Voltage staircase in a current-biased quantum-dot Josephson junction

Abstract

We calculate the current-voltage (I-V ) characteristic of a Josephson junction containing a resonant level in the weakly coupled regime (resonance width small compared to the superconducting gap). The phase φ across the junction becomes time dependent in response to a DC current bias. Rabi oscillations in the Andreev levels produce a staircase I-V characteristic. The number of voltage steps counts the number of Rabi oscillations per 2π increment of φ, providing a way to probe the coherence of the qubit in the absence of any external AC driving. The phenomenology is the same as the Majorana-induced DC Shapiro steps in topological Josephson junctions of Choi et al. [Phys. Rev. B 102, 140501(R) (2020)]-but now for a nontopological Andreev qubit.

Quantum Control via Landau-Zener-Stückelberg-Majorana Transitions

“…However, there are limitations; in particular, the system needs to preserve coherence long enough. This may take place in superconducting weak links, where the Andreev levels as a function of time display avoided-level crossing (Douçot et al, 2020;Gorelik et al, 1998;Mélin et al, 2019;Mélin and Douçot, 2020;Oriekhov et al, 2021); there, it was pointed out that the microwaveinduced LZSM interference should be revealed as a significant source of energy absorption; for a mini review, see (Roy, 2013). Similar studies of coherent interference effects were done for Schwinger vacuum pair production (Akkermans and Dunne, 2012), many body localized systems , and photoisomerization reaction (Duan et al, 2016).…”

Microwave response of an Andreev bound state

“…From Eq. (32) we see that Re χ IQ vanishes at timereversal symmetric points ϕ = 0, π. As a consequence of particle-hole symmetry, Re χ IQ also vanishes at g = 0.…”

“…( 29)]. Our Hamiltonian smoothly interpolates between the Hamiltonian of a quantum dot weakly coupled to the superconducting leads (Γ ∆) [31,32] and the Hamiltonian of a short tunnel junction (Γ ∆) [15][16][17]. Next, in Sec.…”

Microscopic theory of the current-voltage characteristics of Josephson tunnel junctions

“…Both voltage staircases and hystereses are experimentally observed in highquality Josephson junctions [20][21][22][23][24]. In the presence of a qubit formed in the junction, voltage staircases and hystereses have recently been predicted in the DC currentbiased case [25][26][27]. In a genuine Josephson junction, this effect is not yet understood but explained by us below.…”