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Acta Physica Sinica

Research of the impact of group velocity dispersion on the second-order correlation of entangled light field

Han Xiao-chun, Jingzheng Huang, Chen Fang, Zeng Gui-Hua

Published Jan 1, 2015• 0 citations
Publisher

Abstract

In the experiment presented in the paper, HBT (Hanbury-Brown and Twiss) interferometer is used to measure the second-order correlation function (G2) for two entangled photons, denoted as signal and idle ones, generated by the spontaneous parametric down-conversion process. When an extra optical fiber is inserted in the signal's path, the arrival times of these two photons are different, so that the length of the fiber can be estimated by measuring the time offset in the G2 function.#br#As the laser light we used is not monochromatic, the experimental result is affected by the group velocity dispersion (GVD). Light of different wavelength has different velocity and leads to different travelling time in the fiber. Through calculation, we find that the G2 function of each wavelength has the same shape but different center time offset. Thus, the final G2 function, as a superimposition of the functions with different wavelengths, is broadened in a long-distance measurement, which seriously reduces the estimation accuracy. We analyze this phenomenon in both theory and experiment, and the experimental results fit our theoretical simulations quite well.#br#In the theoretical analysis, we find that the group velocity dispersion introduces an additional time offset to the final G2 function which is proportional to the total time offset. In our experiment, this additional time offset is about 1% of the total time offset. In particular, this effect results in a 63600 ps extra time offset, which can be compensated in post process, with a time accuracy of about 1 ps.#br#This paper focuses on the G2 function affected by the group velocity dispersion, and also calculates the additional time offset produced by group velocity dispersion, and thus gives a method to compensate the additional time offset through calculation.

DOI
10.7498/aps.64.070301

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In the experiment presented in the paper, HBT (Hanbury-Brown and Twiss) interferometer is used to measure the second-order correlation function (G2) for two entangled photons, denoted as signal and idle ones, generated by the spontaneous parametric down-conversion process. When an extra optical fiber is inserted in the signal's path, the arrival times of these two photons are different, so that the length of the fiber can be estimated by measuring the time offset in the G2 function.#br#As the laser light we used is not monochromatic, the experimental result is affected by the group velocity dispersion (GVD). Light of different wavelength has different velocity and leads to different travelling time in the fiber. Through calculation, we find that the G2 function of each wavelength has the same shape but different center time offset. Thus, the final G2 function, as a superimposition of the functions with different wavelengths, is broadened in a long-distance measurement, which seriously reduces the estimation accuracy. We analyze this phenomenon in both theory and experiment, and the experimental results fit our theoretical simulations quite well.#br#In the theoretical analysis, we find that the group velocity dispersion introduces an additional time offset to the final G2 function which is proportional to the total time offset. In our experiment, this additional time offset is about 1% of the total time offset. In particular, this effect results in a 63600 ps extra time offset, which can be compensated in post process, with a time accuracy of about 1 ps.#br#This paper focuses on the G2 function affected by the group velocity dispersion, and also calculates the additional time offset produced by group velocity dispersion, and thus gives a method to compensate the additional time offset through calculation.
We study the interference structure of the second-order intensity correlation function for polarization-entangled two-photon light obtained from type II collinear frequency-degenerate spontaneous parametric down conversion (SPDC). The structure is visualized due to the spreading of the two-photon amplitude as two-photon light propagates through optical fiber with group-velocity dispersion (GVD). Because of the spreading, polarization-entangled Bell states can be obtained without any birefringence compensation at the output of the nonlinear crystal. Instead, proper time selection of the intensity correlation function is required. A birefringent material inserted at the output of the nonlinear crystal (either reducing the initial e-o delay between the oppositely polarized twin photons or increasing this delay) leads to a more complicated interference structure of the correlation function.
Quantum networking, distributed quantum sensing and computing, financial markets, and position navigation and timing of satellites, require high precision clock synchronization. Existing quantum two-way time transfer protocols rely on identical wavelengths at each location. In this letter we derive and experimentally validate a heterogeneous wavelength quantum two-way time transfer protocol that eliminates the need for matched entangled-photon sources. The difference in propagation time is explicitly accounted for by incorporating the group refractive index to the calculations. Using a custom-built spontaneous parametric down-conversion photon-pair source, we separate signal and idler with wavelength division multiplexing, while maintaining strong frequency anti-correlation between signal and idler. We show that the dispersion effects on the second-order correlation function can be removed with the addition of dispersion compensation fiber. We performed quantum time transfer between two independent atomic clocks separated by a 15 km fiber spool with a time deviation of 658 fs at 0.2 s averaging time and 3.9 ps at 1 s averaging time. These results demonstrate a pathway for high precision time transfer in heterogeneous networks.
Recently the engineering of the entanglement for photon pairs generated during the spontaneous parametric down conversion process (SPDC) can be achieved via manipulation of pump wavelength behind a \c{hi}(2)-based type II SPDC process [1]. Such effect is used in this paper for demonstration of non-classical dispersion cancellation phenomenon in both local and nonlocal detections, theoretically. The following results are analytically achieved: I) For local detection, if narrow pump laser (highly entangled photons) are used, the dispersive broadening cancelation is directly depends on the degree of entanglement. The higher entanglement degree, the more compensation occurs. The results indicate that by increasing the FWHM of the pump the impact of the entanglement degree is decreased in such a way that for a pump with FWHM=4 nm the entanglement has no effect on the broadening. Therefore, the dispersive broadening is only depends on the temporal walk-off between generated photon pairs and the pump. II) For nonlocal detection, it is also shown that entanglement cancels the dispersive broadening if and only if each of the generated paired photons propagate through dispersive material with identical length with opposite group velocity sign.
A new approach to measure the second order correlation function g(2) and the coherence time was investigated. The g(2) was calculated from the photon pair time interval distribution by direct numerical self-convolution with the high order correction. The accuracy of this method was examined using an optical fiber based Hanbury-Brown-Twiss interferometer with a pseudo-thermal light source. We found that the significance of the high order correction is related to the factor Īτc, which is the overlapping of the photon wave packets. A novel technique was also demonstrated to measure the coherence time τc of a light source using the random phase modulation. This method is more suitable for a weak light source with a long coherence time using a simple experimental setup.
Summary form only given. Photon pairs entangled in different degrees of freedom are of great interest for quantum communication. In long distance fiber based communications, time-energy entanglement [1] is preferred over polarization entanglement due to its robustness against polarization mode dispersion due to the fiber propagation. On the other hand, the measurement of time-energy entanglement is more complex than that of polarization. In this work we convert the quantum correlation of time -energy entangled photons into polarization entanglement using unbalanced Michelson interferometers. Time correlated photons are generated thorough spontaneous parametric down conversion of a laser of wavelength 405nm in a second order nonlinear crystal (β-barium borate). Correlated photons carrying horizontal polarization are converted to diagonal polarization and send to a Michelson interferometer (Fig. la) with a polarizing beam splitter. In both arms of the interferometer, one quarter -wave plate oriented at 45° is kept so that the returning photons are converted from horizontal to vertical and vice -versa. The output of the interferometer yields co -polarized photons (HUI and VV) with the same relative time of arrival. The anti -correlated photons (HV and VH) exit the interferometer with different relative arrival time due to the unbalanced interferometer arms. A coincidence window less than the photon travel time for the path length difference will fi lter out the anti -correlated photons. We ensure that the coherence length of the pump laser is larger than the path length difference such that the co -polarized bi-photon state coherently adds up to the so called Bell state.
High-order photon correlations of light fields are important for characterizing the quantum nature. Since Hanbury Brown and Twiss conducted the pioneering experiments in the 1950s, the HBT effect has inspired extensive research on high-order photon correlation in quantum optics, quantum information, and quantum imaging. The Single-photon counting module is one of the most widely used single-photon detectors. Due to its high detection efficiency and low dark counts in the visible and near-infrared region, it is reasonably chosen for basic research on quantum mechanics. Many researches have demonstrated that the maximum value of second-order photon correlation g(2)(τ) at zero delay (τ = 0) can be used to distinguish different light fields. Therefore, the HBT scheme containing two single photon detectors have been widely used in many advanced studies, such as space interference, ghost imaging, single photon detection with high efficiency, etc. However, higher-order photon correlations g(n) (n > 2) can reveal more measurable characteristics of light fields, such as information about the non-Gaussian scattering process, the skewness and kurtosis of photon number distribution, etc. When the extended HBT scheme is used to measure higher-order photon correlations, the experimental conditions including quantum efficiency and background noise greatly affect the photon correlation measurement. The influences of the counting rate and resolution time of the detection system on the measurements are also very important and cannot be ignored. Therefore, the comprehensive considering of various influence factors is necessary for accurately measuring the high-order photon correlations and also a challenge. In this paper, we present a method based on double Hanbury Brown-Twiss scheme for the accurate measuring of high-order photon correlations g(n) (n > 2). The system consists of four single photon counting modules and is used to detect and analyze the joint distribution probability of temporal photon correlation. Considering the effects of the background noise and overall efficiency, theoretically, we analyze the correlations of the third- and fourth-order photon with the incident light intensity, squeezing parameter and photon number respectively for thermal state, coherent state, squeezed vacuum state, and Fock state. Meanwhile, experimentally we study the influences of resolution time and counting rate on correlations of the coherent state and thermal state with third- and fourth-order photon. On condition that the resolution time is 210 ns and the counting rate is 80 kc/s, the correlations of third and fourth-order photon with the thermal state at zero time delay are accurately measured, and the relative statistical deviations of the measured vales from the theoretical values are 0.3% and 0.8%, respectively. In addition, the third- and fourth-order photon correlations of the thermal state at different delay times are also observed. It is demonstrated that the high-order photon correlations of light fields are measured accurately by comprehensively analyzing various influencing factors. This technique provides a promising and useful tool to investigate quantum correlated imaging and quantum coherence of light fields.