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Journal of Optics B Quantum and Semiclassical Optics

An eight-port detector with a local oscillator of finite intensity

A. Cives-esclop, Alfredo Luis, Luis Lorenzo Sánchez-Soto

Published Jul 31, 2000• 3 citations
Publisher

Abstract

We present a quantum analysis of the action of an eight-port detector with a local oscillator of finite intensity. Resorting to the formalism of generalized measurements, we derive a family of states that determines the statistics of the measurement for any input state. We also give a general expression for this family in the Fock basis and discuss some interesting limiting cases.

DOI
10.1088/1464-4266/2/4/311

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We present a quantum analysis of the action of an eight-port detector with a local oscillator of finite intensity. Resorting to the formalism of generalized measurements, we derive a family of states that determines the statistics of the measurement for any input state. We also give a general expression for this family in the Fock basis and discuss some interesting limiting cases.
It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically. Using recent rigorous results on the quantum theory of homodyne detection observables, we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.
The balanced homodyne detector is the paradigm of phase-sensitive detection schemes in quantum optics. We study the effects of a quantum local oscillator in a coherent state for this detector when it is coupled to a single signal mode. We calculate explicit general expressions for the output statistics of the difference current of this detector (applicable even to non-classical states), and compare them to the statistics of the so-called quadrature-phase amplitude. We show that the naive condition that the number of quanta in the local oscillator be much larger than the number in the signal is not sufficient to ensure that the homodyne detector approximates an ideal detectorof the quadrature-phase amplitude, further, we derive explicit conditions for this approximation to be achieved when the signal is a coherent state or a superposition of coherent states.
Abstract Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible value of the observable. The study of this setup in the frame of von Neumann’s quantum mechanical measurement process has a remarkable result: already after the interaction of the measured system with the detector array without collapse, exactly one detector is indicating a detection. Each single detector indicates either 0 or 1 detection, and no superposition can be attributed to it.