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Physical Review A

Precision measurement scheme using a quantum interferometer

Taesoo Kim, Jacob Dunningham, Keith R. Burnett

Published Nov 1, 2005• 15 citations
Publisher

Abstract

We present a scheme that makes use of quantum mechanical entanglement to significantly enhance the measurement precision accessible by interferometers. This is achieved by making use of a special type of interferometer composed of two ``quantum beam splitters,'' which each transform the input particles into a macroscopic superposition at the outputs. We show that this technique not only enables phase measurements to be made with Heisenberg limited precision, but also overcomes the major practical problems of detector inefficiencies and imperfect beam splitters. It may provide a promising route to implementing sub-shot-noise limited measurement schemes in the laboratory.

DOI
10.1103/physreva.72.055801

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We present a scheme that makes use of quantum mechanical entanglement to significantly enhance the measurement precision accessible by interferometers. This is achieved by making use of a special type of interferometer composed of two ``quantum beam splitters,'' which each transform the input particles into a macroscopic superposition at the outputs. We show that this technique not only enables phase measurements to be made with Heisenberg limited precision, but also overcomes the major practical problems of detector inefficiencies and imperfect beam splitters. It may provide a promising route to implementing sub-shot-noise limited measurement schemes in the laboratory.
In recent work we proposed a quantum interferometer and showed how it could be used to significantly enhance the resolution that could be achieved in measurement schemes. In this paper, we outline a detailed scheme on how these quantum interferometers could be implemented. We also analyze the effects of dissipation and of imperfect detectors and show that this scheme is remarkably robust to both. This suggests that quantum interferometers may provide a promising route for implementing sub-shot-noise limited measurements in the laboratory.
We analyze a nonconventional interferometer that is formed with a parametric amplifier and a beam splitter for beam splitting and recombination. Because the outputs from a parametric amplifier are entangled and their quantum noise is correlated, the employment of the beam splitter will superimpose the two quantum fields and the destructive interference will lead to the subtraction of the quantum noise and to noise reduction in the output of the interferometer and hence an improvement of the signal-to-noise ratio (SNR) beyond the standard quantum limit or the shot noise limit. Furthermore, the injection of a squeezed state into the idler port of the parametric amplifier will lead to further improvement of the SNR. We will discuss the possibility of reaching the Heisenberg limit in such an interferometer. We find that the injection of a coherent state will degrade the performance in reaching the Heisenberg limit, whereas a squeezed state injection can improve it by a factor of 2 at best.
A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.
Conventional interferometers usually utilize beam splitters for wave splitting and recombination. These interferometers are widely used for precision measurement. Their sensitivity for phase measurement is limited by the shot noise, which can be suppressed with squeezed states of light. Here we study a new type of interferometer in which the beam splitting and recombination elements are parametric amplifiers. We observe an improvement of 4.1±0.3 dB in signal-to-noise ratio compared with a conventional interferometer under the same operating condition, which is a 1.6-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. The improvement is due to signal enhancement. Combined with the squeezed state technique for shot noise suppression, this interferometer promises further improvement in sensitivity. Furthermore, because nonlinear processes are involved in this interferometer, we can couple a variety of different waves and form new types of hybrid interferometers, opening a door for many applications in metrology. Interferometers play a key role in precision measurements and metrology. Here, the authors demonstrate a new type of interferometer that replaces the standard beam splitter elements with parametric amplifiers, which provides enhanced performance compared with a Mach–Zehnder interferometer.
Advancements in physics are often motivated/accompanied by advancements in our precision measurements abilities. The current generation of atomic and optical interferometers is limited by shot noise, a fundamental limit when estimating a phase shift with classical light or uncorrelated atoms. In the last years, it has been clarified that the creation of special quantum correlations among particles, which will be called here useful entanglement, can strongly enhance the interferometric sensitivity. Pioneer experiments have already demonstrated the basic principles. We are probably at the verge of a second quantum revolution where quantum mechanics of many-body systems is exploited to overcome the limitations of classical technologies. This review illustrates the deep connection between entanglement and sub shot noise sensitivity.