The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.
The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.
An important part of optical sensing is interferometry, where direct or homodyne detection at the output of an interferometer yields information about small phase shifts. Classical interferometry operates at the shot-noise limit (SNL), caused by the photon structure of light and reached when an interferometer is fed with coherent light. The use of nonclassical light at the input of an interferometer enables overcoming the SNL. In particular, squeezed light is known to be less noisy than coherent light. An interferometer fed with strongly squeezed light can, in principle, provide the phase sensitivity at the Heisenberg limit, the ultimate limit allowed by the laws of physics. However, this supersensitive operation is strongly degraded by loss – both inside the interferometer and outside it, at the stage of detection. While the former (internal loss) seems to be inevitable, the latter (detection loss) can be overcome, and we demonstrate it in our recent experiment. The clue is to amplify light at the interferometer output using a phase-sensitive optical parametric amplifier. This device does not introduce additional noise, but it amplifies the fragile quantum signal and thus makes it tolerant to loss at the detection stage. In a proof-of-principle experiment, we build a polarization Mach-Zehnder interferometer and feed it with coherent light in one port and a squeezed vacuum in another port. At one output port, we amplify light with an optical parametric amplifier and measure a phase sensitivity of 13 mrad for 1500 photons in the interferometer. This result, achieved with 50% detection efficiency, overcomes the SNL by 3 dB. Moreover, by using stronger amplification, we can overcome the SNL under detection efficiency as low as 13%. Our results outline a way to use squeezed light for real-life sensing, where the detection efficiency cannot be very high, especially in spectral ranges like middle-infrared or terahertz.
Semi-classical noise characteristics are derived for the cascade of a non-degenerate phase-insensitive (PI) and a phase-sensitive (PS) fiber optical parametric amplifier (FOPA). The analysis is proved to be consistent with the quantum theory under the large-photon number assumption. Based on this, we show that the noise figure (NF) of the PS-FOPA at the second stage can be obtained via relative-intensity-noise (RIN) subtraction method after averaging the signal and idler NFs. Negative signal and idler NFs are measured, and <2 dB NF at >16 dB PS gain is estimated when considering the combined signal and idler input, which is believed to be the lowest measured NF of a non-degenerate PS amplifier to this date. The limitation of the RIN subtraction method attributed to pump transferred noise and Raman phonon induced noise is also discussed.
This paper investigates the gain characteristics of coherent optical amplifiers that amplify only one of two quadrature phase components in an input signal light according to the phase of pump light. It is constructed around a Mach-Zehnder interferometer with Kerr media. To heuristically obtain the design parameters of the coherent optical amplifier, small-signal analysis is adapted to the Mach-Zehnder interferometer with Kerr media. The theoretical results are then compared to experimental results and shown to agree well, which confirms the validity of this design approach. By utilizing low-loss and high-nonlinearity silica fiber as the Kerr medium and optimizing its length, a coherent optical amplifier is constructed that yields high-gain (up to 26 dB) operation.
A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.
We present a semi-classical approach for predicting the quantum noise properties of fiber optical parametric amplifiers. The unavoidable contributors of noise, vacuum fluctuations, loss-induced noise, and spontaneous Raman scattering, are included in the analysis of both phase-insensitive and phase-sensitive amplifiers. We show that the model agrees with earlier fully quantum approaches in the linear gain regime, whereas in the saturated gain regime, in which the classical equations are valid, we predict that the amplifier increases the signal-to-noise ratio by generating an amplitude-squeezed state of light. Also, in the same process, we analyze the quantum noise properties of the pump, which is difficult using standard quantum approaches, and we discover that the pump displays complicated dynamics in both the linear and the nonlinear gain regimes.
Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text W. Imajuku and A. Takada, "Theoretical noise figure of phase-sensitive amplifier using Mach-Zender interferometer with lossy Kerr media," in Optical Amplifiers and their Applications, S. Kinoshita, J. Livas, and G. van den Hoven, eds., Vol. 30 of Trends in Optics and Photonics (Optical Society of America, 1999), paper ThD2. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article