EIT as phase modulator

based on these studies as the theoretical framework remains valid for ultra-low probe intensities also.

5.6. EIT as phase modulator

In the EIT cell an amplitude modulation of the strong coupling field is transferred to the weak, possibly single-photon probe field. Single-photon probe beam amplitude modula-tions will be experimentally shown in chapter 6, but the modulation transfer in general is also an outcome of the theoretical treatment in section 5.2.2. Besides an amplitude mod-ulation of the probe, the EIT effect will also result in a cross-phase modmod-ulation. Some preliminary studies were performed in order to investigate the influence of the coupling laser on the probe laser phase under EIT conditions. To allow phase measurements the experimental setup from figure 5.6 was extended by a Mach-Zehnder interferometer around the EIT cell, as shown in detail in figure 5.9.

QWP

Figure 5.9.: Details of the setup for EIT phase measurements. The Mach-Zehnder inter-ferometer is stabilized by a counter-propagating auxiliary 850 nm laser using a dichroic mirror (DM) and a feedback loop with piezoelectric elements in one arm. The dashed line encloses a rigid setup of polarizing optics to close the Mach-Zehnder interferometer and obtain an interference signal for active arm-length stabilization, see text for more info. A single-mode fiber in front of the photo detector ensures spatial mode matching of probe and reference beam in order to increase the interferometer’s visibility.

In front of the EIT cell the probe laser is split into two components, one passes the EIT cell and the other is used as phase reference. The interferometer is actively stabilized using a mirror mounted on a piezoelectric element in the reference arm and a counter-propagating auxiliary laser at 850 nm, i.e., far off-resonant from the coupling and probe transitions. The auxiliary laser light was produced using another external-cavity laser system (Toptica DLpro) with a typical linewidth of only 100 kHz and very low drift due to ambient temperature changes ( 100 MHz/K) and good isolation against acoustics and vibrations. As a result of the particular experimental configuration needed for the

EIT effect, the auxiliary laser leaves its output port of the interferometer with different polarization of its two parts which traveled the probe and the reference arm. Thus, in order to measure interference some further optical components are required to separate these two superimposed beams, change one beam’s polarization and superimpose them again in front of a photodiode. To ensure that virtually no arm length fluctuations occur in this part of the beam path, all optics are integrated in a small rigid aluminium structure of∼30 mm diameter. Using this configuration, arm length fluctuations of the probe or reference arm directly result in changes of the interference signal detected by the photodiode.

At first, the Mach-Zehnder interferometer itself was checked. Therefore, without the EIT cell in place the reference arm of the interferometer was linearly scanned and the interferometer visibility was studied by monitoring the probe laser interference at its output port. As shown in figure 5.10, the visibility is very good, it was found to be

>0.98.

Figure 5.10.: Scan of the reference arm in the Mach-Zehnder interferometer. The blue line shows the applied scan voltage, the black dots the measured interfer-ence and the red curve a fitted sinus curve. The visibility is>0.98.

Now, for EIT cross-phase modulation measurements the reference arm-length was ac-tively stabilized using the auxiliary laser interference signal as reference. With active stabilization the probe laser interference signal was found to be virtually constant. The EIT configuration was established by adjusting coupling and probe laser frequency to match their respective transitions while a continuous wave probe beam of 20µW and 2 mW coupling power was used. Behind the EIT cell the superimposed probe and refer-ence signal was detected by a fast, low-noise photo detector (Hamamatsu C4777). The EIT cell was operated at 54^◦ C in order to increase the EIT transmission modulation amplitude, albeit at the cost of lower overall transmission. Figure 5.11 (A) shows the intensity at one output of the Mach-Zehnder interferometer under resonant EIT condi-tions. A pronounced temporal intensity fluctuation is apparent. This fluctuation is only present if the EIT cell is in place and a resonant coupling beam is present, as several test measurements proved.

5.6. EIT as phase modulator

Figure 5.11.: (A) Interference signal of the probe laser measured at one output of the Mach-Zehnder interferometer (see figure 5.9) under resonant EIT condi-tions. (B) Comparison of the Fourier transform of the signal in (A) (red curve) with the normalized Fourier transform of the direct beat-note signal between the coupling laser and the stabilized probe (black curve). The beat note signal was obtained by down-mixing via a local oscillator of≈9.2 GHz.

A common broad spectral feature (see text) between 5M Hz and 7M Hz is clearly visible. For comparison, the inset shows the normalized Fourier transformation of the direct beat-note signal of the probe laser with itself.

The sharp features at 385 kHz and 930 kHz and at 7, 7.6, 8.2, 8.7 MHz are attributed to the laser frequency stabilization electronics.

In order to gain further insight a Fourier transformation of the measured intensity fluctuation signal was performed, which is shown as red curve in figure 5.11 (B). As reference, a beat-note signal between the coupling laser and the stabilized probe laser was measured using direct detection by a 10 GHz photo diode and down-mixing via a local oscillator of ≈9.2 GHz. Its Fourier transformation is plotted as black curve in figure 5.11 (B). The data for the red and for the black curve were recorded simultaneously using two channels of a digital storage oscilloscope with 20M samples record length.

Thereafter, the Fourier transformation was performed on both data sets individually.

It is apparent that both signals almost overlap, apart from a linear decline of the red curve towards higher frequencies, which suggests a 3 dB bandwidth of 10 MHz for the modulation observed in figure 5.11 (A). In particular, a characteristic broad frequency component between 5M Hz and 7M Hz, which reflects a side-band produced by the loop-filters in the phase-lock electronic, occurs in both curves. This measurement shows that there is cross-phase modulation between the coupling and the probe laser [173], as this characteristic broad frequency component is not present on the probe beam before it passes the EIT cell, which is proven by a test measurement shown in the inset of figure 5.11 (B). Here, the beat-note signal of the probe laser with itself is shown. It was measured at the output of the Mach-Zehnder interferometer with the EIT cell being removed, the characteristic frequency component between 5M Hz and 7M Hzis absent.

With a blocked coupling beam in front of the EIT cell the modulation is also not present.

It is important to note that the cross-phase modulation between coupling and probe laser cannot be achieved by electronic modulation, e.g., by detecting the coupling laser and feeding this signal on an EOM to modulate the probe field. However, a coherent modulation mediated by EIT is required.

5.7. Discussion and short summary

Cross-phase modulation between coupling and probe laser was observed. Due to the coherent nature of the modulation also non-classical correlations, e.g., as present in a squeezed pump beam, can be transferred to the probe beam. Cross-phase modulation is thus a possible tool to transfer quantum correlations between strong light beams and weak beams, possibly single photons. Cross-phase modulations were proven through a characteristic frequency component caused by the phase-locking electronics which mod-ulated the coupling laser. Without EIT, this frequency component is present on the coupling beam only, but it is visible as phase-modulation on the probe beam behind the EIT cell as soon as the EIT effect occurs. Although selective and controlled phase manip-ulations were prevented in these first experiments by the superimposed noise modulation on the coupling beam, this can be overcome by a more stable laser source [174, 175].

In addition, using AOM [176] or EOM generated coupling laser sidebands as probe field and a selective coupling beam modulation in front of the EIT cell instead of the two separate phase-locked lasers might be a reasonable enhancement for this experiment.

A fast active coupling laser amplitude fluctuation compensation, e.g., by using another AOM, might also be needed.

Whereas cross-phase modulation between weak, possibly single-photon fields were al-ready discussed and demonstrated [149, 177, 150], it might also be possible to utilize cross-phase modulation between a stronger coupling field and a weak, possibly single-photon field. Possible applications may concern transfer of quantum correlations between quadrature components of two strong beams to correlations between a quadrature com-ponent of a strong beam and the phase of a single photon. An example would be to use one arm of two entangled beams as coupling laser in an EIT configuration and to map its amplitude fluctuation on the phase of a single photon using a Mach-Zehnder

5.7. Discussion and short summary interferometer in the same way as shown in figure 5.9. Except for an additional de-tector in the second arm of the interferometer the setup is similar to the one used by Lobino et al. [178] for quantum tomography of a light pulse stored in ⁸⁷Rb vapor. In that paper an extra noise component of the stored and retrieved state was attributed to the population exchange between atomic ground states of the EIT Λ-system while the light was stored and the coupling field was switched off. Here, the effect of the coupling field itself on the probe field was analyzed, and a combination of the two experiments is certainly aspired.