Controlled Saturation by Separate Saturation Beam

In this section an additional, so-called saturation beam is introduced. It is exactly overlapped with the probe beam and only shifted in frequency by a few MHz. The overlap of the two beams is ensured by transferring them to the cavity in the same single mode fiber. They are generated by two independent AOM benches. This avoids unwanted sum and difference frequency generation as it would occur when driving one AOM with two frequencies. Since the stabilization of the probe and saturation beam is done after the fiber, where both beams are overlapped, a sample-and-hold technique has to be applied. Before the atoms are launched via the atomic fountain towards the cavity the probe beam PID control is used to sample the power level of the probe as well as the saturation beam independently and one after the other. During each of these gauging cycles the respective other beam is completely turned off. The determined output power values of the PID controller during this process are then stored by the experimental control system and can be activated during the experimental sequence when needed. Once an atom is captured, a similar switching measurement as described previously (cf. Section 6.7) is used. During the cool intervals the saturation beam is completely turned off and the intensity control of the probe beam is handled in the regular PID configuration. During the short probe intervals the previously stored intensity settings for the probe and saturation beam are activated and the otherwise applied feedback is switched off. After a certain number of repetitions of cool and probe intervals the atom is kicked out of the cavity. In the subsequent check and reference intervals the saturation beam as well as the probe beam are activated.

The additional saturation beam is used to independently saturate the atom inside the cavity from the probe beam and hence acts as if the coupling of the atom and the cavity is dynamically controlled. A low power of the probe beam is chosen such that the atom is not saturated by this beam. The saturation beam is positioned frequency wise close to one of the normal modes of the atom enabling saturation even at lower powers. The actual frequency relative to the coupled

Free-space Atomic Antiresonance 7.8 Saturation Measurements

system is depicted in the inset of Figure 7.9. As done in the previous section, the probe beam is scanned in frequency and the phase of the coupled system compared to the empty cavity is measured. The data in the plot has been post-selected with a qualification of 20%. Scans for three different power levels of the saturation beam are depicted. The indicated power levels are referenced to the empty cavity photon number, which is around one order of magnitude larger than the actual photon number at the position of the saturation beam for the coupled system.

The scan at low saturation power (blue line) does not show any significant deviation from a scan without saturation beam. This is expected since the intensity of the beam is still slightly below the saturation photon number of the atom. The situation changes clearly for higher intensity levels as depicted by the green and red curve. Here, the atom is saturated leading to a clear reduction of the phase shift.

Figure 7.9: Influence of saturation beam on the normal-mode spectrum. Normal-mode spectra for various intensity settings of the saturation beam are depicted. A switching measurement of the phase shift of the coupled system with respect to the empty cavity is carried out. A qualification of 20% is chosen. The inset shows the position of the saturation beam in a theoretically computed spectrum.

The change in the phase of the transmitted probe beam depending on the power of the saturation beam can also be employed as an efficient means to control the phase of the transmitted beam with a weak saturation beam. A phase scan where the detuning of the probe as well as the saturation beam is fixed is plotted in Figure 7.10. Here only the intensity of the saturation beam is altered. The detuning of the two beams relative to the cavity resonance can be seen in the inset. The frequency of the saturation beam is again chosen close to the position of one of the

-20 -15 -10 -5 0 5 10 15 20

7.8 Saturation Measurements Free-space Atomic Antiresonance

normal mode to efficiently saturate the atom D_pc 2p=12 MHz. The probe beam is set a few MHz above the empty cavity resonance. Here the phase shift of the coupled system compared to the empty cavity is largest. The power of the saturation beam results from an actual measurement of the transmitted power obtained from the heterodyne data taken during the reference intervals at the end of the sequence. The values are scaled to their respective empty cavity value. The power region around 0.01 empty cavity photons was hard to probe since the PID is not aligned to function properly for such small light intensities; in the case the set-point was adjusted to such power levels the output of the PID produced an output, which corresponds to around 0.001 empty cavity photons. Readjusting the PID to work in this power regime would significantly limit its frequency response to values in the few kHz region or cause a saturation of the PID at higher trap powers.

In Figure 7.10 the phase dependency of the transmitted probe beam as a function of the power of the saturation beam is shown. For this plot a qualification of 3% is used to post-select the data. A logarithmic scaling is chosen for the x-axis of the plot. It illustrates nicely saturation effects as they occur for the single atom. An exponential decay serves can be fitted to the negative experimental values of the phase shift measured at higher intensities of the saturation beam, i.e. above 0.05 empty cavity photons. The result is shown as diagonal red line. A

saturation-beam intensity I_sat,beam (empty cavity photons)

Figure 7.10: Controlling the phase of the transmitted probe beam by the saturation beam intensity. The phase shift of the transmitted probe beam for the coupled system with respect to the empty cavity is plotted as a function of the saturation beam intensity (logarithmic scaling). The intensity of the saturation beam is measured behind the cavity and plotted in units of the empty cavity photon number.

Free-space Atomic Antiresonance 7.8 Saturation Measurements

horizontal red line marks the value of –95 degrees, measured for the unsaturated atom. For an effective coupling of g_eff 2p=13 MHz the saturation intensity amounts to 0.027 intracavity photons. For the selected experimental parameters this value corresponds to a saturation beam intensity of 0.18. Here the phase of the transmitted probe beam also shows a clear increase in the experimental data. The measured phase shift varies from values below –95 degrees for a very weak saturation beam to values above –35 degrees for high saturation. The saturation beam thus enables to shift the phase of the probe beam by more than 60 degrees. While this phase shift is achieved for a very low intensity level of the saturation beam, it still does not permit to generate phase control with just a single photon. The main reason for this is the incoupling efficiency of the beam into the cavity at the respective detuning which is below 10% in combination with the missing phase matching with the light in the cavity. However, this phase measurement shows the implementation of a nonlinear process on the few photon level.

Atomic Antiresonance and Parametric Feedback in a Strongly Coupled Atom-Cavity Quantum System