To execute the quantum storage or manipulation process, we allow control fields to re-ceive the switching signal as shown Fig.5.9, then further activate the quantum storage or manipulation process which is shown in Fig.5.11.
5.6.1 Quantum storage process
In the storage process, we fix the optical depth of our system at α ∼ 55 and set the delay time ratio η = Td/Ts ∼ 3 that is in order to store all biphoton wavefunction into the atomic medium(see the discussion in Chapter4). The width of our biphoton wavefunction is around Ts ∼ 25ns and therefore Td ∼ 75ns[see Fig.5.14case(c)]. Once the delay time of slow light is determined, the control beam starts to receive the switching signal from idler photons. Here we set a storage time of 100 ns and the reading power is the same with writing power(Pr = Pw ∼ 16mW). Follow the setting as given above and also after an integral time of 2.5 hours, we successfully observed the biphoton wavefunction after the quantum storage process. The result is illuminated in Fig.5.16.
Quantum storage
700 800 900 1000 1100 1200
0 20 40 60 80 100 120 140 160
Coincidence counts
Time(ns)
Slow light
Storage
Figure 5.16: Quantum storage and slow light of biphoton wavefunction. In the measure-ment, the detection window is 500 ns the time bins of 5 ns. In the cases of slow light and storage, the area represents the numerical simulation based on Eqs.4.65and the solid lines are the raw experimental data. The storage process is showed by the region of ”quantum storage” with a storage time of around 100 ns.
doi:10.6342/NTU201901825 Based on Fig.5.16, we can estimate the storage efficiency of ∼36% which is slightly
lower than slow light efficiency of 56%. The source of efficiency reduction was owing to: the leakage of signal photons in the writing phase, the system decoherence rate γgsof 0.065 ± 0.01Γ and the photon switching effect due to off-resonance driving by the con-trol fields(see Ref.[6] and appendixA.2). On the other hand, the biphoton wavefunction is stretched in time domain since the finite EIT-bandwidth(i.e., broadening effect) that we have discussed in Chapter 4. Illuminatingly, although the broadening effect makes the biphoton wavefunction unclear, the broader temporal distribution of biphoton wave-function corresponds the frequency distribution is narrowed by passing through the EIT-medium. That result exactly is the function of a narrow-bandwidth filter[67]. In order to quantitative this behavior, here we evaluate the bandwidth of slow light and storage by estimating the FWHMs of G(2)s,i(τ ), and we have 1.8 MHz and 2.3 MHz, respectively.
Notice the bandwidth of input biphoton wavefunction is ∼6.2 MHz which is measured in Fig.5.5. And we can clearly discover the bandwidth is narrowed by EIT-medium. In addition, since the leakage in the writing process, the bandwidth of storage has a grain of difference with the slow light pulse.
In order to express the non-classical correlation of the photon pair after interacted with EIT-medium, here we estimate the g(2)s,i(τd) for slow light and storage process and we find the values of 7.20 and 5.87, respectively. According to the estimation of gs,i(2)(τd), that illustrates our EIT-quantum memory preserved the non-classical correlation of gs,i(2) > 2.
However, we still can observe that those values of gs,i(2) are less than the case of input photons of 47. The sources of reduction include three reasons. First, the leakage of the control beam in the reading phase will increase the noise photons and further reduce the signal-to-noise ratio. The second reason is the efficiency of EIT-memory is not unitary, that makes the retrieval photon numbers be limited. The final, the broadening effect re-sulted in G(2)s,i(τ ) become blurry in the coincidence window. The first two points belong to technical issues that can be solved by using a high extinguish ratio filter and high-efficiency quantum memory[6], respectively. About the third issue of broadening effect, we have discussed in Chapter 4. In that time, we have talked about the manipulation process can control the profile of biphoton wavefunction, and further improve the quan-tum fidelity of output photons by correcting the broadening effect. In addition, since the manipulation process allows us to use different reading power to reconstruct the bipho-ton wavefunction, that process provides the function to manipulate the temporal-mode of biphoton wavefunction. For instance, a stronger reading power in reading phase in-crease the group velocity of biphoton wavefunction, and that makes the temporal-mode of biphoton wavefunction is squeezed which correspond to the clear signal-to-noise ratio.
That makes in the manipulation process also can improve the non-classical nature gs,i(2)and
lets the process become more valuable.
5.6.2 Manipulation process
Since here we already prove our system has the ability to execute the process of quantum storage and also illuminate a clear interaction between photons and atoms, therefore, to implement the manipulation process is very straightforward. By changing the setting of Pr in Fig.5.9, that is very easy to control the conditions in the reading phase. In the experiment, we utilize a series of Prto reconstruct the biphoton wavefunctions. The result as shown in Fig.5.17.
In Fig.5.17, the numbers in the figure corresponding to the ratio between reading power to writing power, ξr/w ≡ Pr/Pw. Therefore, the case (c) of ξr/w = 1 represents the light storage process. The first thing we have noticed in Fig.5.17 is the behavior of biphoton wavefunctions are manipulated in the process. In those cases of ξr/w 6= 1, the biphoton wavefunctions are manipulated and expressed the properties that differ from the case of slow light(or ξr/w = 1). We can observe that by increasing the factor of ξr/w, the biphoton wavefunctions are compressed since the group velocities are increased in the reading phase[Fig.5.17(d)∼(f)]. For the opposite case of Fig.5.17 (b) of ξr/w < 1, we have a broader G(2)s,i in the temporal-mode which corresponded to a narrower bandwidth of biphotons. That case shows the manipulation process can control the temporal-mode of biphoton wavefunctions and further control the bandwidth of biphotons.
On the other hands, we expect the non-classical correlation which expresses the signal-to-noise ratio of G(2)s,i also is manipulated in this process. In the ideal case, the biphoton wavefunction becomes centralized in the high-ξr/w case and further illuminate the non-classical correlation g(2)s,i. However, in the real experimental setup, we can observe the noise photons are increased as following the Pr as increasing. This imperfect issue may shroud the biphoton wavefunction and reduce the non-classical correlation gs,i(2). Further-more, although we can see the biphoton wavefunction becomes centralized in high-ξr/w
case, however, the signal-to-noise ratio seen like not enhance by the process. In fact, the main reason that we have already been discussed before, since the structure of en-ergy levels in cesium D2-line involved the excited states |F = 5i, that results in the photon-switching effect in the EIT-QM and further decrease the storage efficiency. This Pr-dependent limitation of efficiency will destroy the non-classical nature of output pho-tons.
In order to clarify the behavior of biphoton wavefunction in the manipulation process, we systematic analysis the experimental results in Fig.5.17 in the next section, includ-ing the bandwidth, the storage efficiency, the non-classical correlation, and the quantum fidelity.
doi:10.6342/NTU201901825
0.7 0.8 0.9 1.0 1.1 1.2
Delay time(s) 40
80 120 160 200 240 280
0
Coincidence counts
(a) Slow light
(b) 0.72
(c)1
(d)2.22
(e) 3.54
(f) 5.12
(g) 5.72
(h) 8.70 Quantum
storage 320
Figure 5.17: Manipulation process of biphoton wavefunction based on EIT-QM. The yel-lows solid lines represent the theoretical simulation based on Eqs.4.65. The gray bar is are the raw data of coincidence counts. The detection window is 500 ns with time bins of 5 ns. The total wave counts are 30000.