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We experimentally demonstrate generation of a squeezed vacuum at 800 nm with a Sagnac loop fiber interferometer. When negative dispersion is properly added to an input laser pulse to compensate for the fiber dispersion, the level of squeezing is improved. A squeezed vacuum of 0.45dB is obtained at a dispersion of -0.0157 ps2 for the 1.5 m-long fiber loop. Since the squeezed vacuum is degraded by guided acoustic-wave Brillouin scattering (GAWBS), the noise level of the squeezing is improved by -0.3dB at a liquid nitrogen temperature. We also demonstrate generation of photon number squeezing at -1.3 dB.
©2009 Optical Society of America
1. Introduction
Experiments in quantum optics utilizing coherent light have been playing an important role in development of quantum information processing as well as those with single photon sources. So far, deterministic quantum teleportation has been demonstrated only with entangled light generated from a couple of squeezed vacuum beams [1]. Squeezed vacuum light is generated from optical parametric oscillators. Squeezing levels of >-4.8 dB may enable us to establish a quantum teleportation protocol of a squeezed state [2]. Third-order optical nonlinearity of optical fibers can also generate squeezed pulses. Squeezed vacuum pulses [3–5] and polarization squeezing [6] have been generated using Sagnac fiber interferometry at a wavelength of 1.5 µm, at which soliton pulse propagation at the anomalous dispersion wavelengths maintains high optical intensity throughout the propagation in a fiber and results in higher squeezing levels. Quantum information processing using fiber optics and teleportation via optical fibers will be achievable with entangled light of a fiber source.
In principle, soliton pulse propagation is not essential for generating squeezed pulses from optical fibers. Nishizawa et al. reported squeezed vacuum pulse generation with a mode-locked 100-ps 1.064 µm Nd:YAG laser [7]. Since Si photodiodes offering more efficient quantum efficiency than photodiodes at 1.5 µm are available at shorter wavelengths than 1 µm, generation of entangled photon pairs at 800 nm using a second-harmonics of a Ti:sapphire laser (800 nm) has actively been studied with a parametric down conversion scheme. Since normal glass fibers exhibit positive dispersion at 800 nm, so far no experimental result has been reported on squeezed pulse generation at 800 nm using fiber optical nonlinearity, except for the experiments utilizing photonic crystal fibers exhibiting negative dispersion at 800 nm [8]. At 800 nm a transform limited laser pulse is immediately broadened within a few cm of the conventional glass fiber. Therefore, only self-phase modulation induced within such a short length can effectively contribute to pulse squeezing.
In this paper, production of squeezed vacuum laser pulses at 800 nm is studied with a Sagnac fiber interferometer using a Ti:sapphire femtosecond laser. By applying a relatively short optical fiber and adding negative chirping to the incident laser pulse to compensate for the fiber dispersion, we succeeded to demonstrate squeezed pulse generation even at 800 nm.
2. Numerical model calculation
We calculated temporal waveform, spectrum and quadrature squeezed level for various input laser pulses and fiber lengths by employing the following nonlinear Schrödinger equation (NLSE) model solved by a back-propagation method [9]:
This equation considers fiber dispersion, Kerr effect and stimulated Raman scattering (SRS). βn is n-th dispersion and γ is fiber nonlinearity. fr means the ratio of the molecule vibration to occupy the Kerr effect and f r=0.18 is used for normal silica fiber. h(t) is the Raman response function. In this equation, we used the intermediate broaden model [8] as a response function.
Since the squeezing level obtained through nonlinear fiber propagation depends on the pulse broadening characteristics associated with self-phase modulation and SRS, it is not straightforward to describe the dependence of squeezing performance on the parameters such as fiber dispersion coefficient, fiber length, input laser energy, and laser pulsewidth. It is especially true for laser pulses at the anomalous dispersion wavelength, since those parameters change soliton pulse formation. However, in general, if the input laser pulse is a transform limited pulse at 800 nm, higher input peak intensities, shorter laser pulses, or smaller dispersion coefficients always induce higher self-phase modulation, which results in higher squeezing levels, since the squeezing obtained by 800 nm laser pulses is determined during the first few cm. On the other hand, stimulated Raman scattering becomes more prominent for intense laser pulses.
In the analysis condition of pulse propagation at 800 nm, we assumed that silica fiber is single mode at 800 nm, and β2=40 ps2/km, β3=0.1 ps3/km. This equation ignores dispersion more than fourth-order. The fiber nonlinear constant γ is 12.3 W-1km-1. On the other hand, we used β2=-20.0 ps2/km, β3=0.1 ps3/km in calculations for laser pulses at 1.55 µm. In the model calculations, interference at a -3dB fiber coupler between two laser pulses propagating in the clockwise and the counter-clockwise directions in a Sagnac fiber loop is modeled as ideal interference. Since the completely same nonlinear propagation, which induces frequency chirping and spectral broadening, can be obtained for both propagations, the ideal destructive interference is obtainable in an actual experimental setup.
First, we calculate squeezing levels for input pulses with a center wavelength at 800 nm and a pulse width of 100 fs. Figure 1(a) shows squeezing and anti-squeezing levels obtained when the pulse propagates through a 1.2 m fiber at 800 nm. Peak intensity of the input pulse is 1,011 W. This pulse corresponds to an N=1 soliton at the pulse width of 100 fs for a fiber with the same dispersion profile but with a negative sign. When ignoring the stimulated Raman scattering in the model, the squeezing level is almost saturated for fiber lengths longer than 40 cm. Squeezing and anti-squeezing levels reach -10.4 dB and 12.3 dB, respectively, after 1.2 m fiber propagation. Therefore, although the pulse width significantly spreads due to the positive dispersion in the fiber, longer length propagation still gradually increases the squeezing level.
Next, we investigate the influence of stimulated Raman scattering, which becomes significant at input pulse widths of less than 100 fs. Figure 1(a) shows also the squeezing and anti-squeezing levels calculated by including the stimulated Raman scattering effect for laser pulses at 800 nm. The squeezing level is degraded by only 1 dB. Propagation beyond 50 cm still increases the squeezing level, since pulse broadening eliminates the influence of stimulated Raman scattering. This is a definite advantage for the pulse wavelength at positive dispersion.
Fig. 1. Numerical model calculation of squeezed vacuum considering Raman scattering at (a) 800 nm and (b) 1.5 µm. Cross and square plots show the anti-squeezed noise level obtained with and without Raman, respectively. Triangle and diamond plots show the squeezed noise level obtained with and without Raman, respectively.
Figure 1(b) shows the squeezing and anti-squeezing levels calculated for laser pulses at 1.55 µm. The fiber length is set at 2.53 m for 1.55 µm pulses, which corresponds to a 10-soliton length for an input pulse width of 100 fs. For 1.55 µm pulses, the squeezing level is significantly degraded by 10 dB due to stimulated Raman scattering because the short laser pulse width is maintained through the entire fiber length. It will be not adequate to judge the performance of squeezed vacuum generation between 800 nm and 1.55 µm only from these calculation results, since many parameters have not been optimized yet. However, SRS becomes more prominent for intense laser pulses. Therefore, even if the length of the fiber is increased to more than 1 m for 1.55 µm laser pulses, accumulated phase modulation does not contribute to increase squeezing due to SRS noise.
When the input pulse is at a Fourier transform limited pulse (FTL pulse), the pulse width gets wider during fiber propagation at 800 nm. When the input pulse is negatively chirped before launching, the pulse will be compressed at a certain position in the fiber. Thus, the whole optical nonlinear effect offered during fiber propagation changes as a function of the initial amount of negative chirp. Figure 2 shows the calculation result of squeezing and anti-squeezing levels for various amounts of initial negative chirping. In these calculations, the stimulated Raman scattering effect is included. When the pulse compression point approaches the center of the fiber (0.024 ps2 in Fig. 2), the effective self-phase modulation through the entire fiber propagation becomes maximum, and thus the squeezing level is improved by 3 dB.
Fig. 2. Dependence of squeezed vacuum predicted by the numerical model upon dispersion compensation: (a) squeezing; (b) anti-squeezing. Dispersion of -0.024 ps2 corresponds to that of the half-length fiber
Fig. 3. Numerical model calculation results of (a) temporal waveform and (b) spectrum at various points in the 1.2 m-long optical fiber length. The input laser pulse is negatively chirped with the dispersion of −0.024 ps2.
Figure 3 shows changes in temporal waveforms and spectra during the fiber propagation. The input pulse has the proper negative dispersion so that the pulse becomes an FTL pulse at the center of the fiber. It is noteworthy that the spectrum of negatively chirped laser pulses is narrowed by the self-phase modulation. Therefore, the peak power of the compressed pulse at the center of the fiber is lower than the peak power of the FTL input laser pulse as shown in Fig. 3(a). Due to this pulse broadening (spectral narrowing), the best squeezing is obtained by adding the dispersion of -0.02 ps2, not -0.024 ps2 in Fig. 2.
In our model calculations, it is shown that more than -10 dB quadrature squeezing is obtainable for both 800 nm and 1.55 µm ultrashort laser pulses using fiber nonlinear optics. However, there is a large discrepancy between the model calculations and squeezing levels obtained so far in experiments reported by many researchers. The major source of the discrepancy is excessive noise caused by guided acoustic-wave Brillouin scattering (GAWBS), which has been ignored in model calculations. Nishizawa et al. theoretically analyzed the effect of GAWBS in optical fibers on squeezed vacuum formation, although SRS was excluded in their numerical model [10]. Currently, Corney et al. included the GAWBS effect in the numerical modeling for squeezing at 1.55 µm in an empirical manner [11]. However, so far, no detailed modeling has been developed to theoretically analyze the excess noise of GAWBS, such as dependence on the wavelength.
3. Experimental setup
Our experiment employs a Sagnac fiber interferometer with a variable fiber coupler as shown in Fig. 4. We used s polarization to maintain single mode, 1.2 m-long fiber (SM85P PANDA: Corning) for the Sagnac loop. The dispersion parameter of the fiber is β2=22.6 ps2/km. The advantage of the fiber Sagnac loop (Canadian Instrumentation & Research) is that we can automatically generate a local oscillator (LO) pulse with the same pulse width and spectrum as a squeezed vacuum pulse at constructive interference at the coupler. It is of prime importance to obtain high interference visibility at a balanced homodyne detection. In our setup, however, the 20 cm-long fiber sleeve will slightly change the duality. The laser source is a Ti:sapphire femtosecond laser (Maitai, Spectra Physics). The center wavelength is 810 nm, pulse width is 100 fs and repetition rate is 79.2 MHz.
Fig. 4. Experimental setup of squeezed vacuum: F. R.; Faraday Rotator, LPF; Low-Pass Filter and S. A.; Spectrum Analyzer.
A Faraday rotator (FR) is placed in front of the fiber interferometer to eliminate the pulse reflected at the fiber edge. To adjust the initial chirping of input laser pulses, we employed an asymmetric 4-f optical layout. The highest negative dispersion attained by this 4-f layout is -0.029 ps2. A squeezed vacuum pulse is mixed with an LO pulse at PBS and measured by homodyne detection. The sum and difference ac photocurrents of the two detectors were recorded by an RF spectrum analyzer (ADVANTEST Q8384) at 10 MHz with a bandwidth of 100 kHz, a video bandwidth of 100 Hz that averaged over 100 measurement cycles after a RF amplifier (SA-230F5), and a low-pass filter (Mini-circuit BLP15) with a cut-off frequency of 79.2 MHz. An optical mount equipped with a PZT is used to control the relative phase between the signal and the LO pulses. We used an additional FR in the SV pulse path to compensate for the dispersion caused by the FR in the LO pulse path. By adding the FR in the SV pulse path, the visibility of interference was improved from 66% to 91%. The discrimination factor at the coupler is 1: 286.
4. Results of squeezed pulse generation
First, we measured dependence of squeezing and anti-squeezing levels upon the second-order dispersion added to the input pulses. The results are shown in Fig. 5. The input laser power is 16 mW. Without any pre-compensation for the positive dispersion, no squeezing is observed. When only the positive dispersion (0.0058 ps2) corresponding to the sum of the dispersion of the FR and the fiber sleeve was compensated, the quadrature noise became slightly lower than the SNL. The highest squeezing of -0.45 dB was obtained with the pre-compensation at -0.0157 ps2. Since the positive dispersion of the half-length fiber loop is estimated at -0.0194 ps2, the amount of dispersion compensation to generate the maximal squeezing does not generate the FTL pulse at the center of the fiber loop.
The experimentally obtained squeezing level is much lower than the numerical model calculation. The major source of this discrepancy is caused by excessive noise of GAWBS in the fiber. So far, GAWBS noise has been reduced by operating a pumping laser at higher repetition rates of >1 GHz [3] or by deactivating phonons at low temperatures <77 K. Recently, it was claimed that micro-structures of photonic crystal fibers are effective to suppress GAWBS [13]. Figure 6 shows squeezing and anti-squeezing levels obtained when part (~70 %)) of the fiber loop was immersed in liquid nitrogen. The total length of the fiber loop is 1.2 m. The pre-compensation level and the input laser power were kept constant at 0.0157 ps2 and 16 mW, respectively. By cooling the fiber, the squeezing and anti-squeezing levels were improved by 0.3 dB and 1.2 dB, respectively. Since the anti-squeezing exhibits substantial excess noise, GAWBS is still a major source degrading the SV performance.
Fig. 5. Dependence of relative noise level of squeezed vacuum pulses upon dispersion compensation: (a) squeezing; (b) anti-squeezing.
Figure 7 shows dependence of the LO spectrum on dispersion compensation. The spectrum becomes narrower when dispersion compensation increases. Therefore, due to the spectrum narrowing caused by self-phase modulation upon a negatively chirped laser pulse, the highest phase modulation, which results in the highest squeezing, is obtained at lower pre-dispersion compensation.
Nishizawa et al. suggested from their numerical model calculation including GAWBS noise that broadened pulses suffer larger degradation of squeezing due to GAWBS noise, and a nearly fundamental soliton pulse is optimum to get the largest squeezing at 1.5 µm even if GAWBS noise is significant [10]. Since GAWBS, being a linear process, introduces less noise in a shorter fiber since it grows in proportional to the fiber length and the relative noise is independent of intensity. From this discussion, 800 nm pulses which spread within a few cm of a fiber will exhibit more significant degradation of squeezing due to GAWBS noise than 1.5 µm laser pulses, if the fiber length is kept same. However, since we could reduce the fiber length down to ~10 cm for obtaining sufficient squeezing levels for 800 nm laser pulses as shown in Fig. 1(a), 800 nm pulse lasers may have a merit in reduction of relative GAWBS noise.
To confirm that the 1.2 m-long Sagnac fiber loop and the non-soliton propagation of an 800 nm pulse can induce sufficient nonlinear phase modulation, we measured photon number squeezing [14] using the same experimental set up but with an asymmetric branching ratio of 93:7 at the fiber coupler. The photon number squeezing can be measured with the balanced homodyne detector without a local oscillator beam. In principle, discrete transverse phonon modes lead to spectrally structured phase noise in a laser pulse transmitted through a fiber. In direct photon number variance detection, therefore, GAWBS phase noise is not limitation.
Figure 8 shows the photon number squeezing levels measured for various amounts of pre-dispersion compensation as a function of input laser power. At room temperature, we obtained the highest photon number squeezing of -1.3 dB at a dispersion compensation of -0.0052 ps2. The pre-dispersion level is much lower than that required for the highest SV. In the asymmetric fiber loop, different input laser power launched to the clockwise and counterclockwise directions causes different spectrum after fiber propagation. Therefore, the two pulses cannot interfere with a high fidelity. Figure 9 shows the spectra of the transmitted pulse from the input port after interference at the coupler when the highest photon number squeezing was obtained.
Thus, in photon-number squeezing with a Sagnac fiber loop, the influence of phase noise caused by GAWBS is smaller, but the power-dependent change in the spectrum during fiber propagation prevents from generating higher squeezing levels.
Fig. 8. Experimental results of photon number squeezing. Amount of pre-dispersion compensation is (a) 0 ps2, (b) 0.00519 ps2, (c) 0.0108 ps2, and (d) 0.0159 ps2, respectively.
5. Conclusion
We experimentally examined squeezed vacuum and photon-number squeezing for femtosecond laser pulses at 800 nm using a 1.2 m-long Sagnac fiber loop. When the positive dispersion of the fiber is properly compensated for before launching so that the FTL pulse is obtained around the center of the fiber loop, the non-soliton propagation can still cause sufficient phase modulation for vacuum squeezing. The major obstacle to generating higher squeezed vacuum levels predicted by model calculation is excess noise caused by GAWBS in the fiber. We obtained the highest squeezed vacuum level of -0.45 dB, which is the first SV pulse at 800 nm obtained by a femtosecond laser pulse at a normal dispersion wavelength with nonlinear fiber optics. The photon-number squeezing was also obtainable with the nonlinear fiber optics. However, the power-dependent spectrum modulation prevents generating higher photon-number squeezing levels.
References and links
1. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998). [CrossRef] [PubMed]
2. N. Takei, T. Aoki, S. Koike, K. Yoshino, K. Wakui, H. Yonezawa, T. Hiraoka, J. Mizuno, M. Takeoka, M. Ban, and A. Furusawa, “Experimental demonstration of quantum teleportation of a squeezed state,” Phys. Rev. A 72, 042304-1–7(2005). [CrossRef]
3. C. X. Yu, H. A. Haus, and E. P. Ippen, “Soliton squeezing at the gigahertz rate in a Sagnac loop,” Opt. Lett. 26, 669–671 (2001). [CrossRef]
4. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons”, Phys. Rev. Lett. 66, 153–156 (1991). [CrossRef] [PubMed]
5. K. Hirosawa, Y. Momose, H. Ushio, Y. Fujiwara, and F. Kannari, “Purification of squeezed vacuum pulse generated from a Sagnac loop fiber using linear optics and conditional homodyne detection,” Jpn. J. Appl. Phys. 48, 034001-1–6 (2009). [CrossRef]
6. J. Heersink, T. Ganber, S. Lorenz, O. Glockl, N. Korolkova, and G. Leuchs, “Polarization squeezing of intense pulses with a fiber-optic Sagnac interferometer,” Phys. Rev. A 68, 013815-1–9 (2003). [CrossRef]
7. N. Nishizawa, S. Kume, M. Mori, T. Goto, and A. Miyauchi, “Squeezed light generation with 1.064 µm Nd:YAG laser and 0.85 µm single-mode fiber“, Jpn. J. Appl. Phys. 33, 138–143 (1994). [CrossRef]
8. K. Hirosawa, H. Furumochi, A. Tada, F. Kannari, M. Takeoka, and M. Sasaki, “Photon number squeezing of ultrabroadband laser pulses generated by microstructure fibers,” Phys. Rev. Lett. 94, 203601-1–4 (2005). [CrossRef]
9. Y. Lai and S. S. Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817–829 (1995). [CrossRef] [PubMed]
10. N. Nishizawa, Y. Matsuo, M. Mori, T. Goto, and H. Nishimoto, “Effect of guided acoustic wave Brillouin scattering on pulsed squeezing in optical fibers with nonlinearity and dispersion,” 4, Opt. Rev. 453–458 (1997). [CrossRef]
11. J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, “Simulations and experiments on polarization squeezing in optical fiber,” Phys. Rev. A 78, 023831-1–18 (2008). [CrossRef]
12. D. Hollenbeck and C.D. Cantrell, “Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function,” J. Opt. Soc. Am. B 19, 2886–2892 (2002). [CrossRef]
13. D. Elser, U. L. Andersen, A. Korn, O. Glockl, S. Lorenz, Ch. Marquardt, and G. Leuchs, “Reduction of guided acoustic wave Brillouin scattering in photonic crystal,” Phys. Rev. Lett. 97, 133901-1–4 (2006). [CrossRef]
14. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446–2449 (1998). [CrossRef]
