Unavoidable decoherence in semiconductor quantum dots

Phonon-induced unavoidable decoherence of orbital degrees of freedom in quantum dots is studied and the relevant time scales are estimated. Dephasing of excitons due to acoustic phonons and, in a polar medium, to optical phonons, including anharmonic effects and enhancement of the effective Fröhlich constant due to localization, is assessed for typical self-assembled quantum dots. Temporal inefficiency of Pauli blocking due to lattice inertia is predicted. For quantum dots placed in a diluted magnetic semiconductor medium a magnon-induced dephasing of a spin is also estimated in accordance with experimental results.

Figure 1

Spectral intensity vs energy (Fourier representation of the correlation function) for the averaged dot dimension $l=6\mathrm{nm}$ (upper), the temperature evolution of LA phonon sideband (middle), and satellite-emission LO phonon peak (lower). Only the LA sideband grows in this temperature range; absorption processes are unimportant for LO phonons at low temperatures (left satellite peak corresponding to LO phonon absorption is smaller by a few orders of magnitude than that for emission and of a similar size as the emission peak for $T>80\mathrm{K}$); the satellite LO peak grows significantly due to the enhancement of the Fröhlich constant in a QD (b) in comparison to its bulk value (a) (cf. Appendix ).

Figure 2

Modulus of the correlation function $\mid ⟨a\left(t\right)a^{†}\left(0\right)⟩\mid$ (the fidelity measure of the ground excitonic state) vs time for rising temperatures. The three plots correspond to small, medium, and large QD’s and contain curves corresponding to the same set of temperatures as given in the upper plot. For the small QD, the experimentally observed fidelity loss for $0.2\mathrm{ps}$ pulse exciton in a QD (Ref. 18) is well reproduced.

Figure 3

The typical shape of the modulus of the correlation function for LO and LA phonons simultaneously. The oscillations correspond to the gap of LO phonons.

Figure 4

Left: the modulus of the correlation function for dynamics with LA (upper) and LO (lower) phonons only. Right: dressing time vs averaged QD dimension $l$ for the LA channel (upper) showing linear dependence and for the LO channel (lower) with quadratic dependence on $l$.

Figure 5

(a)–(c) The shape of the LO phonon replica for damped (solid line) and free (dashed line) LO phonons for three effective dot diameters. (d)–(f) The corresponding envelopes of the LO phonon beats after ultrafast excitation. The dot diameters are $l=3\mathrm{nm}$ (a), (d), $l=6\mathrm{nm}$ (b), (e), and $l=12\mathrm{nm}$ (c), (f). In all the cases the zone-center LO phonon lifetime is ${\tau }_{\mathrm{LO}}=9.2\mathrm{ps}$.

Figure 6

Time of formation of an excitonic magnetic polaron (EMP) in a DMS QD $[\mathrm{Zn}\left(\mathrm{Mn}\right)\mathrm{Se}∕\mathrm{Cd}\mathrm{Se}]$, i.e., the time of the QD exciton-spin dressing with magnons, vs dot dimension. The dependence on dot dimension $d$ is parabolic and sensitive to dopant concentration $\left(x_{\mathrm{i}}\right)$ and band-hole concentration $\left(x_{\mathrm{p}}\right)$ in DMS’s.

Figure 7

The electron (solid line) and hole (dashed line) probability density for the exciton ground state, compared to a noninteracting particle (dotted line).

Figure 8

Left: the coupling constants for LA phonons, obtained from the anisotropic wave function (solid line) and from isotropic approximation (dashed line). Right: the coupling constants for LO phonons.

Figure 9

Effective Fröhlich constant vs QD diameter for self-assembled $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ QD’s. Solid circles: data extracted from a Huang-Rhys parameter for a pyramid-shape QD with base length 19, 17, $15\mathrm{nm}$ (Ref. 39). Open circle: for an extremely small QD, $5–9\mathrm{nm}$ (Ref. 40) (from Huang-Rhys parameter). Square: from FIR attenuation in magnetic field measurement (Ref. 16).