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^{1,2}, A. J. Bennett

^{1,a)}, I. Farrer

^{2}, D. A. Ritchie

^{2}and A. J. Shields

^{1}

### Abstract

We have studied the variation in fine-structure splitting (FSS) under application of vertical electric field in a range of quantum dots grown by different methods. In each sample, we confirm that this energy splitting changes linearly over the field range we can access. We conclude that this linear tuning is a general feature of self-assembled quantum dots, observed under different growth conditions, emission wavelengths, and in different material systems. Statistical measurements of characteristic parameters such as emission energy, Stark shift, and FSS tuning are presented which may provide a guide for future attempts to increase the yield of quantum dots that can be tuned to a minimal value of FSS with vertical electric field.

This work was partly supported by the EU through the IST FP6 Integrated Project QESSENCE. EPSRC provided support for MAP.

### Key Topics

- Quantum dots
- 61.0
- Electric fields
- 13.0
- Excitons
- 7.0
- Photonic entanglement
- 5.0
- Self assembly
- 5.0

## Figures

Electric field dependence of the exciton photon energy for (a) sample A, (b) sample B, (c) sample C, and (d) sample D showing the parabolic Stark shift of the exciton emission energy, from which the Stark parameters pX and βX are extracted, of a typical QD selected randomly from each sample. The lower panels show the magnitude of the fine structure splitting, |s|, for (e) sample A, (f) sample B, (g) sample C, and (h) sample D illustrating the linear shift in |s|, from which is extracted, of three typical QDs in each sample.

Electric field dependence of the exciton photon energy for (a) sample A, (b) sample B, (c) sample C, and (d) sample D showing the parabolic Stark shift of the exciton emission energy, from which the Stark parameters pX and βX are extracted, of a typical QD selected randomly from each sample. The lower panels show the magnitude of the fine structure splitting, |s|, for (e) sample A, (f) sample B, (g) sample C, and (h) sample D illustrating the linear shift in |s|, from which is extracted, of three typical QDs in each sample.

Observation of avoided crossings in the neutral exciton states of quantum dots tuned with electric field. (a), (b), and (c) magnitude of the fine structure splitting, |s|, in a single QD from samples A, B, and D, respectively, as a function of electric field. In each case the minimum value of |s| is approximately 2 μeV and so is sufficient to show entangled photon emission. (d), (e), and (f) show the corresponding orientation of the eigenstates, relative to the [110] crystalline axis, as the QDs are tuned through their minimum |s|.

Observation of avoided crossings in the neutral exciton states of quantum dots tuned with electric field. (a), (b), and (c) magnitude of the fine structure splitting, |s|, in a single QD from samples A, B, and D, respectively, as a function of electric field. In each case the minimum value of |s| is approximately 2 μeV and so is sufficient to show entangled photon emission. (d), (e), and (f) show the corresponding orientation of the eigenstates, relative to the [110] crystalline axis, as the QDs are tuned through their minimum |s|.

## Tables

Summary of the behavior of the exciton emission energy and fine structure splitting of QDs in each of the four sample types, A, B, C, and D. For all parameters, the value given is the mean average over all the QDs studied in the corresponding type. The columns contain the exciton emission energy, E 0 X; Stark shift parameters, z-dipole moment, p X, and polarizability, βX; fine structure splitting at zero electric field, s(F = 0); and the rate at which the fine structure splitting is tuned with electric field, .

Summary of the behavior of the exciton emission energy and fine structure splitting of QDs in each of the four sample types, A, B, C, and D. For all parameters, the value given is the mean average over all the QDs studied in the corresponding type. The columns contain the exciton emission energy, E 0 X; Stark shift parameters, z-dipole moment, p X, and polarizability, βX; fine structure splitting at zero electric field, s(F = 0); and the rate at which the fine structure splitting is tuned with electric field, .

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