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Abstract
We have generated a stable and continuously tunable single frequency (420 nm) coherent blue light (CBL) by the cavity-enhanced four-wave mixing process in Rb vapor. With the bow-tie-type ring cavity, the output power was 3.3 mW, two orders of magnitude higher than that of the CBL generated by the single-pass four-wave mixing process. The measured power stabilities of the 420 nm CBL operated at 2.5 mW and 1.5 mW for 1000 s were 2.89% and 1.88%, respectively. Under the scanning pump laser frequency, the continuously tunable range of the generated CBL reached 1.68 GHz without mode hopping. The measured beam qualities of the generated laser were $M_{x}^2 = 1.117$ and $M_{y}^2 = 1.179$. The excellent performance of the 420 nm CBL was characterized by velocity transfer spectroscopy with 780 nm probe laser. This high quality short wavelength coherent light is potentially applicable to photon-atom interactions in quantum optics and fundamental research fields.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Stable coherent short wavelength lasers corresponding to resonance atomic transitions are widely applied in quantum information science [1], fundamental research [2], and sensitive atomic imaging [3,4]. Short wavelength lasers are also extremely promising for information processing applications such as underwater communications [5], high density storage [6], and lithography [7]. However, the wavelength of tunable single frequency diode lasers is typically limited to 660 - 1500 nm, and the generation of short wavelength lasers is challenging. The nonlinear frequency conversion technique, currently one of the most promising methods, is an attractive option for realizing short wavelength coherent lasers [8].
Short wavelength lasers are typically generated by second-harmonic generation (SHG) of a near-infrared input laser in a nonlinear crystal. However, the laser wavelength generated by SHG largely depends on the input laser wavelength, and special wavelengths that resonate with the atomic transitions are missed. Different atomic states and alkali metals can also generate various wavelengths [9]. Alkali atoms are an important nonlinear medium [10] for generating short wavelength lasers. The four-wave mixing (FWM) process in gaseous alkali atoms allows the generation of short wavelength lasers that resonate with atomic transitions. Furthermore, FWM inherits all the good properties of the input lasers: high beam quality, low noise level, and narrow linewidth [11].
Frequency up-conversion in the FWM process of alkali atoms was pioneered by Zibrov et al. [9]. Recently, frequency up-conversion in atomic systems has shown great potential for quantum frequency conversion in two lasers or single laser two-photon excitation systems [12–14]. The single laser two-photon excitation system requires no complicated optical adjustment to meet the phase matching condition or complex pump laser system, both of which limit the applicability of two lasers excitation systems. Therefore, it has a more compact structure and is more widely employed than two lasers excitation systems. The CBL generated by single continuous-wave emission have a narrow linewidth, but their low output power degrades the conversion efficiency. Although a resonant cavity with strong circulating power can effectively increase the frequency conversion efficiency [15,16], generating stable and continuously tunable single frequency short wavelength coherent lights by the cavity-enhanced FWM process remains a challenging task in quantum optics.
In this work, we generated tunable 420 nm CBL by the cavity-enhanced FWM process in Rb vapor, and investigated the dependencies of their power outputs on the atomic density and input pump laser power. The CBL power was maximized at 3.3 mW at a pump laser power of 1.25 W. The achieved power was two orders of magnitude higher than that obtained by the single-pass FWM process. Moreover, the frequency and output power of the CBL were remarkably stable and the beam quality was high. The narrow linewidth of the CBL has a large tunable range without mode hopping. The tunable short wavelength coherent light produced by the cavity-enhanced FWM process promises great prospects for quantum optics and lithography.
2. Experimental setup
To generate CBL, we excited the diamond-type energy levels in Rb atoms by the cavity-enhanced FWM process (see Fig. 1(a)). When a 778 nm strong pump laser excites the $5S_{1/2} - 5D_{5/2}$ two-photon transition, a 5.23 $\mu$m field corresponding to the $5D_{5/2} - 6P_{3/2}$ transition is produced through amplified spontaneous emission. This two-photon excitation process is detuned by approximately 1 THz from the intermediate $5P_{3/2}$ state. The 420 nm coherent light is simultaneously generated when the phase matching relation 2 $\times$ $k_{NR}$ = $k_{IR}$+ $k_{BL}$ is satisfied, where $k_{NR}$, $k_{IR}$ and $k_{BL}$ are the wave vectors of the 778 nm, 5.23 $\mu$m and 420 nm radiations, respectively.
Fig. 1. (a) Energy levels involved in the FWM process of the rubidium atoms, and (b) the experimental setup. M: mirror; HV: high voltage amplifier; L: lens, F: 420 nm bandpass interference filter; HWP: half wave plate; QWP: quarter wave plate; PBS: polarization beam splitter; PD: photodiode; TC: temperature controller; WM: wavelength meter.
The experimental setup is depicted in Fig. 1(b). The pump laser for the parametric FWM process was a 778 nm continuous-wave diode laser (DLC TA pro, Toptica) with an output power up to 1.25 W. The pump laser excites the $5S_{1/2} - 5D_{5/2}$ two-photon transition. The pump beam is split into two beams by a half wave plate (HWP1) and a polarizing beam splitter (PBS1). The weaker of the two beams monitors the pump laser frequency by two-photon transition fluorescence spectroscopy [17], and the strong beam is coupled to the bow-tie-type ring cavity for the FWM process. The polarization of the incident beam is adjusted by a quarter wave plate, which improves the efficiency of the cavity-enhanced FWM process [18]. The background light is blocked by a 420 nm bandpass interference filter (F) placed after the cavity. The frequency of the generated CBL is measured by a wavelength meter (WS-7, HighFinesse). The absolute accuracy is 60 MHz and the wavelength deviation sensitivity is 2 MHz.
The bow-tie-type ring cavity is composed of two flat mirrors (M1 and M2) and two plano-concave mirrors (M3 and M4) with a 100 mm radius of curvature. All mirrors are highly reflective at 778 and 420 nm except for the input coupler mirror M1, with a power transmission of 8% at 778 nm. Meanwhile, the power transmission of the plano-concave mirror M4 is 94% at 420 nm. The total cavity length (approximately 500 mm) corresponds to a free spectral range of 0.6 GHz. Mirrors M3 and M4 are separated by approximately 105 mm. The optical beam waist, calculated by the ABCD matrix formalism, is approximately 38 $\mu$m. This distance is adjusted through a lens with a focal length of 400 mm, realizing mode matching for the enhancement cavity. The efficiency of mode matching the pump laser to the enhancement cavity is up to 98%. A (10 $\times$ 10 $\times$ 10) mm$^{3}$ Rb vapor cell is placed in the central position between the two concave mirrors. The temperature of the vapor is accurately controlled by a self-feedback system with an accuracy of 1$^{\circ }$C.
M3 is mounted with a piezo-electric transducer (PZT) that actively locks the cavity length to the 778 nm laser by the dither-locking technique [19]. When the pump laser is injected into the enhancement cavity, its weak part leaks into M2 and is sampled by an amplified photodiode (PDA36A-EC, Thorlabs). A 34 kHz sinusoidal modulation is applied to the PZT by a lock-in amplifier (SR830, Stanford Research Systems). The sampled signal mixes with the local oscillator and passes through the low pass filter, producing an error signal that is fed back to the PZT. The generated 420 nm CBL is frequency tuning continuously by scanning the pump-laser frequency.
3. Experimental results and discussions
The enhancement effect of the cavity-enhanced FWM process was investigated by characterizing the CBL output power. The dashed and solid purple curves in Fig. 2 plot the output powers of the single-pass and cavity-enhanced processes, respectively, as a function of 778 nm laser frequency. The two-photon transition fluorescence spectroscopy (blue curve in Fig. 2) is the frequency reference of the 778 nm laser. Judging from the cavity resonant signal (gray curve in Fig. 2), the finesse of the cavity was approximately 27. The atomic density of the vapor was 3.2 $\times$ $10^{14}$ cm$^{-3}$, and the pump power was 1.25 W. In the single-pass FWM process, the CBL was produced near the two-photon transition frequency when the 778 nm laser frequency was scanned across the $5S_{1/2} - 5D_{5/2}$ transition. The maximum CBL output power of the single-pass FWM process was only 10 $\mu$W. In the cavity-enhanced FWM case, the CBL was generated with a narrow linewidth around the cavity resonant frequency position, and the output power of the CBL was greatly enhanced. The peak output power was 1.35 mW, two orders of magnitude higher than in the single-pass FWM process.
Fig. 2. The CBL power as a function of 778 nm laser frequency in the single-pass FWM process (purple dashed line) and the cavity-enhanced FWM process (purple solid line). The blue line is the fluorescence spectrum signal (frequency reference), and the gray line is the cavity resonant signal.
The circulating power in the ring cavity depends on the power injected into the cavity and the cavity characteristics, and is given by [20]:
where $P_{c}$ and $P_{0}$ are the laser powers of the circulating and incident pumps, respectively, $R$ is the reflectivity of the input coupler mirror, and $T_{c}$ is the transmission through the vapor cell. The reflectivity of the input coupler mirror in the experiment was 92%, and the transmission of the vapor cell was 80.3%; consequently, the circulating power was four times higher than the original incident power.Next, the generated CBL power was characterized by varying the input pump laser power. The result is shown in Fig. 3(a). The atomic density was 1.35 $\times$ 10$^{15}$ cm$^{-3}$. The CBL output power increased with pump laser power, and a clear quadratic relationship was observed below 1.0 W [13,18]. The CBL power growth slowed at higher laser, indicating that the cavity-enhanced FWM process was approaching saturation. The previous studies can also clearly reveal this deduction [15,16]. Figure 3(b) plots the CBL output power as a function of vapor atomic density at fixed pump power (1.25 W). The CBL output power increased with atomic density, but again, the growth was suppressed at high atomic densities. The dependencies of the CBL power on both the pump laser power and atomic density suggest a saturation point in the cavity-enhanced FWM process. Saturation can be explained by competition between the forward ($5S - 5P - 5D - 6P - 5S$) and reverse ($5S - 6P - 5D - 5P - 5S$) FWM processes, which limits the CBL generation [21]. A higher output power can be achieved by the improved experimental setup, such as a vapor cell coating with higher blue light transmittance and an optimized structure cavity.
Figure 4(a) presents the frequency tunable feature of the generated CBL at an atomic density of 1.35 $\times$ 10$^{15}$ cm$^{-3}$ and a pump laser power of 1.25 W. The frequencies of the pump laser and generated CBL were centered at 385.282 and 713.284 THz, respectively. The generated CBL linewidth is mainly limited by the temporal coherence of the applied laser field [22,23], we evaluate the linewidth of the blue light is less than 2 MHz with the pump laser linewidth is less than 1 MHz. The continuous mode hop free tuning range of the CBL reached 1.68 GHz when the pump laser was scanned over 0.89 GHz. As the CBL was emitted from diamond energy levels under the four-photon resonance condition, the frequency of the FWM fields must satisfy $\omega _{CBL}$ = 2 $\times$ $\omega _{NR}$ - $\omega _{IR}$, where $\omega _{NR}$, $\omega _{IR}$, and $\omega _{CBL}$ are the frequencies at 778 nm, 5.23 $\mu$m and 420 nm, respectively. When $\omega _{IR}$ is fixed in the near-resonant stepwise excitation FWM process, the expected detuning ratio of $\omega _{NR}$ to $\omega _{CBL}$ is 2 (i.e., $\Delta \omega _{CBL}$ = 2$\Delta \omega _{NR}$) [24]. However, after multiple measurements in our experiments, these two detunings were related as $\Delta \omega _{CBL}$ $=$ (1.89 $\pm$ 0.03)$\Delta \omega _{NR}$. This result can be attributed to the distant detuning (1 THz) of the 778 nm pump laser from the intermediate state in the excitation process, which is consistent with previous results [22,24]. Figure 4(b) shows the CBL power stability measured over 1000 seconds. The power stability depends on the power stability of the incident pump laser, the atomic density stability, and the performance of the locking system. At the CBL output powers of 1.5 and 2.5 mW, the root mean square values were 1.88% and 2.89%, respectively. Under the existing experimental conditions, improving the performance of the locking system is the key way to improve the stability of output light power. To our knowledge, we report the first experimental demonstration of a stable CBL generated by the cavity-enhanced FWM process with alkali atoms.
Fig. 4. (a) Continuous frequency-tuning curves of the 778 and 420 nm beams, and (b) root mean square (RMS) fluctuations of the output blue light at 2.5 and 1.5 mW, respectively.
Figure 5 shows the beam quality $M^{2}$ of the generated CBL. Along the x and y axes, the beam qualities were $M_{x}^{2}$ = 1.117 and $M_{y}^{2}$ = 1.179, respectively, higher than those of crystal-based frequency conversion lasers [25]. Such high beam quality is beneficial for coupling into fibers in further applications. Using the generated 420 nm CBL, we also obtained the rubidium V-type $5S_{1/2} - 6P_{3/2} - 5P_{3/2}$ velocity transfer spectroscopy, which is rarely reported because stable high power 420 nm lasers were previously lacking. The generated CBL resonates with the $^{87}$Rb $5S_{1/2} (F = 2) - 6P_{3/2}(F^{\prime \prime } = 3)$ transition, realizing a coupling beam. Also, a certain number of atoms can be pumped into the $6P_{3/2}(F^{\prime \prime } = 2)$ and $6P_{3/2}(F^{\prime \prime } = 1)$ energy levels through the Doppler effect. The 780 nm probe beam was scanned across the $^{87}$Rb $5S_{1/2} (F = 2) - 5P_{3/2}$ transition, and two beams (a 20 $\mu$W probe beam and a 300 $\mu$W coupling beam) were impacted on the 5 cm-long rubidium vapor in a counter-propagation configuration. The absorption of the weak probe beam was detected by a photodiode. A typical experimental result is shown in Fig. 6. The three obvious transition peaks in the velocity transfer spectroscopy (purple curve) correspond to $^{87}$Rb $5S_{1/2} (F = 2) - 6P_{3/2} (F^{\prime \prime } = 1, 2, 3)$ hyperfine transitions. The saturation absorption spectrum of the $^{87}$Rb $5S_{1/2} (F = 2) - 5P_{3/2}$ transition (red line) is the frequency reference. The obtained frequency interval between $6P_{3/2} (F^{\prime \prime } = 3)$ and $6P_{3/2} (F^{\prime \prime } = 2)$ with 45.13 MHz well agree with previous research [26]. The velocity transfer spectrum reflects the stable frequency, narrow linewidth, high and stable power characteristics of the generated blue light.
Fig. 5. Measured beam quality $M^{2}$ of the output CBL. Black squares and red dots are the experimental data along the x and y axis, respectively. The inset is the beam profile of the CBL.
Fig. 6. Obtained velocity transfer spectroscopy signal (purple line) of $5S_{1/2} -6P_{3/2} - 5P_{3/2}$ transition and the saturation absorption spectrum of the $^{87}$Rb $5S_{1/2} (F = 2) - 5P_{3/2}$ transitions (red line). The insets are the simplified diagram of the key components of the optical setup and the corresponding energy levels. M: mirror; BS: beam splitter; PD: photodiode.
4. Conclusions
We experimentally demonstrated a continuously tunable, single frequency 420 nm CBL generated by the cavity-enhanced FWM process in Rb vapor. The output power was maximized at 3.3 mW under a pump power of 1.25 W. The power stabilities of the CBL, measured over 1000 seconds, were 2.89% and 1.88% at output powers of 2.5 and 1.5 mW, respectively. Meanwhile, the beam qualities of the CBL were $M_{x}^{2}$ = 1.117 and $M_{y}^{2}$ = 1.179. The frequency of this 420 nm CBL was continuously tuned by locking the cavity to the pump laser. The continuous tuning range reached 1.68 GHz without mode hopping. Finally, a velocity transfer spectroscopy signal was observed in a three-level V-type system using the stable 420 nm CBL and the 780 nm continuous-wave laser. The generated tunable 420 nm CBL was deemed suitable for further experiments in quantum optics. The lab-based device promotes the progress in new type of laser-like source radiations at unique wavelengths which is not easily accessible.
Funding
National Key Research and Development Program of China (2017YFA0304203); National Natural Science Foundation of China (61875112, 62075121, 91736209); the Program for Sanjin Scholars of Shanxi Province; Key Research and Development Program of Shanxi Province for International Cooperation (201803D421034); 1331KSC.
Disclosures
The authors declare no conflicts of interest.
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