Flux-Dependent Crossover between Quantum and Classical Behavior in a dc SQUID

In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as the “Münchhausen effect.” We implement such a system by shunting one of the two junctions of a dc SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the “Münchhausen effect.”

Figure 1

(a) Equivalent circuit of the investigated asymmetric dc SQUID. The parameters of the Josephson junctions are their critical currents $I_c$, normal resistances $R$, and intrinsic capacitances $C$. ${\mathrm{JJ}}_1$ is additionally shunted by a large capacitance $C_0$. $L$ is the loop inductance of the SQUID. (b) Optical microscope picture of the studied dc SQUID. The bias current lines are fabricated as microstrips one on top of another in order to minimize their mutual inductances with the gradiometric SQUID loop made as a figure of “8”.

Figure 2

2D potential landscape of a dc SQUID with two identical junctions for $k=0.17$ at a normalized bias current $j=0.2$ and at ${\mathrm{\Phi }}_{\text{ext}}=0$. The dashed white line indicates the bisectrix where ${\phi }_1={\phi }_2$.

Figure 3

Temperature and flux dependence of the mean switching current. Circles indicate measured values, lines are guides to the eye. The black oval and rectangle indicate data points used for the fitting of TA and MQT rates, respectively. The dashed line is the calculated fluctuation free critical current corresponding to the state with zero magnetic flux quanta in the loop. The given temperatures are fit results and deviate from the cryostat temperature as explained later in the text.

Figure 4

(a) TA rates at ${\mathrm{\Phi }}_{\text{ext}}/{\mathrm{\Phi }}_0=-0.24$. (b) MQT rates at ${\mathrm{\Phi }}_{\text{ext}}/{\mathrm{\Phi }}_0=0.24$ for the three lowest temperatures. Measured TA and MQT rates are in color, fit results for the respective temperatures in black.

Figure 5

Dependence of the switching current $I_{\text{sw}}$ on flux ${\mathrm{\Phi }}_{\text{ext}}$ for positive and negative current polarity. The bars represent the recorded switching current histograms. The intensity of gray illustrates the number of counts per current bin. Dashed lines display the theoretically expected behavior in the absence of fluctuations for the extracted critical currents.