Microwave-Cavity-Detected Spin Blockade in a Few-Electron Double Quantum Dot

We investigate spin states of few electrons in a double quantum dot by coupling them to a magnetic field resilient NbTiN microwave resonator. The electric field of the resonator couples to the electric dipole moment of the charge states in the double dot. For a two-electron state the spin-triplet state has a vanishing electric dipole moment and can therefore be distinguished from the spin-singlet state. This way the charge dipole sensitivity of the resonator response is converted to a spin selectivity. We thereby investigate Pauli spin blockade known from transport experiments at finite source-drain bias. In addition we find an unconventional spin-blockade triggered by the absorption of resonator photons.

Figure 1

(a) False-colored scanning electron micrograph of the DQD region. The colored gates are used to form a DQD (circles) and a QPC. One gate (orange) extends to a resonator. Ohmic contacts to the 2DEG are indicated with crossed squares. $V_{\mathrm{sd}}$ is the DQD bias voltage. (b) Normalized resonant resonator transmission $(A/A_{\max }{)}^2$ as a function of $V_L$ and $V_R$ at $B=0$ and $V_{\mathrm{sd}}=0$ for $t/h=3.4\mathrm{GHz}$ (main figure) and $t/h=4.5\mathrm{GHz}$ (inset). Changing voltages along the dashed green or red line independently tunes $ϵ$ or $\delta$. The dots mark triple points. (c) Bare charge qubit energy $E_q$ (blue) and resonator energy $h{\nu }_r$ (black) as a function of $\delta$ for $2t<h{\nu }_r$ (left) and $2t>h{\nu }_r$ (right).

Figure 2

Left (right) column: $2t>h{\nu }_r$ ($2t<h{\nu }_r$). (a)–(b) Normalized resonator transmission at ${\nu }_p\simeq {\nu }_r$. $A_{\max }^2(B)$ is the bare resonator transmission. Insets: theoretical simulation with the same axes and plot ranges as in the main figures. (c) Cut of (a) at $B=300\mathrm{mT}$. $A_0^2$ is extracted from a Lorentzian fit (solid line). (d) Cut of (b) at $B=300\mathrm{mT}$ with two Lorentzian fits (solid line) of amplitudes $A_{\pm }^2$ at $\delta \approx {\delta }_{\pm }$. (e)–(f) Singlet-triplet energy spectrum as a function of $\delta$ for $B=300\mathrm{mT}$. $|g⟩$ (blue) and $|e⟩$ (green) are the spin-singlet qubit ground and excited states. The spin-triplet states are marked in black. Dashed line: qubit ground state offset by the resonator energy.

Figure 3

(a) $A_0^2(B)$ (blue), $A_{+}^2(B)$ (green), and $A_{-}^2(B)$ (red) with standard errors and theory fits (solid lines). (b) $B_0(t)$ and $B_{\pm }(t)$ compared to theory (solid line). The data points extracted from the fits in (a) are marked in color. The error bars in $t$ account for the $\delta$ lever arm error. For $B_{0,+}$ we show the standard errors of the fits as in (a), for $B_{-}$ maximum error estimates from repeated measurements.

Figure 4

(a)–(b) Normalized resonator transmission at ${\nu }_p\simeq {\nu }_r$ as a function of $\delta /{\delta }_{+}$ for $B=800\mathrm{mT}$, $t/h=3.7\mathrm{GHz}$, $V_{\mathrm{sd}}=300\mu \mathrm{V}$ in (a) and $V_{\mathrm{sd}}=-300\mu \mathrm{V}$ in (b). The dots indicate the zero bias triple points. Insets: theory for ${\mathrm{\Gamma }}_R=100\mathrm{MHz}$, ${\mathrm{\Gamma }}_L=1\mathrm{MHz}$, ${\mathrm{\Gamma }}_s=1.3\mathrm{MHz}$, $t/h=3.7\mathrm{GHz}$, and ${ϵ}_{\mathrm{TP}}=510\mu \mathrm{eV}$ with the same axes and plot ranges as in the main panels. (c)–(e) Energy level diagrams with the source (${\mu }_s$), drain (${\mu }_d$) and DQD state electrochemical potentials at $ϵ$ indicated by the corresponding star in (a)–(b). DQD states electrochemical potentials indicated with respect to (0,1) for the two electron states and with respect to state $x$ for the three-electron states $(1,2{)}_x$. Transitions involving a spin flip are marked with a cross.