1. 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 28D 5/2 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. Non-degenerate Four-Wave Mixing through Rydberg States in a MOT Experimental Apparatus J. O. Day, E. Brekke, T. G. Walker University of Wisconsin – Madison Support from NSF 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. 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. Future Work: Dipole Blockade 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. Dipole Blockade Jaksch et al. PRL 85, 2208 (2000) and Lukin et al. PRL 87 037901 (2001) The small waists of the recompressed state makes the HAT an ideal system for seeing mesoscopic dipole blockade. Over the width of the cloud (  x =300 nm,  z =8  m) the dipole-dipole shift is >10 MHz for n=60. 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) 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. 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. Transition Linewidth Rydberg-Detuned Four-Wave Mixing 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. 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 non- phase-matched photons when the 1015 nm de-excitation laser is resonant with the nD-6P3/2 transition. By contrast, we observe phase- matched 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. Rydberg De-excitation 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 phase- matching 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 0.2 o. HAT Facts: Recompressed size:300nm x 300nm x 8  m Recompressed density:2x10 15 atoms/cm 3 Recompressed number:~2000 atoms/microtrap 100  m Talbot Fringe microtraps Nondestructive image of the HAT taken with Spatial Heterodyne Imaging 5 [5] S. Kadlecek, J. Sebby, R. Newell, T. G. Walker, Opt. Lett 26, 137 (2001). Loaded from a vapor cell MOT with 3x10 8 Rb-87atoms. [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) 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]. Excitation Scheme HAT Experiments