−αΓ γgs|Ωc|2 + (4δ2gs+ γgs2 )Γ
(|Ωc|2+ Γγgs− 4δgeδgs)2+ (2δgeγgs+ 2δgsΓ)2
, (5.3)
where Γ = 2π × 5.23MHz in cesium D2-line, the control field is set at on-resonant in the transition of |F = 4i → |F0 = 4i, and thus two-photon detuning is equal to δge. In Fig.5.7, we applied a 100µs pulse of weak coherent light to probe the transmission of light. By analyzing the spectrum, we estimated the optical depth of 60.6 ± 5 with the control field Rabi frequency of 1.73Γ. The decoherence rate is 4.4 × 10−3Γ in this case.
5.4 Testing the connection between the photon source and quantum memory
So far, we have respectively introduced and verified the photon-source and quantum mem-ory, now it’s time to connect two different systems. In Fig.5.8, we illustrate the setup of
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-4 -3 -2 -1 0 1 2 3 4
0.0 0.2 0.4 0.6 0.8 1.0
Transmission
One-photon detuning ()
Figure 5.7: Transmission as a function of one-photon detuning in the EIT-spectrum. The parameters are estimated as: α = 60.6, Ωc= 1.73Γ and γse= 0.0044Γ.
quantum storage and manipulation of single photons. The setup combines the photon-pair source and quantum memory. In order to let two systems communicate with each other, we implement three additional setups, including (i) a 150 m fiber that links signal photons to the QMs, (ii) the switching signal from the SPCMi to the AOM2 and (iii) the measurement of coincidence counts between SPCMiand SPCMQM.
5.4.1 Switching signal for quantum storage
We first pay attention to the setup (ii). Since the SPDC-based photon source relies on the idler photons to herald the random creation of signal photons, however, we should provide the same information for QM lab to switch-off the control fields when signal photons are coming, and further complete the storage process. Therefore, we here send the switching signal from the SPCMi to the AOM2 for switching the control field. In order to realize this process, we design a simple schematic block for quantum storage switching. The schematic block is shown in Fig.5.9. In the process of Fig.5.9, idler photon detection will follow the sequence of AOM1 switching(Fig.5.2), however, in the quantum storage experiment, that only need to detect the idler photons during the time when the cold atoms are ready. Therefore, we need the function that similar to an AND-gate to process the idler and cold atoms signals. The cold atoms signal is provided by the Bit-EIT that come from the pulse and digital word generator(Spincore). To realize the AND gate and also monitor the signal simultaneously, we first use the power splitter to share the signals of SPCMi
AOM1
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Figure 5.8: Experiment setup of quantum storage and manipulation. (a) The photon-pair source laboratory. (b) The quantum memory laboratory. In the photon-photon-pair source laboratory, the signal photons are switched to a 150 m fiber and lead the photons to be sent to the QMs lab. Therefore, the function of SPCMsis switched-off(the light painting).
On the other hands, in the quantum storage setup, the idler photon that is detected by SPCMi not only play the role of heralding the creation of signal photons, but also possess a function of informing the switching signal to control fields for switching off and -on, and further accomplish the quantum storage process. In the quantum memory laboratory, the responsibility of detection is accountable at SPCMQM since the incoming light fields are single photons.
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Figure 5.9: Schematic block diagram of the switching for the quantum storage. SW: RF Switches, Fun.: function generator, DG535: digital delay generator. Spincore: pulse and digital word generation.
and Bit-EIT to the oscilloscope for AB-trigger. On the other hands, the signal of SPCMi is used to as TTL for SW1 to switch the Bit-EIT. The Bit-EIT is set as a 20 µs square pulse which is much greater than the SPCMi pulse of 20 ns, therefore, the output of the SW1 will be a new signal in which the idler signal is limited to the Bit-EIT interval. In other words, the setup of SW1 provides a function of the AND gate.
After the process of AND signal, we use this signal to be the trigger of DG535(digital delay generator) and further generate the synchronous A and AB signals. The signal AB is an inverse square pulse which is used to determine the control fields switching profile, therefore, the width of AB will correspond to the storage time. However, here we didn’t send the AB to the AOM2 directly. The reason is that we want to conveniently switch the modes between quantum storage and classical storage(store the weak laser light).
Therefore, we send the AB signal to the SW3 then combine with Bit-conl. that is used to control the sequence of the control field in classical storage. Further, by using the Bit-Q/C, we can control the storage-modes of quantum or classical very convenient.
In order to realize the manipulation process, the power of control fields in the writing and reading phase need to be controlled. Here we use the signal A from DG535 to switch the SW2 and further to select the different powers for reading(Pr) or writing(Pw). How-ever, in our experimental setup, the control field also plays a role of optical pumping, that makes the power of control fields are not arbitrary. In order to overcome this issue, we prepare another function generator to provide power for optical pumping, furthermore, the Bit-pump is used to control the power in the phase of optical pumping or storage pro-cess in SW4. Final, the SW5 receive the TTL signal form SW3 which decide the storage process, moreover, the input signal from SW4 determine the power for reading and writ-ing. Therefore, final we have a controllable signal for controlling the storage time and manipulation conditions.
The switching setup for the quantum storage provides a scheme to store the randomly generated signal photons. However, there exists an issue of the whole process takes about 200 ns to switch-off the control field(contain the AOM2device and electric circuit). This issue results in a limitation for signal photons, that is the signal photons must delay of at least 200 ns to wait for the switching process completing. In order to compensate this time delay due to the switching setup, therefore, that born the setup (i) in Fig.5.8and we will introduce that setup in the next section.
doi:10.6342/NTU201901825
5.4.2 Time delay due to optical path and external efficiency of quan-tum storage setup
The setup (i) is a long fiber with a length of 150 m. This fiber guide the signal photons to the QM lab and also provides the time delay for waiting for the switching process. In order to measure the time delay which contributes by the fiber, we measure the two-photon correlation function further to compare the cases of G(2)s,i(τ ) in the photon source(Fig.5.1) and in the QM lab[Fig.5.8, setup(iii)]. The result as shown in Fig.5.10
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Photon source Arrived to QM lab
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Figure 5.10: Measurement of biphoton wavefunction in photon source laboratory(gray) and quantum memory laboratory(yellow) with a pump power of 0.16 mW. In this case, the cesium atoms in without loaded in the QM lab. The optical delay is around 800 ns, including a 150 m fiber and, Etalon filter and 4.8 m in the free space.
We can observe a clear optical delay of around 800 ns, including a 150 m fiber, Etalon filter and 4.8m in the free space. This delay provides the buffer to let us can successfully execute the switching process. Based on the result in Fig.5.10, we set the switching pro-cess is executed at 865 ns to storage all biphoton wavefunction and further to manipulation the properties of biphotons.
In Fig.5.10, we also can perceive the attenuation of biphoton wavefunction since there are few unavoidable losses in the experimental setup. The attenuation not only reduces the detection rate but also decrease the non-classical correlation of biphotons. In order to more carefully understand the source of losses, here we progressively measure the losses and further define the external efficiency. The external efficiency ηExt is defined as the ratio between the signal photons output from the photon source laboratory, and
the photons coupled to the single-mode fiber for SPCMi that after passing through the quantum memory setup. And that can be expressed of
ηExt = ηpol× ηop× ηeta× ηf ib× ηBP = 32.2(5)%, (5.4) where ηpol represents the transmission of a polarizer of 76%. The optical elements loss ηop ∼ 89.4% which include the lenses for MOT-coupling, the defective coating on the MOT cell, and the three irises for blocking the scattering light. Another filtering setup is the etalon cavity which provided favorable isolation for the unwanted frequency. The total extinction ratio is 129.1 dB(include all filter setup). However, the filter setup causes the transmission of the signal photons is reduced to ηeta ∼ 60% by the etalon. ηf ib denotes the single-mode-fiber-coupling efficiency of 88.8%. The transmission of the band-pass filter is ηBP ∼ 90%.
Since the losses as given above may affect the nonclassical correlation of biphotons, here we based on those conditions of losses further measure the nonclassical correlation gs,i(2) once again in the quantum memory system, the result as shown by the yellow dots in Fig.5.6. We can see the reduction between the measurement in the photon source and the quantum memory system. The optimal pump power is observed at 0.16 mW and the non-classical correlation g(2) ∼ 47. We also estimate the detection rate of 1.69 kHz/mW in this case.
After the examination of systems, next, we start to introduce the final setup of the pulse sequence for operating the quantum storage system.
5.4.3 Pulse sequence of the system
The pulse sequence of the quantum storage system combines the sequence of photon source and the atomic system. That is illuminated in Fig.5.11.
The process of quantum storage as follows: when the MOT be prepared to serve as quantum memory, the pump beam for photon source is switched from a high power(40mW) to low power of 0.16mW for SPDC process. At the same time, AOM1 turn on to lead idler and signal photons to SPCMi and quantum memory laboratory, respectively. When SPCMi detect an idler photon, on one hand, the switching process that we introduced in Fig.5.9 be activated and further send a switching signal to the control field. On other hands, that indicates the photon is coming. After waiting for 865 ns for the single-photon propagation, control beam be switched-off and store the signal single-photons by EIT-memory. With a storage time 100 ns, the control beam is switched-on to retrieve single-photon again. By applying a series of variable power of control beam for EIT-memory, the waveform of photon-pair can be manipulated. Final, the manipulated signal
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0.96ns 0.86ns 0ns
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Figure 5.11: The pulse sequence of quantum storage and manipulation. We can see that is only 20µs experimental time for quantum storage and manipulation. Since the repetition rate of the atomic system is 8Hz, the real-time of the experimental process is around 1 to 2 hours to integrate enough data.
tons are detected by SPCMQM and reconstruct the biphoton wavefunction by coincidence measurement of SPCMQM and SPCMi.
Here we give a short summary for the section. In this section, we have done the examination for the quantum storage system before the execution of quantum storage.
We found the optimal condition for pump power of 0.16 mW and generate the photon-pair with a non-classical correlation gs,i(2)(0). The detection rate is 1.69 kHz/mW in the quantum memory laboratory. In order to realize the synchronize between control field switching and photon-pair generation, we develop the switching process that introduces in Fig.5.9. However, the time delay due to the electric circuit that makes the switching cannot be executed on time. To overcome this issue, we used the 150 m fiber to increases the delay of signal photons. After making sure the timing of arriving of signal photons, we are ready to follow the process in Fig.5.11 to realize quantum storage of single photons from cavity-SPDC.