Frequency (GHz)

1. coupling capacitor Qubit FBAR resonator 25 mK resonator Z-pulse ampl. (a.u.) Frequency (GHz) Pulse length (ns) Qubit tuning (a.u.) Quantum mechanical resonatorsAndrew N. Cleland, University of California-Santa Barbara, DMR 0605818 FBAR resonator nres = 6.1 GHz Q = 258 We have developed ultrahigh frequency mechanical resonators, high enough in frequency that when cooled to near absolute zero, we have demonstrated for the first time that these can be operated in their quantum “ground state”, the lowest possible energy permitted by quantum mechanics. Top left: Image of 6.5 GHz mechanical FBAR resonator. Top right: Measurement of resonance of resonator at 6.1 GHz, using standard measurement equipment. Center left: Scheme for measuring resonator in quantum ground state, using a quantum bit as measurement tool. Center right: Measurement of qubit resonance; red box shows splitting due to fixed frequency resonator, at 6.15 GHz. This resonator has been cooled to its quantum ground state, the first time this has been accomplished. Bottom left: Generation and detection of a single phonon, the quantum of mechanical vibration; blue/red oscillations correspond to oscillation of qubit state as qubit exchanges single energy quantum with mechanical resonator, as a function of qubit tuning (vertical axis) and interaction time (horizontal axis). Bottom right: Preparation of coherent phonon state in resonator, measured using qubit. Vertical axis is amplitude of coherent state generation (proportional to average number of phonons in pulse), horizontal axis is qubit-resonator interaction time. Again, this is a first time measurement of a coherent phonon state. This work is under preparation for publication. Transmission |S21|2 5.8 6.0 6.2 6.4 Frequency (GHz)

2. Quantum mechanical resonatorsAndrew N. Cleland, University of California-Santa Barbara, DMR 0605818 The undergraduate and graduate students engaged in NSF-funded research programs will form an important part of the nation’s scientists for the next four decades. Future advances in science and technology in the U.S. will stem directly from the education and knowledge gained from programs such as this one. Our work directly or indirectly involves two graduate students and one postdoctoral researcher (Chris McKenney, Aaron O’Connell and Max Hofheinz), and likely 1-2 undergraduates will participate over the course of the program.