Similar to graphene, CNTs posses an orbital (valley) degree of freedom, arising from the two inequivalent Dirac points K, K′ in the Brillouin zone. ( 2) below, the linear combination is set by the phase of the tunneling matrices which couple the quantum dot to the leads. We notice that while in the optical setup it is the coherent drive that defines the linear combination yielding the DS 1, in the transport setup the effect is more subtle. Here we demonstrate that such a situation has been realized in a CNT-based quantum dot. The spontaneous formation of a coherent superposition of system eigenstates (the dark state) suppresses these transitions, despite the presence of the driving. There is a close analogy between the experiment generating dark states in atoms and the one discussed here: In both cases the coupling to an external drive (the laser fields for the atom, the DC bias for the quantum dot) enables inelastic transitions among three energy eigenstates of the isolated system. For opposite bias no suppression takes place. This allows electrons to enter the DS from the left while preventing them to leave it to any of the two leads. The coherent superposition of two degenerate states results in a coupled state (CS) and a DS which is decoupled from the right lead. 1a for the case of a positive electrochemical potential drop between left and right leads. The situation is illustrated in the quantum dot setup of Fig. This in turn yields a characteristic current suppression as the bias voltage or the gate voltage are tuned. Under given conditions, tunneling events into and out of the dot successively trap the system in a DS, i.e., a coherent superposition of the degenerate levels which is decoupled from one of the leads. The effect requires the presence of quasi orbitally degenerate states which can form coherent superpositions. In this work we report the experimental realization of the second all-electrical realization of CPT in a single carbon nanotube (CNT) quantum dot. A second possibility is, similar to the original optical experiment, CPT in a linear superposition of energy eigenstates, predicted for highly symmetric triple quantum dot setups 14, 15 or for molecular junctions with intrinsic orbital degeneracies 16, 17, 18. Several proposals have predicted trapping in a coherent superposition of spatially localized states under appropriate bias conditions, 7, 8, 9, 10, 11 whose signatures have been observed in vertical double dot experiments 12, 13. Since localization of the electrons in the DS also implies a vanishing current through the double quantum dot, this allows the electrical detection of CPT by recording variations of the current as the microwaves parameters are tuned.Īll-electrical realizations of CPT are also desirable. Proposals 3, 4, 5 have considered microwave irradiated double quantum dot analogs of the seminal experiment 6. Quantum dots offer the possibility to engineer artificial atoms and molecules by proper circuit design, and hence to probe CPT in effective Lambda-systems. In the stationary limit, the DS is occupied with probability one and the CPT is perfect. By proper detuning of the lasers, the system has a finite probability to decay into a coherent superposition of the low-lying states which is decoupled from the light, a so-called dark state (DS). The light beams coherently excite the atom from two low-lying states to a common excited state. Coherent population trapping (CPT) occurs in three-level, Lambda-type atomic systems coupled to two quasi-resonant electromagnetic modes 1, 2.
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