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arXiv:1112.0855

Two-Photon Correlation of Spontaneously Generated Broadband Four-Waves Mixing

Rafi Z. Vered, M. Rosenbluh, Avi Pe’er

Published Dec 5, 2011• 0 citations
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Abstract

We measure the time-energy correlation of broadband, spontaneously generated four wave mixing (FWM), and demonstrate novel time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband (>100nm), sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down conversion, its unique dependence on pump intensity due to self and cross phase modulation effects, yields spectral and temporal structure in the correlations. While these effects are minute compared to the time duration and bandwidth of the FWM sidebands, they are well observed using sum frequency generation as a precise, ultrafast, wide-bandwidth correlation detector.

DOI
10.48550/arxiv.1112.0855

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Summary form only given. Generation of correlated photon pairs by spontaneous parametric four-wave mixing (FWM) in photonic crystal fibres (PCF) opens the way for many applications, particularly for fibre-based quantum communication devices. In degenerate FWM, two pump photons at frequency ωρare annihilated to produce simultaneously a signal photon at ωsand an idler photon at ωi, such as ωs+ ωi= 2ωp(energy conservation). This process occurs with high efficiency only if the phase-matching condition (i.e. momentum conservation) is satisfied [1].The group-velocity dispersion (GVD) of the silica-core PCF used in our experiments (fig.1.a, inset) has been experimentally determined by a time-of-flight measurement for wavelengths from 740 nm to 930 nm. The result is consistent with the analytical calculation provided by Saitoh and Koshiba [2]. Particularly, we estimate the zero-dispersion wavelength of the PCF: λZDW = 834 nm. From this GVD measurement, we deduce the phasematching curve given in fig.1.a, on which we note that there is a vertical asymptote at λp - 832 nm. Thus, FWM should not be observed if the pump wavelength λp is lower than this limit value. Our experimental observations are very different from this prediction. Indeed, by injecting inside the fundamental mode of a 1.3-m-long PCF hyperbolic secant picosecond pulses (with an intensity-FWHM duration of about 2 ps) at λinj = 815 nm with a 80-MHz repetition rate, we actually observe a spontaneous parametric FWM phenomenon (with sidebands generated around 925 nm and 745 nm), and moreover with a clear frequency dissymmetry with respect to the injected pulse frequency (ωinj = 2ππc/λinj) (fig.1.b): generated signal and idler frequencies ωs and ωi do not satisfy ωs + ωi = 2ωinj.A systematic study of this frequency-dissymmetric phenomenon shows that it occurs only when the injected pulse peak power (Pinj) is higher than a threshold value Pth, and that Pth increases when λinj decreases from λZDW. This variation of Pth as a function of λinj can be understood by considering the key role played by self-phase modulation (SPM) in the observed phenomenon. Indeed, the frequency-dissymmetric signal and idler waves are generated only when the spectral broadening (due to SPM) of the injected pulses is sufficient to reach a threshold wavelength λth (i.e. a threshold frequency ωth) of the order of 832 nm. This value corresponds to the position of the vertical asymptote in the phase-matching curve. Finally, we observe that ωs + ωi - 2ωth when Pinj Pth. All these observations highlight the fact that, when the injected pulse peak power Pinj is high enough, spectral broadening by SPM is sufficient to get a part of the injected pulse spectrum higher than the threshold value λth, and thus this part of the spectrum can play the role of pump in an efficient FWM process (i.e. with the phasematching condition satisfied). It is important to note that this phenomenon advantageously presents an extension of the spectral range on which an efficient FWM process can occur: instead of being restricted to injected pulse wavelengths higher than the zero-dispersion wavelength λZDW of the fibre (or at least, higher than a threshold wavelength λth of the order of λZDW), experimenters can work with lower wavelengths, providing the availability of a high enough peak power and/or interaction length to sufficiently broaden (by SPM) the injected pulse spectrum.

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We measure the time-energy correlation of broadband, spontaneously generated four wave mixing (FWM), and demonstrate novel time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband (>100nm), sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down conversion, its unique dependence on pump intensity due to self and cross phase modulation effects, yields spectral and temporal structure in the correlations. While these effects are minute compared to the time duration and bandwidth of the FWM sidebands, they are well observed using sum frequency generation as a precise, ultrafast, wide-bandwidth correlation detector.
We measure the time-energy correlation of broadband, spontaneously seeded four-wave mixing (FWM), and demonstrate time-frequency coupling effects; specifically, we observe a power-dependent splitting of the correlation in both energy and time. By pumping a photonic crystal fiber with narrowband picosecond pulses we generate FWM in a unique regime, where broadband (>100>100>100 nm) sidebands are generated that are incoherent, yet time-energy correlated. Although the observed time-energy correlation in FWM is conceptually similar to parametric down-conversion, its unique dependence on pump intensity due to self- and cross-phase-modulation effects yields spectral and temporal structure in the correlations. While these effects are minute compared to the time duration and bandwidth of the FWM sidebands, they are well observed using sum-frequency generation as a precise, ultrafast, wide-bandwidth correlation detector.
We observe time-correlated four photons within a correlation window of 20ns from spontaneous four-wave mixing via a double-Lambda scheme in a cold cloud of Rb-87 atoms. In contrast to high-power pulsed pumping of chi^(2) nonlinear processes in crystals, our scheme generates correlated four-photon states by direct continuous-wave pumping at nominal powers. We verify the presence of genuinely correlated four-photon states over accidentals by higher-order intensity cross-correlation measurements and accidental subtraction. We infer a time-correlated four-photon generation rate of 2.5(4)x10^6 counts per second close to saturation. The photons produced are near-resonant with atomic transitions, and have a bandwidth in the order of MHz, making them readily compatible with quantum networking applications involving atoms.
Summary form only given. Generation of correlated photon pairs by spontaneous parametric four-wave mixing (FWM) in photonic crystal fibres (PCF) opens the way for many applications, particularly for fibre-based quantum communication devices. In degenerate FWM, two pump photons at frequency ωρare annihilated to produce simultaneously a signal photon at ωsand an idler photon at ωi, such as ωs+ ωi= 2ωp(energy conservation). This process occurs with high efficiency only if the phase-matching condition (i.e. momentum conservation) is satisfied [1].The group-velocity dispersion (GVD) of the silica-core PCF used in our experiments (fig.1.a, inset) has been experimentally determined by a time-of-flight measurement for wavelengths from 740 nm to 930 nm. The result is consistent with the analytical calculation provided by Saitoh and Koshiba [2]. Particularly, we estimate the zero-dispersion wavelength of the PCF: λZDW = 834 nm. From this GVD measurement, we deduce the phasematching curve given in fig.1.a, on which we note that there is a vertical asymptote at λp - 832 nm. Thus, FWM should not be observed if the pump wavelength λp is lower than this limit value. Our experimental observations are very different from this prediction. Indeed, by injecting inside the fundamental mode of a 1.3-m-long PCF hyperbolic secant picosecond pulses (with an intensity-FWHM duration of about 2 ps) at λinj = 815 nm with a 80-MHz repetition rate, we actually observe a spontaneous parametric FWM phenomenon (with sidebands generated around 925 nm and 745 nm), and moreover with a clear frequency dissymmetry with respect to the injected pulse frequency (ωinj = 2ππc/λinj) (fig.1.b): generated signal and idler frequencies ωs and ωi do not satisfy ωs + ωi = 2ωinj.A systematic study of this frequency-dissymmetric phenomenon shows that it occurs only when the injected pulse peak power (Pinj) is higher than a threshold value Pth, and that Pth increases when λinj decreases from λZDW. This variation of Pth as a function of λinj can be understood by considering the key role played by self-phase modulation (SPM) in the observed phenomenon. Indeed, the frequency-dissymmetric signal and idler waves are generated only when the spectral broadening (due to SPM) of the injected pulses is sufficient to reach a threshold wavelength λth (i.e. a threshold frequency ωth) of the order of 832 nm. This value corresponds to the position of the vertical asymptote in the phase-matching curve. Finally, we observe that ωs + ωi - 2ωth when Pinj Pth. All these observations highlight the fact that, when the injected pulse peak power Pinj is high enough, spectral broadening by SPM is sufficient to get a part of the injected pulse spectrum higher than the threshold value λth, and thus this part of the spectrum can play the role of pump in an efficient FWM process (i.e. with the phasematching condition satisfied). It is important to note that this phenomenon advantageously presents an extension of the spectral range on which an efficient FWM process can occur: instead of being restricted to injected pulse wavelengths higher than the zero-dispersion wavelength λZDW of the fibre (or at least, higher than a threshold wavelength λth of the order of λZDW), experimenters can work with lower wavelengths, providing the availability of a high enough peak power and/or interaction length to sufficiently broaden (by SPM) the injected pulse spectrum.
Abstract Effects of ultrafast nonlinear optics are shown to play a significant role in photon-pair generation by spontaneous four-wave mixing (FWM) of broadband photon packets in an optical fiber. When extended to this regime, the models of photon-pair generation can stay consistent with energy and photon-number conservation only when the frequency dependence of nonlinear wave coupling is included, giving rise to a shock-type waveform dynamics and a strong asymmetry in FWM sideband amplification. Resonant energy transfer from soliton transients to dispersive waves, accompanied by Cherenkov-type radiation, is shown to open a channel whereby FWM output photons are lost from entanglement generation pathways.