Improving the Quality of Heisenberg Back-Action of Qubit Measurements made with Parametric Amplifiers

A. Metelmann, Archana Kamal

B. A. Levitan

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.

Keith Krause

Gary W. Spetz

Limitations on the sensitivity for detecting a weak classical force acting on a harmonic oscillator are imposed by the quantum mechanical properties associated with a "standard" amplitude-and-phase measurement and, classically, by the back reaction noise associated with the finite noise temperature of the amplifier used to process the measurement. These are known as the "standard quantum limit" and the "standard amplifier limit", respectively. We present the theoretical motivation behind the quest to circumvent these limits, and examine a single-transducer back-action evading measurement scheme designed to perform a phase-sensitive coupling to the oscillator, with the concomitant circumvention of the standard amplifier limit via the "squeezing" of amplifier back reaction noise. The applicability of squeezing in the detection of gravitational radiation is explored via the dependence of detection sensitivity on the physical temperature and quality factor of the resonant-bar gravitational radiation antenna, on the noise temperature of the amplifier, and on the squeezing factor of the back-action evading measurement; the success of back-action evasion in improving upon the optimum amplitude-and-phase detection sensitivities depends critically upon these parameters. Using the LSU superconducting dual-cavity accelerometer as a test platform, we present direct evidence for the establishment of a phase-sensitive coupling to an oscillator, along with a variety of indirect corroborating evidence. This data indicates that our phase-sensitive measurement scheme is indeed more sensitive to one component of the oscillator than to the other component. We also present the first evidence for the existence of back-action evasion of amplifier back reaction noise. We show theoretical expectations and experimental results for the dependence of squeezing on: input signal phases, amplitudes, and frequencies; amplifier back reaction levels; background noise; mechanical oscillator frequency; and coherent carrier contribution at the cavity resonance frequency. Squeezing factors of up to fifteen were achieved by our back-action evading measurement scheme.

Archana Kamal, Adam Henry Marblestone, Michel Devoret

We present the theory of a Josephson parametric amplifier employing two-pump sources. Our calculations are based on input-output theory, and can easily be generalized to any coupled system involving parametric interactions. We analyze the operation of the device, taking into account the feedback introduced by the reaction of the signal and noise on the pump power, and in this framework, compute the response functions of interest---signal and idler gains, internal gain of the amplifier, and self-oscillation signal amplitude. To account for this back action between signal and pump, we adopt a mean-field approach and self-consistently explore the boundary between amplification and self-oscillation. The coincidence of bifurcation and self-oscillation thresholds reveals that the origin of coherent emission of the amplifier lies in the multiwave mixing of the noise components. Incorporation of the back action leads the system to exhibit hysteresis, dependent on parameters such as temperature and detuning from resonance. Our analysis also shows that the resonance condition itself changes in the presence of back action and this can be understood in terms of the change in plasma frequency of the junction. The potential of the double-pump amplifier for quantum-limited measurements and as a squeezer is also discussed.

Yanbei Chen