Coherence versus interferometric resolution

Coherence is a key concept in optics derived from the statistical nature of real light beams [1–3]. Coherence is usually understood as the principal requisite for good quality interference fringes. In this work we show from a quantum metrological perspective that this is not always the case, so that optimum interference and second-order coherence may become antithetical. More specifically, we focus on interference as a practical procedure to detect and measure minute phase changes. For classical thermal-chaotic light resolution and second-order coherence are proportional both in the classical and quantum domains. This may be expected and traced back to some well-known previous results [1–3]. However, we show that increasing coherence degrades resolution for quantum field states reaching optimum precision, such as squeezed light [4–6]. Some previous works have also noticed differences between quantum and classical visibility [7]. For the sake of illustration we consider the most simple two-beam interferometric schemes, such as the Young interferometer and the 50% lossless beam splitter illustrated in Fig. 1, producing the interference of two harmonic scalar electromagnetic waves with complex amplitudes E1,2. In the quantum domain E1,2 become complex amplitude operators satisfying the commutation relations [Ej ,E † j ] = 1. Throughout we consider the spatial-frequency representation. Although the light beams examined may have large bandwidths, for definiteness we focus on a single spectral component (of random complex amplitude) selected by a suitable filtering. In Sec. II we recall the definition of coherence and resolution. These are applied then to typical classical light in Sec. III and quantum squeezed light improving resolution in Sec. IV. The results are further compared in Sec. V.