A novel method of producing squeezed vacuum uses cross phase modulation between a linearly polarized pump signal and the orthogonal polarized vacuum. Here we report on such cross phase modulation using 1-nJ 150-fs pulses from a low noise stretched pulse laser. The nonlinear medium was a single mode fiber and the noise reduction was 3 dB.
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Quadrature squeezing has been extensively investigated in a variety of configurations[1–4]. Of these, fiber offers an advantage since the squeezing is greatly facilitated by the low insertion loss, high power density and long interaction length. In the past squeezing with pulses in the a low dispersion fiber Sagnac loop has resulted in 5dB of noise reduction below the shot noise level .
In a zero dispersion fiber the squeezing is limited since the squeezing orientation varies along the pulse and the homodyne detection averages the squeezing across the pulse. Squeezing in a negative dispersion fiber[3,5,6] can overcome this limitation with the help of soliton formation in the fiber. In this case the squeezing occurs due to the phase spreading of the pulse[5,6], and is constant across the pulse. A more intuitive explanation for the advantage of dispersion in squeezing experiments has been given in Ref. 7. There it has been shown that both negative and positive dispersion effectively mix different temporal segments of the optical pulse which results in a more uniformly squeezed vacuum across the pulse. Recently soliton amplitude squeezing using spectral filtering has been demonstrated. Soliton quadrature squeezing, which we describe here, is a different process in which the pump and squeezed vacuum are separated and then recombined in a homodyne detector. One of the advantages of this scheme is the utilization of a balanced detector which permits observation of squeezing at lower RF frequencies than possible with amplitude squeezing, since the classical noise associated with the laser is canceled.
One method of separating the vacuum from the pump is by using a Sagnac loop. An alternative method in which a polarized pump squeezes the vacuum polarized in the orthogonal plane, has been demonstrated in semiconductor material[9,10] and examined in optical fiber. Here we describe quadrature squeezing of the orthogonal polarized vacuum in a negative dispersion fiber.
The concept of cross phase modulation squeezing in fiber is schematically shown in figure 1.
An incoming pulse linearly polarized along the x axis, is coupled into a single mode fiber. The χ(3) nonlinearity of the fiber couples the creation and annihilation operators of the y-polarized mode. As a result of the cross phase modulation, the quantum state of the y-polarized mode, which was initially a vacuum state, is transformed into a squeezed vacuum state at the output of the fiber. In order to detect the squeezed vacuum, the pump and vacuum are separated by a polarization beam splitter. The pump polarization is rotated to match the polarization of the squeezed vacuum, and used as the local oscillator in a homodyne detection scheme. The main limitation on the attainable squeezing in this scheme arises from the residual birefringence of the single mode fiber. The birefringence will cause a phase walk-off between the pump and squeezed vacuum, limiting the maximum attainable squeezing. In our system we used standard telecommunication fiber with a beat length of ∼4-m. In order to minimize the phase and/or polarization walk-off the length of the fiber used was 20 cm. By using pulses with a soliton period comparable to the fiber length a nonlinear phase shift of about 1 Rad can be obtained. This amount of nonlinear phase shift should result in 9 dB of noise reduction for an ideal soliton squeezing scheme . Another advantage of using a short fiber is the reduction of the guided wave acoustic Brillouin scattering (GWABS), which scales linearly with fiber length.
The experimental setup is shown in figure 2.
The pulse source was a stretched-pulse laser. The average power from the laser was 100 mW and the repetition rate was ∼30 MHz. The corresponding pulse energy was 3 nJ. The pulses were compressed to 150 fs using a double pass through a silicon prism pair, and injected into an SMF-28 fiber. Soliton effects in the fiber further compressed the pulses. The soliton effects are evident in figure 3 which shows the pulse spectra after the fiber for both low and high optical power.
As a result of the soliton pulse compression the spectrum develops wings which fall off exponentially as expected from a soliton, rather than the Gaussian tail which is typical of stretched pulse lasers . It should be noted that the spectrum of the pulse does not broaden since the pulse was initially chirped and the compression is counteracting the initial chirp.
The maximum power achieved in the fiber was 35mW which resulted in 85 fs pulses at FWHM(full width half maximum), shown in figure 4.
For this pulse width and for the dispersion of the SMF-28 (-22 ps2/km) the soliton period is ∼17 cm. To detect the quadrature squeezing a polarizing beam-splitter separated the pump from the squeezed vacuum. The pump was attenuated with a polarizer and its polarization was rotated to match the vacuum polarization. The pump and vacuum were then detected in a homodyne balanced detector. The amplitude noise of the stretched pulse laser, which was 10dB above the shot noise at 2.5 MHz, was canceled by the balanced detector scheme which had a common mode suppression of 20 dB at up to 5 MHz.
In figure 5 we show the shot noise level which was obtained by blocking the squeezed vacuum port, and the noise level obtained with the squeezed vacuum. To obtain the minimum noise level the delay between the pump and vacuum had to be carefully adjusted to obtain the relative phase for maximum squeezing. At other angles anti-squeezing, i.e. noise levels above shot noise, were observed as shown in figure 6.
The results shown in figure 6 were obtained by modulating the piezo displacer shown in figure two at 20 Hz and synchronizing the scan of the RF spectrum analyzer to the modulation. Since both the local oscillator pulse and the squeezed vacuum emerge from the same fiber the interferometric stability necessary for the homodyne detection can be obtained without active stabilization as also demonstrated in Ref. 9. Due to the short fiber length, and as analyzed in , the noise associated with GWABS spectrum was not evident in our system. The optical power was attenuated with the polarizer to 8-mW and the photocurrent was 4-mA through each of the detectors. The RF noise was measured using an HP 8560E RF spectrum analyzer, with a resolution bandwidth of 10KHz, and an averaging of 30 times. The calculated shot noise level based on the detector photocurrent, resolution bandwidth and transimpedance gain (∼54 dB) was -84 dBm. In addition the shot noise level was verified by using a highly attenuated optical signal. The electronic noise floor was limited by the noise of the transimpedance amplifier and was 20 dB below the measured optical shot noise. The linear dependence of the noise level and the detector photocurrent on the optical power were verified up to 15mW of incident optical power. The average noise reduction from figure 5 was 3 dB. Accounting for the quantum efficiency of the detector and an estimated 1 dB of optical losses, the actual squeezing is 5 dB. The expected noise reduction for this scheme is 6 dB which was obtained from simulations similar to those described in Ref. 10. The bandwidth of the squeezed radiation, as in other schemes employing kerr nonlinearity and short pulses, is defined by the pulse bandwidth and the response time of the nonlinear mechanism. In our case the measurement of the squeezed radiation bandwidth was limited by the 5 MHz bandwidth of our balanced detector.
To summarize, we demonstrated 3 dB of quantum noise reduction using cross phase modulation in a standard single mode fiber. These results demonstrate the viability of using the stretched pulse laser for squeezing experiments since it can provide energetic short pulses with low noise. The squeezing results described in this letter could be improved by using a fiber with a lower residual birefringence.
This paper was supported in part by the Office of Naval Research Grant N00014-92-J-1302
References and links
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