We experimentally demonstrate efficient Raman conversion to respective Stokes and anti-Stokes fields in both pulsed and continuous modes with a Rb-87 atomic vapor cell. The conversion efficiency is about 40-50% for the Stokes field and 20-30% for the anti-Stokes field, respectively. This efficient conversion process is realized with coherent feedback of both the Raman pump and the frequency-converted fields (Stokes or anti-Stokes). The experimental setup is simple and can be applied easily to produce light sources with larger frequency shifts using other Raman media with long coherence time. They may have potential applications in nonlinear optics, Raman spectroscopy and precision measurement.
© 2013 OSA
Efficient nonlinear interaction and frequency conversion at low light intensity are of great interest in many areas of nonlinear and quantum optics because of its potential applications to high-precision spectroscopy and quantum information processing and storage. However, efficient conversion almost always requires high-power pumping because nonlinear coefficients are usually small in a nonlinear medium. In particular for Raman scattering, the conversion efficiency from the Raman pump field to the Stokes field is quite low, which will limit its broad applications. It is known that the Raman process has been widely applied to and has a lot of potential applications in biomedical sciences [1–4], Raman spectroscopy [5, 6] and precision measurement [7–9]. Traditionally, one can increase the conversion efficient by high-finesse optical cavity [10–12] or stimulated Raman process [13, 14]. But these methods are complicated to some degree. Some other techniques such as coherent anti-Stokes Raman spectroscopy (CARS) [15, 16] and surface enhanced Raman scattering [17–19] are used for some specific systems.
In the past two decades, it was discovered that nonlinear conversion can be greatly enhanced in coherent atomic ensembles. One approach is to prepare atomic spin wave before the Raman conversion process, the atomic spin wave acts as a seed to the Raman amplification process for enhanced Raman conversion. Jain et al  and Merriam et al  achieved high frequency conversion efficiencies with the help of an atomic coherence prepared via electromagnetically induced transparency [22, 23]. The conversion efficiency has reached near 40% when the Raman write lasers have intensity as high as several MW/cm2. Recently, we demonstrated a high Raman conversion of 40% with a low pump field intensity of 0.1 W/cm2. This is achieved by first preparing a spatially distributed atomic spin wave in Rb-87 vapor with another Raman laser [24, 25]. Nonlinear conversion efficiency can be enhanced with coherent medium prepared by counter-propagating fields and efficient intrinsic feedback [26–29]. Zibrov et al  observed 4% conversion efficiency with laser intensity of 0.1W/cm2. However, these schemes need other fields to prepare the atomic spin waves or can only operate in pulse mode because of the special need for preparing the atomic medium.
In this paper, we experimentally demonstrate a simple and efficient Raman conversion scheme with coherent feedback. The conversion efficiency of the scheme is as high as 50% for the Stokes field and 30% for the anti-Stokes field with pump field power as low as a few hundreds of microwatt in both pulsed and continuous wave (CW) modes. The mechanism for the efficient conversion is the constructive interference due to the coherent feedback. It relies on the creation of the atomic coherence between the two lower states [30, 31] and the phase correlation between the atomic coherence and converted field in Raman scattering . By beating two converted fields generated from a common Raman pump field, we observe a narrow line width of 10 kHz, which is determined by the decoherence time of the atomic spin wave in the medium.
2. Experiment setup
The Raman conversion process studied in our experiment is based on an atomic medium with a lambda-shaped energy level structure [see Figs. 1(b) and 1(c)]. The schematic diagram of our efficient Raman conversion process is shown in Fig. 1(a). The Raman pump laser P is injected into the atomic ensemble and interacts with atoms along the forward direction. The generated converted field (CFF), either Stokes or anti-Stokes, and the atomic spin wave start from the spontaneous process, and then build up along the long cigar-shaped atomic medium defined by the Raman pump field in the forward direction. The atomic spin wave stays in the cell, the CFF and P fields propagate out together and both are reflected back to the atomic medium by a flat mirror for feedback. The subsequent Raman process in the backward direction will be stimulated by the reflected CFF and enhanced by the previously produced atomic spin wave at the same time. An interference effect occurs between the backward converted fields produced by these two mechanisms because of the phase correlation between the CFF field and the atomic spin wave . The co-propagation of the two reflected fields will lead to in-phase constructive interference and thus greatly enhance conversion efficiency . Notice that in this efficient conversion process, in addition to the phase relation between the two reflected fields, the atomic coherence is also crucial because the previously generated atomic coherence, no matter it is generated by the forward or backward Raman process, can enhance the subsequent forward and backward Raman process at the same time. The scheme works equally well for Stokes and anti-Stokes process.
In our experiment, 87Rb atoms are the atomic medium contained in a 50mm long glass cell with paraffin coating. The cell is placed inside a four-layer magnetic shielding to reduce stray magnetic fields and is heated up to 70° using a bifilar resistive heater. The energy levels of 87Rb atom are given in Figs. 1(b) and 1(c) together with laser frequencies. The lower two energy states |g> and |m> are the hyperfine split ground states |52S1/2, F = 1, 2> with a frequency difference of 6.87GHz and the two higher energy states |e1> and |e2> are the excited states (|52P1/2, F = 2>, |52P3/2, F = 3>). An optical pumping field (OP) is used to prepare the atoms in either |g> or |m> state. P is the Raman pump field with a diameter of 1.0 mm. Figure 1(b) is for Stokes generation while Fig. 1(c) is for anti-Stokes generation. If we tune all laser frequency (P and OP) as shown in Fig. 1(b), P couples the states |e1> and |g>, the frequency of the converted field is equal to the frequency of P minus 6.87GHz, corresponding to Stokes field generation. Likewise, the situation in Fig. 1(c) corresponds to anti-Stokes field generation. The frequency of the converted field is equal to the frequency of P plus 6.87GHz. After the mirror feedback, the backward converted field and pass-through pump field are separated by a polarization beam splitter (PBS) because their polarizations are orthogonal to each other. The frequency converted field is measured by photo-detector and monitored by oscilloscope directly. The responsivity of the detector is 20volt/mW, calibrated with the help of an optical power meter and oscilloscope in experiment. It is easy to achieve the power of the converted fields from the volt value on the scope. By divided the power of the converted field by the input P field, the conversion efficiency could be achieved.
3. Experiment results
Firstly, we perform the experiment in pulsed mode with a timing sequence shown in Fig. 1(d). P and OP lasers are chopped into pulses by acoustic-optic modulators (AOM, not shown). The optical pumping pulse (OP) lasts 200 microseconds to prepare all atoms in the ground state |g> or the state |m>. Then the P laser turns on for 1000 microseconds and interacts with the atomic ensemble to generate the Stokes or anti-Stokes light. The long P pulse makes sure that we have the full length of the Stokes/anti-Stokes pulse. The temporal behavior of the converted fields is shown in Fig. 2(a). The intensity peaks quickly and decreases with the time mainly due to the decay of the atomic coherence and partly to the atom depletion. The decay time is consistent with the population decay time of 500 microseconds for the paraffin cell (measured by optical pumping). We also did this pulsed experiment in a regular cell, the converted fields only last several microseconds, consistent with the population decay time of a regular cell. The inset in Fig. 2(a) is a frequency analysis of the generated field by a Fabry-Perot cavity (FP). Almost all part is the generated field with a small leaked P also shown. We measure the conversion efficiency from P laser to the generated field and the results are given in Fig. 2(b). The efficiency ranges around 40-50% for Stokes and 20-30% for anti-Stokes, depending on the power of P.
So far, most of the Raman conversion experiments involving atomic spin wave were done in pulsed mode because of the special need for preparing the atoms in the |g> or |m> state to start the Raman process. But in the application of the precision measurement and quantum optics, CW sources with good coherence are preferred. So next, we perform the experiment in continuous wave (CW) mode by applying continuously the OP field and P field. A steady frequency-converted field is generated as shown in Fig. 2(c). The conversion efficiency is almost the same as the pulsed case, as shown in Fig. 2(d) where we plot the efficiency as a function of the power of P. In the CW mode, we can check the tuning range of the generated field by scanning the frequency of P. The result is shown in Fig. 3 together with the absorption spectrum of 87Rb for frequency calibration. The right black and left red curves are for the Stokes and anti-Stokes fields, respectively. The red and black curves each consist of three peaks, which match well the Raman gain profile. The two large side peaks correspond to blue and red detuned Raman process, respectively. The small middle peak is due to the crossover of the two hyperfine lines of 52S1/2, F 52P1/2, F’ = 1, 2 transitions. The frequency difference between 52P1/2, F’ = 1,2 energy levels is 800MHz, while the Doppler broadening at cell temperature of 70 degree is about 600-700MHz. From this figure, we obtain a tuning range of 3.0 and 4.0GHz for anti-Stokes and Stokes, respectively.
In the CW mode, we are able to look at the coherence property of the converted field. To do this, we split P into two beams and convert each beam to Stokes field. We then superimpose the two generated fields for interference. AC Stark effect leads to a slight difference between the frequencies of the two generated fields because of the difference in power and geometry in the interaction of the two beams with atoms. So we observe a beat signal shown in the inset of Fig. 4. Fourier transformation of the beat signal is recorded by a spectrum analyzer and shown in Fig. 4. The line width of the beat signal is about 10kHz, corresponding to a coherence time of 500 microseconds. This is in the same order as the decoherence time of atoms in a paraffin-coated cell. Narrower linewidth could be achieved by lowering the cell temperature or filled the paraffin cell with a bit of buffer gas .
Finally, to show the enhancement effect of the coherent feedback, we add a PBS between the flat mirror and the cell to separate the pump field P and the forward generated field. We reflect back only the pump field P. The experimental arrangement is shown in Fig. 5(a). The efficiency is given in Figs. 5(b) and 5(c) for the pulsed and CW cases, respectively. The efficiency is around a few percent, an order of magnitude smaller than the scheme with feedback of both the pump field and the forward generated field. This clearly demonstrates the advantage of the scheme with feedback.
In conclusion, we have demonstrated an efficient way to make Raman conversion with feed-back. The conversion efficiency is about 50% for Stokes field and 30% for anti-Stokes field with as little as a few hundreds of microwatt of Raman pump. It is interesting to note that this scheme is somewhat similar to the enhancement scheme due to spatially built atomic spin wave . But the main difference is that in the current experiment, there is a Stokes field injected in the opposite direction and both the feedback fields are coherent to the original fields. Our current scheme improves on that of Ref . in that it can be operated in stable CW mode and the geometry is a lot simpler. Such a scheme can replace traditional techniques such as EOM and AOM to obtain good coherent lights with a large frequency shift for studying light interaction with atoms such as the EIT effect for manipulation of atomic spin waves  and Raman atomic interferometer .
This work was supported by the National Basic Research Program of China (973 Program grant no. 2011CB921604), the National Natural Science Foundation of China (grant numbers 11004058, 11004059, 11129402, 11234003, and 11274118) and Supported by Innovation Program of Shanghai Municipal Education Commission (grant no. 13ZZ0361), the fundamental research funds for the central universities.
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