A method to determine the phase-space distribution of a pulsed molecular beam

Abstract We demonstrate a method to determine the longitudinal phase-space distribution of a cryogenic buffer gas cooled beam of barium-fluoride molecules based on a two-step laser excitation scheme. Temporal resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msub> <mml:mi mathvariant="normal">Π</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> state around 860 nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msub> <mml:mi mathvariant="normal">Π</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> transition around 797 nm. Molecules in the D -state are detected background-free by recording the fluorescence from the D − X transition at 413 nm. A temporal resolution of 11 μs and a velocity resolution of 6 m s −1 is obtained. In order to calibrate the absolute velocity, we have determined the Doppler free transition frequencies for the X − A and X − D transitions with an absolute accuracy below 0.3 MHz. The high resolution of the phase-space distributions allows us to observe a variation of the average velocity and velocity spread over the duration of the molecular beam pulse. Our method hence gives valuable insight into the dynamics in the source.