Optimal Mach-Zehnder phase sensitivity with Gaussian states

Abstract

We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared in respect with the quantum Cramér-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any apriori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fisher information has the consequence of imposing the input phase-matching conditions. We discuss in detail when each scenario yields an optimal performance. Realistic detection scenarios are also considered and their performance compared to the theoretical optimum. The impact of the beam splitter types employed on the optimum phase-matching conditions is also discussed. We find a number of potentially interesting advantages of these states over the coherent plus squeezed vacuum input case.

Single- versus two-parameter Fisher information in quantum interferometry

“…yielding in the balanced case the well-known shot-noise limit ∆ϕ [24,31,37]. This limit has been shown to be achieved with difference-intensity [24,33,37] single-mode intensity [33,37] as well as balanced homodyne detection schemes [36,37].…”

“…where ℑ denotes the imaginary part [36]. Throughout this work we assume that the input port 1 is never in the vacuum state, i. e. n 1 = 0.…”

“…One reason that the single parameter QFI might be considered over-optimistic or artificial is that usual detection schemes cannot go beyond the QCRB given by a two-parameter QFI approach [31,33,37]. Even the balanced homodyne detection, although having access to an external phase reference, cannot exceed this limit if the interferometer is balanced [36,37].…”

“…Among them we can cite the coherent plus squeezed vacuum input state [18,41,42], a popular choice also due to its use in gravitational wave detection [3][4][5][6][7]. The squeezed coherent plus squeezed vacuum input state [43] has been shown to bring a gain in phase sensitivity due to the second squeezer [34,36]. This gain, however, becomes marginal in the experimentally interesting scenario of high input coherent power and limited squeezing factors.…”

“…In this work we focus on two detection schemes. The difference-intensity detection scheme is often considered in the literature [24,33,34,36,37] and it is a good example of a detection method not having access to an external phase reference. We thus expect its performance to be limited by the two-parameter QFI.…”