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Journal of Physics Conference Series

Direct spectral analysis of environmental noise in SQUID and SQUBIT type circuits using a Josephson bifurcation amplifier

Grégoire Ithier, Giovanna Tancredi, P. J. Meeson

Published Dec 8, 2014• 0 citations
Publisher

Abstract

The Josephson Bifurcation Amplifier is a threshold detector that may be viewed as a 1-bit analog-to-digital converter. Such a device is subject to two random processes, firstly the bifurcation itself is a dynamical process that is subject to quantum or thermal fluctuations that broaden the threshold, secondly the device is immersed in an environment that induces low frequency parametric noise. We have developed a new measurement technique that quantitatively and directly links the environmental noise spectrum to the spectrum calculated from the repetitively acquired binary output of the Josephson Bifurcation Amplifier. The technique has considerable advantages over the NMR techniques presently in common use for studies of qubit decoherence and the techniques used for SQUIDs. It is non-dissipative, enabling operation in the milliKelvin range, it has a wide bandwidth, it is operated at low photon numbers, and its sensitivity approaches the shot noise limit of a weak continuous measurement.

DOI
10.1088/1742-6596/568/5/052021

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The Josephson Bifurcation Amplifier is a threshold detector that may be viewed as a 1-bit analog-to-digital converter. Such a device is subject to two random processes, firstly the bifurcation itself is a dynamical process that is subject to quantum or thermal fluctuations that broaden the threshold, secondly the device is immersed in an environment that induces low frequency parametric noise. We have developed a new measurement technique that quantitatively and directly links the environmental noise spectrum to the spectrum calculated from the repetitively acquired binary output of the Josephson Bifurcation Amplifier. The technique has considerable advantages over the NMR techniques presently in common use for studies of qubit decoherence and the techniques used for SQUIDs. It is non-dissipative, enabling operation in the milliKelvin range, it has a wide bandwidth, it is operated at low photon numbers, and its sensitivity approaches the shot noise limit of a weak continuous measurement.
We introduce a new and quantitative theoretical framework for noise spectral analysis using a threshold detector, which is then applied to a superconducting device: the Josephson bifurcation amplifier. We show that this new framework provides direct access to the environmental noise spectrum with a sensitivity approaching the standard quantum limit of weak continuous measurements. In addition, the accessible frequency range of the spectrum is, in principle, limited only by the ring down time of the resonant mode. This on-chip noise detector is non-dissipative and works with low probing powers, allowing it to be operated at low temperatures ( mK). We exploit this technique for measuring the frequency fluctuations of our device and find a low frequency noise with an amplitude and spectrum compatible with a dielectric origin.
We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of a rf-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high sensitivity, low backaction, and the absence of on-chip dissipation. Pulsed microwave reflection measurements on nanofabricated Al junctions show that actual devices attain the performance predicted by theory.
The fundamental noise limit of a phase-preserving amplifier at frequency [Formula: see text] is the standard quantum limit [Formula: see text]. In the microwave range, the best candidates have been amplifiers based on superconducting quantum interference devices (reaching the noise temperature [Formula: see text] at 700 MHz), and non-degenerate parametric amplifiers (reaching noise levels close to the quantum limit [Formula: see text] at 8 GHz). We introduce a new type of an amplifier based on the negative resistance of a selectively damped Josephson junction. Noise performance of our amplifier is limited by mixing of quantum noise from Josephson oscillation regime down to the signal frequency. Measurements yield nearly quantum-limited operation, [Formula: see text] at 2.8 GHz, owing to self-organization of the working point. Simulations describe the characteristics of our device well and indicate potential for wide bandwidth operation.
Crossover between thermal and quantum noise in the externally-pumped Josephson-junction parametric amplifiers is theoretically followed. Two different approaches are used for the analysis : i. Josephson junction is replaced with its RSJ model with the equilibrium source of fluctuations; ii. microscopic theory of the tunnel junctions is used, which takes into account not only thermal and quantum but also shot noise. Because of inconvenience of the noise temperature TNfor the amplifier sensitivity characterization in the quantum limit, we express our results in terms of the figure ΘNwhich is essentially the amplifier output noise energy, reduced to its input (in the classical limit,\Theta_{N}=k_{B}T_{N}). For the nondegenerate amplifier, the minimum value of ΘN. equals hω/2 and is due to quantum noise (zero-point oscillations) in the idle-frequency resonator of the amplifier. For the degenerate amplifier, sensitive to only one quadrature component of the input signal, ΘNcan be made much less than the above "quantum limit" even at operation temperatures much higher thanh\omega/k_{B}, if the Josephson junction characteristic frequency ωcis high enough,h\omega_{c}\gsimk_{B}T. Our analysis of the experimental situatlon shows that the values\Theta_{N}<h\omega/2can be achieved using two-dimensional arrays of a large number (N\simeq100) single-tunnel-junction interferometers with low inductances, inductively coupled to a microwave cavity.
We review the theory, fabrication, and implementation of the Josephson bifurcation amplifier (JBA). At the core of the JBA is a nonlinear oscillator based on a reactively shunted Josephson junction. A weak input signal to the amplifier couples to the junction critical current I(0) and results in a dispersive shift in the resonator plasma frequency omega(p). This shift is enhanced by biasing the junction with a sufficiently strong microwave current I(rf) to access the nonlinear regime where omega(p) varies with I(rf). For a drive frequency omega(d) such that Omega=2Q(1-omega(d)/omega(p))>3, the oscillator enters the bistable regime where two nondissipative dynamical states O(L) and O(H), which differ in amplitude and phase, can exist. The sharp I(0) dependent transition from O(L) to O(H) forms the basis for a sensitive digital threshold amplifier. In the vicinity of the bistable regime (Omega<3), analog amplification of continuous signals is also possible. We present experimental data characterizing amplifier performance and discuss two specific applications--the readout of superconducting qubits (digital mode) and dispersive microwave magnetometry (analog mode).
Critical current fluctuations with a 1∕f spectral density (f is frequency) are potentially a limiting source of intrinsic decoherence in superconducting quantum bits (qubits) based on Josephson tunnel junctions. Prior measurements of this noise were made at nonzero voltages whereas qubits are operated in the zero voltage state. We report measurements of 1∕f noise in a dc superconducting quantum interference device first, coupled to a resonant tank circuit and operated in a dispersive mode at zero voltage, and, second, operated conventionally with a current bias in the voltage regime. Both measurements yield essentially the same magnitude of critical current 1∕f noise.