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arXiv:quant-ph/9912072 · Physical Review A

Nonclassical correlations of photon number and field components in the vacuum state

Holger Friedrich Hofmann, Takayoshi Kobayashi, Akira Furusawa

Published Jun 13, 2000• 9 citations
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Abstract

It is shown that the quantum jumps in the photon number $\mathrm{n\ifmmode \hat{}\else \^{}\fi{}}$ from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component $◯$ of the vacuum light field state are strongly correlated with the quadrature component measurement results. This correlation corresponds to the operator expectation value $〈◯\mathrm{n\ifmmode \hat{}\else \^{}\fi{}}◯〉$ which is equal to one-fourth for the vacuum even though the photon number eigenvalue is zero. Quantum nondemolition measurements of a quadrature component can thus provide experimental evidence of the nonclassical operator ordering dependence of the correlations between photon number and field components in the vacuum state.

DOI
10.1103/physreva.62.013806

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It is shown that the quantum jumps in the photon number n\ifmmode^\elseˆ\fi\mathrm{n\ifmmode \hat{}\else \^{}\fi{}}n\ifmmode^\elseˆ\fi from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component ◯◯◯ of the vacuum light field state are strongly correlated with the quadrature component measurement results. This correlation corresponds to the operator expectation value 〈◯n\ifmmode^\elseˆ\fi◯〉〈◯\mathrm{n\ifmmode \hat{}\else \^{}\fi{}}◯〉〈◯n\ifmmode^\elseˆ\fi◯〉 which is equal to one-fourth for the vacuum even though the photon number eigenvalue is zero. Quantum nondemolition measurements of a quadrature component can thus provide experimental evidence of the nonclassical operator ordering dependence of the correlations between photon number and field components in the vacuum state.
It is shown that the quantum jumps in the photon number https://www.w3.org/1998/Math/MathML" display="inline"> n ^ from zero to one or more photons induced by backaction evasion quantum nondemolition (QND) measurements of a quadrature component https://www.w3.org/1998/Math/MathML" display="inline"> x ^ of the vacuum light field state are strongly correlated with the quadrature component measurement results. This correlation corresponds to the operator expectation value https://www.w3.org/1998/Math/MathML" display="inline"> x ^ n ^ x ^ , which is equal to one-fourth for the vacuum even though the photon number eigenvalue is zero. QND measurements of a quadrature component can thus provide experimental evidence of the nonclassical operator ordering dependence of the correlations between photon number and field components in the vacuum state.
Finite resolution quantum nondemolition (QND) measurements allow a determination of light field properties while preserving some of the original quantum coherence of the input state. It is thus possible to measure correlations between the photon number and a quadrature component of the same light field mode. Nonclassical features emerge as photon number quantization is resolved. In particular, a strong anti-correlation of quantization and coherence is observable in QND measurements of photon number, and a correlation between measurement induced quantum jumps and quadrature component measurement results is obtained in QND measurements of quadrature fluctuations in the photon vacuum. Such nonclassical correlations represent fundamental quantum properties of the light field and may provide new insights into the nature of quantization itself.
The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime, quantization appears as a weak modulation of measurement probability. In this regime, the measurement result is strongly correlated with the amount of phase decoherence introduced by the measurement interaction. In particular, the accidental observation of half integer photon numbers preserves phase coherence in the light field, while the accidental observation of quantized values increases decoherence. The quantum mechanical nature of this correlation is discussed and the implications for the general interpretation of quantization are considered.