1. Introduction

Current studies in the generation of squeezed laser pulses are motivated by the possibility of using highly squeezed pulses to create and distribute continuous-variable entanglement for quantum communication applications [1]. 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 as well as optical parametric oscillators can generate squeezed pulses. Squeezed vacuum pulses [3–5] and polarization squeezing [6] have been generated using fiber interferometry at a wavelength of 1.5 μm, at which soliton pulse propagation maintains high optical peak power throughout the propagation in a conventional single-mode glass fiber. In general, fiber lengths of 5-80 m have been used. However, soliton pulse propagation is not essential for generating squeezed pulses from optical fibers. More experiments have been carried out at ~800 nm with a parametric down-conversion scheme to generate entangled photon pairs since quantum information can be stored or exchanged with alkli atom systems at this wavelength range. Very recently, we reported that a squeezed vacuum (SV) laser pulse at 800 nm was generated for the first time with a 1.5-m-long Sagnac fiber interferometer using a Ti:sapphire femtosecond laser [7]. By compensating for the fiber dispersion, we obtained a SV pulse of –0.45 dB. The major obstacle to generating higher SV levels predicted by model calculation is the excess noise caused by GAWBS in the fiber. Therefore, in our previous experiment, we kept the optical fiber at a liquid nitrogen temperature, although the noise level of the squeezing was only improved by −0.3 dB at 77 K [7].

A significant improvement in the fiber-based production of SV pulse generation at ~800 nm came with the implementation of much shorter fibers. At 800 nm a transform limited laser pulse is immediately broadened within a several cm of conventional glass fiber. Therefore, only self-phase modulation induced within such a short length can effectively contribute to pulse squeezing [7]. Further propagation only linearly increases GAWBS noise in the laser pulses. This paper reports the production of SV laser pulses at 810 nm with a short fiber interferometer at room temperature. We successfully reduced GAWBS noise compared with longer fiber lengths and demonstrated squeezed vacuum pulse generation at >2 dB. The influence of launched laser energy was also studied.

2. Experiment

Our experiment employed a single-pass fiber interferometer, as shown in Fig. 1 , which has been employed for generating photon number squeezing [8] or polarization squeezing [6]. The similar single-pass fiber interferometer was used by Milanovic et al. [9] to generate polarization squeezed pulses at 810 nm. They employed a 1-m-long photonic crystal fibers for which the zero-dispersion wavelength lies at 700 nm. Although in principle there is no difference between SV generation where squeezing is observed in a certain polarization mode and polarization squeezing using a single-pass fiber interferometer, SV pulse has not been extracted yet at ~800 nm with this scheme.

 

Fig. 1 Experimental setup of squeezed vacuum pulse generation at 810 nm.

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We used a polarization maintaining (PM) fiber, PM780-HP(NUFERN). Optical nonlinearity constant γ was 8.51 W⁻¹km⁻¹. The second- and third-order dispersions of the fiber at 810 nm were β ” = 38.1 ps²/km and β ”’ = 0.1 ps³/km, respectively. The laser source was a Ti:sapphire femtosecond laser (Maitai, Spectra Physics). The center wavelength was 810 nm, the pulse width τ ₀ was 100 fs (full width at half maximum), and the repetition rate was 79.2 MHz. A typical optical fiber exhibits the GAWBS spectrum that consists of many discrete resonant peaks starting at ~20 MHz, extending to an effective bandwidth of ~1 GHz. Therefore, in principle, laser sources whose pulse repetition rate is higher than 1 GHz can suppress the GAWBS noise using a fiber interferometer [3]. However, such high pulse repetition rates may not be useful in such quantum protocols as post selection schemes [10,11]. Within the available laser wavelength tuning range of ~10 nm, we could not find any clear dependence of SV generation on the center wavelength. Therefore, we fixed the center wavelength at 810 nm during the experiment described in this paper.

To adjust the initial chirping of the input laser pulses, we prepared a prism-pair pulse stretcher. Then, two ultrashort pulses of identical optical power were coupled into the two orthogonal polarization axes of the fiber, respectively. The total injected laser power and its precise balance were controlled by using a half wave plate (HWP1) and a polarization beam splitter (PBS1). Since the pulses propagate with significantly different group velocity in the two orthogonal polarization axes, they were launched at different times in the fiber so that they overlap at the fiber output. Relative delay is introduced by adding separate optical delay for the two orthogonal polarization modes in the interferometer. This arrangement also prevents cross-phase modulation between the two pulses in the fiber. Moreover, short separation distance between the two pulses (< 1 ns) can partially cancel the GAWBS noise induced in the two pulses at the output of the fiber interferometer since the effective bandwidth of the GAWBS noise is ~1 GHz, as described before. Townsend and Pousite experimentally revealed that at least 7-dB reduction in GAWBS noise is achievable with closely spaced orthogonal polarization pulses [12]. Consequently, at the other end of the fiber, we obtained two independent Kerr squeezed beams with approximately identical quadrature noise properties. At the fiber output, the two pulses are recombined using a half wave plate (HWP3). The typical extinction ratio for the recombined output beam is 1:200. The recombined output pulses are passed through the phase shifter, which consists of a couple of quarter wave plates (QWP3 and 4) and a half wave plate (HWP5) [5]. Using the phase shifter, the phase difference between the orthogonal polarization components, which are the LO and SV pulses, can be arbitrarily varied. The polarization directions are rotated by a half wave plate (HWP4) before the polarization beam splitter (PBS2), and the LO and SV are divided into two equal parts. Then the sum and difference AC photocurrents of the two photodiodes (HAMAMATSU) are recorded by an RF spectrum analyzer (ADVANTEST Q8384) at 21 MHz with a bandwidth of 100 kHz after an RF amplifier (NF circuit SA-230F5) and a band-pass filter (Mini-circuit SBP21.4 + ) for 19.2-23.6 MHz. We verified that the balanced homodyne detectors were not saturated by optical powers up to 50 mW (625 pJ/pulse) in the experiments. The configuration yields a total measured detection efficiency of 72%, where contributing factors include net transmission loss through various optical elements (8.3%), photodiode quantum efficiencies (equivalent losses of 19%), and visibility (equivalent losses of 1%). When correcting for the detection loss to estimate the actual squeezing magnitudes, we also considered the contribution of dark current noise, which depends on input laser power [13]. The dark noise equivalent loss changes from 58% to 5% as the launched laser power to the fiber changes from 3 mW to 60 mW.

3. Results and discussion

Experimental results are shown in Fig. 2 . We measured the quantum-noise reduction for fiber lengths of 20, 40, and 80 cm. Noise reduction was maximized by adjusting the relative phase between the LO and SV pulses by rotating the middle HWP5 of the phase shifter. The highest noise reduction was obtained with a 20-cm-long fiber at an input laser power of ~20 mW (250 pJ/pulse). In general, during laser pulse propagation through a single-mode optical fiber in the normal dispersion regime, the spectral broadening due to self-phase modulation saturates at a certain spectrum width. Further propagation simply increases only the pulse width and noise. The proper propagation distance L _opt has been estimated in the study of compression of optical pulses chirped by self-phase modulation in normal dispersion fibers as follow [14]:

 

Fig. 2 Plots of experimental data of noise reduction from shot noise level as a function of launched laser pulse energy to fiber. Fiber lengths were varied to 20 (circles), 40 (triangles), and 80 cm (squares).

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Figure 3 shows the numerical model prediction obtained for fiber lengths of 20 and 40 cm using a quantum nonlinear Schrödinger equation [7]. The plots are the same experimental data of Fig. 2 except that the linear loss as well as the dark current noise contribution was corrected. The model equation considers fiber dispersion, the Kerr effect, and stimulated Raman scattering. However, the GAWBS noise was not included. The model prediction shows that higher input laser powers monotonically improved the noise reduction for both the 20- and 40-cm-long fibers. The predicted highest noise reduction reached 10 dB at 60 mW. The discrepancy between the model calculation and our experimental results increased with the input power increases or the fiber length is increases because the magnitude of the GAWBS noise is proportional to the pulse energy and fiber length. Therefore, the major obstacle to generate such higher SV levels predicted by model calculation is the excess noise caused by GAWBS in the fiber.

 

Fig. 3 Open circle plots indicate numerical model calculation of squeezed vacuum generation from (a) 20-cm-long and (b) 40-cm-long optical fibers considering Raman scattering at 800 nm. Solid circle plots correspond to experimental data shown in Fig. 2 except that detection efficiency is corrected.

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The launched laser power in our experiment is much higher than similar SV generation using a long fiber interferometer at 1.5 μm, where the launched laser pulse is adjusted at the soliton power and sufficient phase modulation is obtained through long fiber propagation. In our experiment, since the fiber length was limited to 20-40 cm, more intense laser powers are required to get sufficient phase modulation to generate SV pulses. Since GAWBS noise is proportional to the laser pulse energy, whereas the squeezing magnitude is induced by the χ⁽³⁾ effect and is proportional to the peak intensity of the pulse, GAWBS noise can be reduced using shorter laser pulses. On the other hand, squeezing deterioration is attributed to Raman noise when the laser pulse is shorter since Raman noise increases in proportion to the laser intensity. However, when we examined the contribution of Raman noise in the numerical model calculation [7], it was shown that Raman noise is not significant in our experimental condition since pulse broadening eliminates the influence of stimulated Raman scattering. This is a definite advantage for the pulse wavelength at positive dispersion.

Figure 4 shows the experimental results of the noise reduction when the positive dispersion of the fiber was pre-compensated by the prism pair so that the shortest pulse was achieved at the middle length of the fiber. The effect of dispersion compensation is significant, and the highest noise reduction of 2.1dB was obtained with the 40-cm-long fiber at an input power of 12 mW. At this launched laser power, the Shot noise level is higher than the electrical noise by 6.78 dB. When the detection efficiency as well as the dark noise equivalent loss was corrected, this noise reduction corresponds to −4.8 dB SV. The dispersion pre-compensation also improved the squeezing levels obtained with 20-cm-long and 80-cm-long fibers. However, the highest improve was obtained for a 40-cm-long fiber.

 

Fig. 4 Plots of experimental data of squeezed vacuum obtained with a 40-cm-long fiber. Open circles show squeezed and anti-squeezed noise without fiber dispersion compensation. Solid circles show squeezed and anti-squeezed noise with fiber dispersion compensation. The detection efficiency is not corrected.

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In principle, for the soliton pulse squeezing, the nonlinear phase is constant for the pulse envelope. For the normal dispersion regime, however, the nonlinear phase cannot equally distribute over the pulse envelope and temporally varies. Therefore, this temporally dependent phase may degrade the magnitude of observed squeezing in balanced homodyne detection. However, since the magnitude of the observed squeezing is always weighted by the temporal intensity of the LO pulse at homodyne detection, the highest phase modulation at the pulse peak is always dominant. Therefore, it will not be a disadvantage of SV pulse generation using optical fibers at the normal dispersion regime.

Photonic crystal fibers can achieve anomalous dispersion at ~810 nm. Milanovic et al. reported that the highest polarization squeezing of −3.3 dB was obtained at 810 nm using a photonic crystal fiber for which the zero-dispersion wavelength lies at 700 nm [9]. Moreover, photonic crystal fibers could reduce GAWBS acoustic scattering noise by their tailored cross-sectional geometries and, thus, their vibrational properties [15]. Therefore, further optimization in both fiber parameters and pumping lasers will improve SV magnitude at ~810 nm.

4. Conclusion

In conclusion, we demonstrated SV laser pulse generation at 810 nm using a fiber nonlinear polarization interferometer. At 810 nm, the effective fiber length can be shortened to 40 cm since further fiber propagation only increases the GAWBS noise. Although higher laser intensities are required to obtain sufficient phase modulation within such a short fiber length, this operation condition is suitable for 810-nm femtosecond laser pulses to generate higher SV pulses. Maximum noise reduction of 2.1 dB was observed. When the detection efficiency as well as the dark noise equivalent loss was corrected, this noise reduction corresponds to −4.8 dB SV.