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arXiv:0903.1415 · Physical Review A

Quantum state measurements using multipixel photon detectors

I. Afek, Adi Natan, O. Ambar, Yaron R. Silberberg

Published Apr 28, 2009• 92 citations
arXivHTMLPDF

Abstract

The characterization and conditional preparation of multiphoton quantum states require the use of photon-number resolving detectors. We study the use of detectors based on multiple avalanche photodiode pixels in this context. We develop a general model that provides the positive operator value measures for these detectors. The model incorporates the effect of cross talk between pixels which is unique to these devices. We validate the model by measuring coherent-state photon-number distributions and reconstructing them with high precision. Finally, we evaluate the suitability of such detectors for quantum state tomography and entanglement-based quantum state preparation, highlighting the effects of dark counts and cross talk between pixels.

DOI
10.1103/physreva.79.043830

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The characterization and conditional preparation of multiphoton quantum states require the use of photon-number resolving detectors. We study the use of detectors based on multiple avalanche photodiode pixels in this context. We develop a general model that provides the positive operator value measures for these detectors. The model incorporates the effect of cross talk between pixels which is unique to these devices. We validate the model by measuring coherent-state photon-number distributions and reconstructing them with high precision. Finally, we evaluate the suitability of such detectors for quantum state tomography and entanglement-based quantum state preparation, highlighting the effects of dark counts and cross talk between pixels.
In this paper, we reconstructed the positive operator-valued measure (POVM) of a photon-number-resolving detector (PNRD) based on a multi-pixel photon counter (MPPC) by means of quantum detector tomography (QDT) at 791 nm and 523 nm, respectively. MPPC is a kind of spatial-multiplexing PNRD with a silicon avalanche photodiode (Si-APD) array as the photon receiver. Experimentally, the quantum characteristics of MPPC were calibrated at 2 MHz at two different wavelengths. The POVM elements were given by QDT. The fidelity of the reconstructed POVM elements is higher than 99.96%, which testifies that the QDT is reliable to calibrate MPPC at different wavelengths. With QDT and associated Wigner functions, the quantum properties of MPPC can be calibrated more directly and accurately in contrast with those conventional methods of modeling detectors.
We present the characterization of a multi-pixel detector (SiPM, Hamamatsu) in the presence of dark-count and cross-talk effects. Our description yields a self-consistent calibration of the device, based on the light under investigation, which is used to evaluate shot-by-shot detected-photon numbers including dark-counts and cross-talk. The analysis allows us to reliably reconstruct the detected-photons statistics of different light states by taking into account the modifications introduced by detector features. Finally we quantify photon-number correlations in bipartite states and use the data to produce conditional states: only if dark-count and cross-talk effects can be neglected, the experimental results match theory.
Development of reliable photon-number-resolving detectors (PNRDs), devices that are capable of distinguishing 1,2,3… photons, is of a great importance for quantum optics and its applications. A new class of affordable PNRD is based on multipixel photon counters (MPPCs). Here we review results of experiments on using MPPCs for direct characterization of squeezed vacuum (SV) states, generated via parametric downconversion. We use MPPCs to measure the second-order normalized intensity correlation function (g(2)) and directly detect the two-mode squeezing of SV states. We also present a method of calibration of crosstalk probability in MPPCs based on g(2) measurements of coherent states.
A longstanding goal in quantum optics has been to realize a photon-number-resolving detector that efficiently counts the number of photons in an optical field. This goal has been largely met with the development of transition edge sensors which can count up to roughly 20 photons with efficiencies over 95%. This thesis presents three experiments that employ these detectors to characterize and prepare quantum states of light. Firstly, we develop a weak-field homodyne detector. By replacing the photodiodes conventionally used in homodyne detection with transition edge sensors, we experimentally implement a versatile measurement device that can tune between photon counting and quadrature measurements. We study the transition between these complementary measurement regimes and determine the minimum local oscillator strength needed to perform quadrature measurements. Secondly, we use the weak-field homodyne detector as a quantum state engineering tool. We propose a scheme to prepare a wide range of definite parity states, including two- and four-component Schrödinger cat states of arbitrary size with nearly perfect fidelity. Thirdly, we perform optical interferometry using quantum states of light with the aim of surpassing the maximal precision achievable with classical light, i.e. the shot-noise limit. We propose and experimentally implement a scheme that uses high-gain squeezed vacuum sources and transition edge sensors to prepare loss-tolerant entangled states containing up to 8 photons. While our achieved precision does not unconditionally (i.e. without post-selecting on certain measurement trials) surpass the shot-noise limit, our results do demonstrate the robustness of these entangled states to loss despite their size.
Photon-number-resolving detectors with hundreds of pixels are now readily available, while the characterization of these detectors using detector tomography is computationally intensive. Here, we present a modified detector tomography model that reduces the number of variables that need optimization. To evaluate the effectiveness and accuracy of our model, we reconstruct the photon number distribution of optical coherent and thermal states using the expectation-maximization-entropy algorithm. Our results indicate that the fidelity of the reconstructed states remains above 99%, and the second- and third-order correlations agree well with the theoretical values for a mean number of photons up to 100. We also investigate the computational resources required for detector tomography and find out that our approach reduces the solving time by around half compared to the standard detector tomography approach, and the required memory resources are the main obstacle for detector tomography of a large number of pixels. Our results suggest that detector tomography is viable on a supercomputer with 1 TB RAM for detectors with up to 340 pixels.
We propose a design for a photon-counting detector that is capable of resolving multiphoton events. The basic element of the setup is a fiber loop, which traps the input field with the help of a fast electro-optic switch. A single weakly coupled avalanche photodiode is used to detect small portions of the signal field extracted from the loop. We analyze the response of the loop detector to an arbitrary input field and discuss both the reconstruction of the photon-number distribution of an unknown field from the count statistics measured in the setup and the application of the detector in conditional-state preparation.