Frequency dependence of coherently amplified two-photon emission from hydrogen molecules

We investigate how the efficiency of coherently amplified two-photon emission depends on the frequency of one of the two emitted photons, namely the signal photon. This is done over the wavelength range of 5.048–10.21 $\mu \mathrm{m}$ by using the vibrational transition of parahydrogen. The efficiency increases with the frequency of the signal photon. Considering experimental errors, our results are consistent with the theoretical prediction for the present experimental conditions. This study is an experimental demonstration of the frequency dependence of coherently amplified two-photon emission, and also presents its potential as a light source.

Figure 1

Energy diagram of $\mathrm{p}\text{−}{\mathrm{H}}_2$. The energy difference between the $v=0$ and $v=1$ states corresponds to a wavelength of 2403 nm. The 532.2 nm and 683.6 nm pulses are used for the Raman transition. The two-photon detuning $\delta$ can be shifted by changing the wavelength of the 683.6 nm pulses. ${\omega }_{\mathrm{trig}}$ is the frequency of the trigger pulses for TPE. ${\omega }_{\mathrm{sig}}$ is the frequency of the TPE signal.

Figure 2

Experimental setup.

Figure 3

(a) Example of a measured TPE signal spectrum. The wavelength of the trigger field is 4423 nm, and the center wavelength of the TPE signal is 5262 nm. (b) The blue circles indicate the center wavelengths of TPE signal spectra measured at various trigger wavelengths. The red line indicates the calculated variation.

Figure 4

(a) Examples of measured TPE signal energies for various trigger energies. The blue circles, orange squares, red diamonds, and green triangles represent the data for $({\lambda }_{\mathrm{trig}},{\lambda }_{\mathrm{sig}})=(4423,5263)\mathrm{nm}$, $(4001,6018)\mathrm{nm}$, $(3578,7318)\mathrm{nm}$, and $(3302,8827)\mathrm{nm}$, respectively. The error bars indicate standard errors. The solid lines are linear fits to the data. (b) TPE efficiency. The orange circles represent efficiency as defined by the energy ratio of the TPE signal to the trigger at each TPE signal frequency. They correspond to the slopes determined by the linear fits in (a). Each error bar indicates $1\sigma$ of the slope of the linear fit. The blue diamonds represent efficiency as defined by the photon-number ratio of the TPE signal pulse to the trigger pulse.

Figure 5

Experimental data and fit results for the TPE efficiency as defined by the energy ratio as a function of the TPE signal frequency. The orange circles represent the same experimental data as those in Fig. 4. The red solid line and the blue dashed line are the fits of Eq. (1) and $A{\omega }_{sig}^2$, respectively. The shaded area represents a coherence fluctuation of $+7/-16\%$.