– 12 –

Clear differences in the interference patterns have been detected when 2/h is changed from 3 to 10 GHz.

We have performed extensive modelling of a CPB dynamics using Bloch equations in order to calculate the role of Berry phase in the LZ-interference conditions. We find that Berry phase plays a clear role when the CPB is driven simultaneously by charge and phase drives. This would be the Berry phase in the stationary frame, in contrast to the usual case of a rotating frame.

#### MULTIPHOTON SIDE BAND COOLING USING A CHARGE-PHASE QUBIT

D. Gunnarsson, P. Hakonen Yu. Makhlin, A. Paila, J. Sarkar, J. Tuorila, and E. Thuneberg

The coupling between the oscillating motion of an atom (e.g. LC-resonator) and atomic transitions (two level system) can be employed for sideband cooling, as has been demonstrated in quantum optics and nanomechanical resonators. By driving atomic transitions by a detuned rf-signal so that extra energy has to be supplied from the kinetic motion of the resonator, the vibrational motion can be slowed down. We have demonstrated that, the sideband cooling principle works using strongly coupled charge-phase qubits, and even multiphoton resonances can be employed for this purpose.

The relaxation of our charge-phase qubit is quite strong, leading to broad resonances, but individual sidebands can well be resolved. In contrast to the usual sideband cooling configurations, we are driving the oscillator to be cooled at its resonant frequency, in order to read out information out from the qubit + oscillator system. Consequently, sideband cooling and heating are visible in our measurements as damping and amplification of the oscillation amplitude of the resonator. Our analysis is based on semiclassical analysis, in which the dynamics of the qubit is simulated numerically on the basis of Bloch's equations and electrical circuit laws for the resonator. We find a pretty good agreement between the simulation and the experiment, which allows us to account accurately for the main experimental findings. Damping of motion is found up to multiphoton resonances of order 10.

#### LANDAU-ZENER INTERFEROMETRY IN CIRCUIT QED

P. Hakonen, A. Paila, J. Sarkar, and M. Sillanpää

We are developing a new version of the Landau-Zener interferometric measurement. The goal is to bring the qubit level separation near to resonance with the LC-resonator frequency, thereby strengthening the coherent phenomena between the two quantum objects. The realization of this experiment will be based on lumped elements, which facilitates exceptionally strong coupling between the qubit and the resonator.

#### SQUID AMPLIFIERS

D. Gunnarsson, P. Hakonen, and M. Sillanpää

We have continued the development of our second generation GHz SQUID amplifiers designed in collaboration with VTT. The amplifiers work as designed and they give a gain of 20 dB when using power matching circuits at the input and output. With noise matching at the input, a gain of 15 dB is expected from these devices. Improved version of the amplifier is planned to be designed in summer 2008 in collaboration with the VTT spin-off company Aivon Ltd.

#### BLOCH OSCILLATING TRANSISTORS (BOT)

Annual Report 2007