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arXiv:1602.09048 · Physical Review A

Electric dipole coupling in optical cavities and its implications for energy transfer, up-conversion, and pooling

Michael D. LaCount, Mark T. Lusk

Published Jun 8, 2016• 8 citations
arXivHTMLPDF

Abstract

Resonant energy transfer, energy transfer up-conversion, and energy pooling are considered within optical cavities to elucidate the relationship between exciton dynamics and donor-acceptor separation distance. This is accomplished by using perturbation theory to derive analytic expressions for the electric dipole coupling tensors of perfect planar and rectangular channel reflectors---directly related to a number of important energy-transfer processes. In the near field, the separation dependence along the cavity axis is not influenced by the cavity and is essentially the same as for three-dimensional free space. This is in sharp contrast with the reduced sensitivity to separation found in idealized low-dimensional settings. The cavity dynamics only correspond to their reduced-dimensional counterparts in the far field where such excitonic processes are not typically of interest. There is an intermediate regime, though, where sufficiently small cavities cause a substantial decrease in separation sensitivity that results in one component of the dipole-dipole coupling tensor being much larger than those of free space.

DOI
10.1103/physreva.93.063811

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Resonant energy transfer, energy transfer up-conversion, and energy pooling are considered within optical cavities to elucidate the relationship between exciton dynamics and donor-acceptor separation distance. This is accomplished by using perturbation theory to derive analytic expressions for the electric dipole coupling tensors of perfect planar and rectangular channel reflectors---directly related to a number of important energy-transfer processes. In the near field, the separation dependence along the cavity axis is not influenced by the cavity and is essentially the same as for three-dimensional free space. This is in sharp contrast with the reduced sensitivity to separation found in idealized low-dimensional settings. The cavity dynamics only correspond to their reduced-dimensional counterparts in the far field where such excitonic processes are not typically of interest. There is an intermediate regime, though, where sufficiently small cavities cause a substantial decrease in separation sensitivity that results in one component of the dipole-dipole coupling tensor being much larger than those of free space.
The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub- and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.
The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub-and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.
We study the dynamics of excitonic states in one dimensional, dimer and trimer, and two dimensional arrangements of colloidal quantum dots using a density-matrix approach.The dots are coupled via a dipole-dipole interaction akin to the Förster mechanism.Coherent oscillations of tuned donor dots are shown to appear as plateaus in the acceptor dots, and therefore in their optical response.This behavior provides one with an interesting and unique handle to monitor the quantum state of clusters in an eavesdroping arrangement.A trimer cluster in a symmetrical loop shows steady states in a shorter characteristic time than the typical radiative lifetime of the dots.Breaking the symmetry of the loop results again in damping oscillatory states in the donor dots and plateaus in the eavesdropping/acceptor dot.The use of realistic parameters allows direct comparison with recent experiments and indicates that coherent state monitoring is possible in real experiments.Estimates of the Förster coupling V F are obtained from a microscopic description of the exciton levels in the quantum dot.We present results for different materials CdS, CdSe, GaAs, and InP as function of dot features.V F shows a nonmonotonic variation with dot sizes and a maximum value that depends on the specific dot sizes, material parameters, and dot separation.We also study the effect of the orientation factor on coherent energy transfer from a donor quantum dot to an acceptor quantum dot by calculating the polarization of the acceptor dot.We study how the measurement of the ac-ceptor polarization can be used to determine the relative orientation between the donor-acceptor pair.We also find that Förster coupling between dots results in a polarization memory transfer.
Strong coupling between molecular excitations and quantized electromagnetic fields in optical cavities provides a powerful means to control the physical and chemical properties of molecular systems. Here, we study electron transfer (ET) dynamics in cavity-coupled molecules using the numerically exact hierarchical equations of motion (HEOM) method, which captures nonperturbative and non-Markovian effects beyond standard perturbative theories. We identify distinct resonance and collective effects associated with polariton formation and show that the ET rate saturates in the strong-coupling regime, a feature not captured by perturbative approaches. We further extend the cavity-modified ET model by incorporating the nuclear-coordinate dependence of molecular electric dipole moments, which gives rise to a three-body interaction involving molecular electronic and vibrational degrees of freedom and cavity photons. This vibronic polariton formation leads to non-monotonic, oscillatory dependencies of the ET rate on the light-matter coupling strength and cavity frequency, which we attribute to quantum interference among multiple transfer pathways. These findings establish cavity-modified electron transfer as a multichannel quantum process governed by the interplay of electronic, vibrational, and photonic degrees of freedom.
We compute the energies of the interaction between two atoms placed in the middle of a perfectly reflecting planar cavity, in the weak-coupling nondegenerate regime. Both inhibition and enhancement of the interactions can be obtained by varying the size of the cavity. We derive exact expressions for the dyadic Green's function of the cavity field which mediates the interactions and apply time-dependent quantum perturbation theory in the adiabatic approximation. We provide explicit expressions for the van der Waals potentials of two polarizable atomic dipoles and the electrostatic potential of two induced dipoles. We compute the van der Waals potentials in three different scenarios: two atoms in their ground states, two atoms excited, and two dissimilar atoms with one of them excited. In addition, we calculate the phase-shift rate of the two-atom wave function in each case. The effect of the two-dimensional confinement of the electromagnetic field on the dipole-dipole interactions is analyzed. This effect depends on the atomic polarization. For dipole moments oriented parallel to the cavity plates, both the electrostatic and the van der Waals interactions are exponentially suppressed for values of the cavity width much less than the interatomic distance, whereas for values of the width close to the interatomic distance, the strength of both interactions is higher than their values in the absence of cavity. For dipole moments perpendicular to the plates, the strength of the van der Waals interaction decreases for values of the cavity width close to the interatomic distance, while it increases for values of the width much less than the interatomic distance with respect to its strength in the absence of cavity. We illustrate these effects by computing the dipole-dipole interactions between two alkali atoms in circular Rydberg states.
We develop a theory of exciton energy transfer dynamics between two quantum dots in a planar microcavity. We study the dynamics of quantum dot excitons in three different cases: (i) a single dot coupled only to cavity modes, (ii) two dots coupled to cavity modes, and (iii) two dots coupled to cavity modes and to acoustic phonons. In the latter case, we focus on the process of phonon-assisted inelastic exciton energy transfer between the quantum dots. We take into account phonon effects by introducing a light-matter Hamiltonian with operators describing the exciton-photon-phonon coupling and we truncate the Hilbert space by assuming that at most one excitation is present in the system. Using this approach we simulate the exciton dynamics with realistic parameters in the zero temperature limit. From the dynamics we extract the dependence of the characteristic energy transfer rate as a function of the interdot separation. This theoretical approach can be used to optimize exciton energy transfer by designing structures with engineered photon and phonon density of states.