Measuring Back-action of a Single Qubit on its Nuclear Spin Environment Through Spin-echo Correlations

Decoherence of a qubit arising from its interaction with an environment is of great practical and fundamental interest. Commonly the effects of the environment are described as a classical, fluctuating field whose dynamics is unaffected by the qubit. A fully quantum description, on the other hand, implies some back-action from the qubit on the environment. Here we show direct experimental evidence for such a back-action for an electron-spin-qubit in a GaAs quantum dot coupled to an environment of order 10⁶ nuclear spins. We are able to detect the back-action of a single qubit-environment interaction whose duration is comparable to the qubit’s coherence time by a correlation measurement technique. We perform two Hahn spin-echo measurement (SE_1/2), between which the qubit is reinitialized and manipulated but not measured. The correlations between SE₁ and SE₂ are strongly affected by the nuclear-spin dynamics during the intermediate manipulation. The complete suppression or revival of the correlation depending on the choice of intermediate qubit sequence shows the action of a single electron spin on the nuclear spins. Quantifying such back-action effects is important for understanding the limitations of semi-classical descriptions of decoherence processes.