Proposed Coherent Trapping of a Population of Electrons in a ${\mathbf{C}}_{60}$ Molecule Induced by Laser Excitation

This Letter demonstrates the possibility of generating coherent population trapping in ${\mathrm{C}}_{60}$. Similar to a three-level $\Lambda$ system, ${\mathrm{C}}_{60}$ has a forbidden transition between the highest occupied molecular orbital (HOMO) ($|a⟩$) and the lowest unoccupied molecular orbital (LUMO) ($|c⟩$), but a dipole-allowed transition between HOMO and $\mathrm{LUMO}+1$ ($|b⟩$) and between $|b⟩$ and $|c⟩$. We employ two cw laser fields, one coupling and one probe. The strong coupling field is switched on first to resonantly excite the transition between $|b⟩$ and $|c⟩$. After a delay, the probe is switched on; the coherent interaction between the coupling and probe fields traps the population in $|a⟩$ and $|c⟩$. This forms a partially dark state in ${\mathrm{C}}_{60}$, analogous to that in atomic vapors. Turning off the coupling field restores ${\mathrm{C}}_{60}$’s absorption. Pulsed lasers work as well. We use two pulses to steer the system into a dark state; when we send in a cw probe field, the electric polarization of ${\mathrm{C}}_{60}$ plunges by five times, in comparison with the noncontrol case. This should be detectable experimentally.

Figure 1

(a) Absorption spectrum of ${\mathrm{C}}_{60}$. The two arrows denote the excitation photon energies for the coupling and probe fields, respectively. The probe is $E_1$, and the coupling $E_2$. Inset: A typical $\Lambda$ system, where the three levels $|a⟩$, $|b⟩$ and $|c⟩$ refer to the ground state, one-photon-allowed and two-photon-allowed excited states. In the single-particle picture, these three levels correspond to the $H_u$, $T_{1g}$, and $T_{1u}$ states, respectively. (b) Population change as a function of time with the coupling field on. The population is trapped between $|a⟩$ and $|c⟩$ by cw lasers. The solid line denotes ${\rho }_{aa}$, the long dashed line ${\rho }_{cc}$, and the two dotted lines refer to ${\rho }_{bb}$. The laser envelopes are shown at the bottom, where the coupling laser is turned on first and then the probe field. (c) Laser-polarization dependence of the population change in level $|c⟩$ at time $t=315\mathrm{fs}$. The coupling polarization changes from the $x$ axis to the $z$ axis, with the $z$ axis along the fivefold symmetry axis. The inset shows the polarization angle. (d) Population change without the coupling field. Here the absorption is restored. The probe field envelope function is shown at the bottom.

Figure 2

(a) CPT induced by the pulse laser fields. Two coupling pulses prepare the system in a dark state. When the cw probe field enters, it becomes much less absorptive. The laser fields are shown at the top. (b) Envelopes of polarization with (solid red line) and without (long dashed line) the coupling pulses. The change in polarization differs by five times.