Rovibronic spectra of molecules dressed by light fields

The theory of rovibronic spectroscopy of light-dressed molecules is presented within the framework of quantum mechanically treated molecules interacting with classical light fields. The numerical application involves the homonuclear diatomic molecule ${\mathrm{Na}}_2$, for which the general formulas can be simplified considerably and the physical processes leading to the light-dressed spectra can be understood straightforwardly. The physical origin of different peaks in the light-dressed spectrum of ${\mathrm{Na}}_2$ is given and the light-dressed spectrum is investigated in terms of its dependence on the dressing field's intensity and wavelength, the turn-on time of the dressing field, and the temperature. The important implications of light-dressed spectroscopy on deriving field-free spectroscopic quantities are also discussed.

Figure 1

Light-dressed diabatic PECs of ${\mathrm{Na}}_2$ obtained with a dressing-light wavelength of $\lambda =657$ nm, which is near resonant with the transition between the $|X00\rangle$ and $|A21\rangle$ states. The energy scale stands for quasienergy. Vibrational probability densities are drawn for the $|X00\rangle |n\rangle$ [continuous black line on the $V_X\left(R\right)+n\hslash {\omega }_1$ PEC], $|X30\rangle |n-1\rangle$ [green dashed line on the $V_X\left(R\right)+(n-1)\hslash {\omega }_1$ PEC], $|X110\rangle |n-1\rangle$ [brown dashed line on the $V_X\left(R\right)+(n-1)\hslash {\omega }_1$ PEC], $|A21\rangle |n-1\rangle$ [black dotted line on the $V_A\left(R\right)+(n-1)\hslash {\omega }_1$ PEC], and $|A91\rangle |n\rangle$ [purple dashed line on the $V_A\left(R\right)+n\hslash {\omega }_1$ PEC] states. Upward and downward pointing vertical arrows represent transitions of absorption and stimulated emission, respectively. The two product states with the largest contribution to the light-dressed state correlating to $|X00\rangle$ at $|E_1|\to 0$ are $|X00\rangle |n\rangle$ and $|A21\rangle |n-1\rangle$.

Figure 2

Absorption (upper panel) and stimulated emission (lower panel) spectra of ${\mathrm{Na}}_2$ dressed with a 657 nm wavelength laser light at 0 K. The stick spectra were computed using Eq. (3) and show transitions from the field-dressed state, which correlates to the $|X00\rangle$ rovibronic ground state in the limit of the dressing-field intensity going to zero. The envelopes shown are obtained by taking the convolution of the stick spectra with a Gaussian function having a standard deviation of $\sigma =50{\mathrm{cm}}^{-1}$.

Figure 3

Progression of selected light-dressed absorption peaks of ${\mathrm{Na}}_2$ dressed with a 657 nm wavelength laser light at 0 K. The upper panel shows peaks originating from the field-free transition $|X00\rangle \to |A71\rangle$, while the lower panel shows peaks which have no field-free counterpart.

Figure 4

Position of the stimulated emission peak near 13 612.5 ${\mathrm{cm}}^{-1}$ as a function of dressing-light intensity for $\lambda =657$ nm. The straight line plotted was obtained by fitting a linear function to the first four data points.

Figure 5

Absorption (left panel) and stimulated emission (right panel) 0-K spectra of ${\mathrm{Na}}_2$ dressed with an $I={10}^8$ W ${\mathrm{cm}}^{-2}$ intensity laser light of different wavelengths.

Figure 6

Light-dressed absorption (upper panel) and stimulated emission (lower panel) spectra of ${\mathrm{Na}}_2$ obtained at different temperatures with a 657 nm wavelength dressing field having 0.05 GW ${\mathrm{cm}}^{-2}$ intensity.

Figure 7

Light-dressed absorption (upper panel) and stimulated emission (lower panel) spectra of ${\mathrm{Na}}_2$ obtained at 0.5 K with 657 nm wavelength dressing fields having different intensities.

Figure 8

Population of the different field-free eigenstates in the wave function for $\lambda =663$ nm wavelength dressing fields of different turn-on time and intensity.

Figure 9

Population of the different light-dressed states in the wave function for $\lambda =663$ nm wavelength dressing fields of different turn-on time and intensity.