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Quantum Characterization of Single Photon Detectors

M. G. Mingolla

Published Jan 1, 2014• 0 citations
Publisher

Abstract

The research activities described in this thesis have basically an experimental profile, and were realized in the Quantum Optics Laboratories of the Optic Division in the Istituto Nazionale di Ricerca Metrologica (I.N.Ri.M.). The experiments presented here are oriented to the characterization of single- and few-photon detectors calibration, exploiting quantum properties. The first chapter has an introductory character, oriented to the study of nonlinear optics phenomena and focused in the spontaneous parametric down conversion (PDC) process. After the quantization of the free electromagnetic field, we recall the quantum theory of PDC. In the second chapter the Klyshko's two-photon calibration technique is presented and applied to an Avalanche Photo Diode (APD) based single photon counting module. Chapter three is an introduction to quantum measurements and quantum operation theories where the concept of positive-operator valued measurement (POVM) is presented. In chapter four, the quantum characterization of a true photon-number resolving detector (PNRD) based on a transition edge sensor (TES) is presented. In this experiment, the POVM of the TES is reconstructed by realizing a tomography of the detection process's quantum operation, using as a probe a set of known coherent states. In the fifth and last chapter, the POVM of a tree type PNRD is reconstructed exploiting strong quantum correlations of PDC twin beams

DOI
10.6092/polito/porto/2531888

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The research activities described in this thesis have basically an experimental profile, and were realized in the Quantum Optics Laboratories of the Optic Division in the Istituto Nazionale di Ricerca Metrologica (I.N.Ri.M.). The experiments presented here are oriented to the characterization of single- and few-photon detectors calibration, exploiting quantum properties. The first chapter has an introductory character, oriented to the study of nonlinear optics phenomena and focused in the spontaneous parametric down conversion (PDC) process. After the quantization of the free electromagnetic field, we recall the quantum theory of PDC. In the second chapter the Klyshko's two-photon calibration technique is presented and applied to an Avalanche Photo Diode (APD) based single photon counting module. Chapter three is an introduction to quantum measurements and quantum operation theories where the concept of positive-operator valued measurement (POVM) is presented. In chapter four, the quantum characterization of a true photon-number resolving detector (PNRD) based on a transition edge sensor (TES) is presented. In this experiment, the POVM of the TES is reconstructed by realizing a tomography of the detection process's quantum operation, using as a probe a set of known coherent states. In the fifth and last chapter, the POVM of a tree type PNRD is reconstructed exploiting strong quantum correlations of PDC twin beams
Quantum optics is central to emerging quantum technologies such as quantum metrology and quantum information. The continuous variable (CV) approach to encoding information in a physical system, for example the electromagnetic field quadratures has significant advantages over discrete variables (DV) encoding. CV offers higher density encoding in a single optical state and on-demand state preparation for example. However, techniques for CV preparation, manipulation and measurement are not as well developed as the corresponding DV approach. In this thesis we present methods to characterize quantum detectors that operate in the CV regime, and discuss their application to CV state preparation. A quantum detector is described by its positive operator valued measure (POVM) set, with one operator for each measurement outcome. We present an experimental scheme for detector tomography, that is reconstruction of the POVM set of an unknown detector by means of measurement outcomes for a set of tomographically complete input states. We use this scheme to experimentally determine the POVM set of an avalanche photodiode (APD) and a time-multiplexed-detector (TMD) and compare the results to models of the detectors. We introduce a weak-homodyne photon-number-resolving detector (PNRD) , which uses a weak local oscillator beam to set a phase reference for the detection process. We develop a theoretical description of the sensitivity regimes for this detector using the Wigner phase space picture. We also present experimental detector tomography for a weak-homodyne detector based on two APDs. In many cases it is sufficient to calibrate the efficiencies of previously characterized PNRDs. We experimentally demonstrate a scheme using correlated photons produced by spontaneous parametric downconversion (SPDC) to determine the efficiencies of PNRDs, based on the photon number statistics of the source. The same SPDC source is also used to demonstrate preparation of photonic states in the photon number basis and for a first proof-of-principle experiment with a weak-homodyne PNRD based on a TMD.
In this work we discuss topics such as the theory of photon detectors, showing its operation mode, characteristics and types. In addition, we also study the quantum detection theory, how photons interact with the detector's atoms, and how the process of single and coincidences counting mode works. We look into the theory of parametric down conversion in order to create a correlated photon source and a single photon source. We also discuss about ghost imaging theory and experiments, since it shows us in a very clear way a direct appplication for a single photons camera. I present the results obtained so far with the camera we have in our laboratory. We detected the photon's cones generated by the parametric down conversion type I and type II. We recorded interference patterns, multiple slit images, and amplitude masks images with few photons. We used the CCD for photon counting in an experiment where an image of an object is obtained through photons that have not interacted with the object, but is part of one of the beams in the stimulated parametric down conversion. One of the great motivators of working with a camera is performing quantum optics experiments where spatial patterns are detected. In this aspect a camera has a greater robustness than single photon APD since it allows us to observe the whole transverse profile of a beam simultaneously, something that is possible only with a set of detectors APDs.
Characterization of quantum states and detectors is a key task in rapidly emerging optical quantum science and technology. First, we introduce and experimentally demonstrate a noise-robust quantum state characterization protocol using photon-number-resolving (PNR) measurements. Unlike conventional continuous variable state tomography methods, our method utilizes computationally efficient semi-definite programming (SDP) and can be used to accurately reconstruct the state even after loss a known loss. The protocol is demonstrated for a weak coherent state as well as a single-photon Fock state. Next, we propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector’s Positive-Operator-Value-Measure (POVM) elements via weak-field homodyne technique. We also report our experimental progress on characterizing a superconducting transition-edge sensor for PNR measurements.
Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.
Ultrafast quantum light pulses with durations of 1ps and below show great promise as information carriers in quantum communication and computation. In future they may also be used to probe physical processes at ultrashort timescales with a resolution beyond the limits of Heisenberg uncertainty. This thesis focuses on the creation and manipulation of quantum light pulses with second order nonlinear optical processes in optical waveguides. In chapter 1. Introduction, we lead the reader towards this work's topic by giving a brief qualitative overview over the EPR paradox, quantum entanglement, three-wave-mixing and quantum light pulses. Chapter 2. Basic concepts familiarizes the reader with the physical concepts and mathematical tools underlying this thesis. In chapter 3. Spectral engineering, we discuss the requirements to produce separable photon pair states with group velocity matching and examine several nonlinear materials widely used for optical waveguide inscription for their suitability to group velocity matching in the telecom wavelength regime. In chapter 4. A PP-KTP waveguide as parametric downconversion source, we give the basic spontaneous parametric downconversion source setup, as well as some initial measurements to characterize the single photon detectors, to demonstrate the production of correlated photons, and to determine the phasematching properties of the PP-KTP source. In the following chapter, 5. Fiber spectrometer, we present the single-photon fiber spectrometer. We discuss the experimental setup and calibration of the device, and measure the joint spectrum of photon pairs from our PP-KTP source. Finally, we investigate the behavior of a joint spectrum measurement of a high mean photon number source with binary detectors. In 6. Two-mode squeezed vacuum source, we characterize spectral correlations of an ultrafast SPDC source with the second order correlation function g². We present the g² measurement results and show that we can control the spectral correlations to produce a two-mode squeezed vacuum state of light. We then determine the mean photon number and gain of the source. 7. Quantum pulse gate: While the previous chapters focus on the creation and characterization of ultrafast quantum pulses of light, we now propose a way to manipulate the mode structure of a given quantum light state. We discuss the concept of an active optical filter sensitive to spectral/temporal pulse shape: The quantum pulse gate. In the final chapter 8. Conclusion and outlook, we recapitulate the main results of this thesis and provide a few pointers towards possibilities for future research building on it.