Practical guide to the statistical mechanics of molecular polaritons

A theoretical approach aimed at the quantum statistical mechanics of a molecular ensemble coupled to a lossless cavity mode is presented. A canonical ensemble is considered and an approximate formula is devised for the Helmholtz free energy correction due to cavity-molecule coupling, which enables the derivation of experimentally measurable thermodynamic quantities. The frequency of the cavity mode is assumed to lie in the infrared range. Therefore, the cavity couples to molecular vibrations and our treatment is restricted to the electronic ground state of the molecule. The method is tested for an analytically solvable model system of one-dimensional harmonic oscillators coupled to the cavity. The performance of the approximation and its range of validity are discussed in detail. It is shown that the leading-order correction to the Helmholtz free energy is proportional to the square of the collective coupling strength. We also demonstrate that the cavity mode does not have a significant impact on the thermodynamic properties of the system in the collective ultrastrong coupling regime (the collective coupling strength is comparable to the frequency of the cavity mode)

VIBRATIONAL QUANTUM GRAPHS AND THEIR APPLICATION TO THE QUANTUM DYNAMICS OF CH5+

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.5]{graph.eps} \end{wrapfigure} The first application of the quantum graph model to vibrational quantum dynamics of molecules is reported. The usefulness of the approach is demonstrated for the astructural molecular ion CH$_5^+$, an enigmatic system of high-resolution molecular spectroscopy and molecular physics, challenging our traditional understanding of chemical structure and rovibrational quantum dynamics. The vertices of the quantum graph correspond to different versions of the molecule (120 in total for CH$_5^+$), while the differently colored edges represent different collective nuclear motions transforming the distinct versions into one or another. These definitions allow the mapping of the complex low-energy vibrational quantum dynamics of CH$_5^+$ onto the motion of a one-dimensional particle confined in a quantum graph. The quantum graph model provides a simple and intuitive qualitative understanding of the intriguing low-energy vibrational dynamics of CH$_5^+$ and is able to reproduce, with just two adjustable parameters related to the two different motions (indicated by the red and blue lines in the figure), the lowest vibrational energy levels of CH$_5^+$ (and CD$_5^+$) with remarkable accuracy

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 60-vertex graph ${\Gamma}_{60}$ with a single edge length parameter. Within this model, the quantum states of CH5+ are obtained in analytic form and are related to combinatorial properties of ${\Gamma}_{60}$. The bipartite structure of ${\Gamma}_{60}$ gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH5+

Born–Oppenheimer approximation in optical cavities: from success to breakdown

The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduced-dimensional models and the use of the Born-Oppenheimer approximation (BOA) may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a one-dimensional model and is generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity

Impact of Cavity on Molecular Ionization Spectra

Ionization phenomena are widely studied for decades. With the advent of cavity technology, the question arises how the presence of quantum light affects the ionization of molecules. As the ionization spectrum is recorded from the ground state of the neutral molecule, it is usually possible to choose cavities which do not change the ground state of the target, but can have a significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the produced ion exhibits conical intersections between its close-lying electronic states which is known to give rise to substantial nonadiabatic effects. We demonstrate by an explicit realistic example that vibrational modes not relevant in the absence of the cavity do play a decisive role when the molecule is in the cavity. In this example, dynamical symmetry breaking is responsible for the coupling between the ion and the cavity and the high spatial symmetry enables a control of their activity via the molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase when less symmetric molecules are considered

VIBRATIONAL QUANTUM GRAPHS AND THEIR APPLICATION TO THE QUANTUM DYNAMICS OF CH5+

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.5]{graph.eps} \end{wrapfigure} The first application of the quantum graph model to vibrational quantum dynamics of molecules is reported. The usefulness of the approach is demonstrated for the astructural molecular ion CH$_5^+$, an enigmatic system of high-resolution molecular spectroscopy and molecular physics, challenging our traditional understanding of chemical structure and rovibrational quantum dynamics. The vertices of the quantum graph correspond to different versions of the molecule (120 in total for CH$_5^+$), while the differently colored edges represent different collective nuclear motions transforming the distinct versions into one or another. These definitions allow the mapping of the complex low-energy vibrational quantum dynamics of CH$_5^+$ onto the motion of a one-dimensional particle confined in a quantum graph. The quantum graph model provides a simple and intuitive qualitative understanding of the intriguing low-energy vibrational dynamics of CH$_5^+$ and is able to reproduce, with just two adjustable parameters related to the two different motions (indicated by the red and blue lines in the figure), the lowest vibrational energy levels of CH$_5^+$ (and CD$_5^+$) with remarkable accuracy