arXiv subjects

Pardeep Kumar

Publications and source records attributed to Pardeep Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Supersolid Rotation in an Annular Bose-Einstein Condensate coupled to a Ring Cavity

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.

cond-mat.quant-gas↗

arXiv2025

A Reformulation of UVN-Flash for Multicomponent Two-Phase Systems with Application to CO2-rich Mixture Transport in Pipelines

Pipeline transport of dense-phase CO2-rich mixtures is a crucial component in carbon capture and storage (CCS). Accurate modeling requires coupling of fluid dynamics and thermodynamics, especially during transient events such as depressurization. In this work, we present a unified framework for two-phase multicomponent transport in pipelines that integrates both aspects. Specifically, we employ the homogeneous equilibrium model (HEM) for modeling the transport of two-phase CO2-rich mixture, with thermodynamic closure provided by a Helmholtz energy-based equation of state. Phase equilibrium calculations are performed using UVN-flash, supplemented with a stability analysis procedure to detect phase separation and generate initial guesses for the phase-equilibrium calculations. Specifically, we introduce a novel tailored UVN-flash routine that aligns with the fluid dynamics formulation. This is achieved by introducing an alternative and better-scaled set of variables for the phase-equilibrium calculations. The proposed framework is applied to the depressurization of tanks and pipelines containing CO2-rich mixtures, demonstrating its effectiveness for CCS-relevant applications.

physics.comp-ph↗

arXiv2025

Phase-adaptive cooling of fringe-trapped nanoparticles at room temperature in hollow-core photonic crystal fiber

Active feedback cooling of levitated dielectric particles is a pivotal technique for creating ultrasensitive sensors and probing fundamental physics. Here we demonstrate phase-adaptive feedback cooling of silica nanoparticles optically trapped in standing-wave potential formed by two co-linearly polarized counterpropagating diffraction-free guided modes in a hollow-core photonic crystal fiber at room temperature. Unlike standard laser intensity- or Coulomb force-based feedback, our approach modulates the relative optical phase between the counterpropagating fundamental modes proportionally to the particle's axial momentum. This generates a Stokes-like dissipative force which effectively damps the center-of-mass motion without introducing excess heating and can also work with uncharged particles. At 2 mbar air pressure, the axial center-of-mass temperature of a 195 nm silica particle is reduced by half upon application of the feedback and to 58.6 K at 0.5 mbar. The measured mechanical spectra agree well with our analytical model, validating the cooling mechanism. We envision this approach will open up pathways towards long-range, coherent control of mesoscopic particles inside hollow-core fibers, offering a fiber-integrated versatile platform for future quantum manipulation.

physics.optics↗

arXiv2025

AGCD-Net: Attention Guided Context Debiasing Network for Emotion Recognition

Context-aware emotion recognition (CAER) enhances affective computing in real-world scenarios, but traditional methods often suffer from context bias-spurious correlation between background context and emotion labels (e.g. associating ``garden'' with ``happy''). In this paper, we propose \textbf{AGCD-Net}, an Attention Guided Context Debiasing model that introduces \textit{Hybrid ConvNeXt}, a novel convolutional encoder that extends the ConvNeXt backbone by integrating Spatial Transformer Network and Squeeze-and-Excitation layers for enhanced feature recalibration. At the core of AGCD-Net is the Attention Guided - Causal Intervention Module (AG-CIM), which applies causal theory, perturbs context features, isolates spurious correlations, and performs an attention-driven correction guided by face features to mitigate context bias. Experimental results on the CAER-S dataset demonstrate the effectiveness of AGCD-Net, achieving state-of-the-art performance and highlighting the importance of causal debiasing for robust emotion recognition in complex settings.

cs.CV↗

arXiv2025

Cavity Optomechanical Quantum Memory for Twisted Photons Using a Ring BEC

We theoretically propose a photonic orbital angular momentum (OAM) quantum memory platform based on an atomic Bose-Einstein condensate confined in a ring trap and placed inside a Fabry-Perot cavity driven by Laguerre-Gaussian beams. In contrast to electromagnetically induced transparency-based protocols, our memory does not require change of internal atomic levels. The optical states are instead stored in the large Hilbert space of topologically protected and long-lived motional states (persistent currents) of the condensate, yielding a storage time three orders of magnitude better than presently available. Further, the use of a cavity provides orders of magnitude more resonances, and hence bandwidth, for reading and writing than internal atomic transitions. Finally, the analogy to cavity optomechanics suggests a natural path to wavelength conversion, OAM transduction, and nondestructive readout of the memory.

quant-ph↗

arXiv2025

A Fast and Robust Reformulation of the UVN-Flash Problem via Direct Entropy Maximization

We investigate the phase equilibrium problem for multicomponent mixtures under specified internal energy (U), volume (V), and mole numbers (N1,N2, . . . ,Nn), commonly known as the UVN-flash problem. While conventional phase equilibrium calculations typically use pressure-temperature-mole number (PTN) specifications, the UVN formulation is essential for dynamic simulations of closed systems and energy balance computations. Existing approaches, including those based on iterative pressure-temperature updates and direct entropy maximization, suffer from computational inefficiencies due to nested iterations and reliance on inner Newton solvers. In this work, we present a novel reformulation of the UVN-flash problem as a direct entropy maximization problem that eliminates the need for inner Newton iterations, addressing key computational bottlenecks. We derive two new novel formulations: 1) a formulation based on entropy and internal energy and (2) an alternative formulation based on Helmholtz free energy. We begin with a stability analysis framework, followed by a reformulation of the UVN flash problem in natural variables. We then introduce our novel approach and discuss the numerical methods used, including gradient and Hessian computations. The proposed method is validated against benchmark cases, demonstrating improved efficiency and robustness.

math.NA↗

arXiv2024

A new temperature evolution equation that enforces thermodynamic vapour-liquid equilibrium in multiphase flows -- application to CO2 modeling

This work presents a novel framework for numerically simulating the depressurization of tanks and pipelines containing carbon dioxide (CO2). The framework focuses on efficient solution strategies for the coupled system of fluid flow equations and thermodynamic constraints. A key contribution lies in proposing a new set of equations for phase equilibrium calculations which simplifies the traditional vapor-liquid equilibrium (VLE) calculations for two-phase CO2 mixtures. The first major novelty resides in the reduction of the conventional four-equation VLE system to a single equation, enabling efficient solution using a non-linear solver. This significantly reduces computational cost compared to traditional methods. Furthermore, a second novelty is introduced by deriving an ordinary differential equation (ODE) directly from the UV-Flash equation. This ODE can be integrated alongside the governing fluid flow equations, offering a computationally efficient approach for simulating depressurization processes.

physics.flu-dyn↗

arXiv2024

Hybrid Rotational Cavity Optomechanics Using Atomic Superfluid in a Ring

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.

quant-ph↗

arXiv2024

Sensing atomic superfluid rotation beyond the standard quantum limit

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.

quant-ph↗

arXiv2024

Local exact controllability to the trajectories of the convective Brinkman-Forchheimer equations

In this article, we discuss the local exact controllability to trajectories of the following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) defined in a bounded domain $\Omega \subset\mathbb{R}^d$ ($d=2,3$) with smooth boundary: \begin{align*} \frac{\partial\boldsymbol{u}}{\partial t}-\mu \Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{2}\boldsymbol{u}+\nabla p=\boldsymbol{f}+\boldsymbol{\vartheta}, \ \ \ \nabla\cdot\boldsymbol{u}=0, \end{align*} where the control $\boldsymbol{\vartheta}$ is distributed in a subdomain $\omega \subset \Omega$, and the parameters $\alpha,\beta,\mu>0$ are constants. 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.

math.AP↗

arXiv2023

Ring Bose-Einstein condensate in a cavity: Chirality Detection and Rotation Sensing

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.

cond-mat.quant-gas↗

arXiv2023

Cavity optomechanical detection of persistent currents and solitons in a bosonic ring condensate

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.

cond-mat.quant-gas↗

arXiv2023

An inverse source problem for convective Brinkman-Forchheimer equations with the final overdetermination

In this paper, we examine an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations or damped Navier-Stokes equations: \begin{align*} \boldsymbol{v}_t-\mu \Delta\boldsymbol{v}+(\boldsymbol{v}\cdot\nabla)\boldsymbol{v}+\alpha\boldsymbol{v}+\beta|\boldsymbol{v}|^{r-1}\boldsymbol{v}+\nabla p=\boldsymbol{F}:=\boldsymbol{f} g, \ \ \ \nabla\cdot\boldsymbol{v}=0, \end{align*} on a torus $\mathbb{T}^d$, $d=2,3$. The inverse problem under consideration consists of determining the vector-valued velocity function $\boldsymbol {v}$, the pressure gradient $\nabla p$ and the vector-valued forcing function $\boldsymbol{f} $. Using the Tikhonov fixed point theorem, we prove the existence of a solution for the inverse problem for 2D and 3D CBF equations with the final overdetermination data for the divergence free initial data in the energy space $ \mathbb{L}^2(\mathbb{T}^d)$. A concrete example is also provided to validate the obtained result. Moreover, we overcome the technical difficulties while proving the uniqueness and H\"older type stability results by using the regularity results available for the direct problem for CBF equations. The well-posedness results hold for $r \geq 1$ in two dimensions and for $r \geq 3$ in three dimensions for appropriate values of $\alpha,\mu$ and $\beta$. The nonlinear damping term $|\boldsymbol{v}|^{r-1}\boldsymbol{v}$ plays a crucial role in obtaining the required results. In the case of supercritical growth ($r>3$), we obtain better results than that are available in the literature for 2D Navier-Stokes equations.

math.AP↗

arXiv2022

Existence, uniqueness and stability of an inverse problem for two-dimensional convective Brinkman-Forchheimer equations with the integral overdetermination

In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \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}:=f \boldsymbol{g}, \ \ \ \nabla\cdot\boldsymbol{u}=0, \end{align*} in a bounded domain $\Omega\subset\mathbb{R}^2$ with smooth boundary $\partial\Omega$, where $\alpha,\beta,\mu>0$ and $r\in[1,3]$. The investigated inverse problem consists of reconstructing the vector-valued velocity function $\boldsymbol{u}$, the pressure field $p$ and the scalar function $f$. For the divergence free initial data $\boldsymbol{u}_0 \in \mathbb{L}^2(\Omega)$, we prove the existence of a solution to the inverse problem for two-dimensional CBF equations with the integral overdetermination condition, by showing the existence of a unique fixed point for an equivalent operator equation (using an extension of the contraction mapping theorem). Moreover, we establish the uniqueness and Lipschitz stability results of the solution to the inverse problem for 2D CBF equations with $r \in[1,3]$.

math.AP↗

arXiv2022

Theory of phase-adaptive parametric cooling

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.

quant-ph↗

arXiv2021

Well-posedness of an inverse problem for two and three dimensional convective Brinkman-Forchheimer equations with the final overdetermination

In this article, we study an inverse problem for the following convective Brinkman-Forchheimer (CBF) equations: \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*} in bounded domains $\Omega\subset\mathbb{R}^d$ ($d=2,3$) with smooth boundary, where $\alpha,\beta,\mu>0$ and $r\in[1,\infty)$. 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 $\boldsymbol{u}$, the pressure field $p$ and the vector-valued function $\boldsymbol{f}$. We have proved the well-posedness result (existence, uniqueness and stablility) for the inverse problem for the 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 $r\geq 1$ in two dimensions and for $r \geq 3$ 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.

math.AP↗

arXiv2021

A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin-Voigt fluids in bounded domains (a hyperbolic type problem). This inverse problem aims to reconstruct the velocity and kernel of the memory term simultaneously, from the measurement described as the integral over determination condition. By using the contraction mapping principle in an appropriate space, a local in time existence and uniqueness result for the inverse problem of Kelvin-Voigt fluids are obtained. Furthermore, using similar arguments, a global in time existence and uniqueness results for an inverse problem of Oseen type equations are also achieved.

math.AP↗

arXiv2020

Ultrafast valley polarization in bilayer graphene

We study theoretically interaction of a bilayer graphene with a circularly polarized ultrafast optical pulse of a single oscillation at an oblique incidence. The normal component of the pulse breaks the inversion symmetry of the system and opens up a dynamical band-gap, due to which a valley-selective population of the conduction band becomes sensitive to the angle of incident of the pulse. We show that the magnitude of the valley polarization can be controlled by the angle of incidence, the amplitude, and the angle of in-plane polarization of the chiral optical pulse. Subsequently, a sequence of a circularly polarized pulse followed by a linearly polarized femtosecond-long pulse can be used to control the valley polarization created by the preceding pulse. Generally, the linearly polarized pulse depolarizes the system. The magnitude of such a depolarization depends on the amplitude, and the in-plane polarization angle of the linearly polarized pulse. Our protocol provides a favorable platform for applications in valleytronics.

cond-mat.mes-hall↗