Non-Markovian Decoherence of Localized Nanotube Excitons by Acoustic Phonons

Christophe Galland, Alexander Högele, Hakan E. Türeci, and Ataç Imamoğlu

Phys. Rev. Lett. 101, 067402 – Published 6 August 2008

Abstract

We demonstrate that electron-phonon interaction in quantum dots embedded in one-dimensional systems leads to pronounced, non-Markovian decoherence of optical transitions. The experiments that we present focus on the line shape of photoluminescence from low-temperature axially localized carbon nanotube excitons. The independent boson model that we use to model the phonon interactions reproduces with very high accuracy the broad and asymmetric emission lines and the weak red-detuned radial breathing mode replicas observed in the experiments. The intrinsic phonon-induced pure dephasing of the zero-phonon line is 2 orders of magnitude larger than the lifetime broadening and is a hallmark of the reduced dimensionality of the phonon bath. The non-Markovian nature of this decoherence mechanism may have adverse consequences for applications of one-dimensional systems in quantum information processing.

Received 18 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.067402

Authors & Affiliations

Christophe Galland, Alexander Högele, Hakan E. Türeci, and Ataç Imamoğlu

Institute of Quantum Electronics, ETH Hönggerberg, Wolfgang-Pauli-Strasse 16, CH-8093 Zürich, Switzerland

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Vol. 101, Iss. 6 — 8 August 2008

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Images

Figure 1
Photoluminescence of a nanotube quantum dot at $T = 4.2 K$ and $P = 300 nW$ (open circles) and the calculated spectrum (solid line) plotted on a logarithmic scale. For the theoretical model, we used the parameters $D_{S} = 14 eV$ , $D_{RBM} = 1.4 eV / Å$ , $ℏ ω_{RBM} = 37.2 meV$ , $Δ E = 44 meV$ , and $T_{fit} = 6.3 K$ . The upper and lower solid blue lines are calculated spectra with identical parameters but $D_{RBM} = 1.8 eV / Å$ and $D_{RBM} = 1.0 eV / Å$ , respectively, demonstrating the precision with which the coupling strength can be determined. The inset shows a time-resolved measurement (dark line). The red line is a biexponential fit of the PL decay revealing a main fast component with characteristic time $t_{1} = 36 \pm 0.2 ps$ and weight $A_{1} = 100 \pm 0.3$ and a vanishingly weak long tail ( $t_{2} = 284 \pm 40 ps$ , $A_{2} = 1.2 \pm 0.2$ ). From the value of $t_{1}$ , we expect a lifetime-limited linewidth of $\sim 0.036 meV$ , in strong contrast to the measured and calculated width of 3.5 meV.Reuse & Permissions
Figure 2
Left panel: Experimental (open circles) and calculated (solid red lines) PL spectra for the same SWNT at different temperatures $T_{mes}$ (the vertical scale is arbitrary). The excitation power was kept constant at $P = 3 μ W$ . The effective temperature used in the simulation is given by $T_{fit}$ ; the other parameters are $D_{S} = 12.7 eV$ and $Δ E = 22 meV$ . Right panel: Emission from another nanotube at constant sample temperature $T = 4.2 K$ . The changes induced by increasing the laser intensity from 4 nW to $40 μ W$ are very well reproduced by increasing the temperature $T_{fit}$ in the model. The parameters for this SWNT are $D_{S} = 13 eV$ and $Δ E = 20 meV$ .Reuse & Permissions
Figure 3
Upper panel: Calculated emission line shapes at $T = 5 K$ for a QD coupled to a phonon bath of dimension $d = 1$ (left) and $d = 3$ (right) are shown. The coupling to a single acoustic phonon branch with linear dispersion ( $v_{s} = 19.9 km / s$ ) is considered. To extend the model to higher dimension, we assume an isotropic coupling of the QD to LA phonons described by the same deformation potential. A lifetime broadening corresponding to $t_{1} = 36 ps$ is introduced. Lower panel: For illustration, fit of the spectrum shown in Fig. 1 (open circles) with only the temperature-dependent [Eq. (4), red line] and the temperature-independent [Eq. (5), blue line] contributions. Each curve is scaled to span the same total area. The inset shows the susceptibility ( $T = 6 K$ ) used to fit the data (black curve), where a deviation from an exponential decay is visible for $t \leq 1 ps$ . The blue curve of the inset shows the same function at $T = 0.1 K$ where the non-Markovian nature of dephasing becomes clearer.Reuse & Permissions

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