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Journal of the Optical Society of America B

Amplification of a polarized single-photon state and determination of resulting polarization correlations

Thomas H. Chyba, N. B. Abraham

Published Feb 1, 1985• 4 citations

Abstract

The photon statistics of a single spatial mode of the optical field (including the two polarization states) resulting from a single-photon state undergoing unsaturated amplification by a two-level medium are derived. Results are compared with those for an idealized noiseless linear amplifier and a conventional quantum-noise-limited amplifier in the limit of no gain. When the amplified field is divided for detection of different polarization states, distinctive polarization biases and correlations are evident on average when the polarization of the input state is constant. However, the results are insufficient to determine the initial polarization state based on a single measurement. If one must average over two orthogonally polarized input states (e.g., an incoherent mixture of either linearly or circularly polarized initial states) as required in the absence of hidden variable information in an Einstein–Podolsky-Rosen experiment, the distinctions are completely erased.

DOI: 10.1364/josab.2.000377

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Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single photon polarization is possible when the gain factor of the amplification is equal to the inverse squareroot of 1-R.

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In an ideal linear amplifier, the output signal is linearly related to the input signal with an additive noise that is independent of the input. The decoherence of a quantum-mechanical state as a result of optical amplification is usually assumed to be due to the addition of quantum noise. Here we show that entanglement between the input signal and the amplifying medium can produce an exponentially-large amount of decoherence in an ideal optical amplifier even when the gain is arbitrarily close to unity and the added noise is negligible. These effects occur for macroscopic superposition states, where even a small amount of gain can leave a significant amount of which-path information in the environment. Our results show that the usual input/output relation of a linear amplifier does not provide a complete description of the output state when post-selection is used.