In the previous section, we have measured the biphoton wavefunctions in the cases of the storage process and manipulation process. We set a few different conditions in manipula-tion and also observed the different reacmanipula-tions of G(2)s,i. In this section, we start to character-ize the properties of G(2)s,i in the manipulation process, including some classical behavior of bandwidth and storage efficiency. The non-classical nature of cross-correlation and the quantum fidelity also is analyzed in this section.
5.7.1 Efficiency and bandwidth controlling
Storage efficiency
For the condition of a fix delay time ratio η ≡ τd/Ts, the storage efficiency in the EIT-QM is only related to the optical depth α(see Chapter4) in an ideal case, however, in the cesium D2-line, the unavoidable photon switching effect add another variable for storage efficiency. Since the photon switching effect is related to the strength of the control field, that can expect that the stronger control fields in the reading phase will correspond to the lower efficiency, and vice versa. In order to understand the relation between Pr and efficiency in the manipulation process, here we analyze the storage efficiency of those cases in Fig.5.17, and we find the behavior as a function of ξr/was shown in Fig.5.18.
In Fig.5.18, that can find all efficiency in the manipulation process is lower than slow light. That is due to the finite rising(or lowing) time of control field switching and result in the leakage in the writing phase. On the other hands, we also observe the decay behavior as a function of ξr/w which shows the photon switching effect depressing the storage efficiency. Here we consider the exponential decay of T0exp(−γsξr/w) to characterize the photon switching effect, where T0is the efficiency at ξr/w = 1. After fitting, the decay rate from photon switching effect γsis determined of ∼0.055. The fitting curve is shown in Fig.5.18. The decay behavior in the manipulation process will strongly affect the non-classical correlation gs,i(2), since the photon loss strongly reduce the signal-to-noise ratio.
We will have a discussion in the following section.
Bandwidth controlling
Now we turn our attention to the temporal-mode of biphoton wavefunctions. The ma-nipulation process can control the temporal-mode of biphoton wavefunctions and further controlling the bandwidth or improving the quantum fidelity(see Chapter4and next sec-tion). For the bandwidth of biphotons, we estimate the biphoton bandwidth by measuring
doi:10.6342/NTU201901825
2 4 6 8 10
0.1 0.2 0.3 0.4 0.5 0.6
Storage efficiency
r/w
Slow light
Figure 5.18: Storage efficiency of manipulation process. Since photon switching effect from off-resonant driving by control beam, a behavior of exponential decay is introduced in the storage efficiency feature. The dashed line represents the efficiency of slow light.
The solid line is exponential fitting for describing photon switching effect. The error bars are considered by assuming Poissonian statistics.
the FWHMs of G(2)s,i(τ ) in Fig.5.17. The analysis is shown in Fig.5.19.
The results clearly demonstrate the bandwidth controlling of retrieval photons. For the case of ξr/w< 1, the bandwidth of biphotons even narrower than slow light. That implies the manipulation process possess the function of the ultra-narrow-band filter. Moreover, since the efficiency is determined by the writing process and the output photon number is independent on Pr[68], the biphoton wavefunction can be completely used without blocking the waveform. On the other hands, follow the ξr/w increase, the bandwidth of output biphoton wavefunction tend to broad. In the case of ξr/w∼ 8.5, the bandwidth even broader than the input G(2)s,i. That corresponds to the compression of biphoton temporal-mode in the manipulation process.
In Chapter4, we have theoretically calculated the manipulation process and also got the solution of the field of Eqs.4.59. The solution gives the result of the bandwidth of output fields is proportional to ξr/w which is also proportional to the EIT-bandwidth in reading phase. Notice that the Eqs.4.59 is already considered the approximations of ne-glecting high-frequency response of EIT. However, in our experimental conditions, the EIT-bandwidth in reading phase is no longer as proportional to ξr/w, since the system α is not high and the Rabi frequency of control field is relatively high. In this experi-mental regime, the behavior of EIT-bandwidth in reading phase is more close topξr/w
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Bandwidth(MHz)
r/w
Input
Slow light
Figure 5.19: Bandwidth of biphoton wavefunction with different R/W power ratio. Fol-low the R/W power ratio increase, the bandwidth of biphoton wavefunction as increase which demonstrated the bandwidth manipulation of heralded single photons. The band-width is evaluated by the reciprocal of FMHW of the numerical fitting in Fig.5.17.
The yellow(gray) dashed lines represent the biphoton wavefunction bandwidth of slow light(input).
doi:10.6342/NTU201901825 proportion. Thus, we consider the fitting curve that proportional topξr/w to fit the
ex-perimental data. Final, a good agreement between the exex-perimental data and theoretical model is shown in Fig.5.19.
After the analysis of the classical behavior of the manipulation process. We have demonstrated the bandwidth or temporal-mode controlling of biphoton wavefunction. In fact, the same process also can be used for classical light and also get the same behavior of bandwidth or efficiency, since those physical quantities are classical. But here, our goal is that we want to further understand the quantum nature of the interaction between EIT-QM and the single photons. Therefore, in the final section, we start to consider the quantum nature of interacted biphotons. Moreover, those experiments will prove the ability to provide non-classical light by the photon source for the atomic QM, and the ability of the preserve of the quantum nature of light by EIT-QM.