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arXiv:cond-mat/0507008

Measurement of Dissipation of a Three-Level rf SQUID Qubit

Shaoxiong Li, Wei Qiu, Zhongyuan Zhou, Matthew H. Matheny, Wei Chen, James E. Lukens, Siyuan Han

Published Jul 1, 2005• 1 citation
arXivHTMLPDF

Abstract

The dissipation-induced relaxation (T_1) time of a macroscopic quantum system - a \{lambda}-type three-level rf SQUID flux qubit weakly coupled to control and readout circuitry (CRC) - is investigated via time-domain measurement. The measured interwell relaxation time of the qubit's first excited state, T_1=3.45+/-0.06 \{mu}s, corresponds to an effective damping resistance of the flux qubit R=1.6+/-0.1 M\{omega} which is much lower than the intrinsic quasiparticle resistance of the Josephson tunnel junction. An analysis of the system shows that although the CRC is very weakly coupled to the qubit it is the primary source of damping. This type of damping can be significantly reduced by the use of more sophisticated circuit design to allow coherent manipulation of qubit states.

DOI
10.48550/arxiv.cond-mat/0507008

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The dissipation-induced relaxation (T_1) time of a macroscopic quantum system - a {lambda}-type three-level rf SQUID flux qubit weakly coupled to control and readout circuitry (CRC) - is investigated via time-domain measurement. The measured interwell relaxation time of the qubit's first excited state, T_1=3.45+/-0.06 {mu}s, corresponds to an effective damping resistance of the flux qubit R=1.6+/-0.1 M{omega} which is much lower than the intrinsic quasiparticle resistance of the Josephson tunnel junction. An analysis of the system shows that although the CRC is very weakly coupled to the qubit it is the primary source of damping. This type of damping can be significantly reduced by the use of more sophisticated circuit design to allow coherent manipulation of qubit states.
It is well known that that superconducting qubits based on Josephson junctions have the advantages of scalability and the qubit states are easy to prepare and control. In addition, demonstration of Rabi oscillations in various superconducting circuits shows that superconducting qubits are promising for scalable quantum information processing. However, despite flexibility of design and fabrication, easier to scale up, and fast gate speed, superconducting qubits usually have much shorter decoherence time than trapped ions, NMR etc. due to the relatively strong interactions between qubits and environment. Recent experiments show that low frequency flux noise is the dominant mechanism of decoherence in superconducting flux qubits. However, despite extensive effort the origin of flux noise is still not well understood. The goal of this work is to identify the source and characterize the property of flux noisein rf SQUID flux qubit through various spectroscopy and time-resolved measurements. Our result show that one can determine all circuit parameters needed for reconstructing qubit Hamiltonian with high accuracy via measurement of macroscopic resonant tunneling (MRT) and photon assisted tunneling (PAT) and that the amount of flux noise in rf SQUID qubits scales linearly with self inductance of the qubits. In addition, we have investigated the dynamics of a three-level flux qubit in incoherent regime. The result demonstrates that treating a multi-level physical qubit, such as the superconducting flux qubit, as an ideal two-level quantum system may be inadequate under certain circumstances.
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.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
We measured the integrated low frequency flux noise (∼1 mΦ0) of an rf SQUID as a flux qubit by fitting the resonant peaks from photon assistant tunneling (PAT). The energy relaxation time Tl between the ground and first excited states in the same potential well, measured directly in time domain, is 3 ns. From these results we identified low frequency flux noise as the dominant source of decoherence. In addition, we found that the measured values of integrated flux noise in three qubits of various sizes differ more than an order of magnitude.
We believe that the best chance to observe macroscopic quantum coherence (MQC) in an rf-SQUID qubit is to use on-chip RSFQ digital circuits for preparing, evolving and reading out the qubit's quantum state. This approach allows experiments to be conducted on a very short time scale (sub-nanosecond) without the use of large bandwidth control lines that would couple environmental degrees of freedom to the qubit, thus contributing to its decoherence. In this paper we present our design of an RSFQ digital control circuit for demonstrating MQC in an rf-SQUID. We assess some of the key practical issues in the circuit design including the achievement of the necessary flux bias stability. We present an "active" isolation structure to be used to increase coherence times. The structure decouples the SQUID from external degrees of freedom, and then couples it to the output measurement circuitry when required, all under the active control of RSFQ circuits.
We report on the first measurements of the intrinsic dissipation in a macroscopic system cooled at very low temperature (35 mK) and operating in the quantum regime. The system under study is an rf SQUID with a high quality Josephson junction. Below 50 mK the tunneling probability of escape from a metastable well vs applied flux presents a series of maxima due to energy level quantization. From the shape of the tunneling probability we can evaluate the intrinsic dissipation related to the overall system as well as the coherence time related to the Rabi oscillations in a future macroscopic quantum coherence experiment.