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A coherent continuous-wave Lyman-α source based on four-wave sum-frequency mixing in mercury vapor has been realized with solid-state lasers. The third-order nonlinear susceptibility is enhanced by the 61S–71S two-photon resonance and the near 61S–63P one-photon resonance. The phase matching curve for this four-wave mixing scheme is observed for the first time. In addition we investigate the two-photon enhancement of the Lyman-α yield and observe that the maxima of Lyman-α generation are shifted compared to the two-photon resonances of the different isotopes.
©2009 Optical Society of America
1. Introduction
Coherent tunable radiation in the vacuum-ultraviolet (VUV) can be generated using four-wave mixing (FWM) in metal vapors and gases [1, 2]. One wavelength of particular interest is at 121.56nm, the Lyman-α transition of atomic hydrogen, and many pulsed Lyman-α sources have been built over the years [3, 4, 5, 6, 7]. Our interest in Lyman-α generation is laser cooling of antihydrogen in a magnetic trap. Antihydrogen production is an established technique, for recent advances see [8, 9]. Trapped antihydrogen, however, has not been detected, yet. Laser cooling of ordinary hydrogen atoms in a magnetic trap has been demonstrated some time ago using a pulsed Lyman-α source [10]. Distinct advantages are expected from laser-cooling using continuous wave (cw) Lyman-α, including reduced spurious pumping into untrapped magnetic substates and higher cooling rates. A first cw Lyman-α source based on FWM in mercury has been described in [11]. This source used three large-frame argon-ion lasers, one of which was frequency-doubled in an external cavity (257nm wavelength), the second one was used to pump a dye-laser (546nm wavelength), and the third one was used to pump a titanium:sapphire laser, again with external frequency doubling (399nm wavelength). Future laser cooling of antihydrogen requires reliable Lyman-α generation in the beam-time environment of an accelerator facility. We have thus set out to replace the dye laser and the argon-ion lasers. In this Letter we present the first results from a second-generation cw Lyman-α source, which is based on solid-state lasers.
Figure 1 shows the FWM scheme and the corresponding mercury energy levels. Three fundamental beams at 254nm, 408nm and 546nm wavelength are used to generate the sum-frequency at Lyman-α. The combination of the ultraviolet (UV) beam at 254nm and the blue beam at 408nm is tuned to the 61S–71S two-photon resonance, which boosts the Lyman-α yield. Tuning the UV beam close to the 61S–63P resonance can increase the nonlinear susceptibility further. The three-photon height at Lyman-α is in between bound states of mercury, the closest of which is the 123P state. Parasitic fluorescence at 1014nm appears due to the decay of population in the 71S state and can be used to monitor the two-photon resonance.
Fig. 1. Energy-level diagram of mercury and the FWM scheme. The UV laser (254 nm) is tuned close to the 61S–63P resonance, the blue laser (408 nm) establishes the two photon resonance with the 71S state. To generate Lyman-α (121.56 nm) the wavelength of the green laser is set to 546 nm. Fluorescence in the infrared (IR) from the 71S–61P decay is used to monitor the two photon resonance.
2. Lasersetup and Lyman-α production
A schematic of the experimental setup is shown in Fig. 2. The laser system producing the three fundamental beams is in the lower part of the figure. The beam at 254nm is produced by a frequency-quadrupled Yb:YAG disk laser (ELS, VersaDisk 1030–50). Frequency-quadrupling is done with two resonant enhancement cavities, the first one using a lithium triborate crystal (LBO) as the nonlinear medium, the second one using a β -barium borate crystal (BBO). Details of this system have been described elsewhere [12]. From 2W of infrared at 1015nm we get up to 200mW of UV radiation. The power of the IR laser is lower compared to earlier experiments [12] due to degeneration of the Yb:YAG disk. The second fundamental beam at 408nm is produced by a frequency-doubled titanium:sapphire laser (Coherent, 899-21), pumped by a frequency doubled Nd:YVO4 laser (Coherent, V10). The external frequency-doubling cavity uses LBO as the nonlinear medium. From 1.3W of IR light at 816nm we get 300mW of blue light. The third fundamental beam at 546nm is produced with a 10W fiber laser system at 1091nm (Koheras, Adjustik and Boostik) and a modified commercial frequencydoubling cavity (Spectra Physics, Wavetrain). This system is capable of producing up to 4W of green light [13]. However, at these high powers amplified back-reflections tend to damage the entrance facet of the amplification fiber. Getting the laser repaired by the manufacturer is tedious and very time-consuming. For the present experiments we therefore operate the fiber laser at 740mW, a very conservative rating, which still gives 280mW of green light.
The astigmatism of each of the fundamental beams is compensated with a pair of cylindrical lenses and the beams are expanded by telescopes to allow tighter focusing. The beams are then overlapped with dichroic mirrors and focused into the mercury cell using a fused silica lens with a focal length of 15cm. The average confocal parameter of the fundamental beams is b=1.6 mm. For technical reasons the mercury region in the cell was chosen to be much larger (about 15mm) then the confocal parameters. Details of the mercury cell are described elsewhere [11]. The Lyman-α beam is separated from the fundamental beams using the dispersion of a MgF2 lens (f=21.5cm at 546nm, f=13cm at Lyman-α). A tiny mirror is placed in the focus of the fundamental beams to reflect them to the side. The Lyman-α focus is several centimeters closer to the MgF2 lens and the Lyman-α beam is wide at the tiny mirror. Therefore, the small mirror just casts a shadow in the Lyman-α beam, causing ≈30% loss. Light from the fundamental beams is suppressed further by three VUV interference filters (Acton, 122-N and 122-XN) and the radiation at Lyman-α is then detected with a solar-blind photomultiplier (Hamamatsu, R6835). We observe a residual background caused by the UV light. This background is eliminated by chopping the green laser at 1Hz and subtracting the background from the Lyman-α signal. The overlap of the fundamental beams is very critical. For the initial alignment the reflections at the entrance window of the mercury cell are steered through a 20µm pinhole. To further improve the overlap of the UV and blue foci and to monitor the two-photon resonance we detect the IR fluorescence at 1014nm produced by the decay of the 71S state. The overlap of the green beam can then be adjusted using the Lyman-α signal. We get 8000 Lyman-α counts/s with laser powers in the mercury cell of 180mW at 254nm, 200mW at 408nm and 260mW at 546nm and with a detuning to the 63P level of the 202Hg isotope of -400 GHz. The overall detection efficiency of Lyman-α due to the MgF2 lens, the small mirror, the filters and the photomultiplier efficiency is 3*10-5. Therefore the Lyman-α power generated is about 0.4 nW. We observed no saturation of the VUV yield which is proportional to the power-product of the fundamental beams. The Lyman-α generated can thus readily be enhanced by increasing the power in the fundamental beams. The power levels required for Doppler-cooling of antihydrogen in a magnetic trap are rather low: With 1nW of Lyman-α we expect cooling times in the order of minutes [15].
Fig. 2. Experimental Setup. Lower part: The laser system to produce the fundamental beams (SHG: Frequency doubling cavity, BSO: beam shaping optics). Upper part: The fundamental beams are focused into the Hg vapor cell. Lyman-α radiation is separated from the fundamental beams and is detected with a photomultiplier (PMT). UV and IR radiation is monitored with photodiodes (PD).
3. Influence of the two-photon resonance
Figure 3 shows the Lyman-α signal and the IR light from the 71S–61P decay as a function of the detuning of the blue laser. The IR light is a measure for the two-photon resonance. The UV detuning to the 63P level of the 202Hg isotope for this measurement is -974 GHz and the temperature of the Hg cell is 498K. Different mercury isotopes contribute to the Lyman-α signal and the two-photon resonance. Line centers and relative abundances of the different isotopes are indicated by vertical bars in the plot.
Fig. 3. (a) Lyman-α signal and (b) fluorescence at 1014nm due to the two-photon resonance as a function of the blue laser detuning. The doted lines are calculations. Vertical bars indicate the positions and abundances of the different isotopes.
The lines in the plot are calculations of the Lyman-α signal and the two-photon resonance. The Lyman-α yield is proportional to the square of the absolute value of the third order susceptibility χ (3). The third order susceptibility, in turn, is proportional to the function S(ω 1+ω 2), which describes the two-photon enhancement [14] including homogenous and Doppler broadening. This function is used to calculate the shape of the Lyman-α signal. The fluorescence due to the two-photon resonance is calculated by solving the optical Bloch equations of a three-level system and convolving the density matrix element of the 71S level with a Doppler distribution. For both calculations the homogenous line-broadening is the sum of the natural line-width and the collision broadening. The fit of the calculation to the experimental data gives a collision broadening of 1.25 GHz for the Lyman-α signal and 2.5 GHz for the two-photon resonance. This difference needs further investigation.
The comparison of the Lyman-α signal and the two-photon resonance in Fig. 3 clearly shows that the two-photon resonance gives a massive Lyman-α enhancement. A subtle difference between both signals is that in the Lyman-α yield the maxima related to the 202Hg and the 199Hg/198Hg isotopes are shifted compared to the two-photon resonance. The peaks in the two-photon resonance signal are at the expected isotope positions. The shift of the Lyman-α peaks appears in both the experimental data and in the calculation. An explanation for this shift is that the Lyman-α waves produced by the nonlinear polarization in the different isotopes can interfere with each other, whereas the fluorescence due to the two-photon resonance in the different isotopes is independent. In the calculation of the VUV yield the complex third-order susceptibilities for the different isotopes are first added and then the square of the absolute value is calculated. Between the resonance positions of the isotopes the third-order susceptibilities are dephased which gives a reduced VUV yield. Outside the region of the two-photon resonance of the isotopes the third order susceptibilities add constructively. This shifts the Lyman-α peaks away from each other.
4. Phasenmatching
Figure 4 shows the Lyman-α signal as a function of the temperature of the mercury cell. The UV laser detuning is -400 GHz and the blue laser is tuned to the two-photon resonance of the 202Hg isotope. The maximum of the Lyman-α yield is at about 470 K, which corresponds to a mercury density of 3.2*1023 m -3. Changing the temperature of the mercury cell changes the number density of mercury atoms N in the Lyman-α production region. This changes the wavevector mismatch Δk=kLy-α-k 254nm-k 408nm- k 546nm which is proportional to N. Optimal phase matching is at bΔk=-4 [16], where b is the confocal parameter. Due to 61S–63P resonance the main contribution to Δk is the dispersion of the UV beam. A smaller detuning to the 61S–63P resonance, compared to earlier experiments [11], leads to an increased dispersion of the UV beam and the optimal phase matching is achieved at lower mercury temperatures. This enables scanning the phase matching curve of this FWM process for the first time without exceeding the maximum temperature of the cell. The calculated phase matching temperature [17] gives a 40K lower temperature than the one measured in Fig 4. This can be explained with a difference between the temperature of the cell and the actual temperature of the mercury vapor. Such an effect has been reported earlier [18].
We observe that during the temperature scan the transmitted UV light detected by photodiode PD UV in Fig. 2 dropped by approximately 20%. This means that even at a detuning of -400 GHz to the 63P level there is significant absorption at high temperatures. Further investigations on how this will limit the Lyman-α enhancement with smaller detunings have to be made.
5. Conclusion
In conclusion, solid state lasers have been used to produce coherent continuous-wave Lyman-α radiation. This is an important step towards a reliable Lyman-α source for laser-cooling of antihydrogen. We gratefully acknowledge support by the BMBF and by the DFG.
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