Development of a laser for chirp cooling of positronium to near the recoil limit using a chirped pulse-train generator

We present the development and characterization of a pulsed $243\text{-nm}$ laser designed for cooling positronium (Ps) to near the recoil limit. The laser, based on the recent chirped pulse-train generator (CPTG) demonstrated by Yamada et al. [K. Yamada et al., Phys. Rev. Appl. 16, 014009 (2021)], outputs a train of pulses with spectral widths of $10\mathrm{GHz}$. The center frequency of each pulse is shifted upward (up-chirped) in time by $4.9\times {10}^2\mathrm{GHz}\mu {\mathrm{s}}^{-1}$. These parameters are determined by the mechanism of chirp cooling, a suitable scheme for cooling numerous Ps atoms to the recoil temperature of laser cooling. To achieve the desired performance, we drove an optical phase modulator in the CPTG with a high modulation depth based on the operating principle of the cooling laser. Time-resolved spectroscopic measurements confirmed that the developed laser satisfies the chirp rate and instantaneous spectral width requirements for efficient chirp cooling. We believe that the experimental demonstration of Ps laser cooling with a pulse energy of hundreds of microjoules has become possible using realistic methods for the generation and velocity measurement of Ps.

Figure 1

Comparison of laser cooling schemes using a laser with a smooth and fixed spectrum and a chirped laser, showing the laser spectra (dashed and dotted curves) and simulated Doppler profile (solid curves) after cooling. For the laser spectra, the horizontal axis shows the laser detuning from $f_{\mathrm{R}}=1233596\text{GHz}$, which corresponds to the average of energy differences between $1{}^3{S}_1$ and $2{}^3{P}_J$ states weighted by each multiplicity of the excited state. The Doppler shift $\mathrm{\Delta }{f}_{\mathrm{D}}$ shown in the horizontal axis was related with Ps velocity $v_{\mathrm{Ps}}$ by $\mathrm{\Delta }{f}_{\mathrm{D}}=f_{\mathrm{R}}{v}_{\mathrm{Ps}}/c$. (a) Case in which the laser spectrum is smooth and fixed. The broadband spectrum is required to be resonant for Ps atoms with a wide range of velocity. The detuning should be as large as its broad spectral width to avoid laser heating. (b) Case in which a chirped pulse train is used. The narrow instantaneous spectral width in chirp cooling allows smaller detuning at the end of the cooling.

Figure 2

Level diagram including the $1{}^3{S}_1$ and $2{}^3{P}_J$ states of Ps, the Doppler width resulted by the recoil, and a laser spectrum for inducing all transitions between $1{}^3{S}_1$ and all sublevels in the excited states.

Figure 3

Schematic of the laser system. The Ti:sapphire pulsed laser is injection seeded by the external cavity diode laser (ECDL), which is a 729-nm continuous-wave (CW) laser, so that the required 243-nm laser can be obtained after the Ti:sapphire multipass amplifier and third harmonic generation (THG) by the lithium triborate (LBO) and beta barium borate (BBO) nonlinear crystals. By driving the electro-optic modulator (EOM) inside the laser cavity, the CPTG outputs a train of pulses. Each pulse has a broad spectral width and carrier-frequency chirp. The output of the CPTG is then diffracted by an acousto-optic modulator (AOM) before being sent to the subsequent stages. The desired part of the CPTG output can be processed by controlling the timing of the pulsed drive of the AOM and the excitation of the multipass amplifier. This pulse chopping can control the duration of the pulse train, which was also used for time-resolved spectroscopy of the laser in this paper. The output is also modulated by the second EOM to make the spectrum dense for the $1S-2P$ transition of Ps.

Figure 4

Comparison between the natural spectral width of the $1S-2P$ transition of Ps and the interval of the discrete spectrum of the laser. The absorption spectrum of Ps that is broadened by the natural spectral width of approximately $50\mathrm{MHz}$ is shown as a centered solid curve. Because the developed CPTG has a discrete spectrum with an interval of $236\mathrm{MHz}$ (dashed curves), there are many Ps atoms whose resonant frequencies are shifted by the Doppler effect and are off-resonant with any spectral component of the laser. Therefore, we generated sidebands with a modulation frequency around the natural spectral width to make the spectrum dense for the transition of Ps. We adopted $78.8\mathrm{MHz}$ as the modulation frequency for the second EOM, which is one-third of the interval of the unmodulated spectrum. The spectra of the modulated laser are shown by the dotted curves.

Figure 5

Ratio of each sideband power to the incident power on the EOM as a function of the amplitude of the driving rf. Peak-to-peak amplitudes are shown on the horizontal axis. The legend indicates the order of the resolved sideband. Sidebands up to the ninth order can be identified and their optical powers can be described well by the theoretical model of phase modulation, which is represented as solid curves. The conversion factor $F_{\mathrm{conv}}$ from the rf amplitude to the modulation depth $\beta$ was universal across all sideband orders and determined to be 0.080 rad/$V_{\mathrm{pp}}$ to ensure that the measurements agreed well with the theoretical predictions. $\beta$ is indicated at the top of the horizontal axis. The maximum $\beta$ confirmed in this test was 9.3 rad.

Figure 6

Schematic setup for measuring the time-resolved spectrum using a streak camera.

Figure 7

Time-resolved spectra of the Ps cooling laser. (a) Spectrum acquired by setting the sweep time to observe all pulses in the train with a duration of hundreds of nanoseconds. Two components with frequencies higher and lower than those of the seed laser were observed. Either component chirps upward (up-chirps) or downward (down-chirps) so that the frequency shifts from the seed frequency become larger. The chirp rates were estimated to be $6\times {10}^2$ and $-5\times {10}^2\mathrm{GHz}\mu {\mathrm{s}}^{-1}$ by fitting the linear functions to the spectral data. The fitted functions are superimposed on the spectrum (dashed lines). (b) Time-resolved spectrum at the beginning of the pulse train, acquired by fast sweeping to achieve better time resolution. The timing of the pulse trains of the two components are shifted by $\frac{1}{2}\frac{2\pi }{{\mathrm{\Omega }}_{\mathrm{m}}}$, as predicted by the theoretical model [19]. They were well synchronized with the timing of the pulsed drive of the EOM. Both (a) and (b) are averaged over 100 shots. The origin of the horizontal axis corresponded to the optical frequency of the third harmonic of the seed laser denoted as $f_{\mathrm{seed}}$. The time resolutions were (a) $23\mathrm{ns}$ at FWHM and (b) 0.7 ns at FWHM. The frequency resolution was $2.3\times {10}^2\mathrm{GHz}$ at FWHM in both spectra.

Figure 8

Time-resolved spectrum with the up-chirp component optimized by adjusting the phase-matching angle. Because the phase-matching bands of both LBO and BBO crystals were centered in the frequency range of the up-chirp component, the THG efficiency for the chirping pulse train was maintained at a high value for a longer duration than that in Fig. 7. The estimated chirp rate was $6\times {10}^2\mathrm{GHz}\mu {\mathrm{s}}^{-1}$, which was obtained by fitting the superposed linear model. The THG efficiency of the down-chirp component was so low that it could not be observed. The time resolution was $23\mathrm{ns}$ at FWHM, and the frequency resolution was $2.3\times {10}^2\text{GHz}$ at FWHM.

Figure 9

Schematic setup for measuring the spectrum of a single pulse. The transmittance of each UV pulse was measured by scanning the etalon angle. To decrease the pileup effect due to the limited bandwidth of the detectors used in our setup, the output of the CPTG was chopped to reduce the number of pulses to be detected.

Figure 10

Time-resolved optical power of the chopped pulse train at $243\mathrm{nm}$. The turn-on timings of the AOM and excitation timing of the multipass amplifier are indicated by solid arrows, and the turn-off timings of the AOM are indicated by dashed arrows. The duration of the pulse train can be controlled to (a) $300\mathrm{ns}$ for the cooling of Ps and (b) approximately $12\mathrm{ns}$ to measure the spectral width of a single pulse. Three pulses are observed in (b). The optical power of the first pulse was decreased by pulse chopping to reduce the pileup effect on the second pulse, whose transmission spectrum was evaluated using an etalon.

Figure 11

Spectrum of a single pulse at approximately $150\mathrm{ns}$ in the pulse train and instrumental functions. The instrumental function was evaluated using the SLM operation of the CPTG with a narrow spectral width. The measured spectrum under the SLM operation is indicated by filled squares. The FWHM of the function was estimated to be $10\mathrm{GHz}$ by curve fitting with a Voigt function, as indicated by the dashed curve. The measured spectrum of a single pulse is indicated by the filled circles. The spectral width of a single pulse was estimated to be 8.9 GHz at the FWHM by subtracting the effect of the instrumental function. The subtraction was performed by the curve fitting of another Voigt function, assuming that the laser spectrum had a Gaussian line shape and was convolved with the instrumental function. The fitted function is indicated by the solid curve. The spectral peaks are intentionally shifted to the origin of the horizontal axis.

Figure 12

Optical frequency of each pulse constituting a UV pulse train. $f_{\mathrm{SLM}}$ denotes the frequency of the SLM operation, which is the same as the third harmonic of the seeded frequency of the CPTG. The filled diamonds show the center frequencies of the extracted pulses. A linear chirp was observed at a rate of $4.7\times {10}^2\mathrm{GHz}\mu {\mathrm{s}}^{-1}$, which was estimated by fitting a linear function (dashed line) to the data.