Homogeneous linewidth narrowing of the charged exciton via nuclear spin screening in an InAs/GaAs quantum dot ensemble

In semiconductor quantum dots, the electron hyperfine interaction with the nuclear spin bath is the leading source of spin decoherence at cryogenic temperature. Using high-resolution two-color differential transmission spectroscopy, we demonstrate that such electron-nuclear coupling also imposes a lower limit for the positively charged exciton dephasing rate, $\gamma$, in an ensemble of InAs/GaAs quantum dots. We find that $\gamma$ is sensitive to the energetic overlap of the charged exciton spin states, which can be controlled through the application of an external magnetic field in the Faraday configuration. At zero applied field, electron-nuclear coupling induces additional dephasing beyond the radiative limit and $\gamma =230$ MHz ($0.95$ $\mu \mathrm{eV}$). Screening of the hyperfine interaction is achieved for an external field of $\approx 1$ T, resulting in $\gamma =172$ MHz ($0.71$ $\mu \mathrm{eV}$) limited only by spontaneous recombination along the dipole-allowed transition. These results are reproduced with a simple and intuitive model that captures the essential features of the electron hyperfine interaction and its influence on $\gamma$.

Figure 1

The sample studied is a single layer of InAs/GaAs self-assembled QDs in a 1.5 $\mu \mathrm{m}$ wide ridge waveguide structure, shown in the schematic diagrams in (a) and (b). Gold electrodes separated by 2 $\mu \mathrm{m}$ are patterned on both sides of the waveguide for capacitance-voltage (C-V) measurements of the device. A magnetic field up to 3 T can be applied along either the growth direction (Faraday configuration, $\theta =\pi /2$) or in the plane of the QDs (Voigt configuration, $\theta =0$), as indicated in (a). Room temperature C-V measurements reveal that the sample is unintentionally $p$ doped, determined by the slope of the dashed line fit to the $1/C^2$ vs gate voltage ($V_g$) data shown in (c). Panel (d) shows photoluminescence spectra of positively charged excitons taken at 4.2 K using 980 nm excitation with increasing power from 50 $\mu \mathrm{W}$ to 3.75 mW. The vertical dashed line indicates the laser wavelength for the differential transmission experiments.

Figure 2

Schematic diagram of the high-resolution differential transmission experimental setup. Acousto-optic modulators (AOMs) shift the narrow-linewidth pump and probe laser beam frequencies by ${\omega }_p$ and ${\omega }_{pr}$, respectively, and the pump amplitude is modulated at a frequency ${\Omega }_p$. The pump and probe beams transmitted through the waveguide are heterodyned with a local oscillator. The differential change in the probe transmission is recorded by a radio frequency spectrum analyzer at the beat-note frequencies ${\omega }_{pr}\pm {\Omega }_p$ vs the pump-probe detuning frequency.

Figure 3

Energy level diagram of the ground state charged exciton transitions. The system ground state consists of a spin-down ($|\Downarrow \rangle$) and spin-up ($|\Uparrow \rangle$) heavy hole that are coupled by a spin-flip relaxation rate ${\Gamma }_h$ and pure spin dephasing rate ${\gamma }_h^{*}$. The positively charged exciton state $|\Uparrow \Downarrow \uparrow \rangle$ ($|\Downarrow \Uparrow \downarrow \rangle$), consisting of a spin-up (spin-down) electron $|\uparrow \rangle$ ($|\downarrow \rangle$) Coulomb-bound to the holes in a spin-singlet state, is accessible via ${\sigma }^{-}$ (${\sigma }^{+}$) polarized excitation from the $|\Uparrow \rangle$ ($|\Downarrow \rangle$) hole state. The charged exciton states can relax to the same hole ground state through dipole-allowed spontaneous recombination at a rate ${\Gamma }_0$. Electron spin relaxation at a rate ${\Gamma }_e$ and pure dephasing at a rate ${\gamma }_e^{*}$ couple the excited states as well as enable the diagonal “dipole-forbidden” recombination pathways through a second-order process characterized by a rate ${\Gamma }_s$.

Figure 4

Power broadening of the homogeneous linewidth for a sample temperature of 4.2 K and a probe power of 2 pW. The homogeneous linewidth is obtained from a Lorentzian fit to the differential transmission line shape, shown in (a) on a logarithmic vertical scale for increasing pump power from 2 pW to 500 pW. (b) The linewidth data (open symbols) are fitted with Eq. (2) (solid line), yielding a zero-power linewidth of ${\gamma }_0=225\pm 7$ MHz ($h{\gamma }_0=0.93\pm 3$ $\mu \mathrm{eV}$) and a saturation power $P_0=50\pm 10$ pW.

Figure 5

(a) Dephasing rate, $\gamma$, as a function of applied magnetic field in the Faraday configuration. Broadening beyond the radiative limit for applied field $\lesssim 1$ T is explained by a simple model shown in (b) describing the electron-nuclear coupling, which assumes that the probability for an electron spin flip is linearly related to the overlap of the charged exciton state distribution functions (given by the shaded area) separated in frequency by $g_e{\mu }_B\mathit{B}/h$. Each distribution is described by a Lorentzian function with HWHM linewidth $\gamma$. The solid line in (a) is Eq. (4) fitted to the data with the fitting parameters ${\Gamma }_{\mathrm{HF}}^0=174$ MHz and $\gamma =169$ MHz. The large-field asymptote corresponds to the intrinsic radiatively limited dephasing rate $\gamma ={\Gamma }_0/2=169$ MHz (0.70 $\mu \mathrm{eV}$). The normalized differential transmission amplitude is shown in (c) as the open symbols. The solid line is Eq. (5) fitted to the data. At $\mathit{B}$ $\approx 0$ T, bidirectional optical spin pumping inhibits shelving of the hole into either spin state, resulting in the maximum transmission amplitude. For increasing $\mathit{B}$ up to $\approx 1.5$ T, the signal amplitude decreases as bidirectional spin pumping becomes inhibited by the broken degeneracy of the $X^{+}$ transitions. At $\mathit{B}$ $\gtrsim 1.5$ T, as the optical spin pumping rate ${\Gamma }_{\mathrm{osp}}$ decreases, spin pumping is suppressed, resulting in a slight recovery of the signal amplitude. In (d), the dipole selection rules and dominant optical transitions in the QDs for weak and strong external field are shown.

Figure 6

(a) The dephasing rate, $\gamma$, and (b) the normalized differential transmission amplitude as a function magnetic field in the Voigt geometry. (c) The dipole selection rules and dominant optical transitions in the QD under strong applied field in the Voigt configuration, where $X$ and $Y$ are the dipole moments aligned along and perpendicular to the Voigt field, respectively.