Control of emission interval and timing in triggered periodic superradiance

Abstract

To achieve more controllable development of coherence in solids, we investigated the effect of a trigger laser tuned to the superradiance transition wavelength on periodic superradiance observed in an Er:YSO crystal. For period control, applying the trigger laser reduced both the superradiance period and its variance, demonstrating enhanced controllability of coherence development dynamics. As the trigger laser power increased, both the period and the number of emitted superradiance photons decreased while maintaining a proportional relationship. This behavior is explained by a reduced superradiance threshold under a constant excitation rate and is reproduced by numerical simulations based on the Maxwell-Bloch equations. For timing control, we found that superradiance could be triggered even when the excitation laser alone was insufficient. This enabled us to control the emission timing of superradiance using short trigger pulses and provided a device capable of generating superradiance at desired timing.

Figures (9)

• Figure 1: (a) Conceptual illustration of conventional (non-periodic) SR. (Top) Temporal change in the population inversion without (blue dotted line) and with (red solid line) a trigger laser. The initial rapid increase represents excitation by the pump pulse, while the trigger laser---either CW or pulsed---serves as a deterministic seed for coherence development. (Bottom) A single SR pulse is shown, with pulse-to-pulse variation indicated. (b) Conceptual illustration of periodic SR. (Top) Temporal evolution of the population inversion without (blue dotted line) and with (red solid line) a trigger laser. Both the excitation and the trigger laser are CW. (Bottom) Periodic SR pulses are shown.
• Figure 2: Energy diagram of Er$^{3+}$ ion doped in YSO crystal. The dashed rounded square shows enlarged views of the $^{4}$I$_{13/2}$ and $^{4}$I$_{15/2}$ states, respectively.
• Figure 3: (a) Example of waveform of observed periodic SR pulses with trigger laser irradiation. The excitation laser is turned on for 40 ms from $t=0$ and the trigger laser is turned on for 10 ms from $t=15$ ms. (b) Example of waveform of observed periodic SR pulses without trigger laser irradiation. (c) Histograms of the peak interval between neighboring pulses with (magenta) and without (green) trigger laser irradiation. The red and blue lines are the Gaussian fits. The data in the time region of $t=15 \sim 25$ ms, during which the trigger laser is irradiated, are used for this plot. (d) Examples of observed single SR pulses with (magenta cross) and without (green X) trigger laser irradiation. The red and blue solid lines are the fit by sech-squared functions. Each peak timing is set as the origin of time.
• Figure 4: (a) Peak interval (left axis, red circle) and pulse area (right axis, blue diamond) at various trigger laser power. (b) Peak height (left axis, green square) and FWHM pulse duration (right axis, black triangle) at various trigger laser power. The error bars are the standard errors. The leftmost points are the values without the trigger laser.
• Figure 5: Reduction to extend two-level system in our model. The states $\ket{1}$ and $\ket{2}$ correspond to the lowest and second lowest Stark levels of the $^{4}$I$_{15/2}$ ground state, respectively. The state $\ket{3}$ corresponds to the lowest Stark level of the $^{4}$I$_{13/2}$ state.