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## Design for an Ideal Measuring Device |

Laboratory of Atomic and Solid State Physics

Cornell University, Ithaca NY 14853

Cornell University, Ithaca NY 14853

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 V

_{1}cos(ωt) + V_{2}sin(ωt) must have a noise voltage given by the “standard quantum limit” [1]

ΔV _{1}= ΔV_{2}>≈ ΔV_{sql}(1)where

ΔV _{sql}= (^{ }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 ΔV

_{1}can be greatly reduced. The uncertainty principle is upheld:

ΔV _{1}ΔV_{2}>≈ (ΔV_{sql})^{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.

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.

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