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Optics Express

Complete temporal mode analysis in pulse-pumped fiber-optical parametric amplifier for continuous variable entanglement generation

Xueshi Guo, Nannan Liu, Xiaoying Li, Z. Y. Ou

Published Nov 2, 2015• 34 citations
Publisher

Abstract

Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.

DOI
10.1364/oe.23.029369

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Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.
Mode matching plays an important role in measuring the continuous variable entanglement. For the signal and idler twin beams generated by a pulse pumped fiber optical parametric amplifier (FOPA), the spatial mode matching is automatically achieved in single mode fiber, but the temporal mode property is complicated because it is highly sensitive to the dispersion and the gain of the FOPA. We study the temporal mode structure and derive the input-output relation for each temporal mode of signal and idler beams after decomposing the joint spectral function of twin beams with the singular-value decomposition method. We analyze the measurement of the quadrature-amplitude entanglement, and find mode matching between the multi-mode twin beams and the local oscillators of homodyne detection systems is crucial to achieve a high degree of entanglement. The results show that the noise contributed by the temporal modes nonorthogonal to local oscillator may be much larger than the vacuum noise, so the mode mis-match can not be accounted for by merely introducing an effective loss. Our study will be useful for developing a source of high quality continuous variable entanglement by using the FOPA.
We theoretically investigate the quantum-noise properties of a pulse-pumped high-gain-fiber optical parametric amplifiers (FOPAs) by using the Bogoliubov transformation in multiple frequency modes to describe the evolution of the nondegenerate signal and idler twin beams. The results show that the noise figure of the FOPA is generally greater than the 3 dB quantum limit unless the joint spectral function is factorable and the spectrum of the input signal well matches the gain spectrum in the signal band. However, the intensity-difference noise of the twin beams, which weakly depends on the joint spectral function, can be significantly less than the shot-noise limit when the temporal modes of the pump and the input signal are properly matched. Moreover, to closely resemble real experimental conditions, the quantum noise of twin beams generated from a broadband FOPA is numerically studied by taking the various kinds of experimental imperfections into account. Our study is not only useful for developing a compact fiber source of twin beams, but also helpful for understanding the quantum-noise limit of a pulse-pumped FOPA in the fiber communication system.
We demonstrate the experimental generation of quadrature amplitude entanglement in the 1550 nm band by using a fiber optical parametric amplifier. The measured noise variances of the difference and sum of the quadrature amplitudes of the pulsed signal and idler twin beams fall below the shot noise limit by about 1 and 0.8 dB (4.2 and 3.6 dB after the correction for efficiency), respectively, showing that the inseparability criterion of Einstein-Podolsky-Rosen entanglement I<2 is satisfied. Our investigation reveals that the quality of the measured entanglement can be further improved by increasing the transmission efficiency of the twin beams and by optimizing the temporal mode matching of the two sets of homodyne detection systems.
Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
By investigating the intensity correlation function, we study the spectral/temporal mode properties of twin beams generated by the pulse-pumped high gain spontaneous four wave mixing (SFWM) in optical fiber from both the theoretical and experimental aspects. The results show that the temporal property depends not only on the phase matching condition and the filters applied in the signal and idler fields, but also on the gain of SFWM. When the gain of SFWM is low, the spectral/temporal mode properties of the twin beams are determined by the phase matching condition and optical filtering and are usually of multi-mode nature, which leads to a value larger than 1 but distinctly smaller than 2 for the normalized intensity correlation function of individual signal/idler beam. However, when the gain of SFWM is very high, we demonstrate the normalized intensity correlation function of individual signal/idler beam approaches to 2, which is a signature of single temporal mode. This is so even if the frequencies of signal and idler fields are highly correlated so that the twin beams have multiple modes in low gain regime. We find that the reason for this behavior is the dominance of the fundamental mode over other higher order modes at high gain. Our investigation is useful for constructing high quality multi-mode squeezed and entangled states by using pulse-pumped spontaneous parametric down-conversion and SFWM.
Field-orthogonal temporal mode analysis of optical fields has recently been developed for a new framework of quantum information science. However, so far, the exact profiles of the temporal modes are not known, which makes it difficult to achieve mode selection and demultiplexing. Here, we report a novel method that measures directly the exact form of the temporal modes. This, in turn, enables us to make mode-orthogonal homodyne detection with mode-matched local oscillators. We apply the method to a pulse-pumped, specially engineered fiber parametric amplifier and demonstrate temporally multiplexed multidimensional quantum entanglement of continuous variables in telecom wavelength. The temporal mode characterization technique can be generalized to other pulse-excited systems to find their eigenmodes for multiplexing in the temporal domain.