Fast simulation for interacting four-level Rydberg atoms: electromagnetically induced transparency and Autler-Townes splitting.

Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4N × 4N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.

Quantum sensing of microwave electric fields based on Rydberg atoms.

Microwave electric field (MW E-field) sensing is important for a wide range of applications in the areas of remote sensing, radar astronomy and communications. Over the past decade, Rydberg atoms have been used in ultrasensitive, wide broadband, traceable, stealthy MW E-field sensing because of their exaggerated response to MW E-fields, plentiful optional energy levels and integratable preparation methods. This review first introduces the basic concepts of quantum sensing, the properties of Rydberg atoms and the principles of quantum sensing of MW E-fields with Rydberg atoms. An overview of this very active research direction is gradually expanding, covering the progress of sensitivity and bandwidth in Rydberg atom-based microwave sensing, superheterodyne quantum sensing with microwave-dressed Rydberg atoms, quantum-enhanced sensing of MW E-field and recent advanced quantum measurement systems and approaches to further improve the performance of MW E-field sensing. Finally, a brief outlook on future development directions is provided.

Identification of orbital angular momentum using atom-based spatial self-phase modulation.

Optical vortex orbital angular momentum modes, namely the twists number of the light does in one wavelength, play a critical role in quantum-information coding, super-resolution imaging, and high-precision optical measurement. Here, we present the identification of the orbital angular momentum modes based on spatial self-phase modulation in rubidium atomic vapor. The refractive index of atomic medium is spatially modulated by the focused vortex laser beam, and the resulted nonlinear phase shift of beam directly related to the orbital angular momentum modes. The output diffraction pattern carries clearly distinguishable tails, whose number and rotation direction correspond to the magnitude and sign of the input beam orbital angular momentum, respectively. Furthermore, the visualization degree of orbital angular momentums identification is adjusted on-demand in the terms of incident power and frequency detuning. These results show that the spatial self-phase modulation of atomic vapor can provide a feasible and effective way to rapidly readout the orbital angular momentum modes of vortex beam.

Geometric pattern evolution of photonic graphene in coherent atomic medium.

The photonic graphene in atoms not only has the typical photonic band structures but also exhibits controllable optical properties that are difficult to achieve in the natural graphene. Here, the evolution process of discrete diffraction patterns of a photonic graphene, which is constructed through a three-beam interference, is demonstrated experimentally in a 5S1/2 - 5P3/2 - 5D5/2 85Rb atomic vapor. The input probe beam experiences a periodic refractive index modulation when traveling through the atomic vapor, and the evolution of output patterns with honeycomb, hybrid-hexagonal, and hexagonal geometric profiles is obtained by controlling the experimental parameters of two-photon detuning and the power of the coupling field. Moreover, the Talbot images of such three kinds of periodic structure patterns at different propagating planes are observed experimentally. This work provides an ideal platform to investigate manipulation the propagation of light in artificial photonic lattices with tunable periodically varying refractive index.

Three-dimensional location system based on an L-shaped array of Rydberg atomic receivers.

The Rydberg atomic receiver, sensing microwave electric field with high sensitivity and broad bandwidth, possesses the potential to be the staple for precise navigation and remote sensing. In this Letter, a Ku-band three-dimensional location system using an L-shaped array of Rydberg atomic receivers is theoretically proposed and experimentally demonstrated, and the proof of principle results show excellent consistency between the location-derived and the setting coordinates. The novel L-shaped array, together with the triangulation method, gives both phase difference and angle of arrival, achieving location of the horn for a signal microwave field in three-dimensional space. The concluded validity of this location system in the testing scene remains at approximately 90% with a theoretical maximum location tolerance of 5.7 mm. Furthermore, the estimation of two different spatiotemporal coordinates for the moving target confirms the velocity measurement capability of the system with errors less than 0.5 mm/s. The proposed location system using a Rydberg atomic receiver array is a verification for the most basic element and can be extended through repetition or nesting to a multi-input-multi-output system as well as multi-channel information processing.

Spatial mapping of the polarization-resolved spectrum based on vector-beam-assisted nondegenerate four-wave mixing.

The introduction of vector beams (VBs), with space-variant polarization, into the polarization-resolved spectrum, provides a convenient and rapid pathway for revealing micro-structure. Here, we realize the spatial mapping of the polarization-resolved spectrum based on VB-assisted nondegenerate four-wave mixing (FWM) in a diamond atomic system of 85Rb. The 780 nm radial VB and 776 nm linearly polarized Gaussian beam serve as the probe and pump beams in the FWM process, respectively. The generated 420 nm coherent blue light (CBL) possesses a space-variant intensity profile due to the spatially polarized atomic medium. Accordingly, the polarization-resolved spectrum can be directly mapped from a single CBL profile and the polarization information of the input 776 nm beam can be accurately extracted. In particular, such nondegenerate FWM based on VB provides a proof of principle for rapid and visual polarization-related detection by converting to a frequency domain where efficient detectors are readily available.

Sensitivity enhancement of nonlinear refractive index measurement by Gaussian-Bessel beam assisted z-scan method.

Characterizing the nonlinear optical properties of numerous materials plays a prerequisite role in nonlinear imaging and quantum sensing. Here, we present the evaluation of the nonlinear optical properties of Rb vapor by the Gaussian-Bessel beam assisted z-scan method. Owed to the concentrated energy in the central waist spot and the constant intensity of the beam distribution, the Gaussian-Bessel beam enables enhanced sensitivity for nonlinear refractive index measurement. The nonlinear self-focusing and self-defocusing effects of the Rb vapor are illustrated in the case of blue and red frequency detunings from 5S1/2 - 5P3/2 transition, respectively. The complete images of the evolution of nonlinear optical properties with laser power and frequency detuning are acquired. Furthermore, the nonlinear refractive index n2 with a large scale of 10-6 cm2/W is determined from the measured transmittance peak-to-valley difference of z-scan curves, which is enhanced by a factor of ∼ 1.73 compared to the result of a equivalent Gaussian beam. Our research provides an effective method for measuring nonlinear refractive index, which will considerably enrich the application range of nonlinear material.

All-optical information conversion in Rb vapor based on the spatial cross-phase modulation.

All-optical information conversion, conveying optical signals without electro-optical transformation, plays a vital role in the all-optical devices and optical communication. We achieve the all-optical information conversion in Rb vapor by utilizing the spatial cross-phase modulation. The refractive index of atomic medium is spatially modulated by the strong switch laser beam, which makes it as a nonlinear focusing lens for the weak signal laser beam. As a result, the far-field diffraction ring patterns of the signal laser beam interacted with atoms can effectively carry the nonlinear phase shift information of the switch laser beam. The channel numbers, channel capacities and channel storage densities of information transmission from switch laser beam to signal laser beam are investigated in the terms of switch laser intensity and vapor temperature. Finally, a special "sxu" alphabetic string, encoded by ASCII code, is introduced to verify this all-optical information conversion scheme. This work paves the way for studying optical information processing and all-optical networking with atomic ensembles.

Tunable high-order Bessel-like beam generation based on cross-phase modulation.

Nonlinear atomic media are promising substitutes for spatial light modulators (SLMs) owing to the high tunability and fast response. We demonstrate the generation of high-order Bessel-like beam based on cross-phase modulation in 85Rb atoms. The atomic medium, whose refractive index is spatially modulated by the focused Gaussian pump beam, acts as a nonlinear focusing lens for the Laguerre-Gaussian probe beam. As a result, the probe beam carries the nonlinear phase shift and is converted into a Bessel-like mode in far-field diffraction. The superior self-healing ability of the generated high-order Bessel-like beam is verified by inserting an obstruction in the beam path, and its high tunability is investigated in terms of the pump beam power and vapor temperature. Furthermore, this novel beam is used in an obstruction-immune rotation sensor to measure the angular velocity. Nonlinear atomic medium as a novel SLM promises considerable application prospects in modulating the light field structure.

Measuring saturable nonlinearity in atomic vapor via direct spatial mapping.

We demonstrate a scheme to measure the saturable nonlinearity of atomic vapor by mapping its nonlinear response function onto a light beam profile. Our analysis shows that a part of a nonlinear optical solution solved in a model governing the nonlinear beam dynamics in atomic vapor can be used to perform this measurement, even in the presence of large absorption. A desired beam profile is achieved by an evolution of a well-known structured beam, namely the Airy beam. Using this simple yet effective method, we retrieve the saturable nonlinear response function of rubidium (Rb) atomic vapor in experiment, and employ it in light propagation simulation that reproduces well observed nonlinear dynamics, which nevertheless cannot be fitted in a strong nonlinear regime with an ideal Kerr approximation. Our method is applicable to a broad spectrum of materials featured with saturable nonlinearities.

Coherent 420 nm light generated by the cavity-enhanced four-wave mixing process in Rb vapor.

We have generated a stable and continuously tunable single frequency (420 nm) coherent blue light (CBL) by the cavity-enhanced four-wave mixing process in Rb vapor. With the bow-tie-type ring cavity, the output power was 3.3 mW, two orders of magnitude higher than that of the CBL generated by the single-pass four-wave mixing process. The measured power stabilities of the 420 nm CBL operated at 2.5 mW and 1.5 mW for 1000 s were 2.89% and 1.88%, respectively. Under the scanning pump laser frequency, the continuously tunable range of the generated CBL reached 1.68 GHz without mode hopping. The measured beam qualities of the generated laser were Mx2=1.117 and My2=1.179. The excellent performance of the 420 nm CBL was characterized by velocity transfer spectroscopy with 780 nm probe laser. This high quality short wavelength coherent light is potentially applicable to photon-atom interactions in quantum optics and fundamental research fields.

Efficient all-optical modulator based on a periodic dielectric atomic lattice.

All-optical devices used to process optical signals without electro-optical conversion plays a vital role in the next generation of optical information processing systems. We demonstrate an efficient all-optical modulator that utilizes a periodic dielectric atomic lattice produced in a gas of 85Rb vapor. Four orders of diffraction patterns are observed when a probe laser is passed through the lattice. The frequency shift of the peak of each diffraction order can be tuned by adjusting the control laser power and two-photon detuning, enabling this device to be used as a multi-channel all-optical modulator. Both theoretical simulations and experimental results demonstrate that this modulator can operate over a frequency band extending from about 0 to 60 MHz. This work may pave the way for studying quantum information processing and quantum networking proposed in atomic ensembles.

All-optical tunable high-order Gaussian beam splitter based on a periodic dielectric atomic structure.

Beam splitting of high-order Gaussian (HOG) beams increases the channel capacity and improves the processing speed of the incoming information. Here a novel all-optical tunable multi-port HOG beam splitter under a periodic dielectric atomic structure is proposed and demonstrated. The original HOG beam is replicated in the output beams. A distinguishable five-port output beam is observed in the experiment, which is beneficial for high-speed optical communications. By tuning the optical properties of this periodic dielectric structure, the spatial position and intensity distribution of each output port are precisely controllable. The splitting ratio δ can be finely adjusted in the range 0 - 4.8. This work provides a new approach for multi-port HOG beam splitters and the basis for all-optical communication.

Tunable optical vortex array in a two-dimensional electromagnetically induced atomic lattice.

Optical vortex arrays (OVAs) containing multiple vortices have been in demand for multi-channel optical communications and multiple-particle trapping. In this Letter, an OVA with tunable intensity and spatial distribution was implemented all-optically in a two-dimensional (2D) electromagnetically induced atomic lattice (EIL). Such a square lattice is constructed by two orthogonal standing-wave fields in 85Rb vapor, resulting in the periodically modulated susceptibility of the probe beam based on electromagnetically induced transparency (EIT). An OVA with dark-hollow intensity distribution based on 2D EIL was observed in the experiment first. This work thus studied the nonlinear 2D EIL process both theoretically and experimentally, presenting, to the best of our knowledge, a novel method of dynamically obtaining and controlling an OVA and further promoting the construction of all-optical networks with atomic ensembles.

Characterization of rubidium thin cell properties with sandwiched structure using a multipath interferometer with an optical frequency comb.

The characterization of the layer properties of multilayered structures has attracted research interest owing to advanced applications in fields of atom-based sensors, ultra-narrow optical filters, and composite films. Here, a robust non-destructive multipath interferometry method is proposed to characterize the features of a thin cell with a borosilicate glass-rubidium-borosilicate glass sandwiched structure using a femtosecond optical frequency comb. The multipath interference method serves as a powerful tool for identification of the layer number and physical thickness of a three-layered structure. Moreover, the global distribution map is obtained by scanning the entire region. Furthermore, the amplitude of sub-Doppler reflection spectra of the rubidium D2 line is confirmed at different target points to validate this method. This result promotes the development of thin-cell-based atomic devices with strong light-matter interaction at atomic scales.

An Integrated Mission Planning Framework for Sensor Allocation and Path Planning of Heterogeneous Multi-UAV Systems.

Mission planning is the guidance for a UAV team to perform missions, which plays the most critical role in military and civil applications. For complex tasks, it requires heterogeneous cooperative multi-UAVs to satisfy several mission requirements. Meanwhile, airborne sensor allocation and path planning are the critical components of heterogeneous multi-UAVs system mission planning problems, which affect the mission profit to a large extent. This paper establishes the mathematical model for the integrated sensor allocation and path planning problem to maximize the total task profit and minimize travel costs, simultaneously. We present an integrated mission planning framework based on a two-level adaptive variable neighborhood search algorithm to address the coupled problem. The first-level is devoted to planning a reasonable airborne sensor allocation plan, and the second-level aims to optimize the path of the heterogeneous multi-UAVs system. To improve the mission planning framework's efficiency, an adaptive mechanism is presented to guide the search direction intelligently during the iterative process. Simulation results show that the effectiveness of the proposed framework. Compared to the conventional methods, the better performance of planning results is achieved.

Optically tunable grating in a V+Ξ configuration involving a Rydberg state.

A novel tunable all-optical grating is realized experimentally in a V+Ξ configuration coherent rubidium thermal vapor. This new energy level structure employs a Rydberg level as the uppermost level and contains two typical electromagnetically induced transparency energy level configurations with the same probe field. Compared with the traditional V-type three-level grating, a significant improvement of the diffraction efficiency of this novel grating was observed. Its improvement was then also demonstrated experimentally by the transition spectrum and theoretically by a comprehensive simulation. The diffraction efficiency gain introduced by the control laser field was tuned with several experimental parameters, such as the atomic density and the control field intensity. And the maximum enhancement rate of first-order diffraction efficiency is proved to be as high as 30%. Such a novel all-optical tunable grating promises to be the new driving force in the advancement of all-optical communications and information technology.

Measurement of the Kerr nonlinear refractive index of the Rb vapor based on an optical frequency comb using the z-scan method.

We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10-6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.

Prognostic and diagnostic value of circRNA expression in colorectal carcinoma: a meta-analysis.

BACKGROUND: Circular RNAs (circRNAs) are research hotspots in the network of noncoding RNAs in numerous tumours. The purpose of our study was to evaluate the clinicopathological, prognostic and diagnostic value of circRNAs in colorectal cancer. METHODS: The PubMed, Cochrane Library, and Web of Science online databases were searched for relevant studies before May 15, 2019. Pooled hazard ratios (HRs) and odds ratios (ORs) with 95% confidence intervals (CIs) were calculated to assess the association between circRNAs expression, and overall survival (OS) and clinical parameters. Pooled sensitivity, specificity, and the area under the curve (AUC) were employed to assess the diagnostic value of circRNAs. RESULTS: A total of 19 studies were enrolled in this meta-analysis, with 11 on clinicopathological parameters, 8 on prognosis and 7 on diagnosis. For clinicopathological and prognostic value, elevated expression of oncogenic circRNAs was correlated with poor clinical parameters (tumor size: OR = 1.769, 95% CI: 1.097-2.852; differentiation grade: OR = 1.743, 95% CI: 1.032-2.946; TNM stage: OR = 3.320, 95% CI: 1.529-7.207; T classification: OR = 3.410, 95% CI: 2.088-5.567; lymph node metastasis: OR = 3.357, 95% CI: 2.160-5.215; distal metastasis: OR = 4.338, 95% CI: 2.503-7.520) and worse prognosis (HR = 2.29, 95% CI: 1.50-3.52). However, elevated expression of tumor-suppressor circRNAs was correlated with better clinical parameters (differentiation grade: OR = 0.453, 95% CI: 0.261-0.787; T classification: OR = 0.553, 95% CI: 0.328-0.934; distal metastasis: OR = 0.196, 95% CI: 0.077-0.498) and favorable prognosis (HR = 0.37, 95% CI: 0.22-0.64). For diagnostic value, the pooled sensitivity, specificity, and AUC were 0.82 (95% CI, 0.75-0.88), 0.72 (95% CI, 0.66-0.78), and 0.82 (95% CI, 0.78-0.85), respectively. CONCLUSIONS: These results indicate that circRNAs may be potential biomarkers for the diagnosis and prognosis of colorectal cancer.

Diagnostic performance of circulating exosomes in human cancer: A meta-analysis.

BACKGROUND: Cancer has become a public health problem with high morbidity and mortality. Recent publications have shown that exosomes can be used as potential diagnostic biomarkers of cancer. However, the diagnostic accuracy and reliability of circulating exosomes remain unclear. The present meta-analysis was conducted to comprehensively summarize the overall diagnostic performance of circulating exosomes for cancer. METHODS: Eligible studies published up to June 27, 2019, on PubMed, Embase, and Cochrane Library were selected for the meta-analysis. All statistical analyses were performed by STATA 15.1 statistical software and Meta-DiSc 1.4. Quality Assessment for Studies of Diagnostic Accuracy 2 tool was used to access the quality of included studies. A bivariate mixed-effects model was applied to calculate the diagnostic indexes from included studies. RESULTS: A total of 5924 participants comprising 3161 cases and 2763 controls from 42 eligible studies were analyzed. The pooled sensitivity, specificity, positive likelihood ratio, negative likelihood ratio, diagnostic odds ratio, and the area under the curve with 95% confidence intervals (95% CI) were as follows: 0.79 (0.75-0.82), 0.81 (0.78-0.84), 4.1 (3.5-4.8), 0.26 (0.22-0.31), 16 (12-21), and 0.87 (0.84-0.89), respectively. Sensitivity analysis suggested no study exclusively contributed to the heterogeneity, and Deeks' funnel plot asymmetry test indicated no potential publication bias (P = .09). CONCLUSIONS: The meta-analysis indicated that circulating exosomes could serve as effective and minimally invasive biomarkers for diagnosis of cancer, especially in patients with hepatocellular carcinoma or ovarian cancer, serum-based samples and exosomal proteins.