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Physical Review A

Laser-induced coherent population trapping in C 60

G. P. Zhang, Thomas F. George

Published Dec 3, 2013• 2 citations
Publisher

Abstract

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 ${\mathrm{C}}_{60}$. If we radiate ${\mathrm{C}}_{60}$ with a cw coupling field first and then with a weak probe field, ${\mathrm{C}}_{60}$ becomes much less absorptive. Turning off the coupling field restores the absorptive nature. Using two coupling pulses, we can prepare ${\mathrm{C}}_{60}$ 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 ${\mathrm{C}}_{60}$, which is of great importance for future experimental investigations.

DOI
10.1103/physreva.88.063808

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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.
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.
We present a general formalism for studying the interaction between laser fields and degenerate-Zeeman-sublevel atoms correct up to the first order in the weak probe field. We derive from this theory the equations of motion for a \ensuremath{\Lambda}-type system involving S1/2{\mathit{S}}_{1/2}S1/2​, F=2\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1\ensuremath{\leftrightarrows}S1/2{\mathit{S}}_{1/2}S1/2​, F=1 transitions in 87Rb^{87}\mathrm{Rb}87Rb atoms. These equations are used to numerically investigate the coherent population trapping (CPT) schemes in the S1/2{\mathit{S}}_{1/2}S1/2​, F=2\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1 transition induced by a linearly polarized pumping field and the electromagnetically induced transparency exhibited in the weak probe spectrum in the S1/2{\mathit{S}}_{1/2}S1/2​, F=1\ensuremath{\leftrightarrows}P1/2{\mathit{P}}_{1/2}P1/2​, F\ensuremath{'}=1 transition. We discuss the effects of the CPT on the probe spectrum with and without the Doppler broadenings by comparing the probe spectrum derived from the real system with that derived from an ideal \ensuremath{\Lambda}-type system. We show that the atoms in the CPT states are shielded from interacting with the probe field while those in the absorbent states make contributions to the weak probe by the Raman anti-Stokes process, and the effect of the real system on the probe field becomes equivalent to the ideal \ensuremath{\Lambda} system only in the strong CPT parameter regime. \textcopyright{} 1996 The American Physical Society.
In order to investigate effects of coherent population trapping (CPT) on electromagnetically induced transparency (EIT), we added an external weak magnetic field to identify a quantization axis. The laser beam whose polarization is parallel to the direction of the external magnetic field and the perpendicular laser are coupled to different transitions. CPT generated by two circular polarization components of the strong coupling beam when the polarization was perpendicular to the quantization axis, was competed with (EIT) so that absorption reduction could be larger than the case without CPT. We investigated the mechanism of steady-state light amplification without inversion using an incoherent pumping laser.
Coherent atomic states prepared by laser field can have quantum interference\nbetween the different transition amplitudes. Therefore, the medium susceptibility\nand optical response can be engineered, leading to many interesting phenomena, such\nas coherent population trapping (CPT), electromagnetically induced transparency\n(EIT), and lasing without inversion (LWI).\nWe studied the coherence effects in various prototype atomic systems, and found\nmany interesting applications. We solved the slow light bandwidth problem by decomposing\nthe pulse and matching each frequency to its EIT window using a magnetic\nfield gradient. We also considered the probe field deflection induced by the driving\nfield distribution in EIT, and showed that even a broadband pulse can be deflected\nwithout serious spreading. In the fast light area, we examined the effects of noise and\nparameter deviations in a bichromatic Raman type white light cavity. Taking advantage\nof the adjustable absorption of EIT, we showed that EIT in a laser cavity can\nhave either first-order or second-order phase transitions. Last but not least, we show\nthat the adiabatic population transfer can be used to reverse the weak measurement\nof an arbitrary field with finite photon number.
We analytically and numerically investigate the response of an open Λ-type atomic system to a probe laser field, where one of the atomic transition is coupled with a double-band radiation reservoir and high- Q defect modes formed by atomic doping. This system can be transparent to a weak probe field being two-photon resonant with the frequency of the defect modes or one of the two band edges, and the high- Q defect modes can even induce an atom–field coherent population trapping (CPT) state without involving the excited state of the atom, in spite of the background decay of the excited state of the atom. The steady-state properties of this CPT are independent of the smoothness feature of the density of modes (DOM) at band edges. However, the CPT never occurs in the absence of any defect even if the DOM is singular at both band edges. We also find that the background decay of the second ground state of the atom will destroy the CPT and increase the probe absorption, but the atomic coherence induced by the defect modes is more robust than that induced by the band edges. The transient properties of the CPT are also studied.