Phase-sensitive detection and the back-action evasion of amplifier force noise

Franco Bordoni, Roberto Onofrio

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.

Kevin Lyons, John C. Howell, Andrew N. Jordan

Roberto Onofrio, Franco Bordoni

After a general review of the analysis already available for back-action evasion schemes a perturbative approach is introduced and applied to a simple case. As a generalization of the back-action evasion schemes the concept of optimal pumping spectrum is introduced: it works for a unified treatment of stroboscopic and continuous quantum nondemolition strategies. Generalized back-action evasion strategies are introduced and studied in simple applications: they open the possibility for developing high-sensitivity schemes for the measurements of small forces. In particular, estimates of the noise figure for generalized back-action evasion transducers are discussed in detail.

H. A. Haus

Khalid Zaheer, Muhammad Suhail Zubairy