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Abstract
Nondegenerate four-wave mixing (NFWM) is a practical and effective technique for generating or amplifying light fields at different wavelengths, and could be used to create color correlation and entanglement. Here we experimentally investigate the NFWM process in diamond atomic system via two-photon excitation with two pumps at 852 nm and 921 nm, demonstrating that a seeded NFWM with a third laser at 895 nm and two self-seeded NFWMs due to amplified spontaneous emission (ASE) occur simultaneously. We compare the two kinds of processes and show that the single- and two-photon detunings hold the key role in distinguishing them. As a result, the enhancement of seeded NFWM is obtained by selecting large one- and two-photon detunings, in which case the ASE induced self-seeded NFWM can be largely suppressed. In contrast, the ASE and its induced NFWM are effectively achieved with one- and two-photon resonant excitations allowing for population inversion for efficient ASE.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Four-wave mixing (FWM), known as an important nonlinear optical effect, has attracted much attention due to its wide applications in phase conjugation [1], optical parametric amplification [2], squeezed light generation [3], and optical frequency conversion [4]. Extensive studies on quantum coherence enhanced FWM in atomic ensembles [5,6] have shown great potential to develop quantum entanglement [7–10], optical storage and quantum memory [11–14]. Such quantum resources and technologies hold the promise in quantum information processing [15–19], quantum communication and networks [20–22].
Compared to the nonlinear-crystal based quantum light resources via spontaneous parametric down-conversion (SPDC) or optical parametric oscillator (OPO), the quantum light generated from FWM in atoms has the frequency with narrow bandwidth matching exactly the atomic transitions. In addition, the nondegenerate FWM (NFWM) in a diamond atomic structure can produce entangled photon pairs or correlated light beams with substantially different wavelengths, which corresponds to the frequencies of different atomic transitions, or corresponds to a telecom window and an atomic transition line simultaneously [23–25]. Such resources can therefore be used to realize atom-based long-distance quantum communication protocols [26,27].
Most of the experimental investigations of NFWM with diamond-type atomic system were realized in cold and warm alkali atoms [24,28–32], generating the infrared (IR) lasers at the wavelengths different from the pump lasers. Also, the generation of blue or ultraviolet (UV) lasers in this atomic system can be obtained [33–40]. Although both of the IR and blue (or UV) lasing productions are frequency up-conversion FWM processes, the underlying physics is very complex to be clearly understood and identified. This can be possibly attributed to the fact that the coherent IR light is obtained due to seeded NFWM, whereas the blue or UV coherent emission is resulted from spontaneous NFWM. Recently, the generation of coherent mid-infrared (mid-IR) light was experimentally demonstrated with the related spontaneous frequency down-conversion NFWM in a diamond-type Rb atoms [41–43], and it was achieved mainly due to the amplified spontaneous emission (ASE), which in turn strengthen the spontaneous NFWM process being recognized as a self-seeded NFWM [43]. The earlier studies of ASE and FWM in cascade three-level atoms excited by a pulsed laser also showed that ASE was suppressed by FWM that causes the other excitation pathway [44,45]. In fact, the multichannel excitations and decays involved in NFWM processes of atoms show the potential in exploring more nonlinear effects, such as heralded narrowband color-entanglement [46] and polychromatic mirrorless lasing in cesium atoms [47].
Due to the complicated hyperfine structure of cesium atoms, more excitation channels are inevitably involved in FWM. In this paper, we present an experimental study of multichannel involved NFWMs in Cs vapor, exploiting the mix of a seeded NFWM and ASE induced self-seeded NFWM. The dependence of single-photon and two-photon detunings on the two different NFWMs is systematically studied to help us better understanding the interplay and competition between the two different processes. As a result, the efficient NFWM frequency conversions for generating 876 nm, 455 nm and 459 nm lasing emissions are obtained in cesium vapor.
2. Experimental setup
The multi-level structure for NFWM is shown in Fig. 1(a), containing one ground level (6S$_{1/2}$), four intermediate levels (7P$_{3/2}$, 7P$_{1/2}$, 6P$_{1/2}$, and 6P$_{3/2}$), and one upper excited level (6D$_{3/2}$). Figure 1(b) shows the scheme of experimental setup. Two pump lasers at 852 nm and 921 nm with horizontal polarization excite the atoms from 6S$_{1/2}$ to 6P$_{3/2}$, and 6P$_{3/2}$ to 6D$_{3/2}$, respectively, then the atoms on the 6D$_{3/2}$ undergo the two-photon decays into the ground level 6S$_{1/2}$ via any one of the four intermediate levels (7P$_{3/2}$, 7P$_{1/2}$, 6P$_{1/2}$, and 6P$_{3/2}$), leading to the fluorescence emissions at 16.2 $\mathrm{\mu}$m, 12.4 $\mathrm{\mu}$m, 455 nm, 459 nm, 876 nm, and 895 nm, which are measured with a grating spectrometer, as shown in Fig. 2. It is shown that the intensities of IR fluorescence at 876 nm and 895 nm are much larger than that of blue fluorescence at 455 nm and 459 nm. Here the fluorescence at 852 nm and 921 nm is corresponding to the pumping decay channels. In our apparatus, the mid-IR fluorescence are not observed as they absorbed through the windows of the vapor cell.
Fig. 1. (a) The relevant energy levels of $^{133}$Cs. (b) A schematic diagram of the setup. The temperature of the vapor cell is controlled at 115$^{\circ }$C. $\theta _1=0.64^{\circ }$; $\theta _2=0.01^{\circ }$; $\theta _3=0.62^{\circ }$; PD, photodetector; SP, spectrometer; PBS, polarizing beamsplitter.
The complex atomic system can be considered as three linked diamond structures, therefore three NFWM processes could happen under the two-photon excitation with 852 nm and 921 nm pump lasers, possibly generating coherent emission pairs at 876 nm and 895 nm, 12.4 $\mathrm{\mu}$m and 459 nm, 16.2 $\mathrm{\mu}$m and 455 nm, respectively. However, only blue coherent emission is observed under two-photon excitation. Though the fluorescence at 876 nm and 895 nm is higher than the others, there is no any of 876 nm and 895 nm collimated light to be observed. It means that the NFWM in the diamond-type levels of 6S$_{1/2} \leftrightarrow$ 6P$_{3/2} \leftrightarrow$ 6D$_{3/2} \leftrightarrow$ 7P$_{3/2}$ (7P$_{1/2}) \leftrightarrow$ 6S$_{1/2}$ is created, whereas the NFWM in the diamond-type levels of 6S$_{1/2} \leftrightarrow$ 6P$_{3/2} \leftrightarrow$ 6D$_{3/2} \leftrightarrow$ 6P$_{1/2} \leftrightarrow$ 6S$_{1/2}$ could not be established during this two-photon excitation.
In order to explore the NFWM process in the different diamond structures, we focus on the spontaneous decay rates for these different transition channels, as shown in Table 1, in which $\Gamma _{\textrm {6D}_{3/2}} \rightarrow \textrm {P}$ are the spontaneous decay rates from 6D$_{3/2}$ to intermediate levels (7P$_{3/2}$, 7P$_{1/2}$, 6P$_{1/2}$), and $\Gamma _\textrm {P} \rightarrow \textrm{6S}_{1/2}$ are the decay rates from intermediate levels to ground level 6S$_{1/2}$. It shows that $\Gamma _{\textrm {6D}_{3/2}} \rightarrow \textrm {7P}_{1/2} (\textrm {7P}_{3/2})$ $\ll$ $\Gamma _{\textrm {7P}_{1/2}} (\textrm {7P}_{3/2}) \rightarrow \textrm {6S}_{1/2} $ (for mid-IR and blue light involved NFWM), which gives the following result that the two-photon decay rates in mid-IR and blue light involved NFWM process meet the population inversion condition between 6D$_{3/2}$ and 7P$_{3/2}$ (7P$_{1/2}$), and as a result, the mid-IR fields at 16.2 and 12.4 $\mathrm{\mu}$m are produced via amplified spontaneous emission (ASE), which, in turn, serve as seeded light to results in self-seeded or self-stimulated NFWM process.
Table 1. Spontaneous decay rate in relevant Cs transitions [48].
On the other hand, since $\Gamma _{\textrm {6D}_{3/2}} \rightarrow \textrm {6P}_{1/2} $ and $\Gamma _{\textrm {6P}_{1/2}} \rightarrow \textrm {6S}_{1/2} $ are in the same order of magnitude, the population inversion between 6D$_{3/2}$ and 6P$_{1/2}$ cannot be established efficiently. As a result, the NFWM via intermediate level 6P$_{1/2}$ cannot occur spontaneously to generate collimated light at 876 nm or 895 nm. In our experiment, we apply a seed laser at 895 nm with vertical polarization at the angle $\theta _2=0.01^{\circ }$ to induce the NFWM, and a collimated light at 876 nm is generated at the angle of $\theta _3=0.62^{\circ }$ determined by the phase matching condition $k_{852}+k_{921}\cos \theta _{1}=k_{895}\cos \theta _{2}+k_{876}\cos \theta _{3}$ in the z direction and $k_{921}\sin \theta _{1}=k_{895}\sin \theta _{2}+k_{876}\sin \theta _{3}$ in the x direction, see Fig. 1(b). The generated 876 nm light with vertical polarization is reflected by PBS while the generated blue light with horizontal polarization can pass through PBS. In this case, there exists a competition between the self-seeded NFWM of generating the blue light and the seeded NFWM of generating the 876 nm light. The efficiency of the seeded NFWM can be significantly improved by adjusting the pump laser detunings to suppress the ASE or self-seeded NFWM, as discussed in the following.
3. Experimental results and discussions
The spectrum of generated blue light for self-seeded NFWM is shown in Fig. 3. It is detected when we scan the frequency of 852 nm laser around the 6S$_{1/2}$ ($F_{1}$=4) $\rightarrow$ 6P$_{3/2}$ transition while keeping the frequency of 921 nm laser resonant on 6P$_{3/2}$ ($F_{3}$=5) $\rightarrow$ 6D$_{3/2}$ ($F_{4}$=5) transition. The outputs of 455 and 459 nm are approximately going in the same directions determined by the phase matching condition $\vec {k}_{852} + \vec {k}_{921}$ = $\vec {k}_\textrm {IR}$ + $\vec {k}_\textrm {BL}$, where $\vec {k}_\textrm {IR}$ is the wave vector of mid-IR emission light at 16.2 $\mathrm{\mu}$m (12.4 $\mathrm{\mu}$m), and $\vec {k}_\textrm {BL}$ is the wave vector of 455 nm (459 nm) blue light. Therefore, it is detected by one photodetector, as shown in the blue line of Fig. 3. The peak of the spectrum is red-detuned about 34 MHz, which means that the maximum output of blue light is obtained with 34 MHz two-photon detunings, i.e. near two-photon resonance.
Fig. 3. The spectrum for generated blue light (blue curve). The red curve is the saturated absorption spectrum (SAS) of 852 nm laser.
Due to the fact that the NFWM in the diamond-type levels of 6S$_{1/2} \leftrightarrow$ 6P$_{3/2} \leftrightarrow$ 6D$_{3/2} \leftrightarrow$ 6P$_{1/2} \leftrightarrow$ 6S$_{1/2}$ can hardly be created only with two-photon excitation. We investigate the seeded or stimulated NFWM via injecting an 895 nm seed laser. The spectra are measured when the frequency of seed laser scan in the vicinity of the 6S$_{1/2}$ ($F_{1}$ = 4) $\rightarrow$ 6P$_{1/2}$ ($F_{2}$ =3, 4) transition. During the measurement, the frequency of 852 nm pump laser is fixed around the transition of 6S$_{1/2}$ ($F_{1}$ = 4) $\rightarrow$ 6P$_{3/2}$ ($F_{3}$ = 5) while the 921 nm pump laser is taken to keep the NFWM signal at its maximum power. As shown in Fig. 4, the maximum of the NFWM signal appears when the 852 nm pump laser is red-detuned about 125 MHz, see Fig. 4(6). At this point, the NFWM signal is appeared at the detunings of the other two lasers $\Delta _{895}=-$125 MHz and $\Delta _{921}=-$125 MHz. From the measurements in Fig. 4, we find that in each figure the maximum efficiency is achieved at the same detunings of three incident beams $\Delta _{852}=\Delta _{921}=\Delta _{895}$.
Fig. 4. Generated 876 nm laser power vs seed-laser detuning (red curves) for different 852 nm detuning of (1) 0 MHz, (2) 20 MHz, (3) 60 MHz, (4) 100 MHz, (5) 115 MHz, (6) 125 MHz, (7) 140 MHz, (8) 155 MHz, (9) 175 MHz, (10) 190 MHz, (11) 210 MHz and (12) 230 MHz red-shift while the 921 nm laser is adjusted around the 6P$_{3/2}$ ($F_{3}$ = 5) $\rightarrow$ 6D$_{3/2}$ ($F_{4}$ = 5) transition. The blue curves are the saturated absorption spectra (SAS) of 895 nm laser.
To get high efficiency of 876 nm laser power, we keep the 852 nm detuning constant at the optimized value of $\Delta _{852}=-$125 MHz around 6S$_{1/2}$ ($F_{1}$ = 4) $\rightarrow$ 6P$_{3/2}$ ($F_{3}$ = 5) transition in the following measurements and scan the remaining two lasers independently. We scan the frequency of the 921 nm diode laser at the rate of 0.02 Hz and 895 nm laser at the rate of 20 Hz. The result is plotted in concise two-dimensional map, see Fig. 5. The NFWM signal can be observed in a wide range of the detunings of the 921nm field while the signal is sensitive to the 895 nm field frequency and the sharp peak of up to 50 $\mathrm{\mu}$W of 876 nm laser is observed for $\Delta _{895}=\Delta _{921}=\Delta _{852}=-$125 MHz. It means that the maximum output of 876 nm laser is obtained with two-photon red detunings of about 250 MHz, that is to say the pump lasers are tuned off single- and two-photon resonance.
Comparing the seeded and self-seeded NFWM processes, we find that when the pump lasers are tuned off resonance, this process dominatingly undergoes a seeded NFWM generating 876nm laser as shown in Fig. 5. However, when the pump lasers are tuned to near two-photon resonance, self-seeded NFWM generating the blue light dominates, as shown in Fig. 3. This competition takes place between multi-channels. Consequently, to get high conversion efficiency of 876 nm laser during this competition, we adjust the pump laser detunings to be tuned off resonance to suppress the population at upper level for possible ASE, as a consequence, the self-seeded NFWMs involved due to the other two decay channels are suppressed.
The frequencies of the generated lights are determined by the frequencies of the pump lights, but the dependencies are different between the two NFWM processes. For the self-seeded NFWM, since the 921 nm pump light is resonant on the 6P$_{3/2}$ $\rightarrow$ 6D$_{3/2}$ transition, the atoms mainly undergo two-step excitation of 6S$_{1/2}$ $\rightarrow$ 6P$_{3/2}$ transition followed by 6P$_{3/2}$ $\rightarrow$ 6D$_{3/2}$ transition, only involving the atoms with velocity near zero [49–51]. The mid-IR from ASE is resonant on the 6D$_{3/2}$ $\rightarrow$ 7P$_{1/2}$(7P$_{3/2}$) transitions, and thus the generated blue lights have detunings from the 7P$_{1/2}$(7P$_{3/2}$) $\rightarrow$ 6S$_{1/2}$ transitions equal to the 852 nm pump light detuning: $\Delta _{455(459)}=\Delta _{852}$. In addition, a small fraction of atoms with nonzero velocity can be excited to the upper 6D$_{3/2}$ state via two-photon excitation. In this case, the ASE mid-IR and the generated blue light have frequencies shifted by the Doppler effect, and the blue light detuning is given by $\Delta _{455(459)}=\frac {\lambda _{852}}{\lambda _{455(459)}}\Delta _{852}$. For the seeded NFWM, since the frequencies of the pump and the seed are known in the experiment, the frequency of the generated 876 nm light is simply obtained from the detunings of the pump and seed lights $\Delta _{876}=\Delta _{921}+\Delta _{852}-\Delta _{895}$. Due to the off-resonant condition, this process can occur in atoms with different velocities.
Checking the dependence of the signal power of seeded NFWM on temperature of vapor cell, as shown in Fig. 6(a), there exists an optimal temperature at approximately 115$^{\circ }$C, in which condition, the density of atoms could be the best case for efficient nonlinear conversion to overcome the absorption loss induced by atoms. When the atomic density is lower than its optimum value, increasing the temperature results in an increase of the density and therefore of the conversion efficiency. The conversion efficiency increases until the reabsorption of the NFWM signal at the end of the cell becomes significant. When the temperature is larger than 145$^{\circ }$C, the atomic density is high enough with higher absorption loss, leading to a low NFWM efficiency.
Fig. 6. Generated 876 nm laser power versus temperature (a) and the powers of each incident lasers (b)-(d). For each individual dependence, the power of one laser is varied between zero and its maximum value, while the other two lasers are kept at P$_{852} =$ 300 mW, P$_{921} =$ 30 mW and P$_{895} =$ 3 mW.
The generated 876 nm laser power as a function of each input beam powers for vapor cell temperature at 115$^{\circ }$C is illustrated in Fig. 6(b)-(d). We use the same experimental condition as before and make the powers of incident beams as varying parameters. From Fig. 6(b) and (d), as the 852 nm and 895 nm input power increased, we observe both a threshold-like behavior along with saturation of the NFWM signal power. What’s more, the 876 nm laser power increases as the 921 nm pump power increases for the available pump power. There will be up higher power of 876 nm laser by strengthening the power of 921 nm laser.
Owing to the fact that the atoms on ground level 6S$_{1/2}$ ($F_{1}$ =3) cannot contribute to the desired NFWM process, a repump laser at 852 nm tuned to 6S$_{1/2}$ ($F_{1}$=3) $\rightarrow$ 6P$_{3/2}$ ($F_{3}$=4) transition is used to repopulate the atoms from 6S$_{1/2}$ ($F_{1}$=3) back to 6S$_{1/2}$ ($F_{1}$=4), greatly improving the frequency conversion efficiency. Figure 7(a) demonstrates the comparison of the generated 876 nm laser power as a function of the 895 nm laser detuning with and without repump laser. The maximum power of 876 nm laser is improved about 2.6 times (130 $\mathrm{\mu}$W) when the repump laser power is 300 mW. We also studied the dependences of generated 876 nm laser power on the repump laser power. The conversion efficiency dramatically increases when the applied repump laser less than 150 mW and as the repump laser power grows the generated 876 nm laser power rises slowly.
Fig. 7. (a) Power of generated 876 nm laser versus detuning of 895 nm laser with (blue curve) and without (without) 852 nm repump laser. (b) Power of generated 876 nm laser versus the repump laser power.
4. Conclusion
In conclusion, we have experimentally studied the multi-channel involved NFWM process in a diamond-type system in hot cesium vapor. Both of the blue and IR coherent emissions due to self-seeded NFWM with ASE and seeded NFWM have been observed. We find that the process dominatingly undergoes a seeded NFWM when the pump lasers are tuned off resonance while self-seeded NFWM generating the blue light dominates when the pump lasers are tuned to near two-photon resonance. The process is inherently suitable for developing nonlinear many-partite systems and many-partite color entanglement preparations.
Funding
National Natural Science Foundation of China (91736209, U1330203); National Key Research and Development Program of China (2018YFA0307200); Natural Science Foundation of Zhejiang Province (LD18A040001).
Disclosures
The authors declare no conflicts of interest.
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