Measuring phonon dephasing with ultrafast pulses using Raman spectral interference

A technique to measure the decoherence time of optical phonons in a solid is presented. Phonons are excited with a pair of time-delayed 80 fs near infrared pulses via spontaneous transient Raman scattering. The spectral fringe visibility of the resulting Raman pulse pair, as a function of time delay, is used to measure the phonon dephasing time. The method avoids the need to use either narrow band or few femtosecond pulses and is useful for low phonon excitations. The dephasing time of phonons created in bulk diamond is measured to be $\tau =6.8\text{ps}$ $\left(\Delta \nu =1.56{\text{cm}}^{-1}\right)$.

Figure 1

Experimental setup. An oscillator pulse is split into two time-delayed pulses and focused through the diamond sample. Not shown, a bandpass filter cleans the oscillator pulse before the diamond and a long-pass filter rejects the pump and transmits the Stokes before the spectrometer.

Figure 2

(Color online) Diamond energy-level schematic. Ground state phonons are excited with the incident 788 nm pump, via a Raman transition, to the optical phonon mode, emitting an 880 nm Stokes pulse.

Figure 3

Example spectral interference for a delay $\tau =0.39\text{ps}$. Spectra of the broadband excitation laser (left) and the Stokes signal of diamond (right). The single pulse data in (a) and (c) show the pump-laser spectrum and the corresponding broadband Raman spectrum, respectively. Spectral interference fringes appear for coherent pulse pairs in (b) and (d).

Figure 4

(Color online) Decoherence measurement. (a) Stokes spectra for two pump pulses with various delays $\tau$, recorded with an 1800 lines/mm grating. The decrease in spectral interference visibility of the Stokes signal is due to decoherence of the optical phonons created. The respective visibilities are plotted in (b), obtained by curve-fitting the spectra. Asterisks denote data points, the continuous line an exponential decay fit. Part (c) shows a high-resolution Raman spectrum for the same diamond (dots) with a Lorentzian fit (line).

Figure 5

(Color online) Power dependence. The power dependence of the Stokes interference visibility (at constant delay $\tau =0.51\text{ps}$, reduced due to a limited alignment) showing that the experiment can be carried out at arbitrarily low phonon excitation levels (the green horizontal line is plotted to guide the eyes). The inset shows the dependence of the Stokes pulse energy on the average pump power (single pump pulses). The linear power dependence shows that the scattering is in the spontaneous Raman regime. The fraction of pump power converted into collinear Stokes light was measured to be less than ${10}^{-8}$.