitation Scheme
5
Strong dipole-dipole interaction allows Rabi excitation of
a single atom in the ensemble, but not 2 (or more) if the
dipole-dipole coupling exceeds the Rabi coupling. This
gives rise to a blockaded region where only one Rydberg
atom should be present. For our Rabi rates, at n = 60, this
corresponds to a region of about 10 µm.
Photon Anti-Bunching
Due to blockade, only one atom can be excited to the Rydberg state and
then to the 6P3/2 state at a time. We can detect the resultant 422 nm
photon from the decay of this atom to the ground state and record the
subsequent arrival times of all of the 422 photons. The probability of
detecting two photons at the same time from a blockaded region should
be very small. Thus, measuring correlations of these photon arrival
times should produce a strong anti-bunching signal.
When the system is phase matched, the decay photon are emitted in the
direction of the detector with high probability, thus increasing the
effective solid angle of the detection system [2]. The waist of these
beams can be reduced to 11 μm, thus producing an extremely small
excitation volume, making it possible to have an almost complete
blockade within this region.
[2] M. Saffman, T. G. Walker, Phys. Rev. A. 66, 065403 (2002)
0
0
HAT Experiments
50
100
150
Dexcitation Laser Frequency (MHz)
6
40x10
Number of atoms in MOT
Jaksch et al. PRL 85, 2208 (2000) and Lukin et al. PRL 87 037901 (2001)
Support from NSF
15
10
Dipole Blockade
University of Wisconsin – Madison
In this work, we use a three-photon near-resonant process in a laser-cooled Rb vapor to achieve non-degenerate phase-matched four-wave mixing using an
intermediate Rydberg state. Rydberg atoms in the 36D5/2 state are efficiently produced using a 780 nm/480 nm two-photon excitation detuned 500 MHz above
the 5P3/2 intermediate state. When a 1015 nm laser stimulates emission down to the 6P3/2 state, the Rydberg atom populations are significantly depleted and
422 nm 6P3/2-5S photons are observed by photon-counting photomultiplier tubes. With the 780 nm, 480 nm, and 1019 nm lasers configured in a non-collinear
phase-matched geometry, we observe a coherent 422 nm phase-matched signal that is up to 10 times larger than the non-phase-matched radiation. These
experiments demonstrate the ability to coherently manipulate ultracold atoms at optical frequencies using Rydberg states.
Rydberg De-excitation
Future Work:
Dipole Blockade
30
We will combine our Anti-Bunching experiment with our previously
developed Holographic Atom Trap (HAT) [3]. After evaporation and
recompression, we have achieved densities of 2x10^15 atoms/cm^3,
the highest ever seen in incoherent matter [4].
20
10
0
0
50
100
150
Dexcitation Laser Frequency (MHz)
Phase-Matched
Four-Wave Mixing
The angles of incidence for the three laser beams are chosen based on the
calculated requirements for phase-matching. In order to determine if phasematching is present, we compare the ratio of the counts in the phase-matched
direction on counter 1, to the off-axis counts of counter 2. The ratio is
normalized by removing the noise background from each counter and
correcting for the much larger solid angle used for counter 2. The incoming
angles of the beams are then adjusted to maximize this ratio. At optimum
conditions, this ratio of counts per unit solid angle was seen to increase to a
value of 40, as shown in the graphs below. The phase-matching was
determined to be sensitive to less than 0.2o.
Spatial Profile of
Phase-Matched Beam
As another check to verify phase-matched four-wave mixing, we can
measure the spatial profile of the output beam. When phase matched,
the counts should be spatially coherent and emitted in a preferred
direction. To measure the spatial extent of the emitted photons, a razor
blade was scanned across the count area. This data corresponds to a
waist of 300 um. We reduce an iris to about 1.5 mm at this position to
limit the background counts into counter 1.
The small waists of the
recompressed state makes
the HAT an ideal
system for seeing mesoscopic
dipole blockade.
Transition Linewidth
Using this method, the four wave transition linewidth was measured at several
different frequencies of current modulation. The following plot shows the
perceived broadening of the transition at longer times scales due to drift in the
laser frequencies. The smallest transition linewidth we observe for 28D5/2 is
7.2 MHz. Currently, our transitions are primarily limited by the 4 MHz
linewidth of our 480 nm laser, though other factors must also contribute.
Over the width of the cloud
(sx=300 nm, sz=8 mm) the
dipole-dipole shift is >10 MHz
for n=60.
[3] R. Newell, J. Sebby, T. G. Walker, Opt. Lett. 28, 14 (2003)
[4] J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, T. G. Walker, Phys.
Rev. A 71, 021401 (2005)
100mm
HAT Facts:
Talbot Fringe
microtraps
60
Phase Matched
50
Random Axis
Phase Matched Axis
x10
3
40
30
Nondestructive image of the HAT
taken with Spatial Heterodyne Imaging5
20
10
0
0
50
100
150
200
No Phase Matching
35
Random Axis
Phase Matched Axis
30
x10
3
25
Recompressed size:
Recompressed density:
Recompressed number:
300nm x 300nm x 8mm
2x1015atoms/cm3
~2000 atoms/microtrap
20
15
Loaded from a vapor cell MOT with
3x108 Rb-87atoms.
10
5
0
0
50
100
150
200
[5] S. Kadlecek, J. Sebby, R. Newell, T. G. Walker, Opt. Lett 26, 137 (2001).