Phase-insensitive Amplifier Research Articles

Characterization of quantum squeezing generated from the phase-sensitive and phase-insensitive amplifiers in the ultra-low average input photon number regime.

We give the general expressions of intensity-difference squeezing (IDS) generated from two types of optical parametric amplifiers [i.e. phase-sensitive amplifier (PSA) and phase-insensitive amplifier (PIA)] based on the four-wave mixing process, which clearly shows the IDS transition between the ultra-low average input photon number regime and the ultra-high average input photon number regime. We find that both the IDS of the PSA and the IDS of the PIA get enhanced with the decrease of the average input photon number especially in the ultra-low average input photon number regime. This result is substantially different from the result in the ultra-high average input photon number regime where the IDS does not vary with the average input photon number. Moreover, under the same intensity gain, we find that the optimal IDS of the PSA is better than the IDS of the PIA in the ultra-low average input photon number regime. Our theoretical work predicts the presence of strong quantum correlation in the ultra-low average input photon number regime, which may have potential applications for probing photon-sensitive biological samples.

Modulation format dependence on transmission reach in phase-sensitively amplified fiber links.

We quantify the maximum transmission reach for phase-insensitive amplifier (PIA) and phase-sensitive amplifier (PSA) links with different modulation formats and show that the maximum transmission reach increase (MTRI) when using PSAs compared to PIAs is enhanced for higher-order modulation formats. The higher-order modulation formats are more susceptible to smaller phase rotations from nonlinearities, and PSAs are efficient in mitigating these smaller phase distortions. Numerical simulations were performed for single- and multi-span PIA and PSA links with single and multiple wavelength channels. We obtain a significant enhancement in the MTRI with PSAs compared to PIAs when using higher-order modulation formats for both the single- and multi-channel systems in single- and multi-span links. We verify the enhancement with a single-span, single-channel system experiment. We also demonstrate, for the first time, a 64-QAM modulation format fiber transmission in phase-sensitively amplified link, with a 13.3-dB maximum allowable span loss increase compared to a phase-insensitively amplified link.

A Cryogenic CMOS Parametric Amplifier

We propose a phase-insensitive parametric amplifier featuring image cancelation and a doubly tuned transformer to enhance its bandwidth. Exploiting the reduced loss of passive components at cryogenic temperatures, the experimental characterization of a prototype shows a power gain of 9 dB with a bandwidth of 1.85 GHz for a pump frequency of 15.6 GHz and an image rejection of ~24 dB at 8.5 K. The amplifier consumes 33 mW in total at 8.5 K.

Cross-Phase Modulation Mitigation in Phase-Sensitive Amplifier Links

We experimentally investigate a wavelength-division multiplexing (WDM) system with a single span of 80 km standard single-mode fiber (SSMF) and a phase-sensitive amplifier (PSA) as a pre-amplifier. Using two channels spaced 25 GHz apart with single-polarization 10-Gbaud quadrature phase-shift keying (QPSK) signal, we show quantitatively that a PSA can mitigate self-phase modulation (SPM) and cross-phase modulation (XPM). With three single-polarization 10-Gbaud QPSK channels spaced 12.5 GHz apart, we verify that PSA can mitigate XPM and also determine an allowed span loss increase of 9.5 dB for the center channel with correlated edge channels for the PSA compared to the phase-insensitive amplifier (PIA) due to the combined improvement from low-noise amplification and nonlinearity mitigation.

Security of continuous-variable measurement-device-independent quantum key distribution with imperfect state preparation

Abstract The state preparation operation of continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol may become imperfect in practical applications. We address the security of the CV-MDI-QKD protocol based on imperfect preparation of the coherent state under realistic conditions of lossy and noisy quantum channel. Specifically, we assume that the imperfection of Alice's and Bob's practical state preparations equal to the amplification of ideal modulators and lasers at both Alice's and Bob's sides by untrusted third-parties Fred and Gray employing phase-insensitive amplifiers (PIAs), respectively. The equivalent excess noise introduced by the imperfect state preparation is comprehensively and quantitatively calculated by adopting the gains of PIAs. Security analysis shows that CV-MDI-QKD is quite sensitive to the imperfection of practical state preparation, which inevitably deteriorates the performance and security of CV-MDI-QKD system. Moreover, a lower bound of the secret key rate is derived under arbitrary collective attacks, and the upper threshold of this imperfection tolerated by the system is obtained in the form of the specific gains of PIAs. In addition, the methods presented will improve and perfect the practical security of CV-MDI-QKD protocol.

Interference-Induced Quantum Squeezing Enhancement in a Two-beam Phase-Sensitive Amplifier.

We experimentally demonstrate a method for realizing quantum squeezing enhancement which is induced by the interference in a two-beam phase-sensitive amplifier (PSA) based on a four-wave mixing process. Compared to the normal phase-insensitive amplifier with an intensity-difference squeezing (IDS) of 8.97±0.24 dB or 8.76±0.26 dB, the IDS of our two-beam PSA is enhanced to 10.13±0.21 dB under the same experimental situation. Furthermore, we study how various parameters influence the quantum squeezing enhancement of the PSA. These results clearly show that the physical mechanism inducing the IDS enhancement of the two-beam PSA is its intrinsic interference nature. Our results may find potential applications in improving the fidelity of quantum information processing and the precision of quantum metrology.

Enhancing continuous variable quantum key distribution with a heralded hybrid linear amplifier

We propose a method to improve transmission distance of continuous-variable quantum key distribution via a heralded hybrid linear amplifier (HLA), involving an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The phase-insensitive amplification of quantum light states may experience a degradation of signal-to-noise ratio (SNR) of 3dB which can be surmounted by the probabilistic amplification process. The new hybrid amplifier allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. Our equipment could clone unknown coherent states with fidelity surpassing the no-cloning limit by abandoning determinism and using probabilistic methods. The setup has a better compatibility with continuous variable protocols as it only uses Gaussian elements and a post-selection algorithm. The hybrid linear amplifier enhances the SNR and hence the transmission distance of the CVQKD protocol is extended. Both the asymptotic secret key rate and the secret key rate in a finite-size scenario are analyzed in this paper.

Improved mitigation of self-phase modulation induced impairments in 28 GBaud phase-sensitive amplified links.

The improved mitigation of self-phase modulation (SPM) induced nonlinear impairments by the use of a multi-span dispersion map optimization in 28 GBaud phase-sensitive amplifier (PSA) links is numerically investigated. We show that a four-span dispersion map optimized PSA link provides 2.1 times reach improvement over a single-span optimized PSA link with a total nonlinear phase shift tolerance increase from 2.1 radians to 8.8 radians. Furthermore, the optimized PSA link increases the maximum transmission reach by 6.9 times compared to a single-span optimized in-line dispersion managed phase-insensitive amplifier (PIA) link and 4.3 times reach extension is achieved compared to a dispersion unmanaged PIA link.

An All-Optical Buffer Based on Non-Degenerate Phase-Sensitive Parametric Amplification

The scheme of an optical buffer exploiting phase-sensitive amplification based non-degenerate four-wave mixing is presented and theoretically analyzed. The noise figure of the proposed buffer is analytically and numerically estimated as a function of the number of circulations inside the buffer cavity. Two principal configurations are studied depending on the position of the amplification unit inside the cavity. The analysis is supported by split-step Fourier simulations, which reveal different aspects of the buffer's operation. The performance is also estimated for modulated signals in terms of Q -factor and compared to buffers utilizing phase-insensitive amplification.

Quantum noise of parametric amplification in a phase-sensitive/insensitive intermediate condition

Phase-sensitive amplification (PSA) is a particular type of optical parametric amplification (OPA) that features a low-noise property such that the quantum-limited noise figure is 0 dB. The PSA operation is typically achieved when the signal and idler spectra are degenerate in optical parametric interactions, i.e., the degenerate OPA condition. However, for a spectrally broadened incident light, these two spectra can be partially degenerate. The present work investigates the noise property of OPA in such conditions in terms of quantum mechanics. The results quantitatively indicate the intermediate properties between PSA and phase-insensitive amplification.

Long-haul optical transmission link using low-noise phase-sensitive amplifiers

The capacity and reach of long-haul fiber optical communication systems is limited by in-line amplifier noise and fiber nonlinearities. Phase-sensitive amplifiers add 6 dB less noise than conventional phase-insensitive amplifiers, such as erbium-doped fiber amplifiers, and they can provide nonlinearity mitigation after each span. Realizing a long-haul transmission link with in-line phase-sensitive amplifiers providing simultaneous low-noise amplification and nonlinearity mitigation is challenging and to date no such transmission link has been demonstrated. Here, we demonstrate a multi-channel-compatible and modulation-format-independent long-haul transmission link with in-line phase-sensitive amplifiers. Compared to a link amplified by conventional erbium-doped fiber amplifiers, we demonstrate a reach improvement of 5.6 times at optimal launch powers with the phase-sensitively amplified link operating at a total accumulated nonlinear phase shift of 6.2 rad. The phase-sensitively amplified link transmits two data-carrying waves, thus occupying twice the bandwidth and propagating twice the total power compared to the phase-insensitively amplified link.

Four-wave mixing in potassium vapor with an off-resonant double- Λ system

We investigate both theoretically and experimentally four-wave mixing (FWM) in hot potassium vapor, generated by a copropagating pump and probe in an off-resonant double-$\mathrm{\ensuremath{\Lambda}}$ system, and present conditions when this atomic system is (1) a strong phase-insensitive parametric amplifier and (2) a source of large-amplitude squeezing. Theoretically, nonperturbative numerical calculations of optical Bloch-Maxwell equations have been solved for a four-level atomic system of K in order to derive the atomic polarization and then amplitudes of propagating optical waves, pump, probe, and conjugate. For potassium, to our knowledge, there are no such comparisons of theoretical and experimental results of gains of twin beams under the large range of FWM parameters as presented here. Results have shown that one-photon detuning has to be slightly larger than the Doppler broadened transition for large gains and strong squeezing. The gain is particularly large for small red two-photon detuning ($\ensuremath{-}2--6\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$) and high K density ($5.5--10\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). Following experimentally and theoretically determined relation between gains, probe transmissions, and squeezing in Rb and Cs, we have found parameters of FWM when maximum squeezing in hot K vapor is expected.

Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier

Discrete modulation is proven to be beneficial to improving the performance of continuous-variable quantum key distribution (CVQKD) in long-distance transmission. In this paper, we suggest a construct to improve the maximal generated secret key rate of discretely modulated eight-state CVQKD using an optical amplifier (OA) with a slight cost of transmission distance. In the proposed scheme, an optical amplifier is exploited to compensate imperfection of Bob's apparatus, so that the generated secret key rate of eight-state protocol is enhanced. Specifically, we investigate two types of optical amplifiers, phase-insensitive amplifier (PIA) and phase-sensitive amplifier (PSA), and thereby obtain approximately equivalent improved performance for eight-state CVQKD system when applying these two different amplifiers. Numeric simulation shows that the proposed scheme can well improve the generated secret key rate of eight-state CVQKD in both asymptotic limit and finite-size regime. We also show that the proposed scheme can achieve the relatively high-rate transmission at long-distance communication system.

Enhanced intensity-difference squeezing via energy-level modulations in hot atomic media

Narrow-band intensity-difference squeezing beams have important applications in quantum metrology and gravitational wave detection. The best way to generate narrow-band intensity-difference squeezing is to employ parametrically-amplified four-wave mixing process in high-gain atomic media. Such IDS can be further enhanced by cascading multiple parametrically-amplified four-wave mixing processes in separate atomic media. The complicated experimental setup, added losses and required high-power pump laser with the increase of number of stages can limit the wide uses of such scheme in practical applications. Here, we show that by modulating the internal energy level(s) with additional laser(s), the degree of original intensity-difference squeezing can be substantially increased. With an initial intensity-difference squeezing of $-8.5\pm0.4$ dB using parametrically-amplified-non-degenerate four-wave mixing process in a three-level $\Lambda$-type configuration, the degree of intensity-difference squeezing can be enhanced to $-11.9\pm0.4$ dB/$-13.9\pm0.4$ dB (corrected for losses) when we use one/two laser beam(s) to modulate the involved ground/excited state(s). More importantly, a maximal noise reduction of $-9.7\pm0.4$ dB (only corrected for electronic noise) is observed below the standard quantum limit, which is the strongest reported to date in phase insensitive amplification in four-wave mixing. Applying the model to quantum metrology, the signal-to-noise ratio is improved by 23 dB compared to the conventional Mach-Zehnder interferometer under the same phase-sensing intensity, which is a 14-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. Our results show a low-loss, robust and efficient way to produce high degree of IDS and facilitate its potential applications.

19pBJ-4 Construction of Phase-Insensitive Amplifier in the Time-Domain Using Homodyne Detection and Feed-Forward Operation

19pBJ-4 Construction of Phase-Insensitive Amplifier in the Time-Domain Using Homodyne Detection and Feed-Forward Operation

Dispersion management for nonlinearity mitigation in two-span 28 GBaud QPSK phase-sensitive amplifier links.

We present an investigation of dispersion map optimization for two-span single-channel 28 GBaud QPSK transmission systems with phase-sensitive amplifiers (PSAs). In experiments, when the PSA link is operated in a highly nonlinear regime, a 1.4 dB error vector magnitude (EVM) improvement is achieved compared to a one-span optimized dispersion map link due to improved nonlinearity mitigation. The two-span optimized dispersion map of a PSA link differs from the optimized dispersion map of a dispersion managed phase-insensitive amplifier (PIA) link. Simulations show that the performance of the two-span dispersion map optimized PSA link does not improve by residual dispersion optimization. Further, by using the two-span optimized dispersion maps repeatedly in a long-haul PSA link instead of one-span optimized maps, the maximum transmission reach can be improved 1.5 times.

Three-way noiseless signal splitting in a parametric amplifier with quantum correlation

We demonstrate that a phase-insensitive parametric amplifier, coupled to a quantum correlated source, can be used as a quantum information tap for noiseless three-way signal splitting. We find that the output signals are amplified noiselessly in two of the three output ports while the other can more or less keep its original input size without adding noise. This scheme is able to cascade and scales up for efficient information distribution in an optical network. Furthermore, we find this scheme satisfies the criteria for a non-ideal quantum non-demolition (QND) measurement and thus can serve as a QND measurement device. With two readouts correlated to the input, we find this scheme also satisfies the criterion for sequential QND measurement.

Catastrophic breakdown of the Caves model for quantum noise in some phase-insensitive linear amplifiers or attenuators based on atomic systems

When considering the effect of quantum noise (QN) in a phase-insensitive linear amplifier or attenuator, it is customary to use the single channel Caves model (SC-CM). Although this model is valid in simple situations, such as the presence of a beam splitter, it is not necessarily valid when a system with many degrees of freedom is involved. In order to address this issue, we consider in this paper various atomic transitions corresponding to amplification or attenuation using the master-equation- (ME-) based approach to model the QN and to compare the results with the SC-CM. For a four-level system that consists of a transition producing a broad gain peak and a transition producing an absorption dip, which results in perfect transparency at the center, we observe a catastrophic breakdown of the SC-CM. We also show that for a general two-level atomic system, the SC-CM does not apply, except in the limiting case when only either amplification or attenuation exists. A special case where the two models predict the same result is a {\Lambda}-type three-level electromagnetically induced transparency (EIT) system in which the QN at zero detuning vanishes while the system is in the dark state. We also study an optically pumped five-level gain EIT system which has a perfect transparency dip superimposed on a gain profile, and yields the negative dispersion suitable for use in enhancing the sensitivity-bandwidth product of an interferometric gravitational wave detector. In this case, we find that, for some set of parameters, the QN is vanishingly small at the center of the dip, and the SC-CM agrees closely with the ME model. However, we also find that for some other set of parameters, the SC-SM model disagrees strongly with the ME model. All these cases illustrate a wide range of variations in the degree of disagreement between the predictions of the SC-CM and the ME approaches.

Quantum noise in parametric amplification under phase-mismatched conditions

This paper studies quantum noise in parametric amplification under phase-mismatched conditions. The equations of motion of the quantum-mechanical field operators, which include phase mismatch under unsaturated conditions are first derived from the Heisenberg equation. Next, the noise figure is evaluated using the solutions of the derived equations. The results indicate that phase mismatch scarcely affects noise property in phase-insensitive amplification while it has a notable effect in case of phase-sensitive amplification.

Quantum noise limits in white-light-cavity-enhanced gravitational wave detectors

Previously, we had proposed a gravitational wave detector that incorporates the white-light-cavity (WLC) effect using a compound cavity for signal recycling (CC-SR). Here, we first use an idealized model for the negative dispersion medium (NDM) and use the so-called Caves model for a phase-insensitive linear amplifier to account for the quantum noise (QN) contributed by the NDM, in order to determine the upper bound of the enhancement in the sensitivity-bandwidth product. We calculate the quantum noise limited sensitivity curves for the CC-SR design, and find that the broadening of sensitivity predicted by the classical analysis is also present in these curves, but is somewhat reduced. Furthermore, we find that the curves always stay above the standard quantum limit. To circumvent this limitation, we modify the dispersion to compensate the non-linear phase variation produced by the optomechanical resonance effects. We find that the upper bound of the factor by which the sensitivity-bandwidth product is increased, compared to the highest-sensitivity result predicted by Bunanno and Chen [Phys. Rev. D 64, 042006 (2001)], is ~14. We also present a simpler scheme (WLC-SR) where a dispersion medium is inserted into the SR cavity. For this scheme, we found the upper bound of the enhancement factor to be ~18. We then consider an explicit system for realizing the NDM, which makes use of five energy levels in M-configuration to produce gain, accompanied by electromagnetically induced transparency (the GEIT system). For this explicit system, we employ the rigorous approach based on Master Equation to compute the QN contributed by the NDM, thus enabling us to determine the enhancement in the sensitivity-bandwidth product definitively rather than the upper bound thereof. Specifically, we identify a set of parameters for which the sensitivity-bandwidth product is enhanced by a factor of 17.66.