Dynamical Control of Macroscopic Quantum Tunneling

We show that the quantum Zeno and anti-Zeno effects are realizable for macroscopic quantum tunneling by current-bias modulation in Josephson junctions (and their analogs in atomic condensates).

Figure 1

Upper inset: tilted potential $U(q)$ [Eq. (6)]; solid line: maximal tilt, $ϵ=1$; dashed line: minimal tilt, $ϵ=0$ [Eq. (5)]. Lower inset: $U$ ($ϵ=0$) is approximated by a binding potential for energies below $U_m$, since tunneling is negligible; $U$ ($ϵ=1$) is divided into the same binding potential and a perturbation $V<0$, allowing tunneling. Main figure: (a) The coupling spectrum $G_{n=12}(\omega )$ (in units of $R_{\mathrm{GR}}/2\pi$) and the modulation function $F_{t=4{\tau }_0}(\omega )$ (in units of ${\omega }_0^{-1}$) multiplied by 2 with ${\tau }_1=1/{\omega }_0$ and ${\tau }_0=5{\tau }_1$, where ${\omega }_0$ is the fundamental (harmonic) oscillation frequency in the well. (b) Same, with $G_{n=15}(\omega )$, ${\tau }_1=0.3/{\omega }_0$, ${\tau }_0=20{\tau }_1$, and $F_{t=4{\tau }_0}(\omega )$ ($\times 4$).

Figure 2

(a) The decay rate $R$ (in units of the unperturbed, golden rule rate $R_{\mathrm{GR}}$), as obtained from the convolution of $F_t(\omega )$ and $G_n(\omega )$ in Fig. 1a, for $n=12$. The rate is plotted as a function of the interruption time ${\tau }_1$ (in units of $1/{\omega }_0$) on a log scale for ${\tau }_0=5{\tau }_1$ (curve 1) and ${\tau }_0=50{\tau }_1$ (curve 2). The domains of QZE, QZE scaling, and AZE are marked. Inset: the evolution of $\ln P(t)$ for level $n=12$; solid line 1: QZE-like decay; solid line 2: AZE-like decay; dashed line: unperturbed decay. (b) Same, for level $n=15$, corresponding to Fig. 1b. Lower inset: decay rate $R$ shows only QZE behavior. Upper inset: $P$ vs total time $t$ (including the lower-tilt period), showing impulsive jumps.