Demos.MolRotation.PendularStates

Model

When a molecule is irradiated by intense laser light, it will undergo a Raman-type transition. In other words, the laser will induce a dynamic dipole moment in the molecule, which in turn interacts with the electric field. This second order effect then leads to alignment of the molecule. This has been first theoretically described in work by Friedrich and Herschbach. They found that the rotation can be described by an effective potential

Here, α is the dynamic polarizability parallel or perpendicular to the molecular axis, θ is the angle with the laser polarization axis, and E(t) is the slowly varying envelope function of the electric field. Hence, the effective (dimensionless!) Hamiltonian that describes the alignment becomes

where ω(t) = αE²(t)/4B, and where B is the rotational constant of the molecule. Typically, the field is modeled as a Gaussian

where the unit of time is ħ/B. In the following, we show how to reproduce the nonadiabatic alignment as a function of the pulse length σ and the maximum field strength Δω as demonstrated in the work of Ortigoso et al.. In the images below, solid, dashed and dotted lines refer to Δω = 100, 400, 900, respectively.

For such rotational problems, the simplest way to represent the wave function is an expansion in spherical harmonics, which is done by a Gauss-Jacobi DVR.

Pendular Eigenstates

If the laser is turned on slowly, the eigenstates of the free rotor will undergo an adiabatictransition to into eigenstates of the effective Hamiltonian, the so-called '''Pendular States'''. Here, we show these eigenstates for Δω=80, obtained from a bound state calculation (i.e. direct diagonalization of the Hamiltonian matrix.

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Short pulse limit

For σ=0.05 we are approaching the non-adiabatic regime. Although very high angular momenta are reached, the alignment is rather moderate, and field-free alignment can be observed after the pulse ends, see also our work on tuning from non-adiabatic to adiabatic interaction.

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Intermediate regime

For σ=0.5, field-free alignment is again observed, except for Δω=400. There, the laser transfers all the population back into the rotational groundstate due to an accidental phase matching, see also our work on tuning from non-adiabatic to adiabatic interaction.

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Long pulse limit

For σ=5 we are approaching the adiabatic regime. Very strong alignment occurs while the laser is turned on, but the initial rotational groundstate is adiabatically restored during the turn-off, see also our work on tuning from non-adiabatic to adiabatic interaction.

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Excited rotational state

If we choose another initial state than the rotational ground state, the alignment behavior also depends on the second rotational quantum number, m. Here, the dashed line corresponds to m=0, dash-dotted line is m=2, dotted line m=4, and the solid line is the average over all m. Note that figure 3 in the above-mentioned reference contains some errors (m=4 should be the m=5 state, and the average is wrong). See also our work on alignment and anti-alignment of rotationally excited molecules

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