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Fuzzy dark matter is a promising alternative to the standard cold dark matter. It has quite recently been noticed, that they can not only successfully explain the large-scale structure in the Universe, but can also solve problems of position and flux anomalies in galaxy strong lensing systems. In this paper we focus on the perturbation of time delays in strong lensing systems caused by fuzzy dark matter, thus making an important extension of previous works. We select a specific system HS 0810+2554 for the study of time delay anomalies. Then, based on the nature of the fuzzy dark matter fluctuations, we obtain theoretical relationship between the magnitude of the perturbation caused by fuzzy dark matter, its content in the galaxy, and its de Broglie wavelength $\lambda _{\mathrm{dB}}$. It turns out that, the perturbation of strong lensing time delays due to fuzzy dark matter quantified as standard deviation is $\sigma_{\Delta t} \propto \lambda _{\mathrm{dB}}^{1.5}$. We also verify our results through simulations. Relatively strong fuzzy dark matter fluctuations in a lensing galaxy make it possible to to destroy the topological structure of the lens system and change the arrival order between the saddle point and the minimum point in the time delays surface. Finally, we stress the unique opportunity for studying properties of fuzzy dark matter created by possible precise time delay measurements from strongly lensed transients like fast radio bursts, supernovae or gravitational wave signals., Comment: 11 pages, 10 figures

The measurement of the parametrized post-Newtonian parameter $\gamma_{\rm{PPN}}$ is a robust test of general relativity (GR). In some modified theories of gravity, $\gamma_{\rm{PPN}}$ may evolve with the redshift and deviate from one at high redshifts. This means that precise constraints on $\gamma_{\rm{PPN}}$ acquired in the solar system experiments could not be sufficient to test such theories and it is necessary to constrain $\gamma_{\rm{PPN}}$with high precision at high redshifts. However, in many approaches aimed at extragalactic tests of GR, the results might be biased due to entanglement of various factors, such as cosmic curvature, cosmic opacity, and the Hubble constant. Strong lensing systems naturally provide a laboratory to test $\gamma_{\rm{PPN}}$ at galactic scales and high redshifts, but there is degeneracy between measured strength of gravity and cosmic distances in the lensing system. Gravitational waves (GWs) from binary neutron star mergers (standard sirens) provide a direct way to break this degeneracy by providing self-calibrated measurements of the luminosity distance. {We investigate the possibility of estimating $\gamma_{\rm{PPN}}$ by combining well measured strongly lensed systems with GW signals from coalescing neutron stars. Such combination provides a cosmological-model independent, relatively pure and unbiased method for the inference of $\gamma_{\rm{PPN}}$ parameter, avoiding the influence of the above factors and the mass-sheet degeneracy in the lens.} Based on the simulated future 55 lensed quasar systems we demonstrated that the precision of $\gamma_{\rm{PPN}}$ parameter obtained by our method could be of order of $\sim 10^{-2}$. One may reasonably expect that our approach will play an increasingly important role in precise testing the validity of general relativity at galactic scales and high redshifts., Comment: 9 pages, 3 figures, submitted to PRD

{{The reappearance of supernova Refsdal with detailed modeling of the lens cluster allows us to measure the time-delay distance,}} which serves as a powerful tool to determine the Hubble constant ($H_0$). We give a cosmological-model-independent method to estimate $H_0$ through Gaussian process regression, using time-delay measurements from this lensed supernova in combination with supernova data from the Pantheon+ sample. {{Using eight mass models for the lens cluster,}} we infer $H_0 = 64.2^{+4.4}_{-4.3} \, \rm{km\,s^{-1}\,Mpc^{-1}}$ and using two cluster models most consistent with the observations, we infer $H_0 = 66.3^{+3.8}_{-3.6} \, \rm{km\,s^{-1}\,Mpc^{-1}}$. Our estimates of the value of $H_0$ are in $1\sigma$ agreement with the results assuming a flat $\Lambda$CDM model and the uncertainties are comparable. Our constraint results on $H_0$ from the eight lens models and the two lens models indicate $2\sigma$ and $1.8\sigma$ tensions with that estimated by Supernova H0 for the Equation of State, respectively. However, our median values of $H_0$ from the two sets of lens models show good consistency with $H_0$ inferred from Planck cosmic microwave background observations assuming $\Lambda$CDM model within $1\sigma$. We also find that our results for $H_0$ indicate $2\sigma$ deviations and $1.7\sigma$ deviations from the constraint results of $H_0$ using six time-delay quasars by H0LiCOW with the same analysis method., Comment: 6 pages, 2 figures

The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once that the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally-feasible system provides a platform to investigate braiding dynamics, the SU(3) physics and the qutrit gates., Comment: 10 pages, 6 figures

Ultralight axion or axionlike particles are one of the most promising candidates for dark matter because they are a well-motivated solution for the theoretical strong $CP$ problem and observational issues on small scales, i.e. the core-cusp problem and the satellite problem. A tiny coupling of axions and photons induces birefringence. We propose the differential birefringence measurements of multiple images of gravitationally lensed fast radio burst (FRB) systems as probes of the Galactic axion dark matter (ADM) background. In addition to general advantages of lensing systems, i.e. alleviating systematics and intrinsic astrophysical dependencies, precise measurements of lensing time delay and polarization angle in gravitationally lensed FRB systems make them a more robust and powerful probe. We show that, with a single lensed FRB system (which may be detected in large numbers in the SKA era), the axion-photon coupling under the ADM background could be constrained to be $g_{a\gamma} < 7.3 \times 10^{-11}~ \mathrm{GeV^{-1}}$ for an axion mass $m_a\sim10^{-20}~\mathrm{eV}$. This will be of great significance in achieving synergistic searches of the Galactic ADM with other astrophysical probes and laboratorial experiments., Comment: 9 pages, 1 figure, to be published in PRD Letter

Strong gravitational lensing provides a natural opportunity to test General Relativity (GR). We propose a model-independent method for simultaneous constraining on Hubble constant ($H_0$) and post-Newtonian parameter (${\gamma_{\rm{PPN}}}$) using strong lensing systems and observational SNe Ia. The time-delay measurements from strong lesning can directly determine the Hubble constant, and the lens distance inferred from the spectroscopic measurement of the stellar kinematics of the deflector galaxy can help us to constrain the post-Newtonian parameter. We seek the Pantheon dataset and reconstruct unanchored distances using Gaussian process regression to achieve the cosmological model-independent GR testing instead of assuming a specific model, which can reduce possible bias on GR testing and measurement of Hubble constant. Combining the reconstructed unanchored distances and the four H0LiCOW lenses datasets, our results are $H_0=72.9^{+2.0}_{-2.3} {\mathrm{~km~s^{-1}~Mpc^{-1}}}$ and ${\gamma_{\rm{PPN}}}=0.89^{+0.17}_{-0.15}$. All the lenses show that there is no obvious evidence to support GR deviation within observational uncertainties. In the subsequent analysis, we consider a ratio of distance ${D_{\Delta t}}/{D^{'}_{d}}$ method to further avoid the influence of $H_0$ on GR testing. The results show that, except J1206 within the $\sim1.2\sigma$ observational uncertainty, the remaining 3 lenses support GR holds within the $1\sigma$ observational uncertainties., Comment: 7 pages, 3 figures, submitted to MNRAS

Absolute distances from strong lensing can anchor Type Ia Supernovae (SNe Ia) at cosmological distances giving a model-independent inference of the Hubble constant ($H_0$). Future observations could provide strong lensing time-delay distances with source redshifts up to $z\,\simeq\,4$, which are much higher than the maximum redshift of SNe Ia observed so far. In order to make full use of time-delay distances measured at higher redshifts, we use quasars as a complementary cosmic probe to measure cosmological distances at redshifts beyond those of SNe Ia and provide a model-independent method to determine $H_0$. In this work, we demonstrate a model-independent, joint constraint of SNe Ia, quasars, and time-delay distances from strong lensed quasars. We first generate mock data sets of SNe Ia, quasar, and time-delay distances based on a fiducial cosmological model. Then, we calibrate the quasar parameters model independently using Gaussian process (GP) regression with mock SNe Ia data. Finally, we determine the value of $H_0$ model-independently using GP regression from mock quasars and time-delay distances from strong lensing systems. As a comparison, we also show the $H_0$ results obtained from mock SNe Ia in combination with time-delay lensing systems whose redshifts overlap with SNe Ia. Our results show that quasars at higher redshifts show great potential to extend the redshift coverage of SNe Ia and thus enable the full use of strong lens time-delay distance measurements from ongoing cosmic surveys and improve the accuracy of the estimation of $H_0$ from $2.1\%$ to $1.3\%$ when the uncertainties of the time-delay distances are $5\%$ of the distance values., Comment: 10 pages, 5 figures, 2 tables, accepted for publication in ApJ

The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. Recently, the Rydberg electrometer has garnered considerable attention due to its exceptional sensitivity, small-size, and broad tunability. This specific quantum sensor utilizes low-entropy laser beams to detect disturbances in atomic internal states, thereby circumventing the intrinsic thermal noise encountered by its classical counterparts. However, due to the thermal motion of atoms, the advanced Rydberg-atom microwave electrometer falls considerably short of the standard quantum limit by over three orders of magnitude. In this study, we utilize an optically thin medium with approximately 5.2e5 laser-cooled atoms to implement heterodyne detection. By mitigating a variety of noises and strategically optimizing the parameters of the Rydberg electrometer, our study achieves an electric-field sensitivity of 10.0 nV/cm/Hz^1/2 at a 100 Hz repetition rate, reaching a factor of 2.6 above the standard quantum limit and a minimum detectable field of 540 pV/cm. We also provide an in-depth analysis of noise mechanisms and determine optimal parameters to bolster the performance of Rydberg-atom sensors. Our work provides insights into the inherent capacities and limitations of Rydberg electrometers, while offering superior sensitivity for detecting weak microwave signals in numerous applications., Comment: 12 pages

The joint detection of GW signals by a network of instruments will increase the detecting ability of faint and far GW signals with higher signal-to-noise ratios (SNRs), which could improve the ability of detecting the lensed GWs as well, especially for the 3rd generation detectors, e.g. Einstein Telescope (ET) and Cosmic Explorer (CE). However, identifying Strongly Lensed Gravitational Waves (SLGWs) is still challenging. We focus on the identification ability of 3G detectors in this article. We predict and analyze the SNR distribution of SLGW signals and prove only 50.6\% of SLGW pairs detected by ET alone can be identified by Lens Bayes factor (LBF), which is a popular method at present to identify SLGWs. For SLGW pairs detected by CE\&ET network, owing to the superior spatial resolution, this number rises to 87.3\%. Moreover, we get an approximate analytical relation between SNR and LBF. We give clear SNR limits to identify SLGWs and estimate the expected yearly detection rates of galaxy-scale lensed GWs that can get identified with 3G detector network., Comment: 9 pages, 7 figures

Strong gravitational lensed quasars (QSOs) have emerged as powerful and novel cosmic probes as they can deliver crucial cosmological information, such as a measurement of the Hubble constant, independent of other probes. Although the upcoming LSST survey is expected to discover $10^3-10^4$ lensed QSOs, a large fraction will remain unresolved due to seeing. The stochastic nature of the quasar intrinsic flux makes it challenging to identify lensed ones and measure the time delays using unresolved light curve data only. In this regard, Bag et al (2022) introduced a data-driven technique based on the minimization of the fluctuation in the reconstructed image light curves. In this article, we delve deeper into the mathematical foundation of this approach. We show that the lensing signal in the fluctuation curve is dominated by the auto-correlation function (ACF) of the derivative of the joint light curve. This explains why the fluctuation curve enables the detection of the lensed QSOs only using the joint light curve, without making assumptions about QSO flux variability, nor requiring any additional information. We show that the ACF of the derivative of the joint light curve is more reliable than the ACF of the joint light curve itself because intrinsic quasar flux variability shows significant auto-correlation up to a few hundred days (as they follow a red power spectrum). In addition, we show that the minimization of fluctuation approach provides even better precision and recall as compared to the ACF of the derivative of the joint light curve when the data have significant observational noise., Comment: 20 pages, 8 figures, 1 table, accepted for publication in ApJ

The past decades have witnessed a lot of progress in gravitational lensing with two main targets: stars and galaxies (with active galactic nuclei). The success is partially attributed to the continuous luminescence of these sources making the detection and monitoring relatively easy. With the running of ongoing and upcoming large facilities/surveys in various electromagnetic and gravitational-wave bands, the era of time-domain surveys would guarantee constant detection of strongly lensed explosive transient events, for example, supernovae in all types, gamma ray bursts with afterglows in all bands, fast radio bursts and even gravitational waves. Lensed transients have many advantages over the traditional targets in studying the Universe and magnification effect helps to understand the transients themselves at high redshifts. In this review article, basing on the recent achievements in the literature, we summarize the methods of searching for different kinds of lensed transient signals, the latest results on detection and their applications in fundamental physics, astrophysics and cosmology. At the same time, we give supplementary comments as well as prospects of this emerging research direction that may help readers who are interested in entering this field., Comment: 23 pages, 4 figures

Since the first gravitational wave (GW) event from binary black hole (BBH) was detected by LIGO-Virgo, GWs have become a useful probe on astrophysics and cosmology. If compact dark matter (DM) objects e.g. primordial black holes, contribute a significant fraction of dark matter at wide mass range, they will cause microlensing in the GW signals with long wavelengths that are distinct from the lensing effects of electromagnetic signals from astrophysical objects. In this paper, we apply the lensing effect of GW from BBH to derive constraints on the abundance of compact DM for the Cosmic Explorer, a third-generation ground-based GW detector. We firstly consider two channels of formation of BBH that contribute to low and high redshift GW sources, including the astrophysical origin BBH scenario, and the primordial origin BBH scenario. Secondly, comparing with the method of optical depth, we use the Bayesian analysis to derive constraints on the abundance of compact DM with different mass function of lens taken into consideration. For a null search with $1000$ detected GW events of BBH, we find that the abundance of compact DM could be constrained to $\lesssim0.1\%$ in the mass range $\geq500~M_{\odot}$ at $68\%$ confidence level. In addition, if a GW event lensed by a compact DM object with $M_{\rm l}\in[100~M_{\odot},300~M_{\odot}]$ is detected in $100$ detected GW events of BBH, we can derive that the estimation of the abundance of compact DM is from $2.3\%$ to $25.2\%$ in this mass range with the Bayesian analysis., Comment: 9 pages, 7 figures. Accepted by MNRAS

The recent rapid growth of the black hole (BH) catalog from gravitational waves (GWs), has allowed us to study the substructure of black hole mass function (BHMF) beyond the simplest Power-Law distribution. However, the BH masses inferred from binary BH merger events, may be systematically 'brightened' or 'dimmed' by the gravitational lensing effect. In this work, we investigate the impact of gravitational lensing on the BHMF inference considering the detection of the third-generation GW detector -- the Einstein Telescope (ET). We focus on high redshift, $z=10$, in order to obtain the upper limits of this effect. We use Monte Carlo (MC) method to simulate the data adopting 3 original BHMFs under Un-Lensed and Lensed scenarios, then recover the parameters of BHMFs from the mock data, and compare the difference of results, respectively. We found that all the parameters are well recovered within one standard deviation(std., 1$\sigma$), and all 3 BHMF models are reconstructed within 68\% credible interval, suggesting that lensing would not change the main structure drastically, even at very high redshifts and with high precision of ET. And the modest influence beyond $50M_{\odot}$, depends on the modeling of the high mass tail or substructure of BHMF. We conclude that the impact of lensing on BHMF inference with ET can be safely ignored in the foreseeable future. Careful handling of lensing effects is required only when focusing on an accurate estimation of the high mass end of BHMF at high redshifts., Comment: 13 pages, 11 figures, accepted by MNRAS

As a completely independent method, the measurement of time delay of strongly lensed quasars (TDSL) are crucial to resolve the Hubble tension. Extensive monitoring is required but so far limited to a small sample of strongly lensed quasars. Together with several partner institutes, Beijing Normal University is constructing a 1.93m reflector telescope at the Muztagh-Ata site in west China, which has the world class observing conditions. The telescope will be equipped with both a three-channel imager/photometer which covers $3500-11000$ Angstrom wavelength band, and a low-medium resolution ($\lambda/\delta\lambda=500/2000/7500$) spectrograph. In this paper, we investigate the capability of Muztagh-Ata 1.93m telescope in measuring time delays of strongly lensed quasars. We generate mock strongly lensed quasar systems and light curves with microlensing effects based on five known strongly lensed quasars, i.e., RX J1131-1231, HE 0435-1223, PG 1115+080, WFI 2033-4723 and SDSS 1206+4332. In particular, RX J1131-1231 is generated with lens modeling in this work. Due to lack of enough information, we simulate the other 4 systems with the public data without lens modeling. According to simulations, for RX J1131-like systems (wide variation in time delay between images) the TDSL measurement can be achieved with the precision about $\Delta t=0.5$ day with 4 seasons campaign length and 1 day cadence. This accuracy is comparable to the up-coming TDCOSMO project. And it would be better when the campaign length keeps longer and with high cadence. As a result, the capability of Muztagh-Ata 1.93m telescope allows it to join the network of TDSL observatories. It will enrich the database for strongly lensed quasar observations and make more precise measurements of time delays, especially considering the unique coordinate of the site., Comment: 17 pages, 15 figures

Quantum transducers that can convert quantum signals from the microwave to the optical domain are a crucial optical interface for quantum information technology. Coherent microwave-to-optics conversions have been realized with various physical platforms, but all of them are limited to low efficiencies of less than 50\%, the threshold of the no-cloning quantum regime. Here we report a coherent microwave-to-optics transduction using Rydberg atoms and off-resonant scattering technique with an efficiency of $82\pm 2\%$ and a bandwidth of about 1 MHz. The high conversion efficiency is maintained for microwave photons range from thousands to about 50, suggesting that our transduction is readily applicable to the single-photon level. Without requiring cavities or aggressive cooling to quantum ground states, our results would push atomic transducers closer to practical applications in quantum technologies., Comment: Nature Photonics(2022)

Gamma-ray bursts (GRBs) at high redshifts are expected to be gravitationally lensed by objects of different mass scales. Besides a single recent claim, no lensed GRB has been detected so far by using the gamma-ray data only. In this paper, we suggest that the multi-band afterglow data might be an efficient way to search for lensed GRB events. Using the standard afterglow model we calculate the characteristics of the lensed afterglow lightcurves under the assumption of two popular analytic lens models: point mass and Singular Isothermal Sphere (SIS) model. In particular, when different lensed images cannot be resolved, their signals would be superimposed together with a given time delay. In this case, the X-ray afterglows are likely to contain several X-ray flares of similar width in linear scale and similar spectrum, and the optical afterglow lightcurve will show rebrightening signatures. Since the lightcurves from the image arriving later would be compressed and deformed in the logarithmic time scale, the larger time delay (i.e. the larger mass of the lens), the easier is to identify the lensing effect. We analyzed the archival data of optical afterglows and found one potential candidate of the lensed GRB (130831A) with time delay $\sim$500 s, however, observations of this event in gamma-ray and X-ray band seem not to support the lensing hypothesis. In the future, with the cooperation of the all-sky monitoring gamma-ray detectors and multi-band sky survey projects, our method proposed in this paper would be more efficient in searching for strongly lensed GRBs., Comment: Accepted for publication in ApJ

Identifying multiply imaged quasars is challenging due to their low density in the sky and the limited angular resolution of wide field surveys. We show that multiply imaged quasars can be identified using unresolved light curves, without assuming a light curve template or any prior information. After describing our method, we show using simulations that it can attain high precision and recall when we consider high-quality data with negligible noise well below the variability of the light curves. As the noise level increases to that of the Zwicky Transient Facility (ZTF) telescope, we find that precision can remain close to $100\%$ while recall drops to $\sim 60\%$. We also consider some examples from the Time Delay Challenge 1 (TDC1) and demonstrate that the time delays can be accurately recovered from the joint light curve data in realistic observational scenarios. We further demonstrate our method by applying it to publicly available COSMOGRAIL data of the observed lensed quasar SDSS J1226-0006. We identify the system as a lensed quasar based on the unresolved light curve and estimate a time delay in good agreement with the one measured by COSMOGRAIL using the individual image light curves. The technique shows great potential to identify lensed quasars in wide field imaging surveys, especially the soon to be commissioned Vera Rubin Observatory., Comment: Matches the published version, 27 pages, 23 figures

The possibility that primordial black holes (PBHs) form a part of dark matter has been considered for a long time but poorly constrained over a wide mass range. Fast radio bursts (FRBs) are bright radio transients with millisecond duration. Lensing effect of them has been proposed as one of the cleanest probes for constraining the presence of PBHs in the stellar mass window. In this paper, we first apply the normalised cross-correlation algorithm to search and identify candidates of lensed FRBs in the latest public FRB observations, i.e. $593$ FRBs which mainly consist of the first Canadian Hydrogen Intensity Mapping Experiment FRB catalog, and then derive constraints on the abundance of PBHs from the null search result of lensing signature. For a monochromatic mass distribution, the fraction of dark matter made up of PBHs could be constrained to $\leq87\%$ for $\geq500~M_{\odot}$ at 95\% confidence level by assuming flux ratio thresholds dependent signal-to-noise ratio for each FRB and that apparently one-off events are intrinsic single bursts. This result would be improved by a three times factor when a conventional constant flux ratio threshold is considered. Moreover, we derive constraints on PBHs with a log-normal mass function naturally predicted by some popular inflation models and often investigated with gravitational wave detections. We find that, in this mass distribution scenario, the constraint from currently public FRB observations is relatively weaker than the one from gravitational wave detections. It is foreseen that upcoming complementary multi-messenger observations will yield considerable constraints on the possibilities of PBHs in this intriguing mass window., Comment: 13 Pages, 9 Figures, 2 Tables, Accepted by ApJ. arXiv admin note: text overlap with arXiv:2103.08510

Strong lensing of gravitational waves (GWs) is attracting growing attention of the community. The event rates of lensed GWs by galaxies were predicted in numerous papers, which used some approximations to evaluate the GW strains detectable by a single detector. The joint-detection of GW signals by a network of instruments will increase the detecting ability of fainter and farther GW signals, which could increase the detection rate of the lensed GWs, especially for the 3rd generation detectors, e.g., Einstein Telescope (ET) and Cosmic Explorer (CE). Moreover, realistic GW templates will improve the accuracy of the prediction. In this work, we consider the detection of galaxy-scale lensed GW events under the 2nd, 2.5th, and 3rd generation detectors with the network scenarios and adopt the realistic templates to simulate GW signals. Our forecast is based on the Monte Carlo technique which enables us to take Earth's rotation into consideration. We find that the overall detection rate is improved, especially for the 3rd generation detector scenarios. More precisely, it increases by ~37% adopting realistic templates, and under network detection strategy, further increases by ~58% comparing with adoption of the realistic templates, and we estimate that the 3rd generation GW detectors will detect hundreds lensed events per year. The effect from the Earth's rotation is weakened in the detector network strategy., Comment: 7pages, 1 figure, accepted by MNRAS