Preparation of Vibrationally Excited H$_{\mathrm{2}}$ in a Coherent Superposition of $M$-States Using Stark Induced Adiabatic Raman Passage (SARP)

We prepare a large ensemble of rovibrationally excited ($v=$1, $J=$2) H$_{\mathrm{2}}$ molecules in a coherent superposition of $M$-states using Stark-induced adiabatic Raman passage (SARP) with linearly polarized single mode pump (532 nm) and Stokes (699 nm) laser pulses of duration 6 ns and 4 ns. A biaxial superposition state, \textbar $\psi $\textgreater $=$1/$\surd $2 [ \textbar $v=$1, $J=$2, $M=$-2\textgreater - \textbar $v=$1, $J=$2, $M=+$2\textgreater ], is prepared using SARP with a sequence of a pump laser pulse partially overlapping with a cross polarized Stokes laser pulse co-propagating along the quantization z-axis. The degree of phase coherence is measured by recording interference fringes in the ion signal produced using the O(2) line of 2$+$1 resonance enhanced multiphoton ionization (REMPI) from the rovibrationally excited ($v=$1,$ J=$2) level as a function of REMPI laser polarization angle. The ion signal is measured using a time-of-flight mass spectrometer. Nearly 60{\%} population transfer from H$_{\mathrm{2}}$ ($v=$0,$ J=$0) ground state to the superposition state in H$_{\mathrm{2}}$ ($v=$1, $J=$2) is measured from the depletion of Q(0) REMPI signal of the ($v=$0,$ J=$0) ground state. The $M$-state superposition behaves much like a multi-slit interferometer where the number of slits, i.e. the number of $M$-states, and their separations, i.e. the relative phase, can be varied experimentally.