Quantum interference and phonon-mediated back-action in lateral quantum-dot circuits

Abstract

Spin qubits have been successfully realized in electrostatically defined, lateral fewelectron quantum dot circuits [1][2][3][4]. Qubit readout typically involves spin to charge information conversion, followed by a charge measurement made using a nearby biased quantum point contact [1,5,6]. It is critical to understand the back-action disturbances resulting from such a measurement approach [7,8]. Previous studies have indicated that quantum point contact detectors emit phonons which are then absorbed by nearby qubits [9][10][11][12][13]. We report here the observation of a pronounced back-action effect in multiple dot circuits where the absorption of detector-generated phonons is strongly modified by a quantum interference effect, and show that the phenomenon is well described by a theory incorporating both the quantum point contact and coherent phonon absorption. Our combined experimental and theoretical results suggest strategies to suppress back-action during the qubit readout procedure.The back-action process considered in this paper involves deleterious inelastic tunneling events between two adjacent dots in a serial double or triple quantum dot (DQD, TQD). The energy difference ∆ between the initial and final electronic dot states is provided by the absorption of a non-equilibrium acoustic phonon, which itself is generated by the quantum point contact (QPC) detector [12]. Such an absorption process between adjacent dots is constrained by the energy conservation condition ∆ = | q|v ph (v ph is the sound velocity, q the phonon wavevector). More subtly, it is also sensitive to the difference in phase, ∆ϕ = d · q, of the associated phonon wave between the two dot positions, with d being the vector connecting the two dot centers [14,15].This q (and hence ∆) dependent phase difference controls the matrix element for phonon-absorption since it determines whether the electron-phonon couplings in each of the two individual dots add constructively or destructively (see Fig. 1) [16]. The result is an oscillatory probability for inelastic electron-transfer events involving phonon-absorption, with constructive interference occurring when ∆φ = (2n + 1)π (where n is an integer).Data showing a pronounced back-action effect are shown in Fig. 2a, which displays the stability diagram measured in charge detection for a few-electron DQD without a voltage drop between its left and right leads. The charge configuration of the quantum dot structures influences the conductance of a nearby QPC because of the capacitive coupling between the dots and the QPC.In order to serve as a charge detector it is necessary to drive a current through the detector QPC which, in turn, leads to the observed detector back-action. Multiple gates fabricated 85 nm above a high-mobility two-dimensional electron system (2DES) are used to define two dots and two QPCs (Fig. 2d). The differential transconductance dI QPC /dV L of the biased charge detectorDj p = FIG. 1: Interference in quantum dot-phonon interactions. a, The back-action charge fluctuations of...

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