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Abstract
We demonstrate the generation of polychromatic and collimated lights at 456 nm, 459 nm, and 761 nm based on cesium (133Cs) 6S1/2 - 6P3/2 - 8S1/2 - 7P3/2, 7P1/2, 6P1/2 - 6S1/2 multi-diamond-type atomic system via two-photon excitation with two IR pump lasers at 852 nm and 795 nm. The 456 nm, 459 nm (7P3/2, 7P1/2 → 6S1/2) collimated blue lights result from the self-seeded four-wave mixing process (FWM), and the 761 nm coherent light (8S1/2 → 6P1/2) is from a seeded FWM process with the injection of a third laser at 895 nm. We measure the dependency of generated polychromatic fields on the temperature of 133Cs vapor cell and the powers of input lasers, clearly demonstrating the competition between the self-seeded FWM and seeded FWM, as they share the same excitation path. This work is helpful to further produce entangled multi-color photons for quantum communication.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Quantum interference effects, such as electromagnetically induced transparency (EIT), lasing without inversion (LWI) and many other fascinating phenomena in atomic medium, can greatly enhance nonlinear susceptibilities compared to that of solid nonlinear-crystal [1–6]. Four-wave mixing (FWM) as an important nonlinear effect is employed to produce entangled photon pairs [7,8], and to transfer orbital angular momentum [9]. In particular, the nondegenerate FWM in a diamond-type atomic system based on alkali atomic gases has been investigated for frequency up and down conversion by using continuous wave pump lasers, which results in the efficient generation of new coherent optical fields from the ultraviolet (UV) region to infrared (IR), even to the terahertz (THz) band [10–16]. These coherent light sources with special wavelengths are widely applied into underwater communication in free space [7,17], remote sensing, and quantum information processing and so on [17–19]. Akulshin et al realized the generation of coherent mid-IR light at 2.21 µm based on 23 Na 3S1/2 - 3P3/2 - 4D5/2 - 4P3/2 - 4S1/2 - 3P3/2 atomic system [13]. The directional THz beams at 3.3 THz and 311 nm UV light are observed via the FWM based on 85Rb 5S1/2 - 5P3/2 - 10D5/2 - 11P3/2 - 5S1/2 atomic system [15]. The collimated UV light at 355 nm and THz radiation at 1.0 THz are generated based on 133Cs 6S1/2 - 6P3/2 - 11D5/2 - 12P3/2 - 6S1/2 atomic system [11]. More theoretical and experimental researches are based on the 85Rb 5S1/2 - 5P3/2 - 5D5/2 - 6P3/2 - 5S1/2 atomic system for the generation of collimated blue light (CBL) at 420 nm, because this is a closed cycling transition system for the FWM experiment [20–25]. Similarly, some experimental studies on the generation of blue light at 456 nm are based on the 133Cs 6S1/2(F = 4) - 6P3/2(F’=5) - 6D5/2(F”=6) - 7P3/2(F’=5) - 6S1/2(F = 4) cycling system [26,27]. Furthermore, in order to enhance the power output and narrow the linewidth of CBL generated by FWM, some methods, such as putting an atomic vapor cell in a ring cavity [28,29] or using velocity-selective hyperfine optical pumping with an additional repumping laser [30,31], are adopted.
At present, most of these researches mentioned above only focus on single FWM process. In fact, multiple FWM processes often coexist due to the presence of some other intermediate excited states inevitably involved in the experimental system, especially when the atoms are pumped to a higher upper state [11,13]. In this work, polychromatic light fields at 456 nm, 459 nm and 761 nm are simultaneously generated via two self-seeded FWM and a seeded FWM processes in the 133Cs 6S1/2 - 6P3/2 - 8S1/2 - 7P3/2, 7P1/2, 6P1/2 - 6S1/2 multi-diamond-type and open atomic system. We also re-evaluate the influence of the repumping laser on the generation of CBL at 456 nm in experiment.
2. Excitation scheme and experimental setup
The relevant optical transitions of 133Cs atoms are shown in Fig. 1 for the generation of polychromatic and collimated light fields via three diamond-structure FWM processes. Some atoms on the ground state 6S1/2 are stepwise excited to the higher excited state 8S1/2 via intermediate state 6P3/2 through two near-resonant pump fields at 852 nm and 795 nm. The collimated blue beams at 456 nm and 459 nm are generated through two self-seeded FWM processes, which are built up by two input pump lasers as well as the 4.2 µm and 3.9 µm radiations from the 8S1/2 → 7P3/2 and 8S1/2 → 7P1/2 transitions through amplified spontaneous emission (ASE), respectively. In addition, as the third laser at 895 nm as seeded light is added, which shares a common hyperfine level with 852 nm pump laser such as the 6S1/2(F = 3) level as indicated by the red dotted line in Fig. 1, another beam of collimated light at 761 nm is produced through a seeded FWM process via the 6P1/2 intermediate state. Of course, the 895 nm laser can also be used as repumping light in most experiments of CBL enhancement via a self-seeded FWM [7,31], where the 895 nm laser and 852 nm pump laser interact with the two different hyperfine sublevels of the 6S1/2 state, as shown by the red solid line in Fig. 1.
The schematic of the experimental setup is shown in Fig. 2. The two pump fields with relatively low power are provided by external cavity diode lasers, and their available power for the FWM experiment are < 30 mW. The frequency of pump light at 852 nm can be locked to one of the hyperfine transitions of 133Cs D2 line by saturated absorption spectroscopy (SAS) in a separate vapor cell, and the frequency detuning of 795 nm pump light driven the 6P3/2 → 8S1/2 transition is controlled by optical-optical double resonance (OODR) spectrum in an auxiliary 133Cs cell [32]. In order to improve the two-step excitation efficiency from the ground state 6S1/2 to excited state 8S1/2, the two pump fields are co-circularly polarized lights by adjusting the respective λ/4 wave plates before the dichroic mirror (DM) as shown in Fig. 2 [21]. The two pump beams are coupled into two single-mode polarization-maintaining fibers for perfect light spots, respectively (not shown in Fig. 2). Then, they are combined into a bichromatic beam on the DM, and focused with a single achromatic lens (L) of focal length 200 mm before entering a 50 mm long 133Cs vapor cell with a diameter of 25 mm, and their spot sizes are about 200 µm in the central region of vapor cell. There is no buffer gas in the 133Cs vapor cell, and its temperature is controlled in the range 30 °C to 150 °C by a pair of flexible polyimide film heaters wrapped around the both ends of the vapor cell and a temperature controller with precision of ±1 °C. The 895 nm laser as repumping laser or seed laser, is tuned to the 133Cs 6S1/2(F = 3) → 6P1/2 transition, and is co-propagating through the heated vapor cell along the direction of pump beams by a polarizing beam splitter (PBS). The generated polychromatic collimated light fields at 456 nm, 459 nm and 761 nm are separated from the applied laser beams at 852 nm, 795 nm and 895 nm by a color filter, triple prism, or grating with 1200 lines/mm, and then are detected by the photomultiplier (PMT), and analyzed by the optical fiber spectrometer (SP) with sensitivity range of 400 nm - 900 nm. From the side of the 133Cs vapor cell, isotropic fluorescence photons with many possible wavelengths are collected into the SP for spectral analysis.
Fig. 2. Schematic diagram of the experimental setup. (PBS: Polarizing beam splitter; HWP: Half-wave plate; QWP: Quarter-wave plate; DM: Dichroic mirror; M: Mirror; Cs cell: Cesium vapor cell; Filter: Optical filter; L: lens; PMT: Photomultiplier tube; SP: Optical fiber spectrometer.)
3. Results and discussion
3.1 Influence of repumping laser on the blue light generated by self-seeded FWM
The frequency of 852 nm pump laser with power of 16 mW before 133Cs vapor cell is locked on the 6S1/2(F = 4) → 6P3/2(F’=5) hyperfine transition, while the frequency of 795 nm pump laser with power of 22 mW is scanned over the 6P3/2 → 8S1/2 transition, the blue light signal at 456 nm (including some weak 459 nm collimated blue light) generated by the self-seeded FWM process with the help of the ASE at 4.2 µm (3.9 µm), is detected by the PMT as shown in Fig. 3, the curve at the top is the OODR spectrum as a frequency reference, and its detuning is relative to the 6P3/2(F’=5) → 8S1/2(F”=4) transition. Some atoms involved in the production of blue light may decay into the 6S1/2(F = 3) hyperfine sublevel by the double resonance optical pumping (DROP) [33] process in our open atomic system as shown in Fig. 1. Even if a closed cycling atomic system such as the 133Cs 6S1/2(F = 4) - 6P3/2(F’=5) - 6D5/2(F”=6) - 7P3/2(F’=5) - 6S1/2(F = 4) system is selected, some atoms can still be accumulated at the 6S1/2(F = 3) level through collisions among atoms and the inner wall of vapor cell, thus repumping the atoms in the 6S1/2(F = 3) dark state back to the self-seeded FWM channel will help to enhance the generation of blue light, which has been proved in some previous 87/85Rb, 133Cs FWM experiments [30,31].
Fig. 3. Collimated 456 nm blue light versus frequency detuning of 795 nm laser with and without 895 nm repumping laser at the temperature of 133Cs vapor cell of 65 °C (a) and 100 °C (b). The top curve is the OODR spectrum as a frequency reference, and the collimated blue light signals are normalized to the level without repumping laser.
In our experiment, when the frequency of an additional 895 nm laser as repumping light with power of 6.5 mW, is tuned to the 6S1/2(F = 3) → 6P1/2(F’=4) resonant transition, the generated CBL enhances about 7 times at the temperature of 133Cs vapor cell of 65 °C, as shown in Fig. 3(a), which is similar to the reported experimental results [30,31]. However, a seemingly counterintuitive phenomenon is firstly observed, only changing the temperature to 100 °C, the generation of blue light is significantly suppressed when the 895 nm repumping laser is tuned on, as shown in Fig. 3(b). The change of temperature is essentially used to control the number density of atoms in the vapor cell, also controlling the number of atoms involved in the FWM process. To a certain extent, the role of repumping laser is equivalent to raising the temperature of vapor cell, allowing more atoms to participate in the FWM process. However, in similar experiments, there is always an optimized temperature for the maximum output power of generated coherent lights with no repumping light [26], as indicated in Fig. 6(a) below. When the temperature is too high, the generated blue light will be weakened or even completely absorbed due to the self-absorption effect. Therefore, when the temperature is increased, the role of repumping light on enhancing the 456 nm CBL output will be reduced, or even the output of blue light is suppressed for the case of exceeding the optimal temperature 95 °C without the 895 nm repumping laser, which is confirmed by the detailed experimental results in Fig. 4. For example, when the temperature is 100 °C, the CBL is suppressed by 1 - 0.66 = 34% at the 895 repumping light power of 6.5 mW.
Fig. 4. Normalized CBL versus the power of 895 nm repumping laser at different temperature 65°C, 75°C, 85°C, 95°C, 100°C, respectively. The frequency of 852 nm pumping laser is resonant on the 6S1/2(F = 4) → 6P3/2(F’=5) transition, and the 795 nm pumping laser is tuned to give maximum CBL without the 895 nm repumping light, while the frequency of repumping light is set to the 6S1/2(F = 3) → 6P1/2(F’=4) transition.
3.2 Polychromatic light fields produced by multiple FWM processes
With the frequencies of 852 nm and 795 nm pump lights adjusted the 133Cs 6S1/2(F = 4) → 6P3/2 → 8S1/2 transitions, the atoms on excited state 8S1/2 decay to the ground state 6S1/2 via different intermediate states such as 7P3/2, 7P1/2, 6P3/2, 6P1/2. In recording the spectrum of generated collimated lights, in order to minimize the influence of isotropic fluorescence as possible as, the input port of SP is placed 50 cm away from the exit window of 133Cs vapor cell. Meanwhile, using a short wavelength-pass color filter (transmittance T > 90% for the 400 nm - 780 nm wavelength range) before the SP, the residual near-IR pump beams after the cell are attenuated, and the results are that the newly generated beams and residual 795 nm pump light could be displayed on the same graph, and the remaining 852 nm pump light is almost completely blocked. As shown in Fig. 5(a), although the intensity of the fluorescence at 761 nm and 895 nm is significantly stronger than that of 456 nm and 459 nm in the fluorescence spectrum, only the CBL at the 456 nm and 459 nm are generated with dual-wavelength frequency upconversions, and the corresponding spectrum is detected by the SP. The light spots of CBL are clearly observed using a grating as shown in the inset of Fig. 5(a), this confirms that the two self-seeded FWM processes via the 7P3/2 and 7P1/2 states are built with the help of ASE at 4.2 µm and 3.9 µm resulting from the population inversion between the 8S1/2 and 7P3/2, 7P1/2 states. Usually, the generated 456 nm collimated light is significantly stronger than the 459 nm light, because the branching ratios 0.27*0.36 for the 8S1/2 → 7P3/2 → 6S1/2 transitions is greater than the ratios 0.14*0.29 for the 8S1/2 → 7P1/2 → 6S1/2 transitions, as shown in Table 1. In fact, the branching ratios 0.21 for the 8S1/2 → 6P1/2 → 6S1/2 transition channel is significantly bigger than the two CBL channels. Therefore, the absence of generated lights at 761 nm and 895 nm means the third FWM process via the 6P1/2 state can not be effectively established, the main reason is that the spontaneous transition probability of the lower transition 6P1/2 → 6S1/2 is one order of magnitude higher than that of the upper transition 8S1/2 → 6P1/2, completely differing from the situation of the above two self-seeded FWM channels via the 7P3/2, 7P1/2 states, as indicated in Table 1.
Fig. 5. The spectra of fluorescence and polychromatic collimated lights under the two-photon excitation of 852 nm and 795 nm pumping lasers without the 895 nm seeded laser (a), and the spectra with the input of seeded laser (b). The two insets show the light spots of generated 456 nm, 459 nm, and 761 nm collimated lasers, and the residual 795 nm, 852 nm pump lasers after passing through the 133Cs vapor cell via a reflective grating with the 1200 / mm lines and a triple prism, respectively. The temperature of 133Cs vapor cell is 90°C.
Table 1. Spontaneous transition probability A and branching ratio in relevant 133 Cs transitions [34]
The frequencies of 852 nm and 795 nm pump lights are tuned on the 133Cs 6S1/2(F = 3) → 6P3/2 → 8S1/2 transitions, and now the 895 nm laser as seed light is resonance on the same hyperfine sublevel 6S1/2(F = 3) with 852 nm pump light, three beams are co-propagating through the heated 133Cs vapor cell in order to easily meet the phase matching condition, as shown in Fig. 2. The 895 nm seed laser together with the two pump lasers at 852 nm and 795 nm create the coherence between the 8S1/2 → 6P1/2 transition instead of ASE, resulting in the generation of the coherent and collimated laser beam at 761 nm, which is originated from the seeded FWM process in the 6S1/2 → 6P3/2 → 8S1/2 → 6P1/2 → 6S1/2 channel. Meanwhile, the collimated blue beams at 456 nm and 459 nm are also generated as the products of two self-seeded FWMs in the 6S1/2(F = 3) → 6P3/2 → 8S1/2 → 7P3/2, 7P1/2 → 6S1/2(F = 3) channels. At the vapor cell temperature of 90°C, the generated polychromatic beams along with residual two pump beams at the end of 133Cs cell are separated through a triple prism, their light spots are visible to eyes, as shown in the inset of Fig. 5(b).
The above three FWM processes share the same pump channel 6S1/2(F = 3) → 6P3/2 → 8S1/2, so we measure in detail the dependence of the generated polychromatic lights at 456 nm, 459 nm, and 761 nm on the experimental parameters. As in previous experiments, there are always an optimized temperature for the generations of all new fields, higher temperature will cause a high number density of atoms so that the generated polychromatic light fields are significantly absorbed before they can exit the vapor cell [26], as indicated by Fig. 6(a). With the increase of 852 nm pump laser power, the intensity of the polychromatic light fields increases slowly at first and then rapidly, exhibiting a threshold-like behavior, as shown in Fig. 6(b). Fig. 6(c) shows that polychromatic light fields keep nearly linear growth with the increase of 795 nm pump laser power, for which the 795 nm pump laser operating in the upper transition easily triggers ASE processes by population inversion between the 8S1/2 → 7P3/2, 7P1/2 transitions, because there are no population on the intermediate 7P3/2, 7P1/2 excited states at the beginning. While for the generation of 761 nm collimated light between the 8S1/2 → 6P1/2 transition, it is induced by the 895 nm seed light. However, with the increasing power of 895 nm seed light, an interesting phenomenon is observed: the generated CBL at 456 nm and 459 nm from self-seeded FWM channels are suppressed, while the 761 nm infrared light from seed FWM channel is linearly enhanced, and their competition between the multiple FWM processes is clearly demonstrated as shown in Fig. 6(d), for which they share the same pumping path.
Fig. 6. Polychromatic coherent and collimated 456 nm, 459 nm and 761 nm laser signal magnitudes versus the temperature of 133Cs vapor cell (a) and the power of 852 nm pump laser (b), 795 nm pump laser (c), 895 nm seeded laser (d). For each individual dependence, the power of one laser varies between zero and its maximum value, while the other two lasers are kept at P852 = 15 mW, P795 = 20 mW and P895 = 8 mW with the temperature of 95 °C. The frequencies of 852 nm and 795 nm pump lasers are resonant on the 6S1/2(F = 3) → 6P3/2 → 8S1/2 transitions, while the 895 nm laser as seeded light is tuned to the 6S1/2(F = 3) → 6P1/2(F’=4) transition.
4. Conclusion
In the experiment of generating the coherent and collimated light field based on the diamond-type FWM process, we clarify and re-evaluate the role of repumping laser, which can enhance the generation of collimated light field often when the temperature of heated vapor cell is lower than the optimal value without repumping light, differing from the results reported in the previous literature [30,31]. In addition, because the atom has many intermediate excited states, and multiple FWM channels usually coexist, resulting in the generation of polychromatic light fields, we experimentally reveal their competition between self-seeded FWM and seeded FWM, and deepen the analysis of results compared with some previous experiments that only consider single FWM channel. These results may be beneficial to the generation of multi-color entangled light fields [7].
Funding
National Natural Science Foundation of China (61975102); Natural Science Foundation of Shanxi Province (20210302123437); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (2019L0101).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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