Design for an Ideal Measuring Device

Abstract:

The Heisenberg uncertainty principle yields a fundamental limit to the accuracy of ordinary measuring techniques. For example, a standard voltmeter applied to the signal V₁cos(ωt) + V₂sin(ωt) must have a noise voltage given by the “standard quantum limit” [1]

ΔV1 = ΔV2 >≈  ΔVsql              (1)

where

ΔVsql = ( Z

∫

B

dω  2π

ℏω 2

)½             (2)

where Z is the impedance of the system, B is the bandwidth of the voltmeter, and ℏ is Planck’s constant over 2π. We show how to evade this limit by measuring only one phase of the signal, while diverting the noise into the other phase. The noise ΔV₁ can be greatly reduced. The uncertainty principle is upheld:

ΔV1ΔV2 >≈ (ΔVsql)2              (3)

We discuss the design of a device having this property, and describe its effect on thermal noise as well as quantum fluctuations. Efforts to demonstrate operation such a device are underway.

1  Introduction

There are several reasons for investigating the absolute limits of performance of measuring devices. For one thing, there are some questions of principle regarding what is or is not measurable. Secondly, experimentalists are always striving to extract data from noise, so a quieter detector has a certain practical appeal. Indeed, there are fields such as gravity-wave detection[1] and low temperature noise thermometry [2] where exceeding the standard quantum limit will be essential. Furthermore, recent progress in SQUID technology [3] and nonlinear optics [4] have reduced extraneous noise sources to the point where construction of a fundamentally new class of detectors is becoming feasible.