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arXiv:1408.0226 · New Journal of Physics

Large gain quantum-limited qubit measurement using a two-mode nonlinear cavity

S Khan, R Vijay, I Siddiqi, A A Clerk

Published Nov 14, 2014• 1 citation
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Abstract

We provide a thorough theoretical analysis of qubit state measurement in a setup where a driven, parametrically-coupled cavity system is directly coupled to the qubit, with one of the cavities having a weak Kerr nonlinearity. Such a system could be readily realized using circuit QED architectures. We demonstrate that this setup is capable in the standard linear-response regime of both producing a highly amplified output signal while at the same time achieving near quantum-limited performance: the measurement backaction on the qubit is near the minimal amount required by the uncertainty principle. This setup thus represents a promising route for performing efficient large-gain qubit measurement that is completely on-chip, and that does not rely on the use of circulators or complex non-reciprocal amplifiers.

DOI
10.1088/1367-2630/16/11/113032

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We provide a thorough theoretical analysis of qubit state measurement in a setup where a driven, parametrically-coupled cavity system is directly coupled to the qubit, with one of the cavities having a weak Kerr nonlinearity. Such a system could be readily realized using circuit QED architectures. We demonstrate that this setup is capable in the standard linear-response regime of both producing a highly amplified output signal while at the same time achieving near quantum-limited performance: the measurement backaction on the qubit is near the minimal amount required by the uncertainty principle. This setup thus represents a promising route for performing efficient large-gain qubit measurement that is completely on-chip, and that does not rely on the use of circulators or complex non-reciprocal amplifiers.
We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity that is used to amplify a dispersively coupled input signal. Focusing on an operating regime that is near a bifurcation point, we derive simple asymptotic expressions describing the cavity's noise and response. We show that the cavity's backaction and imprecision noise allow for quantum-limited linear amplification and position detection only if one is able to utilize the sizable correlations between these quantities. This is possible when one amplifies a nonresonant signal but is not possible in quantum nondemolition qubit detection. We also consider the possibility of using the nonlinear cavity's backaction for cooling a mechanical mode.
We investigate the quantum measurement physics of a system in which a phase-sensitive parametric amplifier is used to directly measure a qubit to which it is coupled dispersively. By analytic calculation of the signal-to-noise ratio, we show that the amplification properties of the paramp can be exploited to achieve on-chip gain of the qubit readout signal, mitigating the damage done to the measurement rate by circulator added noise and losses in between the readout cavity and any following amplification chain. With a different choice of drive phase, we show that when added noise is not a concern, the squeezing properties of the paramp can be used to enhance the measurement rate relative to a standard dispersive readout by reducing the readout noise without corresponding reduction of qubit signal. We then proceed to calculate the back-action dephasing of the qubit by way of a phase-space technique, and find analytic results valid in the long-time limit while numerically handling the finite-time case. We show how in both operating modes, in the long-time limit, the back-action dephasing of the qubit can be made as small as is allowed by quantum mechanics by using using sufficiently many photons in the measurement, i.e.\@ by using a sufficiently strong coherent measurement drive. Crucially, we find that in the presence of experimentally realistic amounts of added noise, the on-chip gain afforded by such a device can be used to come significantly closer to the quantum limit than is possible with a standard dispersive measurement setup, allowing for efficiencies of ~ 75% under conditions that would yield efficiencies <~ 1 % when applying the usual scheme.
A crucial limit to measurement efficiencies of superconducting circuits comes from losses involved when coupling to an external quantum amplifier. Here, we realize a device circumventing this problem by directly embedding an artificial atom, comprised of a transmon qubit, within a flux-pumped Josephson parametric amplifier. This configuration is able to enhance dispersive measurement without exposing the qubit to appreciable excess backaction. Near-optimal backaction is obtained by engineering the circuit to permit high-power operation that reduces information loss to unmonitored channels associated with the amplification and squeezing of quantum noise. By mitigating the effects of off-chip losses downstream, the on-chip gain of this device produces end-to-end measurement efficiencies of up to 80%. Our theoretical model accurately describes the observed interplay of gain and measurement backaction and delineates the parameter space for future improvement. The device is compatible with standard fabrication and measurement techniques and, thus, provides a route for definitive investigations of fundamental quantum effects and quantum control protocols.
A crucial limit to measurement efficiencies of superconducting circuits comes from losses involved when coupling to an external quantum amplifier.Here, we realize a device circumventing this problem by directly embedding an artificial atom, comprised of a transmon qubit, within a flux-pumped Josephson parametric amplifier.This configuration is able to enhance dispersive measurement without exposing the qubit to appreciable excess backaction.Near-optimal backaction is obtained by engineering the circuit to permit high-power operation that reduces information loss to unmonitored channels associated with the amplification and squeezing of quantum noise.By mitigating the effects of off-chip losses downstream, the on-chip gain of this device produces end-to-end measurement efficiencies of up to 80%.Our theoretical model accurately describes the observed interplay of gain and measurement backaction and delineates the parameter space for future improvement.The device is compatible with standard fabrication and measurement techniques and, thus, provides a route for definitive investigations of fundamental quantum effects and quantum control protocols.
High fidelity qubit readout is a cornerstone for quantum information protocols. In traditional superconducting qubit readout, a chain of microwave amplifiers and nonreciprocal components aid in detecting the qubit's state with tolerable added noise and backaction. However, the loss, size, and magnetic field of standard nonreciprocal components have sparked a decades-long search for more efficient and scalable alternatives. One prominent approach employs networks of parametrically coupled modes to achieve nonreciprocity. While this class of devices can be directly integrated with the qubit's readout cavity, current understanding of the resulting single quantum system is substantially lacking. Here we provide a first-principles theoretical tool to understand and design networks of linear modes integrated with embedded qubits. We utilize this theory to inform and analyze the experimental implementation of a qubit readout with an integrated three-mode nonreciprocal system. In doing so, we achieve excellent agreement between the experimental and theoretical qubit measurement and dephasing rates. We then theoretically analyze the same system operated as an integrated nonreciprocal amplifier, predicting high efficiency for reasonable experimental parameters.
We analyze the use of a driven nonlinear cavity to make a weak continuous measurement of a dispersively coupled qubit. We calculate the backaction dephasing rate and measurement rate beyond leading-order perturbation theory using a phase-space approach which accounts for cavity noise squeezing. Surprisingly, we find that increasing the coupling strength beyond the regime describable by leading-order perturbation theory (i.e., linear response) allows one to come significantly closer to the quantum limit on the measurement efficiency. We interpret this behavior in terms of the non-Gaussian photon number fluctuations of the nonlinear cavity. Our results are relevant to recent experiments using superconducting microwave circuits to study quantum measurement.