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arXiv:cond-mat/0303433 · Physical Review Letters

Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Evgeni V. Il’ichev, Nikolai Oukhanski, A. Izmalkov, Th. Wagner, M. Grajcar, H.‐G. Meyer, Anatoly Yu. Smirnov, Alec Maassen van den Brink, M. H. S. Amin, Alexandre M. Zagoskin

Published Aug 28, 2003• 147 citations
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Abstract

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.

DOI
10.1103/physrevlett.91.097906

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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.
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Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in the GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high-quality resonant tank circuit, inductively coupled to the phase qubit. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase qubit), which explicitly account for the back action of a tank circuit. According to the results of our simulations the Rabi oscillations in the MHz range can be detected using the conventional NMR pulse Fourier technique.
Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector---namely, a spectrum of voltage fluctuations and an impedance---are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating-wave approximations. Back-action effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about the frequency and decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behavior as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.
Nonlinear effects in mesoscopic devices can have both quantum and classical origins. We show that a three-Josephson-junction (3JJ) flux qubit in the classical regime can produce low-frequency oscillations in the presence of an external field in resonance with the (high-frequency) harmonic mode $\ensuremath{\omega}$ of the system. Like in the case of quantum Rabi oscillations, the frequency of these pseudo-Rabi oscillations is much smaller than $\ensuremath{\omega}$ and scales approximately linearly with the amplitude of the external field. This classical effect can be reliably distinguished from its quantum counterpart because it can be produced by the external drive not only at the resonance frequency $\ensuremath{\omega}$ and its subharmonics $(\ensuremath{\omega}/n)$, but also at its overtones, $n\ensuremath{\omega}$.
Measurements of three-junction flux qubits, both single flux qubits and coupled flux qubits, using a coupled direct current superconducting quantum interference device (dc-SQUID) for readout are reported. The measurement procedure is described in detail. We performed spectroscopy measurements and coherent manipulations of the qubit states on a single flux qubit, demonstrating quantum energy levels and Rabi oscillations, with Rabi oscillation decay time T Rabi = 78 ns and energy relaxation time T 1 = 315 ns. We found that the value of T Rabi depends strongly on the mutual inductance between the qubit and the magnetic coil. We also performed spectroscopy measurements on inductively coupled flux qubits.