Controlling rotational air lasing lineshape by carrier-envelope offset phase

The carrier-envelope offset phase (CEP) of a few-cycle optical pulse is commonly used to control electron dynamics on the attosecond timescale, whereas lasing spectra from transitions between rotational states are generally emitted over much longer durations, typically nanoseconds. Here, we demonstrate CEP control of the rotational lasing spectra corresponding to the transition from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> <mml:msubsup><mml:mrow><mml:mi>Σ</mml:mi></mml:mrow> <mml:mrow><mml:mi>u</mml:mi></mml:mrow> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msubsup> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup><mml:mrow><mml:mi>X</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> <mml:msubsup><mml:mrow><mml:mi>Σ</mml:mi></mml:mrow> <mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msubsup> <mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup><mml:mrow><mml:mi>N</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> <mml:mrow><mml:mo>+</mml:mo></mml:mrow> </mml:msubsup> </mml:math> cations, transforming its lineshape from a symmetric Lorentzian profile to an asymmetric Fano type-and vice versa. This lineshape modulation arises from the interference between the B-X coherence initiated by the main pulse and the supercontinuum (self seed) by self-phase modulation, resembling an "f-to-3f" interferometry. Additionally, for lasing lines with lower rotational quantum numbers, we observe a stronger coupling between adjacent lasing peaks, which originates from the amplification of both even- and odd-order rotational coherent emission lines. Our study presents a general framework for controlling lasing lineshapes and provides new insights into sub-optical-cycle dynamics in air lasing.