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.
Highlights
Continuous variable (CV) entanglement, whose quadrature-phase amplitudes possess quantum correlation, is an important non-classical light source for studying quantum effects, and a powerful resource for quantum information technologies, such as quantum metrology and quantum imaging [1,2,3,4]
When the joint spectral function (JSF) of the Fiber-optical parametric amplifiers (FOPA) is factorable, i.e., F(ωs, ωi) = φψ(ωi), and the spectra of LOs and LOi satisfy the conditions ALs(ωs) = φ and ALi(ωi) = ψ(ωi), we will obtain the maximum degree of entanglement for a given gain parameter G because r1 = 1 and rk = 0 (k = 1), which means all the energy of twin beams is concentrated in the fundamental mode
CV entanglement of the twin beams generated from a pulse-pumped FOPA by applying the singular value decomposition (SVD) to the JSF
Summary
Continuous variable (CV) entanglement, whose quadrature-phase amplitudes possess quantum correlation, is an important non-classical light source for studying quantum effects, and a powerful resource for quantum information technologies, such as quantum metrology and quantum imaging [1,2,3,4]. The major complexity involved in the pulse-pumped parametric process is the complicated frequency correlation between the signal and idler twin beams [19] This leads to mixed intermode coupling in frequency domain [22] and the mode mismatch between the pulsed local oscillator and signal/idler fields when homodyne detection is utilized for measuring the quadrature components. The rest of the paper is organized as follows: In Sec. II, after briefly reviewing our previous work [22] on the evolution of the output fields generated from a pulse-pumped FOPA, we characterize the temporal mode structure of the signal and idler fields after applying the SVD to JSF and derive the input-output relation of the FOPA in each temporal mode. Temporal mode property of the signal and idler fields generated from a pulse-pumped FOPA
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