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Frontiers in Physics

A Bi-Axial Quantum State That Controls Molecular Collisions Like a Double-Slit Interferometer

William E. Perreault, Haowen Zhou, Nandini Mukherjee, Richard N. Zare

Published May 28, 2021• 6 citations
Publisher

Abstract

To control molecular scattering, we consider hydrogen molecules prepared in a coherent superposition of m states within a single rovibrational (v, j) energy eigenstate using Stark-induced adiabatic Raman passage (SARP). Specifically, SARP can prepare a bi-axial state of the HD molecule in which the HD bond axis exists simultaneously in two possible alignments at right angles to one another with a well-defined relative phase. We show that scattering from this biaxial state will interfere, resulting in a φ -dependent scattering intensity distribution, where φ is the azimuthal angle about the collision velocity direction. Using the scattering matrix extracted from our experiments on the rotationally inelastic collisions of quantum state prepared HD at low temperatures, we calculate the differential scattering cross-section dσ/dΩ, which shows an interference pattern as function of θ and φ in the image plane perpendicular to the collision velocity. The calculated scattering image shows that scattering from the bi-axial state directs molecules along well-defined angles, corresponding to interference maxima. Thus, the bi-axial state behaves like a double slit for molecular scattering. Moreover, by rotating the polarizations of the SARP preparation lasers, we can control the interference thereby altering the scattering angular distribution. This molecular interferometer, which experimentally measures the relative phases of the scattering matrix elements, allows a direct test of theoretical calculations on important, fundamental collision processes.

DOI
10.3389/fphy.2021.671997

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To control molecular scattering, we consider hydrogen molecules prepared in a coherent superposition of m states within a single rovibrational (v, j) energy eigenstate using Stark-induced adiabatic Raman passage (SARP). Specifically, SARP can prepare a bi-axial state of the HD molecule in which the HD bond axis exists simultaneously in two possible alignments at right angles to one another with a well-defined relative phase. We show that scattering from this biaxial state will interfere, resulting in a φ -dependent scattering intensity distribution, where φ is the azimuthal angle about the collision velocity direction. Using the scattering matrix extracted from our experiments on the rotationally inelastic collisions of quantum state prepared HD at low temperatures, we calculate the differential scattering cross-section dσ/dΩ, which shows an interference pattern as function of θ and φ in the image plane perpendicular to the collision velocity. The calculated scattering image shows that scattering from the bi-axial state directs molecules along well-defined angles, corresponding to interference maxima. Thus, the bi-axial state behaves like a double slit for molecular scattering. Moreover, by rotating the polarizations of the SARP preparation lasers, we can control the interference thereby altering the scattering angular distribution. This molecular interferometer, which experimentally measures the relative phases of the scattering matrix elements, allows a direct test of theoretical calculations on important, fundamental collision processes.
The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H 2 and its isotopologues as the target. We prepare the target in a precisely defined rovibrational ( v, j, m ) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational ( v, j ) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.
= 2) was prepared by Stark-induced adiabatic Raman passage, with its bond axis aligned preferentially parallel or perpendicular to the lab-fixed relative velocity. The coexpansion brought the collision temperature down to 1 kelvin, restricting scattering to s and p partial waves. Scattering angular distributions showed a dramatic stereodynamic preference (~3:1) for perpendicular versus parallel alignment. The four-vector correlation measured between the initial and final velocities and the initial and final rotational angular momentum vectors of HD provides insight into the strong anisotropic forces present in the collision process.
Double slits with molecular states Despite decades of research, the role of quantum mechanical effects in molecular scattering has not yet been fully investigated and can still demonstrate fascinating results, even for simple triatomic systems. Zhou et al . show that the entangled bond axis orientations in the biaxial state of a deuterium molecule can act as the two slits of a double-slit interferometer for rotationally inelastic collision with a helium atom, giving rise to quantum interference between two indistinguishable pathways (see the Perspective by Wang and Yang). The present work presents an elegant example of quantum interference in molecular scattering that is conceptually similar to the famous Young’s optical double-slit experiment. The proposed molecular interferometer could be used to coherently control the phases in various molecular processes in future experiments. —YS
Cold molecules provide a unique platform for exploring quantum phenomena. Using the Stark-induced adiabatic Raman passage (SARP) technique, it has, for example, been demonstrated that resonances are sensitive to the initial orientation/alignment of collisional partners at low collision temperatures. In this work, we investigate the stereodynamics of the following rotationally inelastic collision process through full-dimensional quantum scattering calculations, CO ( v 1 = 0, j 1 = 0) + H 2 ( v 2, j 2 = 2) → CO ( v 1 ′ = 0, j 1 ′ = 0) + H 2 ( v 2 ′ = v 2, j 2 ′ = 0), focusing on its dependence on vibrational excitation of a collision partner ( v 2 ). The integral cross-section is shown to be overall vibrationally adiabatic with a slight red shift of 1 cm –1 per v 2 for the four main resonance peaks but with irregular relative scattering amplitudes. The horizontal SARP induces completely different effects on cross-sections for one of the resonances between different vibrational states: a 92.2% suppression for v 2 = 0 versus a 120.7% enhancement for v 2 = 1. Our findings establish vibrational-state-selective engineering as a potential paradigm for cold collision control.
We prepare an ensemble of isolated rovibrationally excited (v = 1, J = 2) H2 molecules in a phase-locked superposition of magnetic sublevels M using Stark-induced adiabatic Raman passage with linearly polarized single-mode pump (at 532 nm, ∼6 ns pulse duration, 200 mJ/pulse) and Stokes (699 nm, ∼4 ns pulse duration, 20 mJ/pulse) laser excitation. A biaxial superposition state, given by [line]ψ(t)⟩ = 1/√(2)[[line]ν = 1, J = 2, M = -2⟩ - [line]ν = 1, J = 2, M = +2⟩], is prepared with linearly but cross-polarized pump and Stokes laser pulses copropagating along the quantization z-axis. The degree of phase coherence is measured by using the O(2) line of the H2 E,F-X (0,1) band via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 210.8 nm by recording interference fringes in the REMPI signal in a time-of-flight mass spectrometer as the direction of the UV laser polarization is rotated using a half-wave plate. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of the Q(0) line of the E,F-X (0,0) band as the Stokes frequency is tuned across the (v = 0, J = 0) → (v = 1, J = 2) Raman resonance.