Geometric Landau-Zener Interferometry

We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence.

Figure 1

(a) Schematic drawing of the “sluice.” (b) Effective magnetic field corresponding to the pumping cycle considered in this Letter. (c) Adiabatic (instantaneous) energies versus time. Avoided level crossings occur at times $t_1=T/4$ and $t_2=3T/4$. Green and red arrows outline two possibly interfering paths.

Figure 2

(a) Pumped charge (in units of $e$) after one cycle versus phase bias and frequency. The parameters are: $E_C/k_B=2.5\mathrm{K}$, $J_{\max }=0.1E_C$, $0.3\le n_g\le 0.7$. Dashed lines enclose the regions where the ground-state population at the end of the cycle is at least 0.9. Dotted lines have the same meaning but they are calculated according to (10) and in the fast-passage approximation ${\tilde{\phi }}_S\approx -\pi /4$. (b) Ground-state population versus time for a case of destructive (dashed line) and constructive (solid line) interference. The pumping frequency is 1.56 GHz for both cases, the phase biases are 0.22 and 3.36, respectively.

Figure 3

Pumped charge per cycle versus time for a case of constructive (squares) and destructive interference (circles), without decoherence (top) and with decoherence induced by zero-temperature gate-charge noise (bottom). Dashed lines are guides for the eye. The pumping frequency is 500 MHz for both cases, the phase biases are ${\varphi }_c=2.4$ and ${\varphi }_d=-1.45$, respectively. We have also assumed a residual Josephson coupling $J_{\min }=\min \{J_L,J_R\}=0.03J_{\max }$.