Strong Gravitational Lensing of Gravitational Waves with TianQin

When gravitational waves pass by a massive object on its way to the Earth, strong gravitational lensing effect will happen. Thus the GW signal will be amplified, deflected, and delayed in time. Through analysing the lensed GW waveform, physical properties of the lens can be inferred. On the other hand, neglecting lensing effects in the analysis of GW data may induce systematic errors in the estimating of source parameters. As a space-borne GW detector, TianQin will be launched in the 2030s. It is expected to detect dozens of MBHBs merger as far as z = 15, and thus will have high probability to detect at least one lensed event during the mission lifetime. In this article, we discuss the capability of TianQin to detect lensed MBHBs signals. Three lens models are considered in this work: the point mass model, the SIS model, and the NFW model. The sensitive frequency band for space-borne GW detectors is around milli-hertz, and the corresponding GW wavelength could be comparable to the lens gravitational length scale, which requires us to account for wave diffraction effects. In calculating lensed waveforms, we adopt the approximation of geometric optics at high frequencies to accelerate computation, while precisely evaluate the diffraction integral at low frequencies. Through a Fisher analysis, we analyse the accuracy to estimate the lens parameters. We find that the accuracy can reach to the level of 10^-3 for the mass of point mass and SIS lens, and to the level of 10^-5 for the density of NFW lens. We also assess the impact on the accurate of estimating the source parameters, and find that the improvement of the accuracy is dominated by the increasing of SNR.Comment: 12 pages, 8 figure

An Opacity-Free Method of Testing the Cosmic Distance Duality Relation Using Strongly Lensed Gravitational Wave Signals

The cosmic distance duality relation (CDDR), expressed as DL(z) = (1 + z)2DA(z), plays an important role in modern cosmology. In this paper, we propose a new method of testing CDDR using strongly lensed gravitational wave (SLGW) signals. Under the geometric optics approximation, we calculate the gravitational lens effects of two lens models, the point mass and singular isothermal sphere. We use functions of {\eta}1(z) = 1 + {\eta}0z and {\eta}2(z) = 1 + {\eta}0z=(1 + z) to parameterize the deviation of CDDR. By reparameterizing the SLGW waveform with CDDR and the distance-redshift relation, we include the deviation parameters {\eta}0 of CDDR as waveform parameters. We evaluate the ability of this method by calculating the parameter estimation of simulated SLGW signals from massive binary black holes. We apply the Fisher information matrix and Markov Chain Monte Carlo methods to calculate parameter estimation. We find that with only one SLGW signal, the measurement precision of {\eta}0 can reach a considerable level of 0.5-1.3% for {\eta}1(z) and 1.1-2.6% for {\eta}2(z), depending on the lens model and parameters.Comment: 15 pages, 7 figure

Measuring the Hubble Constant Using Strongly Lensed Gravitational Wave Signals

The measurement of the Hubble constant $H_0$ plays an important role in the study of cosmology. In this letter, we propose a new method to constrain the Hubble constant using the strongly lensed gravitational wave (GW) signals. By reparameterizing the waveform, we find that the lensed waveform is sensitive to the $H_0$. Assuming the scenario that no electromagnetic counterpart of the GW source can be identified, our method can still give meaningful constraints on the $H_0$ with the information of the lens redshift. We then apply Fisher information matrix and Markov Chain Monte Carlo to evaluate the potential of this method. For the space-based GW detector, TianQin, the $H_0$ can be constrained within a relative error of $\sim$ 0.3-2\%, using a single strongly lensed GW event. Precision varies according to different levels of electromagnetic information.Comment: 8 pages, 4 figure

Storage of multiple single-photon pulses emitted from a quantum dot in a solid-state quantum memory

Quantum repeaters are critical components for distributing entanglement over long distances in presence of unavoidable optical losses during transmission. Stimulated by Duan-Lukin-Cirac-Zoller protocol, many improved quantum-repeater protocols based on quantum memories have been proposed, which commonly focus on the entanglement-distribution rate. Among these protocols, the elimination of multi-photons (multi-photon-pairs) and the use of multimode quantum memory are demonstrated to have the ability to greatly improve the entanglement-distribution rate. Here, we demonstrate the storage of deterministic single photons emitted from a quantum dot in a polarization-maintaining solid-state quantum memory; in addition, multi-temporal-mode memory with $1$, $20$ and $100$ narrow single-photon pulses is also demonstrated. Multi-photons are eliminated, and only one photon at most is contained in each pulse. Moreover, the solid-state properties of both sub-systems make this configuration more stable and easier to be scalable. Our work will be helpful in the construction of efficient quantum repeaters based on all-solid-state devicesComment: Published version, including supplementary materia

Comparative study on saponin fractions from Panax notoginseng inhibiting inflammation-induced endothelial adhesion molecule expression and monocyte adhesion

<p>Abstract</p> <p>Background</p> <p><it>Panax notoginseng </it>is commonly used for the treatment of cardiovascular diseases in China. The present study investigates the effects of three different saponin fractions (<it>ie </it>total saponins, PNS; protopanaxadiol-type saponin, PDS; and protopanaxatriol-type saponin, PTS) and two major individual ingredients (<it>ie </it>ginsenoside Rg₁and Rb₁) from <it>P. notoginseng </it>on the endothelial inflammatory response <it>in vitro </it>and <it>in vivo</it>.</p> <p>Methods</p> <p>Recombinant human tumor necrosis factor-α (TNF-α) was added to the culture medium of human coronary artery endothelial cells (HCAECs) to induce an inflammatory response. A cell adhesion assay was used to determine the effect of the <it>P. notoginseng </it>saponin fractions on endothelial-monocyte interaction. The cell adhesion molecule (CAMs) expression, including ICAM-1 and VCAM-1, in the protein level on the surface of endothelial cells were measured by cellular ELISA. CAMs expression in mRNA level was also assayed by qRT-PCR in the HCAECs and the aorta of rat fed with high cholesterol diet (HCD). Western blotting was used to detect effect of the saponin fractions on CAMs protein expression in HCAECs. In addition, nuclear translocation of p65, a surrogate marker for NF-κB activation, was measured by immunostaining.</p> <p>Results</p> <p>Three saponin fractions and two individual ginsenosides exhibited the inhibitory effects on monocyte adhesion on TNF-α-activated HCAECs and expression of ICAM-1 and VCAM-1 at both mRNA and protein levels <it>in vitro</it>. The saponin fractions exhibited a similar trend of the inhibitory effects on the mRNA expression of CAMs in the aorta of HCD-fed rat <it>in vivo</it>. These inhibitory effect of saponin fractions maybe attribute partially to the suppression of the TNF-α-induced NF-κB activation.</p> <p>Conclusion</p> <p>Our data demonstrate that saponin fractions (<it>ie </it>PNS, PDS and PTS) and major individual ginsenosides (<it>ie </it>Rg₁and Rb₁) have potential anti-atherogenic effects. Among the tested saponin fractions, PDS is the most potent saponin fraction against TNF-α-induced monocyte adhesion as well as the expression of adhesion molecules <it>in vitro </it>and <it>in vivo</it>.</p