Microwave pump-probe spectroscopy of the dipole-dipole interaction in a cold Rydberg gas

Microwave pump-probe experiments starting with a cold gas of Rb $34s$ atoms confirm that cusped line shapes observed in dipole-dipole broadened microwave transitions are due to atoms which are widely separated and exhibit small dipole-dipole energy shifts. When the experiments are interpreted in terms of a nearest-neighbor model, they demonstrate that it is possible to select pairs of atoms based on their separation and orientation.

Figure 1

A typical cusp spectrum observed in $n{s}_{1/2}n{s}_{1/2}\text{−}n{s}_{1/2}n{p}_{1/2}$ microwave transitions from a high-density Rydberg sample. This example is from $n=44$ with a peak atomic density of ${\rho }_0=1.3\times {10}^9{\mathrm{cm}}^{-3}$. Experimental points (dots) and the Lorentzian fit (solid line) are shown.

Figure 2

(a) Schematic energy-level diagram showing the relevant molecular energy levels as a function of internuclear spacing $R$. The internuclear axis is taken to be the axis of quantization. The solid downward arrows show the transitions driven from the initially populated $34s34s$ state by an on-resonant pump pulse, and the dashed downward arrows show the transition driven by an off-resonant pump pulse. The solid upward arrows show the transitions driven by an on-resonant probe pulse, and the dashed upward arrows show the transitions driven by an off-resonant probe pulse. (b) Classical picture of the interacting atomic dipoles. The dashed vertical line is the internuclear axis. In the attractive states the two atomic dipoles are parallel to the internuclear axis, and in the repulsive states the dipoles are perpendicular to the internuclear axis. The microwave field $E$ is randomly oriented relative to the internuclear axis.

Figure 3

Timing diagram of the experiment, showing laser excitation, pump and probe field microwave pulses, the field ionization pulse, and field ionization signals.

Figure 4

Observed $34p$ signal as a function of the probe frequency for no pump pulse (dashed line) and a pump pulse of amplitude $E_0$ (thick solid line) and amplitude $4E_0$ (thin solid line). With pump amplitude $E_0$ only atoms with large internuclear separations are removed from the $34s34s$ state, and the primary effect is the removal of the cusp seen with no pump pulse. With pump amplitude $4E_0$ the entire signal is reduced in size since pairs with smaller internuclear spacings are removed from the $34s34s$ state.

Figure 5

Observed $34p$ signals of Fig. 4 replotted when normalized to a peak signal of 1.0 in all cases (points) and Lorentzian fits (gray lines). In (a), with no pump pulse, there is a cusp on top of the Lorentzian fit. In (b) with pump field $E_0$ the cusp is removed, and in (c), with pump field $4E_0$ the line shape again exhibits a cusp.

Figure 6

Difference between the signals obtained with pump amplitude $E_0$ and no pump pulse (thick line) and difference between the signals obtained with pump amplitude $4E_0$ and no pump pulse (thin line). With pump amplitude $E_0$ only the cusp of the no-pump-pulse signal is removed, while in the latter case the entire signal is reduced.

Figure 7

The effect of on- and off-resonant pump pulses with amplitude $2E_0$. In all three panels the signals with no pump pulse are shown as solid lines, and areas under the signals with the pump pulse are filled. (a) On the $34s\text{−}33p$ resonance the effect is simply an overall diminution of the signal as in the $4E_0$ trace of Fig. 4. (b) With a detuning of $-4.8$ MHz, there is a larger decrease in the signal above the probe resonance frequency than below it. (c) With a detuning of +4.8 MHz there is a larger decrease in the signal below the probe resonance frequency than above it. The asymmetry in (b) and (c) is due to the fact that off-resonant transitions to the $34p33p$ state can be driven, as indicated by Fig. 2.