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arXiv:1012.2794 · Physical Review A

Balancing efficiencies by squeezing in realistic eight-port homodyne detection

Juha-Pekka Pellonpää, Jussi Schultz, Matteo G. A. Paris

Published Apr 15, 2011• 9 citations
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Abstract

We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementation with current technology.

DOI
10.1103/physreva.83.043818

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We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementation with current technology.
We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.
The eight-port homodyne detection apparatus is analyzed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.
The eight-port homodyne detection apparatus is analysed in the framework of the operational theory of quantum measurement. For an arbitrary quantum noise leaking through the unused port of the beam splitter, the positive operator valued measure and the corresponding operational homodyne observables are derived. It is shown that such an eight-port homodyne device can be used to construct the operational quantum trigonometry of an optical field. The quantum trigonometry and the corresponding phase space Wigner functions are derived for a signal field probed by a classical local oscillator and a squeezed vacuum in the unused port.
Squeezed states belong to the most prominent non-classical resources. They have compelling applications in precise measurement, quantum computation, and detection. Here, we report on the direct measurement of 13.8 dB squeezed vacuum states by improving the interference efficiency and gain of balanced homodyne detection. By employing an auxiliary laser beam, the homodyne visibility is increased to 99.8%. The equivalent loss of the electronic noise is reduced to 0.05% by integrating a junction field-effect transistor (JFET) buffering input and another JFET bootstrap structure in the balanced homodyne detector.
Following a recent theoretical proposal [J. Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004)], we experimentally implement a scheme to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. The suggested setup is based on only a tunable beam splitter and a direct single-photon detector to fully characterize the generated Gaussian states. We discuss the experimental implementation of this procedure and compare it to other reference methods. A detailed exploitation of our results highlights some practical limitations of this method. This experimental work is followed by a detailed numerical analysis to derive the conditions required for the procedure to succeed. In particular, it is found that an overall single-photon detection efficiency of about 50% is needed, which is difficult to achieve in the present experiment.
Squeezed light is a non-classical state of light in which the uncertainty in the electricfield strength at certain phases of oscillation is reduced below the vacuum noise level,at the cost of increased uncertainty at other phases. It has applications ranging fromgravitational wave detection to quantum communication, where the bandwidth of thesqueezed states directly limits protocol speed. Squeezed light is commonly measured us-ing balanced homodyne detection, in which the attainable squeezing level is restrictedby the photodetector’s quantum efficiency and dark noise. Currently, no commerciallyavailable photodetector combines high quantum efficiency with low dark noise over alarge bandwidth. This thesis presents the design and construction of a photodetectorintended to address this gap, with the aim of achieving high quantum efficiency and suf-ficient dark noise clearance over at least 1 GHz of bandwidth. The design was guidedby LTspice simulations and implemented on a two-layer printed circuit board. Twocommercially available reference detectors were characterised, illustrating the trade-offbetween high quantum efficiency and large bandwidth. Since the photodiodes for thenew detector had not arrived at the time of completion, its characterisation remains tobe carried out.