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Optics Express

Mechanism and control of rotational coherence in femtosecond laser-driven N2+

Hongbin Lei, Guihua Li, Hongqiang Xie, Qian Zhang, Xiaowei Wang, Jing Zhao, Zhiming Chen, Zengxiu Zhao

Published Jul 10, 2020• 6 citations

Abstract

We investigate the formation of rotational coherence of N2+ resonantly interacting with an intense femtosecond laser field by numerical simulations based on a strong-field ionization-coupling model described with the density matrix formalism. The created N2+ system is unique in many aspects: the variable total population within the pump duration due to the intensity-dependent ionization injection, the readily accessible resonance owing to the effect of Stark shift, and the involvement of a few dozen of quantum states. By regarding the N2+ system as an open and non-stationary Λ-type cascaded multi-level system, we quantitatively studied the dependence of rotational coherence in different electronic-vibrational states of N2+ on the alignment angle θ and the pumping intensity. Our simulation results indicate that the quantum coherence between the neighbouring rotational states of J, J+2 in the vibrational state ν=0, 1 of the ground state of N2+ can be changed from a negative to a positive. The significant contribution of rotational coherence to inducing an extra gain or absorption of N2+ air lasing is further verified by solving the Maxwell's propagating equation. The finding provides crucial clues on how to manipulate N2+ lasing by controlling the rotational coherence and paves the way to studying strong-field quantum optics effects such as lasing without inversion and electromagnetically induced transparency in molecular ionic systems.

DOI: 10.1364/oe.398888

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Physical Review X•Oct 29, 2013•101 citations

We investigate the formation of rotational coherence of N2+ resonantly interacting with an intense femtosecond laser field by numerical simulations based on a strong-field ionization-coupling model described with the density matrix formalism. The created N2+ system is unique in many aspects: the variable total population within the pump duration due to the intensity-dependent ionization injection, the readily accessible resonance owing to the effect of Stark shift, and the involvement of a few dozen of quantum states. By regarding the N2+ system as an open and non-stationary Λ-type cascaded multi-level system, we quantitatively studied the dependence of rotational coherence in different electronic-vibrational states of N2+ on the alignment angle θ and the pumping intensity. Our simulation results indicate that the quantum coherence between the neighbouring rotational states of J, J+2 in the vibrational state ν=0, 1 of the ground state of N2+ can be changed from a negative to a positive. The significant contribution of rotational coherence to inducing an extra gain or absorption of N2+ air lasing is further verified by solving the Maxwell's propagating equation. The finding provides crucial clues on how to manipulate N2+ lasing by controlling the rotational coherence and paves the way to studying strong-field quantum optics effects such as lasing without inversion and electromagnetically induced transparency in molecular ionic systems.

{\mathrm{N}}_{2}^{+}

lasing action involves the creation, evolution, and radiation of ions in intense laser fields. In this paper, we demonstrate that

{\mathrm{N}}_{2}^{+}

lasing intensity can be enhanced by several times or totally suppressed by controlling the ionic creation and radiation processes through manipulation of the coherent molecular rotational wave packets of

{\mathrm{N}}_{2}

and

{\mathrm{N}}_{2}^{+}

with a pump-control scheme. Our results show that if a weak control pulse arrives at the revival moments of the ionic rotational wave packet, the lasing signal can be notably promoted, which is in contrast to observations in previous studies. Meanwhile, the modulation profiles of the lasing signals caused by molecular alignments of

{\mathrm{N}}_{2}

and

{\mathrm{N}}_{2}^{+}

are analyzed at length, revealing the double roles of the weak control pulse in inducing molecular alignment of

{\mathrm{N}}_{2}

or monitoring the amplification of the

{\mathrm{N}}_{2}^{+}

system by controlling electronic and rotational coherence. Moreover, by performing a Fourier transformation of the delay-dependent

{\mathrm{N}}_{2}^{+}

lasing, the rotational wave-packet information of

{\mathrm{N}}_{2}

and

{\mathrm{N}}_{2}^{+}

is simultaneously retrieved.

The existence of electronic coherence can fundamentally change the scenario of nonlinear interaction of light with quantum systems such as atoms and molecules, which, however, has escaped from observation in the investigations of strong field nonlinear optics in the past several decades. Here, we report on the generation of electronic quantum coherence by strong field ionization of nitrogen molecules in an intense 800 nm laser field. The coherence is experimentally revealed by observing a resonant four-wave mixing process in which the two pump pulses centered at 800 nm and 1580 nm wavelengths are temporally separated from each other. The experimental observation is further reproduced by calculating the nonlinear polarization response of N_2^+ ions using a three-level quantum model. Our result suggests that strong field ionization provides a unique approach to generating a fully coherent molecular wavepacket encapsulating the rotational, vibrational, and electronic states.

Coherent control of the multiple wavelength lasing of

{\rm N}_2^ +

: coherence transfer and beyond

Nitrogen molecules pumped by intense femtosecond laser pulses give rise to coherent emission in the forward direction at a series of wavelengths, coined “air lasing.” We demonstrate the coherent control of these emissions via a pair of seeding pulses at two different frequencies at low pressures, revealing a coherence transfer through vibrational motion. It is found that the injection of a 427.8 nm (391.4 nm) seeding pulse results in its amplification at the expense of the 391.4 nm (427.8 nm) signal, demonstrating a competition between the two spectral components of the emission from the upper level population. Moreover, when the delay between the seeding and pump pulses is finely tuned, the coherent control of both transitions is observed via the coherence transfer. A microscopic molecular relaxation model reproduces these observations, highlighting the crucial role of electronic and vibrational coherences, as well as their coupling, during the lasing action.

Multiple gain routes complicate the amplification behaviors of N2+ lasing. A direct comparison of the amplification processes of various lasing lines of N2+ is still lacking to date, mainly because the efficient generation of different lasing lines requires different experimental conditions. In this work, to overcome the limitation, we use an intense polarization-modulated femtosecond laser pulse to simultaneously produce high-intensity N2+ lasing signals at 391 nm and 428 nm, permitting us readily performing their time-domain characterizations. Our results show that the primary amplification of 428-nm lasing is always retarded by a few picoseconds with respect to the probe pulse while the amplification of 391-nm lasing can be basically completed within the probe pulse duration at a relatively high gas pressure, and besides, the time duration of the former sustains several times longer than that of the latter. These observations indicate the non-negligible contribution of the initial electronic coherence established by the pump laser, apart from the external triggering pulse. For the 391-nm lasing, the seed amplification and superradiance can fiercely interplay within the probe pulse duration. However, for the 428-nm lasing, its amplification is in essence Raman-assisted superfluorescence due to the lacking of the initial electronic coherence and a direct triggering pulse. Our findings not only shed light on the physics of N2+ lasing but also promote the relevant studies on the collective emissions in the cascaded multi-level molecular ion system.

We prepare

{{\mathrm{N}}_{2}}^{+}

mostly in the vibrational ground ${X}^{2}{{\mathrm{\ensuremath{\Sigma}}}_{g}}^{+}$ state by an ultraviolet 267-nm pulse and create the free induction decay (FID) of the $B{\phantom{\rule{0.16em}{0ex}}}^{2}{{\mathrm{\ensuremath{\Sigma}}}_{u}}^{+}\ensuremath{-}{X}^{2}{{\mathrm{\ensuremath{\Sigma}}}_{g}}^{+}$(0, 0) transition at 391 nm by a resonant excitation pulse. By controlling the phase shift of the FID using a near-IR control pulse through the dynamical Stark effect and rotational coherence, we reveal that the absorption spectrum of this transition, exhibiting a Lorentzian absorption profile, can be changed into a Fano-type profile, and then, a Lorentzian emission profile, resulting in

{{\mathrm{N}}_{2}}^{+}

lasing. Our results shed light on the long-term controversy over the mechanism of strong-field-induced

{{\mathrm{N}}_{2}}^{+}

lasing and reveal a general route to achieving amplification of light resonantly interacting with molecular ions without population inversion.

When exposed to intense infrared laser pulses of femtosecond duration, molecules such as N

{}_{2}

, CO

{}_{2}

, and H

{}_{2}

O not only become ionized but can also produce lasers as a result of simultaneous population inversion. Scientists look deep into this ``air lasing'' phenomenon in N

{}_{2}

gas and uncover both quantum coherence in the rotational wave packets of the lasing molecular ions and its footprint in the air-laser spectrum.