Multiphoton absorption observed in a superconducting flux qubit

Shiro Saito, Michael Thorwart1, Hirotaka Tanaka, Hayato Nakano, Kouichi Semba,
Masahito Ueda2, and Hideaki Takayanagi
Materials Science Laboratory, Heinrich-Heine-Universitat Dusseldorf1,
NTT Research Professor and Tokyo Institute of Technology2

 Of the recently realized solid-state quantum bits (qubits), the superconducting flux qubit has advantages because its scalability and long coherence time. The qubit consists of a superconducting loop with three Josephson junctions (see Fig. 1). The two states of the qubit correspond to clockwise |0> and counterclockwise |1> superconducting current in the loop. The current involves millions of Cooper pairs, which means that the two states are macroscopically distinct. Hence, this system can realize a superposition between two such macroscopic states. For the first time, we observed multiphoton transitions between the superposition states in the superconducting flux qubit [1].
 Figure 2(a) shows the magnetic flux dependence of the qubit energy levels, where is the flux through the qubit loop and (= ) is the flux quantum. The arrows in the figure represent a microwave with an energy of 9.1 GHz. The qubit can be excited from the ground state to the first excited state by absorbing multiple photons. We remark that the existence of the energy gap at the degeneracy point =1.5 is strong evidence for the superposition between the macroscopically distinct states.
 The qubit was read out by measuring the switching current of a superconducting quantum interference device (dc-SQUID) (see Fig. 1). Figure 2(b) shows the change in the switching current as a function of the magnetic flux under the microwave irradiation. The dc-SQUID detected the change in the qubit state from |0> to |1> induced by magnetic flux. Furthermore, resonant peaks and dips were observed at the expected operating points in Fig. 2(a). The microwave power dependences of the half width at half maxima of the resonant dips were well reproduced by Bloch equations based on a dressed-atom description (see Fig. 3). From this analysis, we found the qubit coherence time to be 5 ns, which is consistent with that obtained from another experiment using a microwave pulse.

[1] S. Saito, et al., cond-mat/0403425.

Fig. 1. Superconducting flux qubit (inner loop) and dc-SQUID for readout (outer loop)
Fig. 3. Microwave power dependence of HWHM of resonant dips. Solid curves represent theoretical simulations.
Fig. 2. (a) Energy diagram of qubit.
  (b) Magnetic field dependence of qubit readout.

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