Effects of disorder on polaritonic and dark states in a cavity using the
disordered Tavis-Cummings model
- URL: http://arxiv.org/abs/2202.06643v1
- Date: Mon, 14 Feb 2022 11:53:53 GMT
- Title: Effects of disorder on polaritonic and dark states in a cavity using the
disordered Tavis-Cummings model
- Authors: Tarun Gera and K. L. Sebastian
- Abstract summary: We consider molecules confined to a microcavity whose dimensions are such that an excitation of the molecule is nearly resonant with a cavity mode.
We find the conditions for the existence of the polaritonic states, as well as expressions for their energies.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We consider molecules confined to a microcavity whose dimensions are such
that an excitation of the molecule is nearly resonant with a cavity mode. We
investigate the situation where the excitation energies of the molecules are
randomly distributed with a mean value of $\epsilon_a$ and variance $\sigma$.
For this case, we find a solution that approaches the exact result for large
values of the number density $\mathscr{N}$ of the molecules. We find the
conditions for the existence of the polaritonic states, as well as expressions
for their energies. The polaritonic states are quite stable against disorder.
Analytical results are verified by comparison with simulations. When
$\epsilon_a$ is equal to that of the cavity state $\epsilon_c$ (on resonance)
the gap between the two polaritonic states is found to increase with disorder,
the increase being equal to $2 \frac{\sigma^2}{\sqrt{\mathscr{N}}|\tilde{V}|}$
where $\tilde{V}$ is the coupling of a molecular excitation to the cavity
state. An analytic expression is found for the disorder induced width of the
polaritonic peak. We results for various densities of states, and the
absorption spectrum. The dark states that exist in the case $\sigma=0$ turn
"grey" in presence of disorder with their contribution to the absorption
increasing with $\sigma$. We analyze the effect of including lifetimes of the
cavity and molecular states and find that in the strong coupling regime, the
width of the polaritonic peaks is dominated by the lifetime effect and that
disorder plays almost no role, if the Rabi splitting is sufficiently large. We
also consider the case where there is (a) orientational disorder as well as (b)
spatial variation of the cavity field and find that they effectively amount to
a renormlisation of the coupling.
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