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

We investigated both theoretically and experimentally dynamic features of a phase-biased charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop. The effective inductance of the qubit was probed by a high-quality tank circuit. In the presence of a microwave power, with a frequency of the order of the qubit energy level separation, an alteration of the qubit inductance was observed. We demonstrate that this effect is caused by the redistribution of the qubit level population. The excitation of the qubit by one-, two-, and three-photon processes was detected. Quantitative agreement between theory and experimental data was found.

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 study the dynamic behaviour of a quantum two-level system with periodically varying parameters by solving the master equation for the density matrix. Two limiting cases are considered: multiphoton Rabi oscillations and Landau-Zener (LZ) transitions. The approach is applied to the description of the dynamics of superconducting qubits. In particular, the case of the interferometertype charge qubit with periodically varying parameters (gate voltage or magnetic flux) is investigated. The time-averaged energy level populations are calculated as functions of the qubit's control parameters.

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.

We implemented experimentally an interferometer-type charge qubit consisting of a single-Cooper-pair transistor closed by a superconducting loop that is in flip-chip configuration inductively coupled to a radiofrequency tank circuit. The tank permits us to readout the qubit state, acting as an inductance measuring apparatus. By applying continuous microwave power to the quantum device, we observed inductance alterations caused by redistributions of the energy-level populations. From the measured data we extracted the energy gap between ground and upper levels as a function of the transistor quasicharge as well as the Josephson phase across both junctions.

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