Figure 1

(a) Short one-channel constriction between two superconducting electrodes (phase difference $\delta ={\delta }_L-{\delta }_R$). (b) Excitation spectrum: besides the usual continuum of states above the energy gap $\Delta$, which extends all across the structure, there is at the constriction a discrete Andreev spin-degenerate doublet with energy $E_A(\delta )$ above the ground state, where quasiparticles can get trapped. (c) Schematic setup: an atomic point contact (red triangles) forms a SQUID with a Josephson junction (green checked box). Phases $\delta$ and $\gamma$ across contact and junction are linked by the flux $\varphi$ threading the loop. The SQUID is biased by a voltage source $V_b$ in series with a resistance $R_b=200\Omega$. The current $I$ is measured from the voltage drop across $R_b$. An on-chip antenna is used to apply fast flux pulses to the SQUID. It is represented on the right-hand side as an inductor current-biased with a source $I_F$. (d) Four possible configurations of a one-channel constriction: ground state (energy $-E_A$), Andreev doublet empty; two odd configurations, with zero energy and definite spin $\pm 1/2$, one quasiparticle added to the contact; last configuration corresponds to spin-singlet double excitation (energy $+E_A$).Reuse & Permissions

Figure 2

Color plot of measured switching probability $P_{\mathrm{sw}}(s,\phi )$ for SQUID with contact transmissions {0.994, 0.10, 0.10}. Top left inset: Measurement protocol. Short prepulses ensure the same initial conditions before each measurement pulse of height $I=s{I}_0$ and duration $t_p=1\mu \mathrm{s}$ (the subsequent lower plateau holds the voltage to facilitate detection). Delay between prepulse and measurement pulse is here $\Delta t=2\mu \mathrm{s}$. Main panel: Black curves represent theoretical predictions [solutions of $P_{\mathrm{sw}}(s,\phi )\equiv 0.5$] for pristine (solid line) and for poisoned contact (dashed line). Lower left inset: Measured $P_{\mathrm{sw}}(s)$ (red dots) at $\phi =0$ [lower horizontal (green) line in main panel]. Upper right inset: Measured $P_{\mathrm{sw}}(s)$ (red dots) at $\phi =0.88\pi$ [upper horizontal (cyan) line in main panel]. In both insets $P_{\mathrm{sw}}^0(s)[P_{\mathrm{sw}}^1(s)]$, the solid [dashed] line is the theory for the pristine [poisoned] contact. In the upper right inset, the intermediate line (gray solid line) is a fit of the data with the linear combination of Eq. (1) with $p=0.36$.Reuse & Permissions

Figure 3

Relaxation time $T_1$ (blue points) and asymptotic poisoning probability $p_{\infty }$ (red points) as a function of the phase $\delta$ imposed for a time $\Delta t$ between prepulse and measurement pulse. Data taken on SQUID with atomic contact {0.994,0.10,0.10} at 30 mK. Measurements at $|\delta -\pi |>0.5\pi$ show very fast relaxation that could not be resolved reliably in our setup. Left inset: $1\mathrm{\text{−}}p$ is the height of the intermediate plateau in $P_{\mathrm{sw}}(s)$. The dashed line represents $P_{\mathrm{sw}}(s)$ found for $\Delta t\gg 100\mu \mathrm{s}$. Right inset: Typical time evolution of $p$, from where $T_1$ and $p_{\infty }$ are extracted.Reuse & Permissions

Figure 4

Relaxation data for five different atomic contacts [transmissions are given in panel (b)]: (a) relaxation time $T_1$, (b) asymptotic poisoning probability $p_{\infty }$, (c) rates ${\Gamma }_{\mathrm{in}}$ and ${\Gamma }_{\mathrm{out}}$ as a function of normalized Andreev state energy $E_A/\Delta$ of most transmitting channel. There is a sharp threshold at $E_A/\Delta \approx 0.5$ for all contacts. The minimal value of $E_A/\Delta$ is $\sqrt{1-\tau }$ (0.08 for the black squares, 0.5 for the orange upside-down triangles) and is reached when $\delta =\pi$, as shown in (d). Inset: Rates ${\Gamma }_{\mathrm{in}}$ (${\Gamma }_{\mathrm{out}}$) are for processes increasing (decreasing) the number of quasiparticles in contact. The relaxation rate from the excited singlet to the ground state is assumed to be much faster than all other rates. The occupation of all four configurations is given in italic letters: $1\mathrm{\text{−}}p$ for the ground state, $p/2$ for each of the odd configurations, and 0 for the excited state.Reuse & Permissions