Spin Noise of Electrons and Holes in Self-Assembled Quantum Dots

We measure the frequency spectra of random spin fluctuations, or “spin noise,” in ensembles of $(\mathrm{In},\mathrm{Ga})\mathrm{As}/\mathrm{GaAs}$ quantum dots (QDs) at low temperatures. We employ a spin noise spectrometer based on a sensitive optical Faraday rotation magnetometer that is coupled to a digitizer and field-programmable gate array, to measure and average noise spectra from 0–1 GHz continuously in real time with $\mathrm{\text{subnanoradian}}/\sqrt{\mathrm{Hz}}$ sensitivity. Both electron and hole spin fluctuations generate distinct noise peaks, whose shift and broadening with magnetic field directly reveal their $g$ factors and dephasing rates within the ensemble. A large, energy-dependent anisotropy of the in-plane hole $g$ factor is clearly exposed, reflecting systematic variations in the average QD confinement potential.

Figure 1

(a) Experimental schematic. Spin fluctuations $\delta S_z(t)$ impart Faraday rotation fluctuations $\delta {\theta }_F(t)$ on the probe laser. $\delta V(t)$ is digitized at $2\mathrm{GS}/\mathrm{s}$, and its power spectrum from 0–1 GHz is computed and averaged continuously on a FPGA. (b) A raw noise power spectrum showing hole spin noise in (In,Ga)As QDs after 600 s averaging (1.2 TB of processed data; corrected for frequency-dependent detector gain). The rms noise floor at 300 MHz is $440\mathrm{\text{picorad}}/\sqrt{\mathrm{Hz}}$, which can be further reduced by smoothing (grey line).

Figure 2

(a) PL spectrum of a QD ensemble (1.58 eV excitation). (b) Faraday rotation noise power spectra versus $B_x$ ($\parallel [110]$), using 2.5 mW, 1.385 eV probe laser. (c), (d) The hole spin noise peak frequency and full width.

Figure 3

(a) Hole spin noise with [110] axis rotated 0°, 45°, and 90° from $B_x$. (b) In-plane anisotropy of $g_{h\perp }$ at 1.386 eV. (c) Energy-dependent anisotropy of $g_{h\perp }$.

Figure 4

(a) Electron spin noise, using 3 mW, 1.377 eV probe laser and additional 1.58 eV linearly polarized illumination. Grey lines are Lorentzian fits; $B_x\parallel [110]$. (b) Peak frequency versus $B_x$.