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Chinese Physics B

Macroscopic resonant tunneling in an rf-SQUID flux qubit

Shanhua Cong, Yiwen Wang, Guozhu Sun, Jian Chen, Yang Yu, Peiheng Wu

Published May 1, 2011• 6 citations
Publisher

Abstract

We have observed the macroscopic resonant tunneling of magnetic flux between macroscopically distinct quantum states in a superconducting flux qubit. The dependences of the macroscopic resonant tunneling on the barrier height of the potential well, the flux bias and the initial state are investigated. Detailed measurements of the tunneling rate as a function of the flux bias reveal the feature of the quantum noise in the superconducting flux qubit.

DOI
10.1088/1674-1056/20/5/050316

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We have observed the macroscopic resonant tunneling of magnetic flux between macroscopically distinct quantum states in a superconducting flux qubit. The dependences of the macroscopic resonant tunneling on the barrier height of the potential well, the flux bias and the initial state are investigated. Detailed measurements of the tunneling rate as a function of the flux bias reveal the feature of the quantum noise in the superconducting flux qubit.
Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than the target well. The rms amplitude of the noise, which is proportional to the dephasing rate 1/tauphi, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.
We experimentally demonstrate the observation of macroscopic resonant tunneling (MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device (rf-SQUID) under a single-cycle sinusoidal driving. The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells. The dynamics of the qubit depends significantly on the amplitude, frequency, and initial phase of the driving signal. We do the numerical simulations considering the intra-well and inter-well relaxation mechanism, which agree well with the experimental results. This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.
We report on measurements of flux and charge noise in an rf-SQUID (superconducting quantum interference device) flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
We have developed a quantitative theory of resonant tunneling of magnetic flux between discrete macroscopically distinct quantum states in superconducting quantum interference device systems. The theory is based on the standard density-matrix approach. Its elements include the discussion of the two different relaxation mechanisms that exist for the double-well potential, and description of the ``photon-assisted'' tunneling driven by external rf radiation. It is shown that in the case of coherent flux dynamics, rf radiation should lead to splitting of the peaks of resonant flux tunneling, indicating that the resonant tunneling is a convenient tool for studying macroscopic quantum coherence of flux.
We report measurements of macroscopic resonant tunneling between the two lowest energy states of a pair of magnetically coupled rf-superconducting quantum interference device flux qubits. This technique provides both a direct means of measuring the energy gap of the two-qubit system and a method for probing of the environment coupled to the pair of qubits. Measurements of the tunneling rate as a function of qubit flux bias show a Gaussian line shape that is well matched to theoretical predictions. Moreover, the peak widths indicate that each qubit is coupled to a local environment whose fluctuations are uncorrelated with that of the other qubit.