Screening Nuclear Field Fluctuations in Quantum Dots for Indistinguishable Photon Generation

A semiconductor quantum dot can generate highly coherent and indistinguishable single photons. However, intrinsic semiconductor dephasing mechanisms can reduce the visibility of two-photon interference. For an electron in a quantum dot, a fundamental dephasing process is the hyperfine interaction with the nuclear spin bath. Here, we directly probe the consequence of the fluctuating nuclear spins on the elastic and inelastic scattered photon spectra from a resident electron in a single dot. We find the in-plane component of the nuclear Overhauser field leads to detuned Raman scattered photons, broadened over experimental time scales by field fluctuations, which are distinguishable from both the elastic and incoherent components of the resonance fluorescence. This significantly reduces two-photon interference visibility. However, we demonstrate successful screening of the nuclear spin noise, which enables the generation of coherent single photons that exhibit high visibility two-photon interference.

Figure 1

(Left panels) (a) Level diagrams for $X^0$; $X^{1-}$ at $B_{\mathrm{ext}}=0\mathrm{T}$; and $X^{1-}$ at $B_{\mathrm{ext}}^{\perp }>0\mathrm{T}$, where $|+⟩$ and $|-⟩$ are the symmetric and antisymmetric neutral exciton eigenstates, respectively, ${\delta }_1$ is the splitting due to the anisotropic part of the electron-hole exchange interaction, and the green arrows represent the driving fields. (b) Plot of the ratio of elastic scattered photons to the total intensity. The points are based on the fits to the RF spectra and the curve is a fit using Eq. (1). (Right panels) High-resolution spectra of (c) $X^0$, (d) $X^{1-}$ at $B_{\mathrm{ext}}^{\perp }=0\mathrm{T}$, and (e) $X^{1-}$ at $B_{\mathrm{ext}}^{\perp }=0.6\mathrm{T}$, above ($\mathrm{\Omega }>{\mathrm{\Omega }}_S$), near ($\mathrm{\Omega }\approx {\mathrm{\Omega }}_S$), and below ($\mathrm{\Omega }<{\mathrm{\Omega }}_S$) the saturation Rabi frequency. The green (red) line is a single (multiple) Lorentzian fit to the elastic (inelastic) component of the RF. The black curve is the total Lorentzian fit. Data are taken from sample 1.

Figure 2

(a) High-resolution spectra as a function of laser detuning $({\mathrm{\Delta }}_L)$ demonstrate that the central peak and sidebands are dependent on the laser energy. (b) The intensity of the detuned spectra reveal a Lorentzian line shape (the red curve). (c) A simulated spectrum based on the four-level model including $B_N$ (the black curve) fit to the experimental data (the black points) for $\mathrm{\Omega }=0.25{\mathrm{\Omega }}_S$. The green line represents elastically scattered photons. The red and blue lines represent the red- and blue-detuned Raman photons as shown in the level diagrams for two different $B_N^{\parallel }$ values. Data are from sample 1. (d) Level diagrams for two different values of $B_N^{\parallel }$. For constant excitation energy, changes in $B_N^{\parallel }$ change the splitting of the Raman transitions from the laser: fluctuations in the Overhauser field result in broadened Raman sidebands.

Figure 3

Second-order correlation measurements on the Zeeman-split $X^{1-}$ transitions at $B_{\mathrm{ext}}^{\perp }=0.6\mathrm{T}$ and $\mathrm{\Omega }=0.5{\mathrm{\Omega }}_S$. Single laser excitation of the (a) blue- and (b) redshifted lines show bunching around $\tau =0$, with decay time $\sim 20\mathrm{ns}$. Simultaneous two-laser excitation (c) shows suppressed bunching, demonstrating that its origin is spin pumping. Data are from sample 1.

Figure 4

Second-order correlation and two-photon interference measurements on (a) $X^0$, (b) $X^{1-}$ at $B_{\mathrm{ext}}=0\mathrm{T}$, and (c) $X^{1-}$ at $B_{\mathrm{ext}}^{\perp }=0.6\mathrm{T}$. Blue (red) solid lines are (deconvolved) fits to the data. Near perfect TPI visibility is observed for $X^0$ and $X^{1-}$ with a screening of nuclear field fluctuations. For $X^{1-}$ at $B_{\mathrm{ext}}=0\mathrm{T}$, $\nu$ is reduced to $\approx 0.67$ due to $B_N$. Data are from sample 2.