Abstract

Quantum-mechanical operators of phase difference between two electromagnetic fields are proposed and their properties are analyzed. The Hermitian phase-difference operators are determined using the operators of interference of the two fields, which appears upon their mixing on a beam splitter. The results of calculations for the measured mean values and dispersions (fluctuations) of the trigonometric functions of the phase-difference operators, which follow from the Pegg–Barnett theory, are compared with the corresponding values for the proposed operators. Calculations and comparison are carried out for the Fock, coherent, and squeezed quantum states of electromagnetic fields. Analysis is performed for quantum microscopic fields with mean values \(\hat {n}\) ~ 1 of the number of photons, which are currently used in quantum technologies. The quantitative agreement between two different theories is demonstrated for the Fock and squeezed states of the fields; in the case of coherent states, an appreciable quantitative difference in the predictions of the theories is observed.

中文翻译：

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量子电磁场的三角相差算符

摘要

提出了两个电磁场之间相位差的量子力学算子，并对其性质进行了分析。埃尔米特相位差算子是使用两个场的干扰算子确定的，这两个算子在分束器上混合时出现。根据Pegg–Barnett理论，将相差算子的三角函数的实测平均值和色散（涨落）的计算结果与所建议算子的相应值进行比较。对电磁场的福克，相干和压缩量子态进行了计算和比较。对平均值为\（\ hat {n} \）的量子微观场进行分析当前在量子技术中使用的光子数量的〜1。两种不同理论之间的定量一致性被证明是针对Fock和场的压缩状态的。在相干态的情况下，在理论预测中观察到明显的数量差异。