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Journal of Modern Optics

Using quantum interferometers to make measurements at the Heisenberg limit

Jacob Dunningham, T. Kim

Published Jan 10, 2006• 24 citations
Publisher

Abstract

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.

DOI
10.1080/09500340500443268

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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 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.
We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.
High-sensitivity interferometers are one of the basic tools for precision measurement, and their sensitivity is limited by their shot noise limit (SNL), which is determined by vacuum fluctuations of the probe field. The quantum interferometer with novel structures can break the SNL and measure the weak signals, such as the direct observation of gravity wave signal. Combining classical interferometers and the optical parametric amplifier (OPA) can enhance the signal; meanwhile, the quantum noise is kept at the vacuum level, so that the sensitivity of the nonlinear interferometer beyond the SNL can be achieved. By analyzing in detail the influence of system parameters on the precision of quantum metrology, including the intensity of optical fields for phase sensing, the gain factor of OPA, and the losses inside and outside the interferometers, the application conditions of high-sensitivity nonlinear quantum interferometers are obtained. Quantum interferometer-based OPAs provide the direct references for the practical development of quantum precise measurement.
Quantum enhancements of precision in metrology can be compromised by system imperfections. These may be mitigated by appropriate optimization of the input state to render it robust, at the expense of making the state difficult to prepare. In this paper, we identify the major sources of imperfection of an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The second of these has received much attention; we show that it is the least damaging to surpassing the standard quantum limit in a optical interferometric sensor. Further, we show that photonic states that can be prepared in the laboratory using feasible resources allow a measurement strategy using photon-number-resolving detectors that not only attain the Heisenberg limit for phase estimation in the absence of losses, but also deliver close to the maximum possible precision in realistic scenarios including losses and inefficiencies. In particular, we give bounds for the tradeoff between the three sources of imperfection that will allow true quantum-enhanced optical metrology
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the shot noise limit and reach the Heisenberg limit. Nevertheless, many of those experiments fail to break even the classical shot-noise limit. Following a recent proposal, we present here the results of optical phase measurements with a photon-number resolving detector using coherent states of up to 4200 photons on average. An additional scheme that can be implemented using standard single-photon detectors is also presented, and the results of the two schemes are compared. These measurements present deterministic single-shot sub-wavelength super-resolution up to 288 better than the optical wavelength. The results follow the classically limited sensitivity, up to 86 times better than the wavelength.