We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.It is becoming clear that artificially fabricated solidstate devices of macroscopic size may, under certain conditions, behave as single quantum particles. We report on the controlled time-dependent quantum dynamics between two states of a micron-size superconducting ring containing billions of Cooper pairs (1). From a ground state in which all the Cooper pairs circulate in one direction, application of resonant microwave pulses can excite the system to a state where all pairs move oppositely, and make it oscillate coherently between these two states. Moreover, multiple pulses can be used to create quantum operation sequences. This is of strong fundamental interest because it allows experimental studies on decoherence mechanisms of the quantum behavior of a macroscopicsized object. In addition, it is of great significance in the context of quantum computing (2) because these fabricated structures are attractive for a design that can be scaled up to large numbers of quantum bits or qubits (3).Superconducting circuits with mesoscopic Josephson junctions are expected to behave according to the laws of quantum mechanics if they are separated sufficiently from external degrees of freedom, thereby reducing the decoherence. Quantum oscillations of a superconducting two-level system have been observed in the Cooper pair box qubit using the charge degree of freedom (4). An improved version of the Cooper pair box qubit showed that quantum oscillations with a high quality factor could be achieved (5). In addition, a qubit based on the phase degree of freedom in a Josephson junction was presented, consisting of a single, relatively large Josephson junction current-biased close to its critical current (6,7).Our flux qubit consists of three Josephson junctions arranged in a superconducting loop threaded by an externally applied magnetic flux near half a superconducting flux quantum Φ 0 = h/2e [(8); a one-junction flux-qubit is described in (9)]. Varying the flux bias controls the energy level separation of this effectively two-level system. At half a flux quantum, the two lowest states are symmetric and antisymmetric superpositions of two classical states with clockwise and anticlockwise circulating currents. As shown by previous microwave spectroscopy studies, the qubit can be engineered such th...

In the emerging field of quantum computation 1 and quantum information, superconducting devices are promising candidates for the implementation of solidstate quantum bits or qubits. Single-qubit operations 2−6 , direct coupling between two qubits 7−10 , and the realization of a quantum gate 11 have been reported. However, complex manipulation of entangled states − such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments 12,13 or cavity quantum electrodynamics 14 − has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.The device was realized by electron-beam lithography and metal evaporation. The qubit-SQUID geometry is shown in Fig. 1a: a large loop interrupted by two Josephson junctions (the SQUID) is merged with the smaller loop on the right-hand side comprising three in-line Josephson junctions (the flux qubit) 15 . By applying a perpendicular external magnetic field, the qubit is biased around Φ 0 /2, where Φ 0 = h/2e is the flux quantum. Previous spectroscopy 16 and coherent timedomain experiments 6 have shown that the flux qubit is a controllable two-level system with 'spin-up/spin-down' states corresponding to persistent currents flowing in 'clockwise/anticlockwise' directions and coupled by tunneling. Here we show that a stronger qubit−SQUID coupling allows us to investigate the coupled dynamics of a 'qubit−harmonic oscillator' system.The qubit Hamiltonian is defined by the charging and Josephson energy of the qubit outer junctions (E C = e 2 /2C and E J = hI C /4e where C and I C are their capacitance and critical current) 16 . In a two-level truncation, the Hamiltonian becomes H q /h = −ǫσ z /2−∆σ x /2 where σ z,x are the Pauli matrices in the spin-up/spin-down basis, ∆ is the tunnel splitting and ǫ ∼ = I p Φ 0 (γ q − π)/hπ (I p is the qubit maximum persistent current and γ q is the superconductor phase across the three junctions). The resulting energy level spacing represents the qubit Larmor frequency F L = √ ∆ 2 + ǫ 2 . The SQUID dynamics is characterized by the Josephson inductance of the junctions L J ≈ 80 pH, shunt capacitance C sh ≈ 12 pF (see Fig. 1a) and self-inductances L sl ≈ 170 pH of the SQUID and shunt-lines. In our experiments, the SQUID circuit behaves like a harmonic oscillator described by H sq = hν p (a † a + 1/2), where 2πν p = 1/ (L J + L sl )C sh is called the plasma frequency and a (a † ) is the plasmon annihilation (creation) operator. Henceforth |βn represents the state with the qubit in the ground(β = 0) or excited ...

We measure the dispersive energy-level shift of an LC resonator magnetically coupled to a superconducting qubit, which clearly shows that our system operates in the ultrastrong coupling regime. The large mutual kinetic inductance provides a coupling energy of ≈ 0.82 GHz, requiring the addition of counter-rotating-wave terms in the description of the Jaynes-Cummings model. We find a 50 MHz Bloch-Siegert shift when the qubit is in its symmetry point, fully consistent with our analytical model.

Microwave spectroscopy experiments have been performed on two quantum levels of a macroscopic superconducting loop with three Josephson junctions. Level repulsion of the ground state and first excited state is found where two classical persistent-current states with opposite polarity are degenerate, indicating symmetric and antisymmetric quantum superpositions of macroscopic states. The two classical states have persistent currents of 0.5 microampere and correspond to the center-of-mass motion of millions of Cooper pairs.

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