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The European Physical Journal Applied Physics

Intensity noise measurement of strongly attenuated laser diode pulses in the time domain

Xuan Quyen Dinh, Romain Alléaume, Liantuan Xiao, François Treussart, Bernard A. Journet, Jean-François Roch

Published Jul 11, 2006• 5 citations
Publisher

Abstract

Developing the ability to characterize photon statistics of light sources has been one of the important driving forces of Quantum Optics. Photon statistics is also a crucial parameter to evaluate of quantum key distribution security. As practical quantum cryptographic systems encode information on faint laser pulses, we present a simple method to measure and calibrate their intensity noise with respect to shotnoise reference. The technique is based on the record of photodetection timetags in the photon counting regime. Two different methods are considered to produce light pulse: first, direct pulsing of a laser diode driving current, second, chopping the CW laser beam emitted by a laser diode with an acousto-optical modulator. As predicted by basic Quantum Optics theory, levels of attenuation used in practical quantum key distribution systems lead in both cases to Poissonian photon number distribution in the generated light pulses.

DOI
10.1051/epjap:2006079

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Developing the ability to characterize photon statistics of light sources has been one of the important driving forces of Quantum Optics. Photon statistics is also a crucial parameter to evaluate of quantum key distribution security. As practical quantum cryptographic systems encode information on faint laser pulses, we present a simple method to measure and calibrate their intensity noise with respect to shotnoise reference. The technique is based on the record of photodetection timetags in the photon counting regime. Two different methods are considered to produce light pulse: first, direct pulsing of a laser diode driving current, second, chopping the CW laser beam emitted by a laser diode with an acousto-optical modulator. As predicted by basic Quantum Optics theory, levels of attenuation used in practical quantum key distribution systems lead in both cases to Poissonian photon number distribution in the generated light pulses.
Faint laser pulses are practical signal sources in quantum key distribution. The photon statistics has been measured by recording every photo-counts moment and leading directly to the Mandel parameter of the photon distribution. Two different types operation of a single mode laser diode have been considered: either direct pulsing of the driving current or CW emission followed by pulse-shaping using an acousto-optic modulator. In both cases, it has been found that for practical attenuations, the photon distribution in each light pulse follows a poissonian statistics.
The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the receiver (Bob's) unit. We apply our method to three QKD systems and estimate their secure key rates.
The direct measurement of the Mandel parameter of weak laser pulses, with 10 ns pulse duration time and the mean number of photon per pulse nˉ\bar nnˉ being approximately 0.1, is investigated by recording every photocount event. With the Hanbury Brown and Twiss detection scheme, and not more than one photon per pulse being detected during the sample time by single-photon counters, we have found that the single mode diode laser with driving current lower than the threshold yields a sub-Poissonian statistics. In addition, when the diode laser driving current is much higher than the threshold, it is validated that the Mandel parameterQ C of the Poissonian coherent state is nearly −nˉ/2 - \bar n/2−nˉ/2 . The experimental results are in good agreement with theoretical prediction considering the measurement error.
Key distribution system using faint laser is very likely to become the first application exploiting the particular properties of single quanta called photons. In experimental key distribution system, it is highly demanded to use single-photon source for secure key distribution. Since there is not yet a laser source capable of producing such faint state, most experiments uses low coherent pulse laser, which is attenuated to produce a mean photon number mu. In this paper, we present an experimental setup to determine the mean photon number using a 300-ps low coherent pulse laser at 1550 nm for a practical crypto system. We will also present the effect of trigger frequency, detection efficiency and dark counts on average photon counts.
We couple noise into the driving current of a laser diode to produce correlated light. We characterize the intensity correlations of the laser with two different techniques: two-detector photon coincidence and analysis of the photocurrent from a single detector. The light exhibits bunching with a magnitude and characteristic time set by the bandwidth and the amplitude of the noise modulating the laser driving current. A simple model based on amplitude modulation of the laser intensity agrees with the measured correlation functions. The bunched light can be used to probe systems that are sensitive to intensity correlations.
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.