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Physical Review Letters

Proposed Coherent Trapping of a Population of Electrons in a C60 Molecule Induced by Laser Excitation

G. P. Zhang, Thomas F. George

Published Dec 19, 2012• 12 citations
Publisher

Abstract

This Letter demonstrates the possibility of generating coherent population trapping in C(60). Similar to a three-level Λ system, 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 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 C(60), analogous to that in atomic vapors. Turning off the coupling field restores 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 C(60) plunges by five times, in comparison with the noncontrol case. This should be detectable experimentally.

DOI
10.1103/physrevlett.109.257401

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This Letter demonstrates the possibility of generating coherent population trapping in C(60). Similar to a three-level Λ system, 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 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 C(60), analogous to that in atomic vapors. Turning off the coupling field restores 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 C(60) plunges by five times, in comparison with the noncontrol case. This should be detectable experimentally.
Coherent population trapping (CPT) and electromagnetically induced transparency in atoms have garnered enormous attention because of their conceptual novelty in quantum optics and potential applications in quantum information processing. Here, we show that CPT can occur in buckminsterfullerene C60{\mathrm{C}}_{60}C60​. If we radiate C60{\mathrm{C}}_{60}C60​ with a cw coupling field first and then with a weak probe field, C60{\mathrm{C}}_{60}C60​ becomes much less absorptive. Turning off the coupling field restores the absorptive nature. Using two coupling pulses, we can prepare C60{\mathrm{C}}_{60}C60​ in a dark state, which is transparent to the probe field. Such a dark state sensitively depends on the laser field amplitude, pulse durations, time delay between two coupling pulses, and laser chirps. Too strong fields refill the ground state, while too long durations overshoot the population and become less effective. There is an optimal delay between two pulses. By employing the first-principles method and solving the Liouville equation dynamically, we scan the vast laser parameter space and find a practical path to coherent population trapping in C60{\mathrm{C}}_{60}C60​, which is of great importance for future experimental investigations.
We observe coherent population trapping (CPT) in a two-electron atom— 174 Yb—using the transition. CPT is not possible for such a transition according to one-electron theory because the magnetic sublevels form a V-type system, but in a two-electron atom like Yb, the interaction of the electrons transforms the level structure into a Λ -type system, which allows the formation of a dark state and hence the observation of CPT. Since the two levels involved are degenerate, we use a magnetic field to lift the degeneracy. The single fluorescence dip then splits into five dips—the central unshifted one corresponds to coherent population oscillation, while the outer four are due to CPT. The linewidth of the CPT resonance is about 300 kHz and is limited by the natural linewidth of the excited state, which is to be expected because the excited state is involved in the formation of the dark state.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We report an experimental observation of coherent population trapping in multilevel dark states prepared in the ground hyperfine states of 87Rb{}^{87}\mathrm{Rb}87Rb atoms confined in a room-temperature vapor cell. The dark states are created by a linearly polarized coupling laser that is tuned to the 87Rb{}^{87}\mathrm{Rb}87Rb D1{D}_{1}D1​ $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1$ or 2 transition and establishes \ensuremath{\Lambda}-type transition chains. The Doppler shift for the \ensuremath{\Lambda}-type transition chains is compensated by the left and right circularly polarized components of the coupling laser. The multilevel dark states that consist of three or two magnetic sublevels among the five degenerate magnetic sublevels in the F=2F=2F=2 ground hyperfine state are probed by a weak probe laser scanned across the same D1{D}_{1}D1​ transition and their existence is manifested by a strong dependence of the probe excitation on the probe polarization. Our experiment demonstrates the importance of coherent population trapping in a laser coupled degenerate multilevel open atomic system, which may play an important role in diverse physical phenomena such as atom cooling and trapping, optical pumping, and multiple laser excitation and ionization of atoms and molecules.
The interaction between a three-level atom and a polychromatic field with an equidistant spectrum (Λ-scheme of the atom--field interaction) has been studied theoretically. It is shown that the interaction of an atom with such a field can be reduced to its interaction with a bichromatic field with additional light shifts of transition frequencies and an additional coupling of the lower atomic levels, which is proportional to the field intensity. Owing to this coupling, the idea of the coherent population trapping can be considered only as an approximation, because the dark state is not an eigenstate of the effective Hamiltonian in the general case of arbitrary dipole moments. The analyzed model gives a simple theoretical interpretation for the formation of the atomic state, which is close to the coherent population trapping, in the radiation field of a femtosecond laser.
We report an experimental study of coherent population trapping and four-wave mixing via multilevel dark states prepared in the ground hyperfine states of 87Rb{}^{87}\mathrm{Rb}87Rb atoms. The dark states are created by \ensuremath{\Lambda}-type coupling chains driven by a linearly polarized pump laser tuned to the D1{D}_{1}D1​ $F=2\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=1$ transition. The Doppler shift in the coupling chains is compensated by the left- and right-circularly polarized components of the pump laser. The multilevel dark states are explored by a probe laser and their existence is manifested by a strong dependence of the probe excitation and four-wave-mixing emission on the probe polarization. Our experiment shows that coherent population trapping in multilevel dark states of a degenerate atomic system should be useful in the coherence control of optical nonlinearity.