Correlation and dephasing effects on the non-radiative coherence between bright excitons in an InAs QD ensemble measured with 2D spectroscopy

Highlights

• Optical 2D spectroscopy is implemented to study an InAs quantum dot ensemble.

• Exchange-mediated splitting of bright excitons is measured with 30 neV resolution.

• With increasing emission energy, the splitting decreases at a rate of $0.1\mathrm{\mu }\mathrm{eV}/\mathrm{meV}$.

• Pure dephasing broadens the interband exciton linewidths beyond the radiative limit.

• The two lowest-energy exciton states exhibit nearly perfectly correlated dephasing.

Abstract

Exchange-mediated fine-structure splitting of bright excitons in an ensemble of InAs quantum dots is studied using optical two-dimensional Fourier-transform spectroscopy. By monitoring the non-radiative coherence between the bright states, we find that the fine-structure splitting decreases with increasing exciton emission energy at a rate of $0.1\mathrm{\mu }\mathrm{eV}/\mathrm{meV}$. Dephasing rates are compared to population decay rates to reveal that pure dephasing causes the exciton optical coherences to decay faster than the radiative limit at low temperature, independent of excitation density. Fluctuations of the bright state transition energies are nearly perfectly correlated, protecting the non-radiative coherence from interband dephasing mechanisms.

Introduction

In semiconductor quantum dots (QDs), the lowest energy electron–hole pair (exciton) has a coherence time up to nanoseconds [1], [2], making QDs promising candidates for forming the building blocks of devices relevant for quantum information [3], [4], [5], [6], [7] and nonlinear electro-optic applications [8]. Without considering the exchange interaction, the lowest-energy exciton state is four-fold spin degenerate, with two optically active ($|\pm 1〉$) and inactive ($|\pm 2〉$) states. Relative to higher-dimensional quantum systems, confinement in QDs increases the strength of the exchange interaction, which couples the spins of the electron and hole [9], [10]. Through short-range exchange, the four-fold degeneracy is lifted and the bright $|\pm 1〉$ states are energetically split from the dark $|\pm 2〉$ states. In QDs that lack cylindrical symmetry of the confinement potential, the long-range exchange interaction couples the $|+1〉$ and $|-1〉$ states to form two orthogonal linearly polarized exciton states, $|\mathrm{H}〉$ and $|\mathrm{V}〉$, that are energetically separated by the so-called fine-structure splitting, ${\delta }_1$. These states are coupled by confinement-enhanced Coulomb interactions, forming a four-level diamond system shown in Fig. 1.

Successful implementation of the aforementioned applications using QDs requires understanding how the physical properties of the QD – including confinement, internal strain and alloying – affect its optical properties. Significant insight in this regard has been obtained in the past decade, either through single QD studies using photoluminescence [10], [11], [12], [13], [14] or by spectrally averaging the ensemble nonlinear response using time-integrated four-wave mixing (FWM) techniques [15]. These studies show that ${\delta }_1$ typically decreases with increasing emission energy (decreasing confinement) at a rate ranging from 0.25 to $2\mathrm{\mu }\mathrm{eV}/\mathrm{meV}$. Anisotropy in the QD confinement potential responsible for ${\delta }_1$ tends to orient $|\mathrm{H}〉$ and $|\mathrm{V}〉$ along the [110] and $[1\overline{1}0]$ crystal axes for samples grown along the [001] direction. Elongation of the QD shape occurring during growth and strain-induced piezoelectric fields [12] are thought to be responsible for the anisotropy, although the dominant mechanism is still under debate [14].

In this work, we demonstrate that ${\delta }_1$ can be measured for all QDs in the inhomogeneously broadened ensemble simultaneously by monitoring the temporal evolution of the coherence [16] between $|\mathrm{H}〉$ and $|\mathrm{V}〉$ using two-dimensional Fourier-transform spectroscopy (2DFTS), which is based on three-pulse transient FWM [17]. The non-radiative $|\mathrm{H}〉–|\mathrm{V}〉$ coherence, which has no optical dipole moment, can be probed optically by coherently exciting the $|0〉–|\mathrm{H}〉$ and $|0〉–|\mathrm{V}〉$ transitions using either two orthogonal linearly polarized pulses or a single circularly polarized pulse. Previous experiments [4], [18], [19], [20] have used this coherence to manipulate exciton spin states and create entangled photon pairs from single QDs. Here we measure the dynamics of this coherence in an InAs QD ensemble and present zero-quantum 2D spectra that reveal the effects of dephasing and correlated scattering on the exchange-split exciton states. We find that within the full-width half-maximum (FWHM) of the inhomogeneous distribution, ${\delta }_1$ decreases with increasing emission energy at a rate of $0.1\mathrm{\mu }\mathrm{eV}/\mathrm{meV}$ and anisotropy in the QD confinement potential responsible for ${\delta }_1$ is oriented along the same crystal axis for all QDs. By comparing the exciton homogeneous linewidth [21], comprised of a narrow Lorentzian zero-phonon line (ZPL) at low temperatures with a broad phonon background at high temperatures, to the population decay rate, we find that additional pure dephasing broadens the linewidth beyond the radiative limit at low temperature, independent of excitation density. Interestingly, the dephasing rate of the $|\mathrm{H}〉–|\mathrm{V}〉$ coherence is equal to the population decay rate of the individual exciton states, indicating that nearly perfectly correlated scattering of $|\mathrm{H}〉$ and $|\mathrm{V}〉$ shields the non-radiative coherence from the pure dephasing mechanisms.