We theoretically propose a photonic orbital angular momentum quantum memory, currently of great interest from the perspective of quantum networks, based on a ring-trapped Bose-Einstein condensate interacting with Laguerre-Gaussian beams. The optical states are stored in the large Hilbert space of topologically protected persistent currents of the condensate. In contrast to earlier work, our proposal uses a cavity, which enhances the light-matter interaction by several orders of magnitude, resulting in high fidelity, convenient detection, and no need to repeat read-write cycles degraded by atom loss. Our scheme avoids using multiple internal atomic states as in generic electromagnetically induced transparency-based protocols and thus bypasses problems like off-resonant photoassociation by the control fields and dephasing effects that limit memory storage time. For optimized parameters, our work yields a storage time 3 orders of magnitude better than presently available and opens the way for exploiting existing advantages of cavity-based noise suppression, wavelength transduction, large bandwidth, and nondestructive readout of the memory.

In the present paper, we study the inverse problem for the two-dimensional convective Brinkman–Forchheimer (CBF) equations with the integral overdetermination condition and discontinuity at the initial moment of time. By CBF equations, we mean the Navier–Stokes equations with an absorption term -(αv+β |v|^r-1v), α , β >0, r∈ [1,+∞ ). Specifically, we approximate the discontinuous overdetermination condition with a continuous one. Following the classical results on the initial layer of singularly perturbed differential equations, we scale the problem in an infinitesimal neighborhood [0,1/n] of the point t=0 , using the fast time variable t= tn∈ [0,1] . In the limit, we obtain ordinary differential equations that provide a new initial velocity for the inverse limit problem in the rest domain.

In this article, we discuss the local exact controllability to trajectories of the convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) in a bounded domain Ω with control supported in a subdomain ω⊂Ω⊂ℝ^d , d ∈{2,3} with smooth boundary. We first present global Carleman estimates and observability inequality for the adjoint problem of a linearized version of CBF equations by using a global Carleman estimate for the Stokes system. This allows us to obtain its null controllability at any time T>0 . We then use the inverse mapping theorem to deduce local results concerning the exact controllability to the trajectories of CBF equations.

We theoretically investigate an annularly confined Bose-Einstein Condensate (BEC) coupled to a four-mirror ring cavity supporting traveling-wave optical modes. Under symmetric driving by counter-propagating Laguerre-Gaussian beams carrying equal and opposite orbital angular momenta, the system realizes supersolid phases coexisting with persistent superfluid circulation. Specifically, we obtain a supersolid state if we start with a BEC of winding number L_p as well as supersolid packets with coherent superpositions of two different BEC L_p values. Under asymmetric pumping, realized with Laguerre-Gaussian beams of different orbital angular momenta, chiral symmetry is broken in the system, resulting in asymmetric cavity field amplitudes, directional density modulations, and tunable rotational dynamics of the resulting supersolid lattice. This leads to rotating supersolid density structures for a single winding-number state, and rotating wave packets for an initial superposition of rotational eigenstates. Finally, we probe the presence of Goldstone and Higgs modes which can be observed using minimally destructive measurements of the cavity output spectrum. Our mean-field theory reveals interference-driven rotation without physical stirring, and distinguishes our work from prior static cavity supersolids. Our results establish the ring cavity annular BEC as a versatile platform for generating chiral quantum matter, implementing rotation-sensing devices and generating atomtronic circuits with supersolids.

In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \begin{document}$ \begin{align*} \boldsymbol{u}_t-\mu \Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nabla p = \boldsymbol{F}: = \boldsymbol{f} g, \ \ \ \nabla\cdot\boldsymbol{u} = 0, \end{align*} $\end{document} in bounded domains \begin{document}$ \Omega\subset\mathbb{R}^d $\end{document} (\begin{document}$ d = 2, 3 $\end{document}) with smooth boundary, where \begin{document}$ \alpha, \beta, \mu>0 $\end{document} and \begin{document}$ r\in[1, \infty) $\end{document}. The CBF equations describe the motion of incompressible fluid flows in a saturated porous medium. The inverse problem under our consideration consists of reconstructing the vector-valued velocity function \begin{document}$ \boldsymbol{u} $\end{document}, the pressure gradient \begin{document}$ \nabla p $\end{document} and the vector-valued function \begin{document}$ \boldsymbol{f} $\end{document}. We prove the well-posedness result (existence, uniqueness and stability) of an inverse problem for 2D and 3D CBF equations with the final overdetermination condition using Schauder's fixed point theorem for arbitrary smooth initial data. The well-posedness results hold for \begin{document}$ r\geq 1 $\end{document} in two dimensions and for \begin{document}$ r \geq 3 $\end{document} in three dimensions. The global solvability results available in the literature helped us to obtain the uniqueness and stability results for the model with fast growing nonlinearities.

Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, in situ, in real-time and with minimal destruction, using a cavity driven with optical fields carrying orbital angular momentum. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing.

We introduce a hybrid optomechanical system containing an annularly trapped Bose-Einstein condensate (BEC) inside an optical cavity driven by Lauguerre-Gaussian (LG) modes. Spiral phase elements serve as the end mirrors of the cavity such that the rear mirror oscillates torsionally about the cavity axis through a clamped support. As described earlier in a related system [P. Kumar et al., Phys. Rev. Lett. 127, 113601 (2021)], the condensate atoms interact with the optical cavity modes carrying orbital angular momentum which create two atomic side modes. We observe three peaks in the output noise spectrum corresponding to the atomic side modes and rotating mirror frequencies, respectively. We find that the trapped BEC's rotation reduces quantum fluctuations at the mirror's resonance frequency. We also find that the atomic side modes-cavity coupling and the optorotational coupling can produce bipartite and tripartite entanglements between various constituents of our hybrid system. We reduce the frequency difference between the side modes and the mirror by tuning the drive field's topological charge and the condensate atoms' rotation. When the atomic side modes become degenerate with the mirror, the stationary entanglement between the cavity and the mirror mode diminishes due to the suppression of cooling. Our proposal, which combines atomic superfluid circulation with mechanical rotation, provides a versatile platform for reducing quantum fluctuations and producing macroscopic entanglement with experimentally realizable parameters.

Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently being investigated in the context of superfluid hydrodynamics, quantum sensing and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work, we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing and quantum information.

In the northern-western Himalayan region of India, the winter vegetable crop, vegetable pea, is pivotal for regional food security and ecological equilibrium. To ensure its sustainable management, it is imperative to discover irrigation methods harmonizing with organic farming practices. Drip irrigation, recognized for precise water delivery and minimal loss, emerges as a promising solution. A field experiment in the Rabi season of 2020 at the Norman E. Borlaug Crop Research Centre, G.B. Pant University of Agriculture and Technology, Pantnagar, scrutinized two irrigation approaches (drip and flood) and assessed six nutrient management combinations in a split-plot design. Compared to flood irrigation, drip irrigation exhibited substantial advantages in irrigation water use efficiency, water productivity, gross return, net returns, and B:C ratio. Particularly, an integrated nutrient management practice (RDF + FYM @2.5 t/ha + vermicompost @ 1t/ha) under drip irrigation resulted in a 29.4% increase in irrigation water use efficiency and a 28.3% rise in water productivity. The highest B:C ratio (3.5) was achieved with RDF + FYM 2.5t/ha + Vermicompost 1t/ha under drip irrigation. This strategy not only enhances water use efficiency and economic returns but also augments soil health, bolstering the long-term sustainability of regional agriculture.

We present numerical simulations of the cavity optomechanical detection of persistent currents and bright solitons in an atomic Bose-Einstein condensate confined in a ring trap. This work describes a novel technique that measures condensate rotation in situ, in real-time, and with minimal destruction, in contrast to currently used methods, all of which destroy the condensate completely. For weakly repulsive inter-atomic interactions, the analysis of persistent currents extends our previous few-mode treatment of the condensate [P. Kumar et al. Phys. Rev. Lett. 127, 113601 (2021)] to a stochastic Gross-Pitaevskii simulation. For weakly attractive atomic interactions, we present the first analysis of optomechanical detection of matter-wave soliton motion. We provide optical cavity transmission spectra containing signatures of the condensate rotation, sensitivity as a function of the system response frequency, and atomic density profiles quantifying the effect of the measurement backaction on the condensate. We treat the atoms at a mean-field level and the optical field classically, account for damping and noise in both degrees of freedom, and investigate the linear as well as nonlinear response of the configuration. Our results are consequential for the characterization of rotating matter waves in studies of atomtronics, superfluid hydrodynamics, and matter-wave soliton interferometry.

Himachal Pradesh state is located in seismically active western Himalayas (India) and its seven districts are in seismic zone V and other in zone IV as per the seismic code of India. Ninety% area of Hamirpur district, the studied area, lies in zone V. Peak ground acceleration (PGA) is one of the most important seismic response parameters in structural seismic design, largely influenced by the sub-soil and input seismic motion characteristics. In the present work, the primary objective is to identify the areas in the district that are prone to amplification of peak ground acceleration and can be delineated for infrastructural planning. Peak ground acceleration is one of the most important parameters used in seismic design of the structures. It is estimated using the computer programme ProShake, wherein the soil parameters from 181 borehole profiles up to 30 m depth and software in-built standard earthquake input motions of magnitude 6.9, 7.0, and 7.2 used as the input parameters. The output peak ground acceleration range from 0.24 g to 0.72 g at the ground surface and from 0.21 g to 0.54 g at a depth of 10 m. There is an attenuation of peak ground acceleration at 30 m depth. The estimation of peak ground acceleration will play an important role in delineating the starta having higher peak ground acceleration amplification. This information can be effectively used for planning of important infrastructure projects like hospitals, educational institutions, and commercial establishments in an economical way in the studied area.

Atomic superfluids confined in a ring provide a remarkable paradigm for quantized circulation. Very recently, a technique based on cavity optomechanics has been proposed [Kumar et al., Phys. Rev. Lett. 127, 113601 (2021)] for sensing and manipulating the rotation of a bosonic ring condensate with minimal destruction, in situ and in real time. Here, we theoretically investigate other coherent interference effects that can be supported by the proposed configuration. Specifically, in the presence of a strong control beam, we analyze the influence of atomic rotation on the transmission spectrum of a weak probe laser through a cavity containing a ring condensate. We present a detailed study of the resulting narrow probe transmission profiles and group delay and show that they can be tuned by means of persistent currents. Our results explore a facet of rotating matter waves and are relevant to applications such as atomtronics, sensing, and information processing.

Mercury (Hg) is among the naturally occurring heavy metal with elemental, organic, and inorganic distributions in the environment. Being considered a global pollutant, high pools of Hg-emissions ranging from >6000 to 8000 Mg Hg/year get accumulated by the natural and anthropogenic activities in the atmosphere. These toxi-cants have high persistence, toxicity, and widespread contamination in the soil, water, and air resources. Hg accumulation inside the plant parts amplifies the traces of toxic elements in the linking food chains, leads to Hg exposure to humans, and acts as a potential genotoxic, neurotoxic and carcinogenic entity. However, excessive Hg levels are equally toxic to the plant system and severely disrupt the physiological and metabolic processes in plants. Thus, a plausible link between Hg-concentration and its biogeochemical behavior is highly imperative to analyze the plant-soil interactions. Therefore, it is requisite to bring these toxic contaminants in between the acceptable limits to safeguard the environment. Plants efficiently incorporate or absorb the bioavailable Hg from the soil thus a constructive understanding of Hg uptake, translocation/sequestration involving specific heavy metal transporters, and detoxification mechanisms are drawn. Whereas recent investigations in biological remediation of Hg provide insights into the potential associations between the plants and microbes. Furthermore, intense research on Hg-induced antioxidants, protein networks, metabolic mechanisms, and signaling pathways is required to understand these bioremediations techniques. This review sheds light on the mercury (Hg) sources, pollution, biogeochemical cycles, its uptake, translocation, and detoxification methods with respect to its mo-lecular approaches in plants.

Assurance of substance abuse in plasma and different parts of the body is vital in clinical and legal toxicology. Detection techniques are evaluated for their appropriateness in scientific and clinical sciences, where extraordinary prerequisites must be met. Recognition and affirmation are for the most part done by gas chromatography-Mass spectrometry (GC-MS) or liquid chromatography (LC-MS), Surface-enhanced Raman spectroscopy (SERS), Magnetic resonance imaging, Positron Emission Tomography, Infrared Spectroscopy, and UV Spectroscopy. Progressed spectroscopic techniques provided helpful quantitative or qualitative data about the natural chemistry and science of exploited substances. These spectroscopic techniques are assumed as quick, precise, and some of them are non-damaging investigation apparatus that may be assumed as a substitution for previously used compound investigation. Spectroscopy with its advances in technology is centralized to novel applications in the detection of abused drug substances and clinical toxicology. These techniques have attracted growing interest as forensic tools for the early detection and monitoring of exploited drugs. This review describes the principle, role, and clinical application of various spectroscopic techniques which are utilized for the identification of drug abuse like morphine, cocaine, codeine, alcohol, amphetamines, and their metabolites in whole blood, plasma, hair, and nails.

Rapid rise in number of industries, anthropogenic activities and advancement in agricultural materials (insecticides, pesticides, herbicides and other chemical fertilizers) on this globe have resulted in the release of various non-essential or toxic heavy metals or metalloids (As, Pb, Cd, Hg, Cr, Ni, etc.) into the environment. Such constant release of noxious heavy metals has become a major challenge in the survival of plants and other living beings. In the current scenario, it has become essential aspect to understand how plants perceive metal stress signals, respond to these stresses and adapt for survival. Molecular-level processes involved in plant defense against heavy metal toxicity hold significant importance for numerous other reasons. It plays a crucial role in preserving environmental health by providing insights that can shape strategies to mitigate heavy metal pollution. It's essential for ensuring food safety, as it can guide the development of crop variants that limit the accumulation of toxic heavy metals. This knowledge can also improve plant health and productivity by aiding in the creation of plants resistant to heavy metals, thereby increasing agricultural output. From a scientific standpoint, it deepens our grasp of plant biology and stress response mechanisms. Finally, it offers potential applications in biotechnology, such as the possibility of designing plants with increased resistance to heavy metals, which would be advantageous in regions with heavy metal-laden soils. Exploratory research into the molecular mechanisms of plant species under HM stress is therefore quite important. In this regard, the present review provides new perspectives on the molecular mechanisms of plant defense under HM stress. This review is a compiled version of recent genomic, transcriptomic, proteomic, metabolomics as well as epigenomic analysis studies through the use of various modern techniques which are mainly focused on regulatory networks by which plants adapted and tolerate heavy metal stress.

We propose an adaptive phase technique for the parametric cooling of mechanical resonances. This involves the detection of the mechanical quadratures, followed by a sequence of periodic controllable adjustments of the phase of a parametric modulation. The technique allows the preparation of the quantum ground state with an exponential loss of thermal energy, similarly to the case of cold-damping or cavity self-cooling. Analytical derivations are presented for the cooling rate and final occupancies both in the classical and quantum regimes.

We present a versatile model of gapped graphene to manipulate valley polarization by using ultrafast linearly polarized pulses of zero areas. First, a circularly polarized pulse of a single oscillation produces a valley-selective population of the conduction band by means of topological resonance. Then we apply a linearly polarized femtosecond-long pulse that changes the valley polarization. The magnitude of such a change depends on the amplitude and the direction of polarization of the pulse. Our protocol provides a favorable platform for applications in valleytronics.