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Journal of the Optical Society of America B

Quantum self-homodyne tomography with an empty cavity

Jing Zhang, Tiancai Zhang, Kuanshou Zhang, Changde Xie, Kunchi Peng

Published Nov 1, 2000• 13 citations
Publisher

Abstract

We develop a scheme to reconstruct the optical quantum state of a single-mode bright light field by using the dispersion characteristics of the empty cavity. The input field has a strong coherent component at frequency ω0, which serves as a local oscillator (LO) to measure its two-sideband mode at ω0±Ω. We control the relative phase of the 0–2π range between the LO and the two-sideband mode by scanning the cavity length, so the optical quantum state is tomographically reconstructed. In the proposed scheme the influence of the space-mode mismatch between the LO and measured mode on the quantum efficiency is eliminated, and this scheme can conveniently be used in some quantum optical systems in which LO field cannot be available.

DOI
10.1364/josab.17.001920

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We develop a scheme to reconstruct the optical quantum state of a single-mode bright light field by using the dispersion characteristics of the empty cavity. The input field has a strong coherent component at frequency ω0, which serves as a local oscillator (LO) to measure its two-sideband mode at ω0±Ω. We control the relative phase of the 0–2π range between the LO and the two-sideband mode by scanning the cavity length, so the optical quantum state is tomographically reconstructed. In the proposed scheme the influence of the space-mode mismatch between the LO and measured mode on the quantum efficiency is eliminated, and this scheme can conveniently be used in some quantum optical systems in which LO field cannot be available.
Considerable interest is growing around self-homodyne techniques. Such techniques allow one to avoid non-unitary detection efficiencies due to inefficient mode matching of the local oscillator. Galatola et al (1991 Opt. Commun. 85 95) proposed one possible scheme of self-homodyne detection of a field with a strong coherent component involving the use of a Fabry-Perot cavity with a perfectly reflecting mirror. We extend the theory to arbitrary cavities, and we observe a remarkable agreement between the theory and the observed data. Using the same setup we performed a tomographic measure of the Wigner function of the field emitted by a laser diode.
The quantum noise in photocurrent fluctuations usually gives incomplete information about the quantum state of spectral sideband modes of bright light beams involved in the detection. Each frequency component of the noise spectrum corresponds to two sideband modes symmetrically located around the bright optical field. In the case of the usual homodyne detection, it limits the ability to recover discriminated information of each mode involved. We theoretically show that complete reconstruction of the two-mode quantum state can be obtained by using phase-locked (coherent) resonator detection, even for non-Gaussian states. We experimentally demonstrate the technique by measuring a two-mode displaced coherent state.
Summary form only given. Considerable interest is growing around self homodyne techniques. Such techniques allow to avoid nonunitary detection efficiencies due to inefficient mode matching of the local oscillator. As proposed by Galatola et al. [1991], one possible scheme of self homodyne detection of a field with a strong coherent component involves the use of a Fabry-Perot cavity with a high reflecting rear mirror. Using this setup we are able to perform a tomographic measure of the Wigner function of the field emitted by a laser diode.
We introduce a method for quantum-state tomography for a pair of optical modes, which we call generalized rotations in phase space. Rather than using a dual-mode local oscillator field for implementing balanced-homodyne detection, as in previous methods, a single-mode local oscillator field can be used in our method, greatly simplifying certain aspects of experiments. The signal field is put through a series of general transformations before entering the detection system where quantum statistics are measured.
A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local oscillator and the signal modes, which is the main limitation to the overall quantum efficiency in conventional homodyning. The feasibility of the measurement is analyzed on the basis of Monte Carlo simulations, studying the effect of nonunit quantum efficiency on detection of the correlation and the total photon-number oscillations of the twin-beam state.