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Optics Letters

Coherent transport of excitons in quantum-dot chains: role of retardation

D. S. Citrin

Published Apr 15, 1995• 38 citations
Publisher

Abstract

A model for the coherent transport of excitons along linear, one-dimensional arrays of quantum dots accounting for spontaneous emission is presented. The interdot coupling is made by means of the coherent emission and reabsorption of photons. The long-range nature of the coupling leads to nontrivial dynamics in the polarization and in the exciton population with qualitatively different behaviors for chains with periods just less than or just greater than integer multiples of half the wavelength of the optical transition. Biexponential radiative decay of an initially well-localized population is predicted.

DOI
10.1364/ol.20.000901

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•Jun 4, 2007•0 citations
A model for the coherent transport of excitons along linear, one-dimensional arrays of quantum dots accounting for spontaneous emission is presented. The interdot coupling is made by means of the coherent emission and reabsorption of photons. The long-range nature of the coupling leads to nontrivial dynamics in the polarization and in the exciton population with qualitatively different behaviors for chains with periods just less than or just greater than integer multiples of half the wavelength of the optical transition. Biexponential radiative decay of an initially well-localized population is predicted.
The optical response of radiatively coupled semiconductor multiple-quantum-well structures is investigated theoretically. It is shown that the transverse optical field leads to a coupling of exciton states within each well which causes a radiative decay and a mixing of excitonic resonances. Simultaneously, the field-induced long-ranged coupling between different wells leads to collective effects that are very sensitive to the detailed geometry of the structure. For a quantum-well spacing equal to an integer multiple of half the optical wavelength inside the medium, it is predicted that the collective effects cause a stimulated decay of electronic excitations that should be observable in either transmission or reflection geometry. On the other hand, in a quarter wavelength structure, the light-induced coupling causes an interwell energy transport and a splitting of the excitonic resonances, that should be observable as quantum beats in the time-resolved transmitted or reflected signal.
We have investigated the coherent dynamics of excitons in a single, a double, and a quintuple quantum-well structure under resonant excitation. In pump-and-probe experiments on the quintuple quantum well we observe a fast decay of the excitonic population within the initial coherent regime. This fast initial population decay is less pronounced for the double quantum well and is almost absent for the single quantum well. The energy linked to the initially lost coherent population is found in the coherent electromagnetic emission induced by the first-order polarization. More specifically, the intensity of this directional light emission increases quadratically with the number of quantum wells. Interference effects and electromagnetic coupling effects between polarizations located in distinct quantum wells probably play a crucial role in the superlinear coherent emission process.
We present a theoretical study of the collective optical effects which can occur in groups of three and four quantum dots. We define conditions for stable subradiant (dark) states, rapidly decaying super-radiant states, and spontaneous trapping of excitation. Each quantum dot is treated like a two-level system. The quantum dots are, however, realistic, meaning that they may have different transition energies and dipole moments. The dots interact via a short-range coupling which allows excitation transfer across the dots, but conserves the total population of the system. We calculate the time evolution of single-exciton and biexciton states using the Lindblad equation. In the steady state the individual populations of each dot may have permanent oscillations with frequencies given by the energy separation between the subradiant eigenstates.
The coherent exciton transport on a class of deterministic and random scale-free networks (DSFNs and RSFNs) generated by simple rules is studied in this paper. The coherent exciton dynamics is modeled by continuous-time quantum walks, and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For DSFNs, the probabilities of finding the excitation at the initial central nodes are nearly periodic, in contrast to the flat behavior found for RSFNs. In the long time limit, the transition probabilities on DSFNs show characteristic patterns with identical values. For RSFNs, we find that the excitation is most likely to be found at the initial nodes with high connectivity. All these features of quantum transport are significantly different from those of the classical transport modeled by continuous-time random walks.
Semiconductor Quantum dots are potentially an attractive source of non-classical light. They can confine bound electron-hole pairs, excitons, in all three spatial dimensions giving them discrete optical emission energies, much like the electronic states in atomic systems. The semiconductor nature of the system allows quantum dots to be integrated into complicated device structures including optical cavities [1] and electrical injection [2]. The radiative exciton emission from a semiconductor quantum dot can provide the simplest form of quantum light, a single photon source [2]. The finite re-excitation time following the radiative decay of an exciton in a quantum dot prevents the dot from emitting more than one photon if excited with a short optical or electronic pulse. In a similar fashion excitation of the biexciton state, consisting of two electrons and holes, in the quantum dot results in the emission of a pair of photons at the energy of the biexciton and exciton transitions. The biexciton state was, in fact, proposed as a possible source of polarisation-entangled photons in 2000 by Benson et al. [3] as it consists of two polarisation-correlated decay paths which could potentially be indistinguishable. The condition of indistinguishability is fundamental to the generation of entangled photons and is, in general, not true of the two decay paths from the biexciton state in a quantum dot; physical anisotropy causes the intermediate exciton states to hybridise and separate in energy providing ‘which-path’ information about the route taken through the biexciton decay. We demonstrate how the splitting between the intermediate exciton states in a single InAs quantum dot can be controlled by growth [4], rapid thermal annealing [5] and the application of an external magnetic field [6]. Each of these three techniques can be used to make the intermediate exciton states degenerate allowing the biexciton decay to produce singe pairs of entangled photons triggered by short laser pulses [7,8]. Entangled photon pair sources are essential for applications such as entanglement based quantum key distribution, and optical quantum computing. For these applications it is important that no more than one entangled photon pair is generated in a cycle, a requirement met by our quantum dot source which is not possible with traditional methods for generating entangled pairs of photons. Entanglement also enables quantum interferometry and metrology, the basis of image resolution beyond that possible with equivalent classical light. Biphoton interferometry using entangled emission from the biexciton decay reveals fringes with half the period of classical light [9], and less that that of the laser. In addition, interferometry suggests that this type of entangled light source is not limited by decoherence, we fine the biphoton is surprising robust against dephasing, in stark contrast to the devastating effect of decoherence upon single photons emitted by similar structures.