Electronic quantum coherence encoded in temporal structures of ${{\mathrm{N}}_2}^{+}$ lasing

We experimently and theoretically investigate temporal structures of ${{\mathrm{N}}_2}^{+}$ lasing at the wavelengths of 391 and 428 nm. Our results show that the resonant interaction of a femtosecond laser with ${{\mathrm{N}}_2}^{+}$ ions with a picosecond dipole relaxation time will induce a long-lasting polarization, which exists in cases of both absorption and amplification of the external seed. The induced polarization will be amplified in population-inverted ${{\mathrm{N}}_2}^{+}$ ions, giving rise to the retarded radiation (i.e., ${{\mathrm{N}}_2}^{+}$ lasing). The temporal profile of the retarded radiation is closely related to the dipole relaxation time, population inversion density, and propagation length. The combined experimental and theoretical study reveals the physical origin of the retarded seed amplification in ${{\mathrm{N}}_2}^{+}$ ions.

Figure 1

Schematic diagram of the experimental setup. DM1, DM2: dichroic mirror with high reflectivity around 400 nm and high transmission around 800 nm; DM3: dichroic mirror with high reflectivity around 266 nm and high transmission around 800 nm; HWP: half-wave plate; L1: $f=20$ cm lens; L2: $f=10$ cm lens; L3, L4: $f=30$ cm lens; L5: $f=15$ cm lens; SP: sapphire plate; BBO1: β-barium borate for double frequency generation; BBO2: β-barium borate for cross-correlation measurements. The inset shows the plasma-channel truncation scheme with a pressure gradient on two sides of the gas chamber.

Figure 2

The spectra of 391 nm seed pulses after passing through ${{\mathrm{N}}_2}^{+}$ ions produced by (a) 0.8 mJ, (b) 1.25 mJ, and (c) 2.4 mJ pump laser pulses. The corresponding temporal profiles are shown in (d)–(f). For comparison, the seed spectra in the absence of the pump laser are indicated with red dashed lines, and the temporal profiles of seed pulses after passing through the plasma channel of argon are shown with red dash-dot lines. For clarity, (d) is illustrated with the logarithmic scale in the inset.

Figure 3

Same measurements as in Fig. 2 but the seed wavelength is tuned to 428 nm and gas pressure is taken as 20 mbar.

Figure 4

(a) Spectral and (b) temporal evolution of 428 nm lasing radiation as a function of the propagation length.

Figure 5

The simulated spectra of 391 nm radiation with (a) $T_2=1\mathrm{ps}$ and (b) $T_2=20\mathrm{ps}$. The corresponding temporal profiles are shown in (c), (d). For comparison, the initial seed spectra and the temporal profiles are indicated with red dashed lines and red dash-dot lines, respectively.

Figure 6

The simulated spectra of 391 nm radiation with different initial population probabilities of (a) $n_X=0.55$, $n_B=0.45$, (b) $n_X=0.4$, $n_B=0.6$. The corresponding temporal profiles are shown in (c), (d). For clarity, (c) is shown with the logarithmic scale in the inset.

Figure 7

The simulated spectra of 428 nm radiation in different initial population probabilities of (a) $n_X=0.45$, $n_B=0.55$, (b) $n_X=0.15$, $n_B=0.85$. The corresponding temporal profiles are shown in (c), (d). For clarity, the logarithmic scale of (c) is shown in corresponding inset.

Figure 8

(a) The simulated spectral and (b) temporal evolution of 428 nm radiation as a function of propagation length.