Spin dynamics in InAs nanowire quantum dots coupled to a transmission line

We study theoretically electron spins in nanowire quantum dots placed inside a transmission line resonator. Because of the spin-orbit interaction, the spins couple to the electric component of the resonator electromagnetic field and enable coherent manipulation, storage, and readout of quantum information in an all-electrical fashion. Coupling between distant quantum-dot spins, in one and the same or different nanowires, can be efficiently performed via the resonator mode either in real time or through virtual processes. For the latter case, we derive an effective spin-entangling interaction and suggest means to turn it on and off. We consider both transverse and longitudinal types of nanowire quantum dots and compare their manipulation time scales against the spin relaxation times. For this, we evaluate the rates for spin relaxation induced by the nanowire vibrations (phonons) and show that, as a result of phonon confinement in the nanowire, this rate is a strongly varying function of the spin operation frequency and thus can be drastically reduced compared to lateral quantum dots in GaAs. Our scheme is a step forward to the formation of hybrid structures where qubits of different nature can be integrated in a single device.

Figure 1

(Color online) Schematics of the two configurations considered in this work. (a) Large-diameter InAs nanowire (pink-gray cylinder) positioned inside and parallel to the transmission line (blue-gray). The disk-shaped quantum dots (QDs) are located in the nanowire and are formed by two InP boundaries (brown-dark gray). Each QD contains only one electron with spin $1∕2$ (green arrows). (b) Two small-diameter InAs nanowires (pink-gray) positioned perpendicularly to the transmission line (blue-gray). The elongated QDs are oriented along the nanowire with one electron in each dot. The QD confinement can be achieved by barrier materials (as shown in brown-dark gray) or by external gates (not shown).

Figure 2

(Color online) The relaxation rate $T_1^{-1}$ as a function of the ratio ${\omega }_Z^{\mathit{eff}}R∕c_l$ for both FSCBs and CSBCs (see text for explanations of FSBCs and CSBCs). Here, $\hslash c_l∕R\simeq 0.6\times {10}^{-4}\mathrm{eV}$ ($c_l\simeq 4\times {10}^3\mathrm{m}∕\mathrm{s}$ and $R\simeq 50\mathrm{nm}$) corresponding to a magnetic field $B\simeq 0.2\mathrm{T}$ for $g=2.5$.

Figure 3

(Color online) The relaxation rate $T_1^{-1}$ as a function of the ratio ${\omega }_Z^{\mathit{eff}}l∕c_s$ for three different ratios $l∕{\lambda }_{\mathit{SO}}$ and with FSBCs (see text).