Landau–Zener–Stückelberg interferometry

Abstract

A transition between energy levels at an avoided crossing is known as a Landau-Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase accumulated between transitions (commonly known as the Stückelberg phase) may result in constructive or destructive interference. Accordingly, the physical observables of the system exhibit periodic dependence on the various system parameters. This phenomenon is often referred to as Landau-Zener-Stückelberg (LZS) interferometry. Phenomena related to LZS interferometry occur in a variety of physical systems. In particular, recent experiments on LZS interferometry in superconducting TLSs (qubits) have demonstrated the potential for using this kind of interferometry as an effective tool for obtaining the parameters characterizing the TLS as well as its interaction with the control fields and with the environment. Furthermore, strong driving could allow for fast and reliable control of the quantum system. Here we review recent experimental results on LZS interferometry, and we present related theory. 3 B. Superconducting qubits 3 C. Fano and Fabry-Perot interferometry using superconducting qubits 4 D. Hamiltonian and bases 4

Motional averaging in a superconducting qubit

“…S4. The LZS interference seen in our system corresponds to the so-called fast passage limit 21 . In this limit, the expression for the occupation probability can be calculated analytically 21 and the result agrees exactly with our equation (5).…”

“…S3. These population oscillations can be alternatively understood as a photon-assisted version of the standard Landau-Zener-Stückelberg interference 20,21 (see Methods and Supplementary Fig. S4).…”

“…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…”

Nonlinear dynamics of two coupled nano-electromechanical resonators

“…By now several types of resonators were successfully considered, like optical two level atoms in quantum cavities [2], artificial Josephson junction qubits [3], atoms seized in ion traps [4], or nano-optomechanical devises [5]. There is a new trend towards nano-electromechanical resonators.…”