Dynamics of Low Density Rydberg GasesExperimental Apparatus

E. Brekke, J. O. Day, T. G. Walker

University of Wisconsin – MadisonSupport from NSF and NASA

A state-dependent stimulated emission probe was used to investigate the coherent and dynamic properties of cold Rydberg atoms. 87Rb atoms were excited to various nl Rydberg states from a MOT via continuous two-photon excitation. A stimulated emission probe laser was then used to bring the Rydberg atoms down to the 6P3/2 state,allowing detection of decay photons as a Rydberg atom detection method. Phase-matched four-wave mixing was also achieved and the angular dependence investigated. This coherent process is optimized when detuned from the Rydberg state, giving as much as 40% phase-matched light. In addition, the stimulated emission probe technique shows that radiative processes dominate the Rydberg population dynamics on a time scale much faster than the natural radiative lifetime. Modeling suggests superradiant emission may be the dominant factor.

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. The red trace of the graph below is the phase-matched direction of counter 1, while the blue trace is the non-phase-matched counter 2.

Superradiance State Model

Future Work:

Single Photon SourceBy focusing the excitation beams to around 10 μm waists, the excitation rates increase dramatically and the excitation volumes are small enough that the entire region can be blockaded. In this regime, the excitation of one atom to the Rydberg prevents the excitation of others. In concert with the four-wave mixing setup, this may allow us to create an on-demand single-photon source. Furthermore, the resultant 420 nm photon is in a different direction than the input photons, making it easier to filter out background light from the desired signal.

Two-Photon Excitation DataIn addition to four-wave mixing, we also investigate Rydberg gas dynamics by

exciting atoms to the Rydberg state via two-photon excitation and then observing trap loss (red trace) from the MOT as well as count rates (blue trace) from the photon counters. In these two-photon scans, the trap loss rate is small (0.2 s-1)

compared to the much larger Rydberg excitation rate (110 s-1). This data, taken at the 28D state, implies that only 1 out of every 500 Rydberg atoms excited is lost

from the trap. Similar numbers are measured for other Rydberg states: 1:50 for the 43D and 58D states, and 1:1000 for the 30S state. This implies that inelastic atom-

atom collisions occur at very low rates for these densities.

We develop a three state model to describe the Rydberg excitation process with a ground state g, a Rydberg excitation state r, and a set of nearby Rydberg states s

which atoms from state r transition to via blackbody radiation, superradiance, and other factors which occur at a total rate γ. By using the 1015 as a state-probe laser, we can bring the atoms in state r down to the 6P3/2 state before they have a chance

to transition to another state. By varying the rate of this de-excitation, we can determine the size of the transfer rate γ.

In these experiments, we determine that the transfer rate is faster than blackbody transfer, atom-atom collisions, electron collisions, or other processes could account

for. We determine that the mechanism that is likely to transfer atoms quickly enough to account for the observed rates is superradiance. Following the work of Dicke [1], we develop a model for superradiance. The calculated transfer rates in

the tables are based on this model.

[1] R. H. Dicke, Phys. Rev. 93, 99 (1954).

Angular Acceptance of Phase-Matched Beam

We generate Rydberg atoms in a 87Rb 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 70 mW of light from a 1015 nm cw diode laser. Two photon counters are used to detect the 420 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.

As a further test of the phase-matched setup, we change the angle of incidence for one of the input beams (in this case, the 780 nm beam) and observe the change in phase-matched counts on the on-axis counter. The counter has a

much larger angle of acceptance than the graph below, which shows a 1.2 mrad (0.09º) angular width where phase-matching occurs. In addition, when changing

the principal quantum number of the Rydberg excitation state from n=28 to n=43, the 780 nm beam needed to be moved by 4.3 0.3 mrad compared to the

expected 4.07 mrad from a k-vector calculation.

Phase-MatchedFour-Wave Mixing

Detuned Four-Wave Mixing

We may also tune the 1015 nm laser above the Rydberg resonance to avoid creating a large population in the Rydberg state. The 480 nm Rydberg excitation laser is then tuned so that

the three-photon process still results in direct excitation to the 6P3/2 state. The result of this is a reduction in the number of phase-matched counts produced, but an increase in the ratio of phase-matched counts to non-phase-matched counts. This implies that large Rydberg state populations cause a dephasing of the four-wave process, even though our Rydberg atom

densities are such (~ 107 cm-3) that atom-atom interactions should not be much of a factor. We have developed a model where we set up a series of state equations for the 4 levels used

in the experiment. By taking account of Rabi frequencies, AC stark shifts, and complex detunings that factor in finite state widths, we calculate the steady-state 6P3/2 population.

This population can be used to calculate the rate of 420 nm photon production.

HAT Facts:

Recompressed size: 300nm x 300nm x 8mRecompressed density: 2x1015atoms/cm3

Recompressed number: ~2000 atoms/microtrap

100m Talbot Fringe

microtraps

Nondestructive image of the HAT taken with Spatial Heterodyne Imaging

Loaded from a vapor cell MOT with 3x108 Rb-87atoms.

HAT Experiments

Emission ProbeCount Rate Data

As the de-excitation rate produced by the 1015 nm stimulated-emission probe increases, we observe an increase in the count rate from the 6P3/2

state. This implies that at high probe intensities Rydberg atoms are brought down to the 6P3/2 state before they can undergo trap loss. We may also

look at the loss rates from the MOT as a function of the stimulated emission rate to determine γ. In this graph, the ratio of decay photon count

rate to the number of ground state atoms present saturates at high probe intensity, which implies that the transfer rate γ is slow compared to the

high probe intensities which produce this saturation. The line on the graph is a fit to our state model, and the chart shows the transfer rates obtained

from this data as compared to our model for superradiance.

Excitation Scheme

Rydberg Level γ (calc) γ (expt)

28D 1.7×105 1.2×105

43D 2.4×105 7.4×104

58D 1.2×105 2.6×104

30S 2.2×105 3.9×105

We have previously produced a high-density Holographic AtomTrap with densities of 2×1015 atoms/cm3. We will use this along

with the four-wave mixing setup to produce small excitation regions which can more easily be blockaded.