Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a continuously observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of Rabi spectroscopy enabled a long coherence time of about 2.5 micros, corresponding to an effective qubit quality factor approximately 7000.

We have observed signatures of resonant tunneling in an Al three-junction qubit, inductively coupled to a Nb LC tank circuit. The resonant properties of the tank oscillator are sensitive to the effective susceptibility (or inductance) of the qubit, which changes drastically as its flux states pass through degeneracy. The tunneling amplitude is estimated from the data. We find good agreement with the theoretical predictions in the regime of their validity.PACS numbers: 85.25. Cp, 85.25.Dq, 84.37.+q, 03.67.Lx Several groups, using different devices, have by now established that superconductors can behave as macroscopic quantum objects.1-3 These are natural candidates for a qubit, the building block of a quantum computer. Qubits are effectively two-level systems with timedependent parameters. One of them is a superconducting loop with low inductance L, including three Josephson junctions (a 3JJ qubit).4 Its potential energy, U = For suitable parameters, U (φ 1 , φ 2 ) has two minima corresponding to qubit states Ψ l and Ψ r , carrying opposite supercurrents around the loop. These become degenerate for Φ x = 1 2 Φ 0 . The Coulomb energy E C (≡ e 2 /2C, with C the capacitance of junction 1) introduces quantum uncertainty in the φ j . Hence, near degeneracy the system can tunnel between the two potential minima.(Since E C ≪ E J ≡ E J1 , we deal with a flux qubit; E C ≫ E J yields a charge qubit. Coherent tunneling was demonstrated in both.)In the basis {Ψ l , Ψ r } and near Φ x = 1 2 Φ 0 , the qubit can be described by the Hamiltonian∆ is the tunneling amplitude. At bias ǫ = 0 the two lowest energy levels of the qubit anticross [ Fig. 1(a)], with a gap of 2∆. Increasing ǫ slowly enough, the qubit can adiabatically transform from Ψ l to Ψ r , staying in the ground state E − . Since dE − /dΦ x is the persistent loop current, the curvature d

Abstract. -A two-level system traversing a level anticrossing has a small probability to make a so-called Landau-Zener (LZ) transition between its energy bands, in deviation from simple adiabatic evolution. This effect takes on renewed relevance due to the observation of quantum coherence in superconducting qubits (macroscopic "Schrödinger cat" devices). We report an observation of LZ transitions in an Al three-junction qubit coupled to a Nb resonant tank circuit.In analogy to their classical counterparts, qubits are effectively two-level systems, with a time-dependent bias enabling one-qubit gate operations. Besides their computational use, this makes them suitable for studying Landau-Zener (LZ) transitions [1,2] (see below eq. (1)). One prominent qubit is a superconducting loop with low inductance L, interrupted by three Josephson junctions (a 3JJ qubit) [3]. Its Josephson energy, U J = 3 j=1 E Jj (φ j ), depends on the phase differences φ j across the junctions. In a small loop, due to magnetic flux quantization, only two φ j 's are independent.The two minima in U J (φ 1 , φ 2 ) correspond to the qubit states ψ L and ψ R , carrying opposite supercurrents around the loop. These become degenerate in the presence of an external magnetic flux Φ e = 1 2 Φ 0 (Φ 0 ≡ h/2e is the flux quantum). The potential U J is sketched in fig. 1a.

We implement the impedance measurement technique (IMT) for characterization of interferometer-type superconducting qubits. In the framework of this method, the interferometer loop is inductively coupled to a high-quality tank circuit. We show that the IMT is a powerful tool to study a response of externally controlled two-level system to different types of excitations. Conclusive information about qubits is obtained from the read-out of the tank properties.

Low noise three-stage pseudomorphic high electron mobility field-effect transistors amplifier were designed for the temperature range below 1 K. A minimum noise temperature TN≈100 mK was measured at an ambient temperature of about 380 mK at frequencies between 1 and 4 MHz for a source resistance of 10 kΩ. The gain of the amplifier was 50 at a power consumption of about 200 μW. The noise parameters of the amplifier are stable to within 30%, for a power consumption in the range of 100–300 μW. Minimum voltage spectral noise density of the amplifier with respect to the input is about 200 pV/Hz1/2 and the corner frequency of the 1/f noise is close to 300 kHz.