Superconducting quantum circuits offer similar functionalities as quantum systems created of single atoms, ions, and spins addressed with optical radiation. The main advantage of their superconducting artificial counterparts is their creation as circuits with controllable properties including coupling to radiation and their level splitting. However due to unavoidable parameter spread, the experimentally achieved values usually deviate from the designed ones. Thus, additional control during the experiment is desirable. We propose to use the dynamic Stark shift for adjusting the energy level splitting of a superconducting quantum bit (qubit) by a detuned microwave signal. The advantage of such a device lays in the universality of the approach, meaning that any type of quantum system featuring an interaction with radiation can be tuned in that way.

For experimental demonstration, we use a standard type flux qubit formed by a superconducting loop that incorporates three Josephson junctions. As shown in the SEM image of Fig. 1, we couple the flux qubit to a coplanar waveguide resonator used as readout device. The energy levels of the qubit can be probed by standard two-tone spectroscopy. The first signal, if in resonance with the qubit, modifies its population. This change in population in turn moderates the eigenfrequency of the coupled qubit-resonator system which can be detected by the second tone. In our experiment a third tone with frequency well above the eigenfrequency of the qubit and the resonator is used to tune the qubit energy level splitting as demonstrated by the experimental results in Fig. 2. 

Having experimentally proven the tuning capability, a key question for the use of the dynamic Stark shift is how strong the underlying mixing of qubit states will contribute to a systematic change in the dynamic properties of the qubit, such as relaxation and decoherence. 

For an accurate description of the level shift, we have developed a theoretical approach also including these modifications of the dissipative dynamics. As we show, the key parameter in the theoretical modeling is the ratio , where is the Rabi frequency of the control tone and its positive and negative frequency detuning from the qubit. While the tuning of the energy levels follows a first order function of r the correction of the dissipative dynamics is of second order. Therefore, we conclude that the dynamic Stark shift can be used for additional qubit control while additionally keeping the other original qubit parameters in the case of large detuning compared to the strength of the control signal.

 

Reference:

G. Oelsner, U. Hübner, E. Il’ichev Controlling the energy gap of a tunable two-level system by ac drive, Physical Review B 101, 054511 (2020)