1.3.1 Photon sources based on atomic ensemble
Since the essence of optical quantum memory is the interface between light field and matter, when we want to find a non-classical light source provided to atomic quantum memory, it is natural to associate directly used atomic medium to produce non-classical light. Spontaneous four-wave-mixing(sFWM) is a process commonly used to generate correlated photon pairs under an atomic platform[21, 22, 23, 24,25, 26, 27]. Its energy level system is shown in the Fig.1.3. First, the atomic population is prepared in the ground state, then the writing pulse drives the transition between |gi → |e1i, and spontaneously emits a writing photon at the transition |e1i → |si. The generation of writing photon indicates that at least one atom has been excited to the ground state and establishes the coherence of the ground states, therefore, when the next reading pulse drives an atomic transition of |si → |e2i. This process can re-convert the ground state coherence of the atom to a reading photon, and further produce a photon pair composed of the reading and writing photon. sFWM not only can be used as a photon-pair source, but it is also a read-only memory[28]. This is because this type of memory does not require any input, and the initial quantum state is spontaneously generated by the writing process. Therefore, in the quantum repeater protocol, this memory is very suitable as a component of the syn-chronous entangled state. On the other hand, since the photon pair is directly generated from the atomic system, its corresponding frequency is already locked in the atomic tran-sition. In addition, the bandwidth also comparable with atomic natural linewidth. These properties make the atomic photon source can be directly provided the nonclassical light for the atomic quantum memory. However, since the problem of the atomic-based light source is that the experimental system is relatively complicated, such makes it difficult to mass-produce and expand to large-scale quantum communication.
doi:10.6342/NTU201901825
Writing
pulse Writing photon
Reading pulse
Reading photon
|𝑔ۧ
ۧ
|𝑠
|𝑒1ۧ
ۧ
|𝑒2
Figure 1.3: Atomic energy level diagram of spontaneous four-wave-mixing.
1.3.2 Solid state photon source
Another relatively simple way to generate photon pairs is to use the spontaneous paramet-ric down-conversion(SPDC) process in nonlinear crystals. The SPDC process is a nonlin-ear optical process that can be performed by injecting a high-frequency pump photon and then converting it to a pair of low-frequency photon pairs, which we call signal and idler photons(see Fig.1.4). The photon pairs produced by this process have a strong correlation.
The dimensions of correlations are based on different crystal designs. They can be related in frequency, spatial or even polarization. Since the experimental system of nonlinear crystals is relatively simple and quite scalable, it is widely used in the preparation of vari-ous non-classical light sources[29,30,31,32]. However, the problem faced by the SPDC system is that the photon pairs generated by the process have too high bandwidth for the atomic system. In general, the SPDC generates a bandwidth of about several hundred GHz to one THz. Relating to the atomic system MHz level, the bandwidth carried by SPDC photons greatly reduces the interaction with the atomic system. That makes the atomic-based quantum memory almost completely lose the opportunity to store SPDC photons.
In order to solve this problem, the most straightforward way is to install a filtering device after the SPDC light source[33]. The filtering device is designed to allow only a specific frequency and a finite linewidth to pass. Therefore, the final output photons can be utilized in the atom system. However, the extra filter device cannot avoid a large loss of photon de-tection rate. In order to solve the problem of SPDC’s excessive bandwidth and low gener-ation rate, in 1999, Z.Y. Ou and Y.J. Lu installed the nonlinear crystal into the cavity[34].
The finite bandwidth of the cavity was used to effectively reduce the bandwidth of the
Pump
field Signal photon
Idler photon
Figure 1.4: Energy level diagram of parametric down-conversion.
photon pair to few ten MHz. On the other hand, the resonant cavity also greatly enhances the efficiency of photon pair generation. Subsequently, many teams used this method to generate photon pairs with narrow linewidths and achieved relatively high photon pair de-tection rates[35,36,37,38, 39,40,41,42,43,44, 45, 46,47,48,49,50,51, 52,53,54].
Among them, Dr. Markus Rambach et al. implemented a 100% duty cycle and ultra-narrow bandwidth photon source based on the cavity-enhanced SPDC[44, 45, 54]. The design of this work will be widely used in the experiment of the photon-atom interface.
The narrow-band photon source is closely related to the form of the resonator. For ex-ample, the higher cavity finesse can suppress the SPDC bandwidth to be narrower so that the output photon has a narrower linewidth. Another way to suppress the linewidth is to use the cavity with a longer length. The longer resonator can reduce the cavity linewidth and further produces narrow-band photon-pairs. However, a longer cavity also means a shorter free spectral range (FSR). This behavior makes resonator possible to cover several resonant modes in the SPDC gain profile, so the photon source under such conditions will output photons in the multimode operation. Inevitably, to use such a multimode photon source under the atomic system, the experimental setup will require the additional filter-ing systems while sacrificfilter-ing the photon detection rate. A clever solution is to design the source as a non-degenerate output[55]. Non-degenerate means that the signal field and the idler field carries two different frequencies. Since the signal field and the idler field each have a different FSR, the conditions for simultaneously resonating in the cavity become extremely strict, which is called the double resonant condition. The double resonant con-dition greatly reduces the resonant modes that allowed in the resonator, so the equivalent
doi:10.6342/NTU201901825
Figure 1.5: Comparison of the parameters of the photon source based on the cavity-SPDC scheme in recent years. *The estimate of spectral brightness for is based on the detection rate without considering technical losses[54]. This figure is captured from reference [51].
FSR will be greatly increased. This behavior is called the cluster effect. When the cluster mode spacing greater than the SPDC gain profile, the photon pair can output the cavity in a single-mode operation, which makes the cavity-enhanced SPDC photon source more capable of being applied to the atomic system.
Based on the above discussion, we can sort out several important parameters as the ba-sis for designing photon sources for atomic systems. These parameters include linewidth, frequency, single/multimode operation, and generation rate of photon pairs. The photon pair generation rate is quite helpful for experiments. The high generation rate can quickly provide photons to reduce the data acquisition time, and increase the signal-to-noise ratio to obtain clear experimental data. For the atomic system, because of the system require-ments for the linewidth of the photon source, here we can introduce the spectral brightness to illustrate the performance of the photon source. Spectral brightness is an important co-efficient of performance which combines the generation rate and the bandwidth of photon source. The definition is defined by the photon-pair counting per pump power(mW) per bandwidth(MHz) per second. According to the definition of Spectral brightness, this quantity can be understood as describing the ability of a photon source to generate the energy concentrated photons. Therefore, spectral brightness is especially meaningful for atomic systems. In Fig.1.5, we compare the spectral brightness of the photon source, and also show such as the wavelength, linewidth, and single or multi-mode property for various works based on the cavity-SPDC scheme during the past 15 years.