Continuous-Time Monitoring of Landau-Zener Interference in a Cooper-Pair Box

Abstract

Landau-Zener (LZ) tunneling can occur with a certain probability when crossing energy levels of a quantum two-level system are swept across the minimum energy separation. Here we present experimental evidence of quantum interference effects in solid-state LZ tunneling. We used a Cooper-pair box qubit where the LZ tunneling occurs at the charge degeneracy. By employing a weak nondemolition monitoring, we observe interference between consecutive LZ-tunneling events; we find that the average level occupancies depend on the dynamical phase. The system's unusually strong linear response is explained by interband relaxation. Our interferometer can be used as a high-resolution Mach-Zehnder-type detector for phase and charge.

Motional averaging in a superconducting qubit

“…Even though O ( o 0 , the qubit can be excited with the low-frequency signal in the presence of an additional highfrequency drive o. This can be seen as a multi-photon transition process involving quanta from both fields (in equation (5)), or, as a photon-assisted Landau-ZenerStückelberg (LZS) interference 18,20,21,36 between the dressed states |k, nS and |m, n À 1S. Let us first consider the multi-photon transition processes associated with the sinusoidal-modulated Hamiltonian, defined in equations (1) and (4),…”

“…However, the system can still perform LZS transitions by absorbing a photon from the driving field. This photon-assisted LZS interference can be seen by transforming the HamiltonianĤ þĤ drive from equation (7) into the frame rotating at o around the z axis (unitary transformation U ¼ expð À ioŝ z /2Þ), where it has exactly the same form (in the RWA) as that of LZS interference 18,21,36 , namelŷ…”

Inverse Landau-Zener-Stückelberg problem for qubit-resonator systems

“…(9) and (11). Figure 3 demonstrates that our formalism is valid for a description of the experimentally measurable quantities: the quantum capacitance or the resonant frequency shift 8,14 (see also Appendix C). Such a description allows to correctly find the position of the resonance peaks in the interferogram and to demonstrate the sign-changing behavior of the quantum capacitance, which relates to the measurable quantities.…”

“…The charge can then be related to the charge-qubit occupation, the derivative of which (under resonant driving) exhibits sign changes. Similar sign-changing response under strong driving was recently studied for qubits probed by an LC (tank) circuit for capacitive coupling 14,15 as well as for inductive coupling 16,17 . Thus, in the first part of this work (Section II) we study the situation where the strong-driving qubit's state is probed by the NR.…”

“…The appearance of the interferogram depends on several factors: the values of the qubit parameters, the model for the dissipative environment (such as Eqs. (13,14) and the parameters α and B), the value of the bias current (which distorts the shape of the resonances, as demonstrated in Ref. [17]).…”