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arXiv:1711.03713

Double balanced homodyne detection

Kouji Nakamura, Masa‐Katsu Fujimoto

Published Nov 10, 2017• 3 citations
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Abstract

In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators $\hat{b}_{1}$ and $\hat{b}_{2}$ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator $\hat{b}_θ$ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.

DOI
10.48550/arxiv.1711.03713

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In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator b^θ:=cos⁡θb^1+sin⁡θb^2\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}b^θ​:=cosθb^1​+sinθb^2​ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator b^θ\hat{b}_θb^θ​ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators b^1\hat{b}_{1}b^1​ and b^2\hat{b}_{2}b^2​ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator b^θ\hat{b}_θb^θ​ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.
Motivated by the readout scheme in interferometric gravitational-wave detectors, we consider the device which measures the expectation value of the photon annihilation and creation operators for output optical field from the main interferometer. As the result, the eight-port homodyne detection is rediscovered as such a device. We evaluate the noise spectral density in this measurement. We also briefly discuss on the application of our results to the readout scheme of gravitational-wave detectors. We call this measurement scheme to measure these expectation values as "double balanced homodyne detection."
The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined, which specifies the directly measured quantum operator in the detection. This specification is necessary to apply the quantum measurement theory to gravitational-wave detections. We clarify the contribution of vacuum fluctuations to the noise spectral density without using the two-photon formulation. We found that the noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not includes those from the local oscillator which depends on the directly measured operators.
Abstract The balanced homodyne detection as a readout scheme of gravitational-wave detectors is carefully examined from the quantum field theoretical point of view. The readout scheme in gravitational-wave detectors specifies the directly measured quantum operator in the detection. This specification is necessary when we apply the recently developed quantum measurement theory to gravitational-wave detections. We examine the two models of measurement. One is the model in which the directly measured quantum operator at the photodetector is Glauber’s photon number operator, and the other is the model in which the power operator of the optical field is directly measured. These two are regarded as ideal models of photodetectors. We first show these two models yield the same expectation value of the measurement. Since there is consensus in the gravitational-wave community that vacuum fluctuations contribute to the noises in the detectors, we also clarify the contributions of vacuum fluctuations to the quantum noise spectral density without using the two-photon formulation which is used in the gravitational-wave community. We found that the conventional noise spectral density in the two-photon formulation includes vacuum fluctuations from the main interferometer but does not include those from the local oscillator. Although the contribution of vacuum fluctuations from the local oscillator theoretically yields the difference between the above two models in the noise spectral densities, this difference is negligible in realistic situations.
The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum backaction noise. Several backaction evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in tabletop quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local-oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.
The possibility of using squeezed states and balanced homodyne detection of gravitational waves is discussed. It is shown that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer. The present analysis describes photon statistics measurements effects related to quadrature balanced homodyne detection showing the advantage of using this scheme for detecting gravitational waves.
Balanced Homodyne Detection (BHD), introduced in the 1970s, enables highly sensitive detection of phase and amplitude variations in weak light. Initially developed as an advanced optical detection technique, it rapidly became essential in quantum optics for accurately quantifying quadrature components and detecting squeezed states at the shot-noise limit. Today, BHD plays a critical role in diverse fields such as high-precision quantum metrology, gigabit speed optical communications, gravitational wave detection, and large-scale quantum information systems. In this study, a BHD simulation was implemented with a 90 phase difference between the local oscillator and the signal, thus enabling the extraction of the phase quadratureP^component of the optical field.