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arXiv:1410.8012 · Europhysics Letters (EPL)

Balanced homodyne detection with on-off detector systems: Observable nonclassicality criteria

Jan Sperling, W. Vogel, G. S. Agarwal

Published Feb 1, 2015• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/0295-5075/109/34001

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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.
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.
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.
We address the problem of measuring nonclassicality in continuous-variable bosonic systems without having access to a known reference signal. To this end, we construct broader classes of criteria for nonclassicality which allow us to investigate quantum phenomena regardless of the quantumness of selected subsystems. Such witnesses are based on the notion of partial normal ordering. This approach is applied to balanced homodyne detection using arbitrary, potentially nonclassical local oscillator states, yet only revealing the probed signal's quantumness. Our framework is compared to standard techniques, and the robustness and advanced sensitivity of our approach is shown. Therefore, a widely applicable framework, well-suited for applications in quantum metrology and quantum information, is derived to assess the quantum features of a photonic system when a well-defined coherent laser as a reference state is not available in the physical domain under study.
We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
We address the problem of constructing witnesses for nonclassical light that are applicable in state-of-the-art photon-counting devices. The key ingredient for the criteria we derive are generalized and directly measurable counting statistics and matrices of counting moments. Beyond common criteria, we find classes of witnesses that are based on half-integer powers of click moments and counts. Remarkably, this leads to an exponential increase of the number of nonclassicality criteria one can construct and apply. With this finding, special attention is payed to probing even and odd parity states, requiring such distinct witnesses. Our method is applicable to spatial and time-bin multiplexing in optical systems, where each spatial and temporal mode can be measured with both on-off detectors and detectors with partial internal quasi-photon-number resolution. Generalizations to multimode scenarios are provided, allowing for the direct measurement of nonclassical correlations and coincidence counts between an arbitrary number of modes.
In this work we generalize the Bochner criterion addressing the characteristic function, i.e., the Fourier transform, of the Glauber-Sudarshan phase-space function. For this purpose we extend the Bochner theorem by including derivatives of the characteristic function. The resulting necessary and sufficient nonclassicality criteria unify previously known moment-based criteria with those based on the characteristic function. For applications of the generalized nonclassicality probes, we provide direct sampling formulas for balanced homodyne detection. A squeezed vacuum state is experimentally realized and characterized with our method. This complete framework---theoretical unification, sampling approach, and experimental implementation---presents an efficient toolbox to characterize quantum states of light for applications in quantum technology.