Figure 1

The rate at which a particle escapes by quantum tunneling out of a metastable potential well has been predicted to strongly increase [3] when the particle carries a spin $1/2$ degree of freedom whose Zeeman energies are position dependent and cross in the barrier, so that the spin can flip while tunneling.Reuse & Permissions

Figure 2

Top: the quantronium circuit [4] is based on a split Cooper pair box (CPB) with charging energy $E_C$, Josephson energy $E_J$, and asymmetry $d$ (see the text), controlled by a gate voltage $U$ and a magnetic flux $\Phi$. For readout, a larger Josephson junction with phase difference $\theta$ is biased by a current pulse $I_b$ able to induce the switching to the voltage state. Bottom left: scanning electron micrograph of the island with the two small junctions. Bottom right: measured energy splitting $E_{01}$ of the two lowest energy eigenstates of the CPB (dots), at $N_g=C_{g}U/2e=1/2$, as a function of $\gamma =\theta +2e\Phi /\hslash$. The dashed and solid lines are fits using $E_J=0.655k_B\mathrm{K}$ and $E_C=0.870k_B\mathrm{K}$, with $d=0$ and $d=0.1$, respectively. At $\gamma =\pi$ (see the arrow), a level crossing or a small gap occurs depending on $d$.Reuse & Permissions

Figure 3

Experimental (dots) and theoretical (lines) amplitudes $I_{60}$ of 100 ns long current pulses giving a switching probability $p=60\%$, as a function of the reduced flux $\varphi$ at $N_g=0$ (top) and $N_g=1/2$ (bottom). The lines are best fits leading to ${\mathcal{E}}_C=0.0051k_B\mathrm{K}$, ${\mathcal{E}}_J=10.2k_B\mathrm{K}$ for the readout junction, and to the CPB asymmetry $d=3.0\%$. The solid (dashed) curve of the bottom panel is a fit calculated with (without) Zener flips. Three regions A, B, and C have to be distinguished (see the text), and $R$ denotes a reference point. Inset: escape temperature $T_{\mathrm{e}\mathrm{s}\mathrm{c}}$ calculated from escape rate measurements performed at $R$ and at $N_g=0$ with 200 ns long current pulses, as a function of the measured temperature $T$. The solid line corresponds to $T_{\mathrm{e}\mathrm{s}\mathrm{c}}=T$, and the dashed line to the theoretical zero temperature limit.Reuse & Permissions

Figure 4

Top panel: experimental (dots) and calculated (lines) values of $s_{60}=I_{60}/{\mathcal{I}}_0$, as a function of the reduced flux $\varphi$, in region B. Error bars are mainly due to gate-charge noise. The curves are calculated with (solid line) and without (dashed line) Zener flips. The right vertical scale results from the conversion of $s_{60}$ into a rate ${\Gamma }_R$ according to the inset (see the text). Arrows indicate the reference point $R$. Inset: escape rate $\Gamma (s_{\max })$ measured (dots) and calculated (line) at $N_g=1/2$ at the reference point $R$. Bottom panel: escape rate enhancement calculated at constant rate ${\Gamma }_{\mathrm{t}\mathrm{o}\mathrm{t}}(\varphi ,s_{60})={\Gamma }_{60}$ by dividing ${\Gamma }_{60}$ by the rate ${\Gamma }_B$ that would be observed at the same $s_{60}$ in the absence of Zener flips.Reuse & Permissions

Figure 5

Average population $P_1$ of the first excited state of the quantronium as a function of the reduced flux $\varphi$, calculated from the difference between the theoretical and experimental $I_{60}$ in and close to region C, where the minimum of $E_{01}$ is crossed during the current ramp, as depicted in the inset. The error bar indicates the systematic error on the plateau.Reuse & Permissions