Jan 14, 1991 - IBM Research Division, Almaden Research Center, 650 Harry Road, Sanjose, California 95120- ... is accomplished using the Kerr nonlinearity.
VOLUME 66, NUMBER 2
PHYSICAL REVIEW LETTERS
14 JANUARY 1991
Squeezed Optical Solitons and R. M. Shelby IBM Research Division, Almaden Research Center, 650 Harry Road, San jose, California 95120-6099
M. Rosenbluh
"'
(Received 15 October 1990)
We have experimentally demonstrated the squeezing of optical solitons, resulting in a detected photocurrent noise power (32 ~ 3)% (1.7 dB) below the shot-noise limit over a broadband of frequencies. The squeezing is accomplished using the Kerr nonlinearity of a polarization-preserving single-mode optical fiber at liquid-nitrogen temperature. Squeezed solitons, 1. 1 dB below the shot-noise limit, were observed at room temperature. PACS numbers:
42. 50. Dv, 42. 50.Qg, 42. 81.Dp
Optical solitons are pulses which propagate in optical fibers without temporal or spectral distortion, owing to a balancing between the second-order dispersion of the refractive index and the nonlinear self-phase-modulation induced by the intensity-dependent refractive index. Classically, this stationary propagation only requires negative group-velocity dispersion and the proper choice of pulse width and shape for a given pulse energy or photon number. However, quantum mechanics imposes fundamental fluctuations of the amplitude and phase of the optical pulse, thus limiting the precision with which this pulse shape can be produced. If the quantum noise on the optical pulse is that of the zero-point or vacuum fluctuations of the field, the uncertainties in the field ampliminitude and phase quadratures are simultaneously mized, the field is a coherent state, and the intensity and phase noise of the pulse are at the classical shot-noise limit. The quantum fluctuations, however, are not stationary with respect to propagation in an optical fiber, even if the classical mean field satisfies the condition for a soliton; rather they evolve under the combined eA'ects of dispersion and self-phase-modulation. Squeezing arises due to self-phase-modulation: Quantum fluctuations of the amplitude cause correlated fluctuations in the phase to be generated as the pulse propagates in the fiber. If the fluctuations of the input pulse are those of the vacuum, the low-frequency amplitude fluctuations remain at the vacuum level under the influence of this purely dispersive nonlinearity, the phase fluctuations become correlated to this vacuum noise, and this quantum correlation manifests itself as squeezing. At the detector, the correlation can produce a destructive interference between the amplitude and phase noise, yielding a noise level below that of the vacuum. We have observed this squeezing experimentally in the propagation of 200fsec solitons in 5 m of optical fiber. The generation of squeezed light, where fluctuations in one quadrature of the electromagnetic field are reduced to less than those of the vacuum, has been demonstrated for both continuous-wave and pulsed laser sources. Numerous schemes have been used, including four-wave mixing in atomic vapors, parametric amplification and oscillation, and the Kerr eAect in optical fibers. The squeezed field can be used to reduce the noise level in
'
sensitive optical experiments, and more than a factor-of2 noise reduction has been observed in prototypes of such experiments. Though optical fibers seem promising as nonlinear media, inelastic light scattering due to thermal fluctuations of the fiber refractive index adds excess phase noise, ' limiting the quantum noise reduction attainable to approximately 12%, even when the fiber is cooled with Pulsed laser light oAers a way to overliquid helium. come these limitations. With pulses sufTiciently short, so that their spectral bandwidth is greater than the bandwidth of the refractive-index fluctuations, the thermal phase noise added by the fiber scales in proportion to the number of photons in the pulse, whereas nonlinear eAects such as squeezing scale in proportion to the peak intensiSince one ty, giving an advantage to short pulses. might expect temporal broadening and/or phase distorto intions due to dispersion and self-phase-modulation terfere with or reduce squeezing, we were led to consider the squeezing of solitons. We report the results here: a detector photocurrent noise level (32~ 3)% below the vacuum noise level, i.e. , 1.7 da below the classical shotnoise level, over the entire bandwidth of our detector sensitivity (3-30 MHz). The squeezing was maximum for conditions near fundamental soliton pulses. For fundamental soliton propagation, hyperbolicsecant-shaped pulses are required, with a photon number n specified uniquely by the fiber second-order dispersion k" = 8 k/8 co, the effective third-order nonlinearity g = 6 to n2/2A, and the pulse duration t p n
=c Ik" I/gtp.
(1)
Here n&=3. 2X10 cm /W is the intensity-dependent refractive index of fused silica, k and co are the propagation constant and frequency of the pulse, and 4 is the effective fiber-core area. The FWHM duration of the pulse is v=1.763(0. Squeezing occurs over a characteristic length given by '
zp
=tp/Ik" = [g(n/tp)] I
proportional to the pulse peak intensity. Thus, each time the pulse duration is halved, the fiber can be shortened by a factor of 4, and the thermal phase noise, which is proportional to n and to the fiber which is inversely
1991 The American Physical Society
153
PHYSICAL REVIEW LETTERS
VOLUME 66, NUMBER 2
length, is reduced by a factor of 2. We produced pulses of 1550-nm wavelength, 200-fsec duration, and 168-MHz repetition rate with an additive(APM) NaC1 color-center laser. ' ' pulse mode-locked When the color-center-laser cavity length and the length of the cavity containing the APM fiber were adjusted to match the mode-locking frequency of the Nd-doped yttrium aluminum garnet pump laser, shot-noise-limited performance could be obtained. The intensity autocorrelation of the pulses was 310 fsec in width, and the spectrum was somewhat asymmetric with a FWHM width of 2. 6 THz, about 30% broader than the transform limit for Gaussian pulses. The conditions necessary for soliton propagation were determined by launching these pulses into 5 or 10 m of York HB1500 polarization-preserving fiber and monitorand spectrum of the ing the intensity autocorrelation output pulses as a function of pulse energy in the fiber. For an average power of 40 m W, corresponding to a pulse energy of 0.24 n3, the emerging pulses displayed spectral and temporal width nearly equal to those of the input, and were at the transform limit for hyperbolic secants, i.e. , autocorrelation width of 240 fsec, corresponding to r =156 fsec, and spectral width of Aco/2rr = 2. 1 THz, yielding h, co = 2.05. For pulse energies above or below this critical value the pulses were ternof porally and spectrally distorted. The manufacturer this fiber quotes a group-velocity dispersion at 1550 nm of D = ~2rrck "/X =16.6 psec/nmkm. For a core area of A = 1 x10 cm, we calculate nkvd =0.28 nJ as the fundamental soliton pulse energy. The apparatus used to demonstrate soliton squeezing is a nonlinear Sagnac interferometer, first suggested for this purpose by Shirasaki and Haus, ' and is shown in Fig. 1. The nonlinear element is a loop of polarizationpreserving fiber into which the pulse train of variable intensity was injected with equal intensities in the two If the intensities are directions. counterpropagating equal in both directions, the linear and nonlinear phase shifts in the fiber are also equal, and the two pulses interfere constructively at the input port of BS2 and destructively at the other, unused port. However, vacuum noise enters through this "unused" port of BS2 and is combined with the incoming laser pulses and their associated As these composite pulses traverse the fluctuations. generate quantumfiber, their intensity fluctuations correlated phase fluctuations via the intensity-dependent refractive index, producing squeezed pulses. When these pulses recombine at BS2, the portion corresponding to the vacuum input is reconstructed at the unused beamsplitter port as a pulse of squeezed vacuum, with nominally zero mean field, while the pulse emerging from the input port is a squeezed "bright" pulse, i.e. , with nonzero mean field. The pulse energy in each direction in the fiber could be adjusted in the experiment from 0 to 1.2 times that of the fundamental soliton. The mean-square fluctuations in each quadrature of
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14 JANUARY 1991
„To Spectrum AnaIyzer
NIP
~
DL
APM
OI
p
Laser
30% BS2 50% A
Fiber
FIG. 1. Soliton squeezing apparatus. 200-fsec, 1550-nm pulses are incident from the right and are controlled in energy by a polarizer (P) and wave plate (WP). They are launched into both ends of the polarization-preserving York HB1550 fiber through beam splitter BS2. Vacuum noise is incident through the other side of BS2. A portion of the emerging pulse is picked oA by beam splitter BS1 to form the local oscillator, is delayed, combined at a nominally 50% beam splitter (BS) with the pulse of squeezed vacuum which emerges from BS2, and detected by InGaAs p-i-n photodiodes and preamps, D1 and D2. The two photocurrent signals are combined in a hybrid junction to form photocurrent sum and difference signals which are recorded by a spectrum analyzer. the squeezed vacuum pulse are measured via balanced homodyne detection, using a portion of the bright pulse as local oscillator (LO). Special care is taken to ensure both spatial and temporal overlap of the LO and the pulse of squeezed vacuum. This method of providing the local oscillator' has the advantage of filtering out any low-frequency phase noise which is common to the squeezed vacuum field and LO field, such as that due to thermal' or acoustic variations of the low-frequency fiber refractive index. The dc photocurrent from each detector (Epitaxx ETX1000) is monitored by a digital voltmeter and a digital oscilloscope. The ac part of the photocurrent signal noise and the is filtered to eliminate low-frequency strong signal at the 168-MHz pulse repetition frequency, saturation of the Signetics NE5212 thus preventing The usable ac bandwidth transimpedance preamplifier. of this detector and preamp extends from about 3 to 50 M Hz. The average optical power on each detector ranged up to 10 mW. The preamp outputs were combined at an rf hybrid junction after adjustable phase shift and attenuation, and either the sum or diff'erence signal noise powers were monitored by an HP8566B spectrum analyzer. The relative phase of the squeezed field and the LO pulse is varied by piezoelectrically translating one mirror as the noise power in a 300-kHz resolution bandwidth is recorded by the spectrum analyzer. After each sweep the memories of spectrum analyzer and digital scope are stored on the disk of an IBM PS/2 computer for subsequent analysis. The shot-noise or vacuum-noise limit was established as a function of the two dc photocurrents through several
VOLUME 66, NUMBER 2
PHYSICAL REVIEW LETTERS 100
calibration
procedures. First, during each data run, the diff'erence photocurrent noise was recorded for a range of LO intensities with the signal port of the balanced detector blocked. The LO noise is itself within 3 dB of the vacuum, as determined by comparison of the noise on the sum and difference outputs from the hybrid junction. Since the common-mode-rejection ratio of the balanced detectors was established in an independent experiment to be greater than 30 dB, this constitutes an In situ determination of the vacuum noise. 6,' 7,' 13 Second, the laser when operated in synchronous pumping mode ii. e. , with no APM fiber) exhibits intensity noise at the vacuum level to within a few percent between 3 and 30 MHz; again this was established by a comparison of the detector sum and diff'erence noise signals. Using this laser source, the detector shot-noise level was calibrated over the entire range of dc currents used in the experiments, including the response of each detector when individually illuminated. This allowed us to account for small variations in the ratio of intensities on the two detectors due to imbalance of the fiber interferometer. Finally, this calibration was compared to the noise observed with the detectors illuminated by a 2. 5-mW, 1S32-nm cw HeNe laser, which is shot-noise limited at frequencies higher than its very narrow cavity bandwidth. All of these vacuum-noise calibrations agreed to within 3% and were stable over the course of several weeks. From the photodetector dc response and the known optical losses of the system, our overall detection quantum e%ciency was estimated to be rl = (75 5)%. The photocurrent difference noise power at 15 MHz (within the 300-kHz resolution bandwidth) is shown in Fig. 2 as a function of the relative phase between the LO and the squeezed vacuum pulse (the absolute phase of the squeezed quadrature was not determined). The noise power is normalized to the calibrated vacuum noise level, and thus expressed in vacuum noise units or VNU. 14 Other experimental parameters were a fiber length of 5 m maintained at liquid-nitrogen temperature for more than 90% of its length, and average laser power of 36 mW propagating through the fiber in each direction. The mean-square uncertainty of one quadrature amplitude increases by a factor of 75 above the vacuum, while that of the orthogonal-quadrature amplitude dips below the vacuum level to 0.68 VNU. The product of these is far above that of a minimum-uncertainty state. This is partly due to the presence of thermal phase noise from the guided acoustic wave Brillouin scattering or to excess phase noise associated with Raman scattering. However, most of the noise in the amplified quadrature originates in the same interaction leading to squeezing, and as shown by earlier numerical simulations, is characteristic of the squeezing of soliton pulses in fibers. Previous measurements of light scattering in optical fibers' provide an estimate of the average thermal phase noise spectral density near zero frequency (scaled apVNU/mWm at propriately for our fiber) of 1.7&&10
~
14 JANUARY 1991
) a
10
0 Q
Z.'
0.
5: Zy (rad. )
FIG. 2. Photocurrent diAerence noise power, normalized to the vacuum level noise power in the same bandwidth is shown as a function of the relative LO phase, h, p. The noise power normalized thus is in vacuum noise units, or VNU. The horizontal solid line is the vacuum noise level or classical shotnoise limit, while the dotted line is the minimum noise of the squeezed soliton of 0.68 VNU. These data were recorded for a pulse energy traveling in each direction in the fiber of 0.21 n3. The resolution bandwidth of the spectrum analyzer was 30 kHz, the video bandwidth was 30 Hz, and the sweep time was 8 s. room temperature. We have measured the thermal noise induced on 2-psec-duration transform-limited pulses by a 5-m-long fiber. Using Eqs. (3.9) and (3. 10) of Ref. 4, we then estimated the bandwidth of the thermal Auctuations, and obtained @=0.001, i.e. , a bandwidth of 2 6Hz in physical units. Upon cooling the fiber to 77 K, the observed phase noise is consistent with a linear temperature dependence, confirming guided acoustic wave Brillouin scattering as the likely origin. ' Numerical simulation of the squeezing process with these thermal-noise parameters yielded a noise level of 0.09 VNU for the squeezed quadrature and 200 VNU for the amplified quadrature, as compared to 0.03 and 200 VNU, respectively, for the case of no thermal noise. Taking into account the detection quantum efticiency of 75%, our measurements suggest that some additional noise source limits the observed squeezing. A likely candidate is the Raman eff'ect. We already see signs of the Raman self-frequency shift 15 for these pulses and fiber lengths. The optimum squeezing occurs for a pulse energy about (10-12)% below that of the fundamental soliton, and this may reAect the increased importance of the Raman eA'ect for higher peak powers. A theoretical estimate of this noise is in proof the relative insiggress. A further confirmation nificance of the thermal phase noise is provided by the observation of (23 3)% squeezing with the 5-m fiber at room temperature. The bandwidth of quantum soliton squeezing is expected to be very large, comparable to the soliton spectral width of 2 THz. Our current balanced detection system is sensitive only between 3 and 30 MHz, limited by preamp response, filtering, and the bandwidth of the
~
PHYSICAL REVIEW LETTERS
VOLUME 66, NUMBER 2
100:
14 JANUARY 1991
Naval Research.
'
Permanent address: Physics Department, Bar-Ilan University, Ramat Gan, Israel. 'A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23, 142
10 =
0
Z'.
OO I
I
I
10
20
~~ ~
Q
I
30
Frequency (MHzj
FIG. 3. Normalized noise power, in VNU, for the squeezed (circles) and the orthogonal or maximum noise quadrature quadrature (squares) observed in individual measurements at each of the frequencies shown, under similar experimental conditions as in Fig. 2. The dotted line indicates a noise level of 0.7 VNU.
hybrid junction. In I ig. 3 we show a plot of the noise minima of the squeezed quadrature and amplified quadrature for several frequencies in this band. These measurements were made by simultaneously scanning the frequency and phase, or by maintaining the phase in the neighborhood of the optimum for squeezing while the frequency was swept. As expected, about 30% squeezing appears at all frequencies investigated. The authors are grateful to M. D. Levenson for his encouragement and insights during the course of this work, and to P. D. Drummond and S. J. Carter for continuing discussions of the theory of soliton squeezing. The authors also wish to thank D. E. Horne for detector design, R. C. Eckardt for the loan of a BBO crystal, . and C. Pollock for discussions on the construction of a NaCl APM laser. This work was supported in part by the 0%ce of
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(1973). 2L. F. Mollenauer, Philos. Trans, Roy. Soc. London Ser. A 3~5, 435 (1985). 3P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B 4, 1565 (1987); P. D. Drummond, S. J. Carter, and R. M. Shelby, Opt. Lett. 14, 373 (1989). 4R. M. Shelby, P. D. Drummond, and S. J. Carter, Phys. Rev. A 42, 2966 (1990). sH. A. Haus and Y. Lai, J. Opt. Soc. Am. 8 7, 386 (1990). 6R. E. Slusher er al. , J. Opt Soc. Am. B 4, 1453 (1987); L. A. Orozco er al. , J. Opt. Soc. Am. B 4, 1490 (1987). L.-A. Wu, M. Xiao, and H. J. Kirnble, J. Opt. Soc. Am. B 4, 1465 (1987); M. Xiao, L. -A. Wu, and H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987). sR. E. Slusher et a/. , Phys. Rev. Lett. 59, 2566 (1987); P. Kumar er al. , Phys. Rev. Lett. 64, 1015 (1990). 9G. J. Milburn er al. , J. Opt. Soc. Am. 8 4, 1476 (1987). ' R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. 8 31, 5244 (1985); S. H. Perlmutter er al. , Phys. Rev. Lett. 61, 1388 (1988); Phys. Rev. B 42, 5294 (1990). ''C. P. Yakymyshyn, J. F. Pinto, and C. R. Pollock, Opt. Lett. 14, 621 (1989). ' M. Shirasaki and H. A. Haus, J. Opt. Soc. Am. B 7, 30
(1990). '3H. P. Yuen and V. W. S. Chan, Opt. Lett. 8, 177 (1983); B. L. Schumaker, Opt. Lett. 9, 189 (1984); J. H. Shapiro, IEEE J. Quantum Electron. 21, 237 (1985). '4This normalization is discussed in the appendix of the last paper of Ref. 10. The noise power in vacuum noise units is inof detection parameters such as bandwidth, dependent amplifier gain, and local oscillator power, is an absolute quantity, and is operationally convenient. '~F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986); J. P. Gordon, Opt. Lett. 11, 662 (1986).
