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Journal of Optics B Quantum and Semiclassical Optics

Coherence and complementarity in a Mach-Zehnder interferometer with two DOPAs

Suc-Kyoung Hong, Chung‐In Um, Kyu-Hwang Yeon, Dukhyeon Kim

Published Sep 2, 1999• 1 citation
Publisher

Abstract

The characteristics of the quantum optical complementarity principle and the coherence of the photons generated in a Mach-Zehnder interferometer with two degenerate optical parametric amplifiers are analysed. The photon statistics and the phase fluctuation of the combined states are analysed in a homodyning Mach-Zehnder interferometer with two degenerate optical parametric amplifiers. By analysing the photon statistics, the mean-square phase fluctuation and the fringe visibility, the complementarity is considered as a function of the gain and input phase, when the amplified input is a coherent state containing one photon, on average. It is also considered when the input is a number state with one photon.

DOI
10.1088/1464-4266/1/5/313

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This paper provides a theoretical analysis of a Mach–Zehnder interferometer (MZI) enhanced by optical parametric amplifiers (OPA) placed inside its arms and fed by a coherent input source. Contrary to most cases found in literature, we perform a wider analysis by considering the MZI unbalanced and two internal phase shifts. We discuss the theoretical best-case phase sensitivity of this setup via the quantum Cramér–Rao bound (QCRB) and we consider scenarios having – or not – access to an external phase reference. We also assess the realistic performance of the OPA-enhanced MZI by employing a balanced homodyne detection (asymmetric and symmetric phase shifts) scheme and a difference-intensity detection scheme. We are thus able to find the optimum beam splitter (BS) transmissivity (transmission coefficient) of the first BS via the quantum Fisher information (QFI), while for the second one, we need to take the detection scheme into account. We are able to find these optimal values for all considered scenarios and thus assess the best-case phase sensitivity provided by this setup.
We present an extension of Glauber's theory of the Mach-Zehnder interferometer with optical amplifiers placed in each of its internal paths. Conditions are derived for the achievement of maximum fringe visibility with amplifiers of general linear characteristics. The effects of the phase-conjugated and the phase-preserved components of the amplified light are elucidated for the contrasting cases of coherent and number-state inputs. Particular attention is paid to the minimization of amplifier noise in the limit of high gain.
This paper investigates the gain characteristics of coherent optical amplifiers that amplify only one of two quadrature phase components in an input signal light according to the phase of pump light. It is constructed around a Mach-Zehnder interferometer with Kerr media. To heuristically obtain the design parameters of the coherent optical amplifier, small-signal analysis is adapted to the Mach-Zehnder interferometer with Kerr media. The theoretical results are then compared to experimental results and shown to agree well, which confirms the validity of this design approach. By utilizing low-loss and high-nonlinearity silica fiber as the Kerr medium and optimizing its length, a coherent optical amplifier is constructed that yields high-gain (up to 26 dB) operation.
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Using the phase space method, we study the quantum interference through a Mach–Zehnder interferometer with an arbitrary-photon Fock state and a coherent state as two inputs. The statistical properties, in terms of the Wigner function, average photon number, photon number distribution and parity, are derived analytically for the field of the individual output port. These results indicate that the output state is actually a statistical mixture between a bunch of Fock state and coherent states. In addition, the phase sensitivity is also examined by using the detection scheme of intensity difference measurement.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.