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arXiv:1508.03142 · Physical Review A

Homodyne detection with on-off detector systems

Tobias Lipfert, Jan Sperling, W. Vogel

Published Nov 16, 2015• 19 citations
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Abstract

Phase-sensitive properties of light play a crucial role in a variety of quantum optical phenomena, which have been mostly discussed in the framework of photoelectric detection theory. However, modern detection schemes, such as arrays of on-off detectors, are not based on photoelectric counting. We demonstrate that the theory of homodyning with such click-counting detectors can be established by using a proper detection model. For practical applications, a variety of typically occurring imperfections are rigorously analyzed and directly observable nonclassicality criteria are studied. Fundamental examples demonstrate the general functionality of our technique. Thus, our approach of homodyne detection with on-off detector systems is able to bridge the gap between imperfect detection and the phase resolution demands for modern applications of quantum light.

DOI
10.1103/physreva.92.053835

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Phase-sensitive properties of light play a crucial role in a variety of quantum optical phenomena, which have been mostly discussed in the framework of photoelectric detection theory. However, modern detection schemes, such as arrays of on-off detectors, are not based on photoelectric counting. We demonstrate that the theory of homodyning with such click-counting detectors can be established by using a proper detection model. For practical applications, a variety of typically occurring imperfections are rigorously analyzed and directly observable nonclassicality criteria are studied. Fundamental examples demonstrate the general functionality of our technique. Thus, our approach of homodyne detection with on-off detector systems is able to bridge the gap between imperfect detection and the phase resolution demands for modern applications of quantum light.
Driven by single photon detection requirements, the theory of arrays of off-on detectors has been developed and applied. However, for a comprehensive characterization of nonclassicality, one also needs phase sensitive properties. This missing link is introduced with the derived theory of phase sensitive click counting measurements. It unifies the balanced homodyne detection for high intensities with the click detection in the few-photon regime. We formulate a hierarchy of nonlinear squeezing conditions to probe quantum effects beyond standard squeezing. Imperfections stemming from fluctuations, detector efficiency, and dark count rates are considered. Experimentally accessible sampling formulas are given. Our theory paves the way towards novel applications of light in quantum metrology.
Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click-counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, a small number of on-off diodes can yield more insight than perfect photon number resolution. Quantum signatures in the particle and wave domain of the quantized radiation field, as shown by photon number and squeezed states, respectively, will be uncovered in terms of negativities of the sampled phase-space functions. Application in the vast fields of quantum optics and quantum technology will benefit from our efficient nonclassicality characterization approach.
Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g., to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator, typically in a coherent state. Such a strong coherent local oscillator may not be readily available, particularly for a massive quantum system like a Bose-Einstein condensate, posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of nonideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond a Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators.
The efficient certification of nonclassical effects of light forms the basis for applications in optical quantum technologies. We derive general correlation conditions for the verification of nonclassical light based on multiplexed detection. The obtained nonclassicality criteria are valid for imperfectly balanced multiplexing scenarios with on-off detectors and do not require any knowledge about the detector system. In this sense, they are fully independent of the detector system. In our experiment, we study light emitted by clusters of single-photon emitters, whose photon number may exceed the number of detection channels. Even under such conditions, our criteria certify nonclassicality with high statistical significance.
The study on photon counting statistics is of fundamental importance in quantum optics. We theoretically analyzed the imperfect detection of an arbitrary quantum state. We derived photon counting formulae for six typical quantum states (i.e., Fock, coherent, squeeze-vacuum, thermal, odd and even coherent states) with finite quantum efficiencies and dark counts based on multiple on/off detector arrays. We applied the formulae to the simulation of multiphoton number detections and obtained both the simulated and ideal photon number distributions of each state. A comparison between the results by using the fidelity and relative entropy was carried out to evaluate the detection scheme and help select detectors for different quantum states.
The measurement of quantum states of light is fundamental for the investigations of Quantum Optics and for the applications of Quantum Information. Here we present the implementation of a novel detection apparatus, that is a homodyne-like detection scheme based on photon-number-resolving detectors. Thanks to its hybrid nature, the apparatus is useful to investigate both the particle-like and wave-like properties of light. We tested the scheme in the measurement of the quadratures of different optical states, namely coherent states and mixtures of coherent states. In particular, we investigate the performance of our scheme compared to that of a standard homodyne detector.