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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 25099–25106
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Photon-number squeezing with a noisy femtosecond fiber laser amplifier source using a collinear balanced detection technique

Shota Sawai, Hikaru Kawauchi, Kenichi Hirosawa, and Fumihiko Kannari  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 25099-25106 (2013)
http://dx.doi.org/10.1364/OE.21.025099


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Abstract

We experimentally demonstrate photon-number squeezing at 1.55 μm using a noisy erbium-doped fiber amplifier (EDFA). We employ a collinear balanced detection (CBD) technique, where the intensity noise at a specific radio frequency is canceled between two pulse trains. In spite of substantially large excess noise (>10dB) in an EDFA due to amplified spontaneous emission, we successfully cancel the intensity noise and achieve a shot noise limit at a specific radio frequency with the CBD technique. We exploit two sets of fiber polarization interferometers to generate squeezed light and observe a maximal photon-number squeezing of −2.6dB.

© 2013 OSA

1. Introduction

Squeezed light is an important resource in the field of quantum information and communication technologies, especially for the realization of entangled states with continuous variables [1

1. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005). [CrossRef]

]. Quantum entangled state with continuous variables plays an important role in quantum information processing and quantum communication, such as deterministic quantum teleportation [2

2. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49(2), 1473–1476 (1994). [CrossRef] [PubMed]

,3

3. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80(4), 869–872 (1998). [CrossRef]

], dense coding [4

4. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881–2884 (1992). [CrossRef] [PubMed]

,5

5. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61(4), 042302 (2000). [CrossRef]

], and entanglement based quantum cryptography [6

6. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991). [CrossRef] [PubMed]

]. In the future, it is desirable to integrate local devices for preparing quantum states and for processing quantum information into small systems consisting of slab waveguides and/or optical fibers. However, coupling loss is inevitable when quantum states of light generated in free space is transferred into an optical fiber or a waveguide. Since continuous-variable entanglement is a fragile resource, its quantum nature will easily be vanished by optical losses. Therefore, generation of squeezed light or entangled states in an optical fiber platform holds a significant merit for future integrated quantum information processing systems which are operated with continuous-variable. Moreover, a fiber-based squeezer using third-order optical nonlinear effects does not need second-harmonic light for pumping, which is essential in OPA squeezers using a waveguide nonlinear material such as PPLN.

Several schemes to generate squeezed light in optical fibers have already been demonstrated, for example i) phase-shifting cavity [7

7. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57(6), 691–694 (1986). [CrossRef] [PubMed]

], ii) spectral filtering [8

8. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77(18), 3775–3778 (1996). [CrossRef] [PubMed]

], iii) balanced interferometers [9

9. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66(2), 153–156 (1991). [CrossRef] [PubMed]

], iv) asymmetric interferometers [10

10. 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(12), 2446–2449 (1998). [CrossRef]

], a two-pulse, single-pass method generating squeezed vacuum [11

11. M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express 2(3), 72–76 (1998). [CrossRef] [PubMed]

,12

12. N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. 41(Part 2, No. 2A), L130–L132 (2002). [CrossRef]

], and polarization squeezing [13

13. J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. 30(10), 1192–1194 (2005). [CrossRef] [PubMed]

]. A nonlinear optical polarization interferometer (NOPI) is a kind of symmetric or asymmetric interferometers which can avoid optical interference between a signal and local oscillator (LO) light in free space and has frequently been employed to generate squeezed light pulses [12

12. N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. 41(Part 2, No. 2A), L130–L132 (2002). [CrossRef]

,14

14. J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys. 40(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]

].

Although entangled light at a wavelength of 1.55 μm is suitable to utilize the present fiber communication network, an erbium-doped fiber amplifier (EDFA), which is the most commonly used 1.55-μm light source in the classical optical communication network, contains substantially high intensity noise due to the beat noise of amplified spontaneous emission. It is impossible to obtain squeezing without removing this excess noise. In fact, so far squeezed light or entangled states at 1.55-μm have been obtained by optical parametric oscillators or Cr:YAG lasers in experiments, but not by noisy EDFAs.

Very recently, Nose et al. proposed a collinear balanced detection (CBD) technique for noise suppression in fiber laser-based stimulated Raman scattering (SRS) microscopy [15

15. K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express 20(13), 13958–13965 (2012). [CrossRef] [PubMed]

]. They experimentally confirmed the noise suppression of the second harmonic of Er-fiber laser pulses by 13 dB and the effectiveness of the CBD technique by SRS imaging of a cultured cell. In this paper, we applied this CBD technique to cancel the intensity noise of femtosecond EDFA light pulses and generated photon-number squeezing at 1.55 μm.

2. Experiment and Results

2.1 Noise reduction with the CBD technique

This technique compensates the intensity noise at a specific radio frequency by pulse splitting and recombination with relative time delay τ. The photocurrent contributed by the pulse trains is given by
I(t)=I1(t)+I2(t)=I1(t)+I1(tt)
(1)
where I1(t) and I2(t) are the photocurrent contributed by the first and second pulses, respectively. Equation (1) does not contain an interference term because no pulses temporally overlap each other. In the Fourier domain, we can obtain
I(w)=I1(w)+I2(w)=I1(w)+I1(w)exp(iwt),    
(2)
where I(ω), I1(ω), and I2(ω) are the Fourier transforms of I(t), I1(t), and I2(t), respectively. Equation (2) indicates that the photocurrents were added up destructively at ω = π/τ. When selecting τ equal to the interval of the pulse train of light, one can reduce the side-band spectral power density at a radio frequency corresponding to the half of the pulse repetition rate. Since in general the quantum noise of light is evaluated in the radio frequency sideband, it is very useful if the intensity noise power at a certain radio frequency is canceled.

When we apply this CBD technique for two pulses split equally at a beam splitter, the pulse is a classically perfect replica of the other. However, in the quantum theory, a vacuum state is always added at the beam splitter to both pulses with a reversed phase (see e.g [16

16. S. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2003).

].). Therefore, the vacuum noise remains even at perfect cancellation by CBD. When the vacuum states added to the signal pulses are phase modulated during nonlinear pulse propagation in an optical fiber, we can extract only the phase modulated vacuum state at perfect cancellation by CBD.

In principle, normal balanced homodyne detection can cancel classical noise of light. However, in actual experiments, since we cannot achieve ideal interference in fiber squeezers, for example in Sagnac fiber loops or NOPIs, there is always some leakage of LO light to the squeezed signal light. This leakage of the noisy LO light hides the reduction of quantum noise to lower than the SNL. Although the noise cancellation takes place only at specific radio frequency, the CBD technique is more useful in noise cancellation than balanced homodyne detection.

First, we demonstrated classical noise cancellation with the CBD technique and compared the noise level with the Shot noise limit (SNL), which was measured by balanced homodyne detection.
Fig. 1 Experimental setup to reduce intensity noise by CBD technique. ATT: attenuator; HWP: half wave plate; PBS: polarization beam splitter; BS: 50:50 beam splitter; AMP: RF amplifier; S.A.: RF spectrum analyzer; PDs: photodiodes.
Figure 1 shows the experimental setup. We used a femtosecond fiber laser (Femtolite, IMRA) as a light source. The center wavelength was 1560 nm, the pulse width was ~160 fs (full width at half maximum, FWHM), and the repetition rate was 47.5 MHz. The noise property is presented in Fig. 2.
Fig. 2 Plots of noise relative to SNL as a function of laser power. Values were recorded at 23 MHz. Square and diamond plots correspond to noise level of original pulse train and delayed and recombined pulse trains with CBD technique, respectively.
The intensity noise of a pulse train generated from the light source is already higher than the SNL by 10 dB at an average optical power of 3 mW. Therefore, it is impossible to obtain squeezing without removing this additional noise. In Fig. 1, the initial pulse train from the light source was split into two pulse trains at a polarization beam splitter (PBS). We added time delay τ = 1/frep, where frep is the repetition rate, to one of the two pulse trains and added another delay (∆τ) to prevent optical interference at the recombination. The two pulse trains with identical optical power were combined at a non-polarized beam splitter (BS).

The photon-number noise was measured by one of the two photodiodes (PDs). The bandwidth of the PDs (KPDE030, KYOSEMI) was 600 MHz. The photocurrents, which are proportional to the photon-number [17

17. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. 48(3), 143–156 (2007). [CrossRef]

] were recorded by an RF spectrum analyzer (ADVANTEST Q8384) with a resolution 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. The experiment was carried out under an average optical power of 5 mW, which was sufficiently lower than the saturation power of the RF amplifier. SNL was measured by splitting one pulse train at PBS2 with a branch ratio of 50:50 and subtracting the photocurrents [17

17. C. Silberhorn, “Detecting quantum light,” Contemp. Phys. 48(3), 143–156 (2007). [CrossRef]

]. Small delay ∆τ was varied from 6.7 ps to 2.5 ns. There was no influence of ∆τ on the noise reduction performance with CBD. Therefore, in the following experiment, the delay ∆τ was kept constant at 6.7 ps unless it is specified. The intensity noise can be canceled at a radio frequency of 23.8 MHz. Figure 2 shows the relative noise levels of the initial pulse train and two pulse trains recorded at 23 MHz. We clearly confirmed that the intensity noise of the two pulse trains was coincident to the SNLs at 23.8 MHz. In Fig. 2, plots for the two pulse trains indicate slightly lower relative noise than the SNL, especially at higher laser powers. These are a measurement error caused by underestimation of the launched laser powers. The deviation in the relative intensity noise measurement itself using a radio frequency spectrum analyzer is ~0.05dB.

Fig. 3 Noise spectra of femtosecond laser pulse trains. Red curve: original pulse train; green curve: delayed and recombined pulse trains with CBD technique; blue curve: shot noise; and purple curve: electric noise.
Figure 3 shows the noise power dependence on the radio frequency measured for ∆τ = 1.67 ns. The intensity noise of the femtosecond pulse train was canceled at 22 MHz, which exactly corresponds to ∆τ = 1.67 ns.

We also measured the noise level after propagation through an optical fiber in a preparatory experiment for squeezed light generation by optical fiber nonlinearity. We used a 3-m-long polarization maintaining (PM) fiber (HB1500G, FIBERCORE). The mode-field diameter was 7.9 μm. We compared the noise reduction performances between two cases. In the first scheme, the two delayed pulse trains were propagated through a common fiber. In the second scheme, they were propagated through separate fibers. The experimental setups are depicted in Fig. 4.
Fig. 4 Experimental setup of intensity noise cancellation after propagation of optical fibers. The left one is in the case of using a common fiber. The right one is in the case of using two separate fibers.
When we used a common fiber, the two pulse trains were recombined at a BS before the fiber launch to let the pulse trains propagate along the same axis of the fiber. Therefore, half of the optical power was wasted at the splitter. On the other hand, in the case of two separate fiber propagations, the two pulse trains were recombined collinearly at a polarization splitter after they were propagated along the fast axis of each fiber.

Fig. 5 Plots of noise relative to SNL measured at 23 MHz as function of laser power. Square plots: original pulse train; triangle plots: two pulse trains after propagating through a common fiber; and diamond plots: two pulse trains after propagating through two separate fibers.
Figure 5 shows the results of the measured noise level recorded at 23 MHz. Small delay ∆τ was adjusted at 6.7 psec. The noise levels of the two pulse trains after propagation through two separate fibers were coincident with the SNLs. We successfully canceled the intensity noise even after propagation through separate fibers. In contrast, the noise levels of the two pulse trains after propagation through a common fiber greatly exceeded the SNLs. The change in ∆τ did not improve the noise reduction performance. Small delay ∆τ of 6.7 ps is sufficiently shorter than the characteristic frequency of the guided acoustic-wave Brillouin scattering (GAWBS), which may be a major noise source through fiber propagation [18

18. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter 31(8), 5244–5252 (1985). [CrossRef] [PubMed]

]. Therefore, the imperfection of the noise cancellation was not caused by GAWBS. Presumably, the SRS noise, which is generated by the preceding pulses in the fiber, is added to the following pulses. The noise added to one of the two pulses cannot be canceled at the electrical detection. Sufficient noise reduction was only obtained using two separate fibers.

2.2 Photon- number squeezing

As a result, we obtained a maximum photon-number squeezing of −2.6 dB when the average power was 4.0 mW as shown in Fig. 7.
Fig. 7 Plots of noise relative to SNL as a function of coupled laser power into the fiber. Square, anti-squeezed noise; diamond, squeezed noise. The values were recorded at 22MHz.
All the measurements in Fig. 7 were obtained at 22 MHz. The average power was the total detected power. In a separate experiment, we also generated a photon-number squeezed pulses using a nonlinear optical polarization interferometer with the same 3-m PM fiber excited by a femtosecond OPO at a 1.55-μm wavelength. The pulse width was ~250 fs (full width at half maximum), and the repetition rate was 79.25 MHz. The original laser pulse train exhibited SNL noise. We obtained a photon-number squeezing of −2.4 dB at a pulse energy of 50 pJ and −3.7 dB at a pulse energy of 190 pJ. Therefore, the squeezing level we obtained in this work using the CBD technique is comparable to that achieved by coherent laser sources.

Fig. 8 Measurement of amplitude noise as a function of radio frequency. Red curve: shot noise; blue curve: noise level of squeezed light when the relative phase difference between orthogonally polarized pulses was swept; green curve: minimum noise level of squeezed light; purple curve: maximum noise level of anti-squeezed light.
Figure 8 shows the noise power dependence on the radio frequency. In this figure, a blue curve shows the change in noise power when a relative phase between the orthogonal polarization pulses was continuously scanned by a PZT driven mirror shown in the setup of Fig. 6. The largest anti-squeezed noise and the lowest squeezed noise measured by keeping the relative phase at a proper value are shown by a purple curve and a green curve, respectively. Noise reduction below the SNL was observed in the band width of ~5 MHz centered at 22 MHz, although the band width was restricted by the band-pass filter. Our optical layout yields a total measured detection efficiency of 83%, where contributing factors include the net transmission loss through various optical elements (1.4%) and photodiode quantum efficiencies (equivalent losses of 16%). The dark noise equivalent loss was 16% at 4.0 mW. When we corrected these equivalent losses, the noise reduction of 2.6 dB corresponds to −4.5 dB photon-number squeezing.

Qualitatively, a vacuum mode that enters through another port of the BS experiences phase modulation while copropagating with a bright pulse train. Amplitude noise, which contains classical EDFA noise, was completely canceled at a specific RF frequency by the CBD technique. Consequently, what we observed in our experiment corresponds to phase-modulated vacuum noise. Therefore, we may be able to extract squeezed vacuum pulses with a modified experimental setup using the CBD technique.

3. Conclusion

We achieved photon-number squeezing at 1.55 μm using a noisy EDFA laser as a light source using the collinear balanced detection technique. Maximum noise reduction of 2.6 dB was observed. When the equivalent losses were corrected, the noise reduction of 2.6 dB corresponds to −4.5 dB photon-number squeezing. This experimental evidence indicates that our scheme makes it possible to observe phase-modulated vacuum noise that entered a beam splitter that separates two pulse trains by electrically canceling the substantial intensity noise of a light source at a specific RF frequency.

References and links

1.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005). [CrossRef]

2.

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49(2), 1473–1476 (1994). [CrossRef] [PubMed]

3.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80(4), 869–872 (1998). [CrossRef]

4.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69(20), 2881–2884 (1992). [CrossRef] [PubMed]

5.

S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A 61(4), 042302 (2000). [CrossRef]

6.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991). [CrossRef] [PubMed]

7.

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57(6), 691–694 (1986). [CrossRef] [PubMed]

8.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett. 77(18), 3775–3778 (1996). [CrossRef] [PubMed]

9.

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66(2), 153–156 (1991). [CrossRef] [PubMed]

10.

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(12), 2446–2449 (1998). [CrossRef]

11.

M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express 2(3), 72–76 (1998). [CrossRef] [PubMed]

12.

N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys. 41(Part 2, No. 2A), L130–L132 (2002). [CrossRef]

13.

J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett. 30(10), 1192–1194 (2005). [CrossRef] [PubMed]

14.

J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys. 40(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]

15.

K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express 20(13), 13958–13965 (2012). [CrossRef] [PubMed]

16.

S. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2003).

17.

C. Silberhorn, “Detecting quantum light,” Contemp. Phys. 48(3), 143–156 (2007). [CrossRef]

18.

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter 31(8), 5244–5252 (1985). [CrossRef] [PubMed]

OCIS Codes
(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(270.6570) Quantum optics : Squeezed states

ToC Category:
Quantum Optics

History
Original Manuscript: July 8, 2013
Revised Manuscript: September 7, 2013
Manuscript Accepted: September 9, 2013
Published: October 14, 2013

Citation
Shota Sawai, Hikaru Kawauchi, Kenichi Hirosawa, and Fumihiko Kannari, "Photon-number squeezing with a noisy femtosecond fiber laser amplifier source using a collinear balanced detection technique," Opt. Express 21, 25099-25106 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25099


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References

  1. S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005). [CrossRef]
  2. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A49(2), 1473–1476 (1994). [CrossRef] [PubMed]
  3. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett.80(4), 869–872 (1998). [CrossRef]
  4. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69(20), 2881–2884 (1992). [CrossRef] [PubMed]
  5. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A61(4), 042302 (2000). [CrossRef]
  6. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett.67(6), 661–663 (1991). [CrossRef] [PubMed]
  7. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broad-band parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett.57(6), 691–694 (1986). [CrossRef] [PubMed]
  8. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, “Observation of optical soliton photon-number squeezing,” Phys. Rev. Lett.77(18), 3775–3778 (1996). [CrossRef] [PubMed]
  9. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett.66(2), 153–156 (1991). [CrossRef] [PubMed]
  10. 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(12), 2446–2449 (1998). [CrossRef]
  11. M. Margalit, C. X. Yu, E. P. Ippen, and H. A. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express2(3), 72–76 (1998). [CrossRef] [PubMed]
  12. N. Nishizawa, K. Sone, J. Higuchi, M. Mori, K. Yamane, and T. Goto, “Squeezed vacuum generation using symmetric nonlinear polarization interferometer,” Jpn. J. Appl. Phys.41(Part 2, No. 2A), L130–L132 (2002). [CrossRef]
  13. J. Heersink, V. Josse, G. Leuchs, and U. L. Andersen, “Efficient polarization squeezing in optical fibers,” Opt. Lett.30(10), 1192–1194 (2005). [CrossRef] [PubMed]
  14. J. Higuchi, N. Nishizawa, M. Mori, K. Yamane, and T. Goto, “Nonlinear polarization interferometer for photon number squeezed light generation,” Jpn. J. Appl. Phys.40(Part 2, No. 11B), L1220–L1222 (2001). [CrossRef]
  15. K. Nose, Y. Ozeki, T. Kishi, K. Sumimura, N. Nishizawa, K. Fukui, Y. Kanematsu, and K. Itoh, “Sensitivity enhancement of fiber-laser-based stimulated Raman scattering microscopy by collinear balanced detection technique,” Opt. Express20(13), 13958–13965 (2012). [CrossRef] [PubMed]
  16. S. Barnett and P. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, 2003).
  17. C. Silberhorn, “Detecting quantum light,” Contemp. Phys.48(3), 143–156 (2007). [CrossRef]
  18. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B Condens. Matter31(8), 5244–5252 (1985). [CrossRef] [PubMed]

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