Creation and Detection of Molecular Schrödinger Cat States: Iodine in Cryogenic Krypton Observed via Four-Wave-Mixing Optics

Abstract

This contribution addresses the experimental observation and  theoretical interpretation of environment-induced decoherence of molecular Schrödinger cat states, as observed for dihalogen molecules embedded in a cryogenic rare gas environment. We specifically address a three-pulse experiment performed on an $\mathrm {I_2}$-krypton system,  involving the coherent creation, by two distinct optical pulses, of a vibrational Schrödinger cat state and its observation through a third pulse which induces a Raman scattering signal that reports on the time-evolving coherence.  Full quantum-mechanical simulations of the combined molecule-plus-environment system under the influence of the external fields are reported, making use of advanced wave packet propagation techniques. As a key quantity, a time-evolving subsystem coherence matrix is characterized, and its evolution as a function of the state preparation is discussed. In line with the experiment, it is found that long-lived coherences can be observed, even though the system-bath coupling is comparatively strong. The system–environment interactions fall into a non-Markovian regime and are determined by a few specific environmental modes that strongly interact with the chromophore. A perspective is given on general implications of these observations for molecular systems embedded in a matrix or solvent environment.

Appendix A: Explicit Form of the B State PES

The protocol for the construction of the B state PES has been described in detail in [7]. Briefly, classical trajectories evolving in the B state are initialized by sampling the positions and momenta $\{ q_i, p_i \}$ from the zero-temperature Wigner distribution associated to the X state minimum,

$$\begin{aligned} W_0(q_i,p_i) = \frac{1}{\pi }\exp \left( - q_i^2 - p_i^2 \right) \ , \end{aligned}$$

(7.30)

which mimics an instantaneous $B \longleftarrow X$ excitation.

A subset of 23 bath modes, which undergo the largest displacements from the initial average phase space position, $q_i = p_i = 0$, is identified and explicitly included in the Hamiltonian. The potential energy surfaces evaluated at geometries sampled along the trajectories are finally fitted to anharmonic polynomial functions so that the terms of (7.2) take the explicit form:

$$\begin{aligned} \mathcal {H}^{(\alpha )}_\mathrm {s} = -\frac{\hbar \omega _1}{2} \frac{\partial ^2}{\partial q_1^2} + \sum _{r = 0}^6 C_{0r}^{(\alpha )} q_1^r \ , \end{aligned}$$

(7.31a)

$$\begin{aligned} \mathcal {H}^{(\alpha )}_\mathrm {b} = -\sum _{i = 2}^{24} \frac{\hbar \omega _i}{2} \frac{\partial ^2}{\partial q_i^2} + \sum _{i = 2}^{24} C_{i0}^{(\alpha )} q_i + \sum _{i,j = 2}^{24} C_{ij0}^{(\alpha )} q_i q_j + \sum _{i,j = 2}^{24} C_{iij0}^{(\alpha )} q_i^2 q_j + \sum _{i = 2}^{24} C_{iiii0}^{(\alpha )} q_i^4 \ , \end{aligned}$$

(7.31b)

$$\begin{aligned} \mathcal {H}^{(\alpha )}_\mathrm {sb} = \sum _{i = 2}^{24} \sum _{r = 1}^3 C_{ir}^{(\alpha )} q_1^r q_i + \sum _{i,j = 2}^{24} \sum _{r = 1}^2 C_{ijr}^{(\alpha )} q_1^r q_i q_j + \sum _{i,j = 2}^{24} C_{iij1}^{(\alpha )} q_1 q_i^2 q_j \ . \end{aligned}$$

(7.31c)