Dynamical Fano-Like Interference between Rabi Oscillations and Coherent Phonons in a Semiconductor Microcavity System

We report on dynamical interference between short-lived Rabi oscillations and long-lived coherent phonons in CuCl semiconductor microcavities resulting from the coupling between the two oscillations. The Fourier-transformed spectra of the time-domain signals obtained from semiconductor microcavities by using a pump-probe technique show that the intensity of the coherent longitudinal optical phonon of CuCl is enhanced by increasing that of the Rabi oscillation, which indicates that the coherent phonon is driven by the Rabi oscillation through the Fröhlich interaction. Moreover, as the Rabi oscillation frequency decreases upon crossing the phonon frequency, the spectral profile of the coherent phonon changes from a peak to a dip with an asymmetric structure. The continuous wavelet transformation reveals that these peak and dip structures originate from constructive and destructive interference between Rabi oscillations and coherent phonons, respectively. We demonstrate that the asymmetric spectral structures in relation to the frequency detuning are well reproduced by using a classical coupled oscillator model on the basis of dynamical Fano-like interference.

Figure 1

Schematic diagram of coupled oscillator model connecting a fast-relaxing RO (broad spectrum) and a slow-relaxing CP (sharp spectrum). $\hslash \mathrm{\Omega }$ and $\hslash \omega$ indicate the RO and CP energies, respectively; ${\mathrm{\Gamma }}_{\mathrm{RO}}$ and ${\gamma }_{\text{CP}}$ are the RO and CP relaxation rates, respectively (${\mathrm{\Gamma }}_{\mathrm{RO}}>{\gamma }_{\text{CP}}$). When the RO and CP are resonant in energy, they couple through the Fröhlich interaction between the LO phonons and the excitonic components of the RO.

Figure 2

(a) Schematic of the CuCl microcavity structure with DBRs. (b) Transmission spectra of the CuCl microcavity for various incident angles at 10 K. The dashed vertical lines denote the energies of the $Z_3$ and $Z_{1,2}$ excitons: $E_{Z(3)}(E_{Z(1,2)})=3.202(3.268)\mathrm{eV}$. The blue dotted line represents the laser pulse spectrum for which the center energy was tuned to the energy midway between the LPB and MPB. (c) Incident angle dependence of peak energies of cavity polariton modes in the CuCl microcavity (open circles) and calculated dispersion relationship of the cavity polaritons (solid curves). The dashed curve gives the dispersion relationship of the cavity photon. The estimated Rabi splitting energies for the $Z_3$ and $Z_{1,2}$ excitons are 26 and 34 meV, respectively.

Figure 3

(a) Oscillatory signals in the CuCl microcavity at various incident pump angles obtained at 10 K. (b) Time-partitioned FT spectra of oscillatory signals observed at incident pump angle of 15°. The black and red curves indicate the time-partitioned FT spectra of the oscillatory signals before and after 1 ps, respectively. The dotted vertical lines indicate the LO phonon frequency of CuCl (${\omega }_{\mathrm{CP}}/2\pi$) and the frequency ($\mathrm{\Delta }\omega /2\pi$) corresponding to the energy difference between the MPB and LPB. (c) Incident angle dependence of intensities of the RO (squares) and CP (triangles) components in the time-partitioned FT spectra before and after 1 ps, respectively. The open circles show the square of the product of the transmission intensities at the LPB and MPB [$(T_{\mathrm{LPB}}{T}_{\mathrm{MPB}}{)}^2$].

Figure 4

(a) FT spectra of oscillatory signals for incident pump angles of 15°, 11°, and 9° observed at 10 K. (b) FT spectra of $f(t)$ calculated at ${\mathrm{\Omega }}_{\mathrm{RO}}/2\pi =4.0$, 6.3, and 8.5 THz. The Fano parameter $q$ estimated by fitting the superposition of a Fano line shape and a Lorentz function to each FT spectrum is shown as a reference, where the red broken line indicates the fitted curve. (c)–(e) Image plots of CWT of oscillatory signals observed at 15°, 11°, and 9°, respectively. (f)–(h) Image plots of CWT of $f(t)$ calculated at ${\mathrm{\Omega }}_{\mathrm{RO}}/2\pi =4.0$, 6.3, and 8.5 THz, respectively. The vertical dashed line indicates the LO phonon frequency of CuCl, ${\omega }_{\text{CP}}/2\pi$. (i)–(k) Temporal variations of $f_{\mathrm{RO}}$ (red line), $f_{\mathrm{RO}+\text{CP}}$ (blue line), and $f(t)$ (black line) at ${\mathrm{\Omega }}_{\mathrm{RO}}/2\pi =4.0$, 6.3, and 8.5 THz.