Generation and quantum control of giant plasmon pulses by transient quantum coherence

Amplified ultrashort laser pulses are useful in many fields of science and engineering. We propose a quantum approach to ultrashort pulse generation using transient quantum coherence that predicts order of magnitude stronger pulses generated with lower input energy than in the steady-state regime. This femtosecond quantum-coherent analog of nanosecond $Q$ switching is not limited by the pulse duration constraints of the latter and, in principle, may be used for a variety of lasers including plasmon nanolasers. This approach, applied to the generation of giant plasmon pulses, could achieve quantum control of plasmon relaxation dynamics by varying the drive-pulse delay, amplitude, and duration. This holds promise for a new control mechanism. We discuss implementations and applications of this source of ultrashort nano-optical studies.

Figure 1

Generation of giant plasmon pulses by quantum-coherent $Q$ switching. (a) Silver nanosphere surrounded by three-level quantum emitters placed in the near field of a dipolar plasmon mode driven by an ultrashort laser pulse. (b) Energy-level diagram reveals the physical mechanisms involved in the quantum-coherent plasmon-pulse-generation process. (c) Temporal profile of the number of plasmons (solid blue curve) with a drive pulse (dashed red curve) arriving at the ${\tau }_d=0.625$ ps delay time after switching of the pump. The inset shows the zoom in and reveals that the generated giant plasmon pulse is significantly shorter than the drive pulse. Principles of the electro-optic (d) and quantum-coherent (e) $Q$-switching: cavity losses (dotted black) are modulated using voltage (dashed red) in a Kerr cell in (d) and using quantum coherence (dashed red) induced by the drive laser pulse (solid red) in the atomic gain medium in (e). Sudden lowering of the cavity loss leads to $Q$-switching and formation of the giant pulse of radiation (solid green). Transient quantum coherence serves the role of the ultrafast $Q$-switch.

Figure 2

Plasmon relaxation oscillations without a drive. (a) Temporal evolutions of the gain medium level populations. (b) Temporal profile of the population inversion on the $|2\rangle \to |1\rangle$ transition $n_{21}$ (dashed red curve) and the number of generated plasmons $N_n$ (solid blue curve). (c) Phase plane description of the relation between population inversion and number of plasmons at various points in time.

Figure 3

Control by the drive-pulse delay. (a) Maximum number of plasmons (dashed red curve) at different time delays of the Gaussian drive pulse with ${\sigma }_d=25$ fs and ${\Omega }_{a0}=24\times {10}^{12}{\mathrm{s}}^{-1}$ with respect to the switching of the pump compared with the number of plasmons without the drive (solid blue curve). Three regimes of plasmon-pulse generation are separated by vertical dashed black lines: I, the first regime of the largest-plasmon-pulse generation; II, the second, spiking regime; and III, the third, stable regime. Also shown are population evolutions ${\rho }_{ii}$, population inversion $n_{21}$, plasmon-pulse profiles $N_n$, and phase plane plots for different time delays for (b), (e), and (h) the first ${\tau }_d=0.4$ ps; (c), (f) and (i) the spiking ${\tau }_d=0.9$ ps; and (d), (g) and (j) the stable ${\tau }_d=3$ ps regimes.

Figure 4

Temporal profiles of the number of plasmons (solid blue curve) with a transient drive pulse (dashed red curve) arriving at different time delays for (a) the first ${\tau }_d=0.4$ ps, (b) the spiking ${\tau }_d=0.9$ ps, and (c) the stable ${\tau }_d=3$ ps regimes, corresponding to Fig. 3.

Figure 5

Control by the drive-pulse amplitude. Maximum number of surface plasmons for the drive-pulse duration ${\sigma }_d=25$ and 75 fs in (a) the stable and (b) first regimes, respectively. Also shown are the population inversion and plasmon-pulse profiles for the stable [with (c) ${\Omega }_{a0}=4\times {10}^{12}{\mathrm{s}}^{-1}$ and (d) ${\Omega }_{a0}=24\times {10}^{12}{\mathrm{s}}^{-1}]$ and first [with (g) ${\Omega }_{a0}=4\times {10}^{12}{\mathrm{s}}^{-1}$ and (h) ${\Omega }_{a0}=24\times {10}^{12}{\mathrm{s}}^{-1}]$ regimes (for the drive-pulse duration ${\sigma }_d=25$ fs). The corresponding phase plane plots are (e) and (f) for the stable and (i) and (j) for the first regimes.

Figure 6

Population evolutions for the drive-pulse duration ${\sigma }_d=25$ fs in the stable [with (a) ${\Omega }_{a0}=4\times {10}^{12}{\mathrm{s}}^{-1}$ and (b) ${\Omega }_{a0}=24\times {10}^{12}{\mathrm{s}}^{-1}]$ and the first [with (c) ${\Omega }_{a0}=4\times {10}^{12}{\mathrm{s}}^{-1}$ and (d) ${\Omega }_{a0}=24\times {10}^{12}{\mathrm{s}}^{-1}]$ regimes corresponding to Fig. 5.

Figure 7

Control by the drive-pulse duration. Maximum number of surface plasmons in (a) the stable and (b) the first regime, respectively. The population inversion and plasmon-pulse profiles for various drive-pulse durations in the stable regime (c) ${\sigma }_d=5$ fs, (d) ${\sigma }_d=37.5$ fs, and (e) ${\sigma }_d=162.5$ fs and in the first regime (i) ${\sigma }_d=5$ fs, (j) ${\sigma }_d=400$ fs, and (k) ${\sigma }_d=25$ ps. Also shown are the corresponding phase plane plots for the (f)–(h) stable and (l)–(n) first regimes.

Figure 8

Temporal profiles of the number of plasmons (solid blue curve) with a transient drive pulse (dashed red curve) for various drive-pulse durations in the stable regime (a) ${\sigma }_d=5$ fs, (b) ${\sigma }_d=37.5$ fs, and (c) ${\sigma }_d=162.5$ fs and in the first regime (d) ${\sigma }_d=5$ fs, (e) ${\sigma }_d=400$ fs, and (f) ${\sigma }_d=25$ ps corresponding to Fig. 7.

Figure 9

Population evolutions for various drive-pulse durations in the stable regime (a) ${\sigma }_d=5$ fs, (b) ${\sigma }_d=37.5$ fs, and (c) ${\sigma }_d=162.5$ fs and in the first regime (d) ${\sigma }_d=5$ fs, (e) ${\sigma }_d=400$ fs, and (f) ${\sigma }_d=25$ ps corresponding to Fig. 7.