Quantum electrodynamical theory of high-efficiency excitation energy transfer in laser-driven nanostructure systems

A fundamental theory is developed for describing laser-driven resonance energy transfer (RET) in dimensionally constrained nanostructures within the framework of quantum electrodynamics. The process of RET communicates electronic excitation between suitably disposed emitter and detector particles in close proximity, activated by the initial excitation of the emitter. Here, we demonstrate that the transfer rate can be significantly increased by propagation of an auxiliary laser beam through a pair of nanostructure particles. This is due to the higher order perturbative contribution to the Förster-type RET, in which laser field is applied to stimulate the energy transfer process. We construct a detailed picture of how excitation energy transfer is affected by an off-resonant radiation field, which includes the derivation of second and fourth order quantum amplitudes. The analysis delivers detailed results for the dependence of the transfer rates on orientational, distance, and laser intensity factor, providing a comprehensive fundamental understanding of laser-driven RET in nanostructures. The results of the derivations demonstrate that the geometry of the system exercises considerable control over the laser-assisted RET mechanism. Thus, under favorable conformational conditions and relative spacing of donor-acceptor nanostructures, the effect of the auxiliary laser beam is shown to produce up to 70% enhancement in the energy migration rate. This degree of control allows optical switching applications to be identified.

Figure 1

Schematic depiction of energy transfer from donor to acceptor. Green arrows represent emission and absorption of energy in donor and acceptor particles. Horizontal red dashed arrow illustrates the interaction of the laser beam with the donor and acceptor. Horizontal orange wavy arrow represents the transfer of energy, mediated by a virtual photon, from the donor to the acceptor. The Greek letters indicate the relevant electronic excited states and 0 the ground state.

Figure 2

Time-ordered Feynman diagrams representing resonance energy transfer between a donor $D$ and acceptor $A$. On each matter vertical line, Greek symbols identify particle electronic excited states, with 0 the corresponding ground state and $r,s$ intermediate matter states. The transfer is mediated by the virtual photon with wave vector $\mathbf{p}$. Panels (a) and (b) illustrate Feynman diagrams for direct RET. (c) One of 24 time orderings representing one type of laser-modified process where both donor and acceptor interact with the auxiliary beam (with wave vector $\mathbf{k})$. (d) The mirror case of (c). (e) One of 24 time orderings representative of LARET interactions where only the donor $D$ interacts with the auxiliary beam. (f) Converse case where only $A$ interacts with the auxiliary beam. In each case (c)–(f), photons are absorbed from and emitted back into the laser beam. Cases (c) and (d) require both donor and acceptor to be sited within the beam: in principle, in (e) or (f), only one of them need be.

Figure 3

Schematics for the (a) direct resonance energy transfer in NW to NW with the orientational factors in Eq. (15) $(R$ is the distance between two NWs), and (b) laser-assisted resonance energy transfer (LARET) in a NW pair.

Figure 4

RDDI strengths of the direct RET (ash colored dashed line), laser-driven RET (pink colored line), and the quantum interference (blue colored line) when $\kappa =1,0,-1$ are shown in (a)–(c), respectively, as a function of the laser intensity.

Figure 5

Transfer rates for energy transfer between nanowires: direct RET (ash colored dashed line), laser-driven RET (red colored line), quantum interference (blue colored line), and the total LARET rate (green colored line) when $\kappa =1,0,-1$ are shown in (a)–(c), respectively, as a function of the laser intensity.

Figure 6

Schematics for the (a) direct resonance energy transfer in QD to QD with the orientational factors in Eq. (26) $(R$ is the distance between two QDs), and (b) laser-assisted resonance energy transfer (LARET) in a QD pair.

Figure 7

RDDI strengths of the direct RET (ash colored dashed line), laser-driven RET (pink colored line), and the quantum interference (blue colored line) when $\kappa =2,0,-2$ are shown in (a)–(c), respectively, as a function of the laser intensity.

Figure 8

Transfer rates for energy transfer between quantum dots: direct RET (ash colored dashed line), laser-driven RET (red colored line), quantum interference (blue colored line), and the total LARET rate (green colored line) when $\kappa =2,0,-2$ are shown in (a)–(c), respectively, as a function of the laser intensity.

Figure 9

(a) The brown and purple solid lines represent the LARET rates; (b) RET rate enhancement factor in QD and NW systems; (c) log-log plot of transfer rate as a function of $\text{log}\left(I\right)$, for three different relative distances (3 nm, 5 nm, 7 nm) between D and A, dashed lines representing the transfer rates for the case of a NW pair. Note that for all the plots from (a)–(c), we consider ${\kappa }_{\mathrm{NW}}=-1$ and ${\kappa }_{\mathrm{QD}}=-2$.