arXiv subjects

S. Ramanan

Publications and source records attributed to S. Ramanan.

At least 19 recordsLinked to original sources

arXiv2026

Hartree shift and pairing gap in ultracold Fermi gases in the framework of low-momentum interactions

In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum dependent interaction that reproduces the s-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well-converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte-Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.

cond-mat.quant-gas↗

arXiv2025

Estimation of deuteron binding energy with renormalization group-based effective interactions using the variational quantum eigensolver

We have obtained the energy of the deuteron on a quantum simulator using the variational quantum eigensolver. We have employed realistic two-body interactions, namely, chiral N4LO and AV$_{18}$, thus incorporating the role of tensor forces. These interactions are subsequently evolved to low resolution scales using the similarity renormalization group approach with parameter $\lambda$. The deuteron ground state energy has been calculated in the truncated harmonic oscillator basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of harmonic oscillator basis states (hence qubits) needed for computing the energy to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing $\lambda$. We have analysed the extent of entanglement between oscillator modes using concurrence as the entanglement quantifier. It is seen that the entanglement decreases as $\lambda$ is lowered from the bare value to $\sim 1.0 \, \text{fm}^{-1}$ independent of the form of the bare interaction and the number of harmonic oscillator basis states.

nucl-th↗

arXiv2025

A machine learning approach to tomographic pattern generation and classification of quantum states of light

Optical tomograms can be envisaged as patterns. The Wasserstein generative adversarial network (WGAN) algorithm provides a platform to train the machine to compare patterns corresponding to input and generated tomograms. Using a deep-learning framework with two convolutional neural networks and WGAN, we have trained the machine to generate tomograms of Fock states, coherent states (CS) and the single photon added CS ($1$-PACS). The training process was continued until the Wasserstein distance between the input and output tomographic patterns levelled off at a low value. The mean photon number, variances and higher moments were extracted directly from the generated tomograms, to distinguish between different Fock states and also between the CS and the $1$-PACS, without using an additional classifier neural network. The robustness of our results has been verified using two error models and also with different colormaps that define the tomographic patterns. We have examined if the training program successfully reflected some of the findings in a recent experiment in which state reconstruction was carried out to establish that the fidelities between an amplified CS, an optimal CS and a $1$-PACS were close to unity, over a range of parameter values. By training the machine to reproduce tomograms corresponding to these specific states, and comparing the mean photon numbers of these states obtained directly from the tomograms, we have established that the variations in these observables reflect the experimental trends. State reconstruction from tomograms could be challenging, in general, since the Hilbert space associated with quantized light is large. The tomographic approach provides a viable alternative to detailed state reconstruction. Our work demonstrates the use of machine learning to generate optical tomograms from which the states can be directly characterized.

quant-ph↗

arXiv2025

Comparing probability distributions: application to quantum states of light

Probability distributions play a central role in quantum mechanics, and even more so in quantum optics with its rich diversity of theoretically conceivable and experimentally accessible quantum states of light. Quantifiers that compare two different states or density matrices in terms of `distances' between the respective probability distributions include the Kullback-Leibler divergence $D_{\rm KL}$, the Bhattacharyya distance $D_{\rm B}$, and the $p$-Wasserstein distance $W_{p}$. We present a novel application of these notions to a variety of photon states, focusing particularly on the $p=1$ Wasserstein distance $W_{1}$ as it is a proper distance measure in the space of probability distributions.

quant-ph↗

arXiv2025

Induced three-neutron interactions with low cutoffs for dilute neutron matter

The properties of dilute neutron matter are mostly determined by the s-wave two-body (2N) interaction, while three-body (3N) interactions are suppressed by the Pauli principle. In a previous work, we showed that it can be advantageous to use renormalization group based effective interactions with cutoffs scaled with the Fermi momentum, especially at low densities. In that case, induced 3N interactions may become important. In this work, we compute the 3N interaction induced by the similarity renormalization group flow of the s-wave 2N interaction. We work in the momentum-space hyperspherical partial wave basis and investigate its convergence properties. Then we study the effect of the induced 3N interaction on the equation of state of dilute neutron matter. We observe that the cutoff dependence of the equation of state is strongly reduced when the effect of induced 3N interaction is included.

nucl-th↗

arXiv2024

Optimal sensing of photon addition and subtraction on nonclassical light

We demonstrate that the Wasserstein distance $W_{1}$ corresponding to optical tomograms of nonclassical states faithfully captures changes that arise due to photon addition to, or subtraction from, these states. $W_{1}$ is a true measure of distance in the quantum state space, and is sensitive to the underlying interference structures that arise in the tomogram after changes in the photon number. Our procedure is universally applicable to the cat and squeezed states, the former displaying the characteristic negativity in its Wigner function, while the latter does not do so. We explicate this in the case of the squeezed vacuum and even coherent states and show that photon addition (or subtraction) is mirrored in the shift in the intensity of specific regions in the tomogram. Further, we examine the dependence of $W_{1}$ on the squeezing parameter, and its sensitivity to different quadratures.

quant-ph↗

arXiv2024

Tomographic entanglement indicators in a coupled oscillator model

We study entanglement in a simple model comprising two coupled linear harmonic oscillators of the same natural frequency. The system is separable in the center of mass (COM) and relative coordinates into two oscillators of frequency $ω_c$ and $ω_r$. We compute standard entanglement measures (subsystem linear entropy and subsystem von Neumann entropy) as well as several tomographic entanglement indicators (Bhattacharyya distance, Kullback-Leibler divergence and inverse participation ratio) as functions of the frequency ratio $η= ω_c/ω_r$, keeping the COM oscillator in the ground state. We demonstrate that, overall, the entanglement indicators reflect quite faithfully the variations in the standard measures. The entanglement is shown to be minimum at $η= 1$ and maximum as $η\to 0$ or $\infty$.

quant-ph↗

arXiv2024

Tomographic markers and photon addition to coherent states of light: Comparison with experiment

Photon addition to quantized light is of immense interest, both experimentally and theoretically. We identify a set of markers that play an important role in the context of photon addition to coherent states of light. These markers are directly computable from optical tomograms. We calculate the amplification gain due to photon addition, and the dependence of quadrature variances on relevant parameters, from the tomograms and compare them with results obtained after state reconstruction in a recent experiment. Our results match well with the fidelity plots reported by the experimenters. Our approach which circumvents state reconstruction could provide a viable procedure to identify specific aspects of photon addition to nonclassical light as well, from the tomograms themselves.

quant-ph↗

arXiv2023

A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems

Entropic uncertainty relations (EURs) have been examined in various contexts, primarily in qubit systems, including their links with entanglement, as they subsume the Heisenberg uncertainty principle. With their genesis in the Shannon entropy, EURs find applications in quantum information and quantum optics. EURs are state-dependent, and the state has to be reconstructed from tomograms (which are histograms readily available from experiments). This is a challenge when the Hilbert space is large, as in continuous variable (CV) and certain hybrid quantum (HQ) systems. An alternative approach is to extract information about the unknown quantum state directly from appropriate tomograms. Many variants of EURs can be computed from tomograms. In the literature many tomographic entanglement indicators (TEIs) that can be calculated from tomograms have been defined. The objectives of this work are as follows: (i) Use the tomographic approach to investigate the links between EURs and TEIs in CV and HQ systems as they evolve in time. (ii) Identify the TEI that most closely tracks the temporal evolution of EURs. We consider two generic systems. The first is a multilevel atom modeled as a nonlinear oscillator interacting with a quantized radiation field. The second is the $Λ$-atom interacting with two radiation fields. The former model accommodates investigations on the role of the initial state of the field and the ratio of the strengths of interaction and nonlinearity in the connection between TEIs and EURs. The second model opens up the possibility of examining the connection between mixed state bipartite entanglement and EURs, when the number of atomic levels is finite. Since the tomogram respects the requirements of classical probability theory, this effort also sheds light on the extent to which TEIs reflect the temporal behaviour of those EURs which are rooted in the Shannon entropy.

quant-ph↗

arXiv2023

Equation of state of superfluid neutron matter with low-momentum interactions

In this work, we calculate the ground state energy of pure neutron matter using the renormalization group based low-momentum effective interaction $V_{\text{low-}k}$ in Bogoliubov many-body perturbation theory (BMBPT), which is a perturbative expansion around the Hartree-Fock-Bogoliubov (HFB) ground state. In order to capture the low-density behavior of neutron matter, it turns out to be better to use a density dependent cutoff in the $V_{\text{low-}k}$ interaction. Perturbative corrections to the HFB energy up to third order are included. We find that at low densities corresponding to the inner crust of neutron stars, the HFB state that includes pairing is a better starting point for perturbation expansion. It is observed that including the higher order perturbative corrections, the cutoff dependence of the ground state energy is reduced.

nucl-th↗

arXiv2021

Manifestations of changes in entanglement and onset of synchronization in tomograms

Quantum state reconstruction for continuous-variable systems such as the radiation field poses challenges which arise primarily from the large dimensionality of the Hilbert space. Many proposals for state reconstruction exist, ranging from standard reconstruction protocols to applications of machine learning. No universally applicable protocol exists, however, for extracting the Wigner function from the optical tomogram of an arbitrary state of light. We establish that nonclassical effects such as entanglement changes during dynamical evolution and the onset of quantum synchronization are mirrored in qualitative changes in optical tomograms themselves, circumventing the need for state reconstruction for this purpose.

quant-ph↗

arXiv2021

Low-momentum interactions for ultracold Fermi gases

We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the s-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired from recent successes of this method in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones. Limitations and possible extensions of the approach are discussed.

cond-mat.quant-gas↗

arXiv2020

Pairing in pure neutron matter

We review the long standing problem of superfluid pairing in pure neutron matter. For the $s$-wave pairing, we summarize the state of the art of many-body approaches including different $nn$ interactions, medium polarization, short-range correlations and BCS-BEC crossover effects, and compare them with quantum Monte Carlo results at low-densities. We also address pairing in the $p$-wave, which appears at higher densities and hence has large uncertainties due to the poorly constrained interactions, medium effects and many-body forces.

nucl-th↗

arXiv2019

Neutron pairing with medium polarization beyond the Landau approximation

We revisit the long-standing problem of the superfluid transition temperature $T_c$ in dilute neutron matter. It is well known that $T_c$ is strongly affected by medium polarization effects (screening) which modify the pairing interaction in the medium. We study these effects within the random-phase approximation (RPA). It turns out that the widely used Landau approximation is sufficient only at densities below about 0.002 fm$^{-3}$. At higher densities, the full RPA leads to stronger screening than the Landau approximation.

nucl-th↗

arXiv2019

Involutions and higher order automorphisms of Higgs bundle moduli spaces

We consider the moduli space $\mathcal{M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a complex semisimple Lie group. This is a hyperkähler manifold homeomorphic to the moduli space $\mathcal{R}(G)$ of representations of the fundamental group of $X$ in $G$. In this paper we study finite order automorphisms of $\mathcal{M}(G)$ obtained by combining the action of an element of order $n$ in $H^1(X,Z)\rtimes \mbox{Out}(G)$, where $Z$ is the centre of $G$ and $\mbox{Out}(G)$ is the group of outer automorphisms of $G$, with the multiplication of the Higgs field by an $n$th-root of unity, and describe the subvarieties of fixed points. We give special attention to the case of involutions, defined by the action of an element of order $2$ in $H^1(X,Z)\rtimes\mbox{Out}(G)$ combined with the multiplication of the Higgs field by $\pm 1$. In this situation, the subvarieties of fixed points are hyperkähler submanifolds of $\mathcal{M}(G)$ in the (+1)-case, corresponding to the moduli space of representations of the fundamental group in certain reductive complex subgroups of $G$ defined by holomorphic involutions of $G$; while in the (-1)-case they are Lagrangian subvarieties corresponding to the moduli space of representations of the fundamental group of $X$ in real forms of $G$ and certain extensions of these. We illustrate the general theory with the description of involutions for $G=\mbox{SL}(n,\mathbb{C})$ and involutions and order three automorphism defined by triality for $G=\mbox{Spin}(8,\mathbb{C})$.

math.AG↗

arXiv2019

Unveiling Regions in multi-scale Feynman Integrals using Singularities and Power Geometry

We introduce a novel approach for solving the problem of identifying regions in the framework of Method of Regions by considering singularities and the associated Landau equations given a multi-scale Feynman diagram. These equations are then analyzed by an expansion in a small threshold parameter via the Power Geometry technique. This effectively leads to the analysis of Newton Polytopes which are evaluated using a Mathematica based convex hull program. Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions like potential and Glauber. Several one-loop and two-loop examples are studied and benchmarked using our algorithm which we call ASPIRE.

hep-ph↗

arXiv2018

Screening and anti-screening of the pairing interaction in low-density neutron matter

We study pairing in low-density neutron matter including the screening interaction due to the exchange of particle-hole and RPA excitations. As bare force we employ the effective low-momentum interaction $V_{low\,k}$, while the Fermi-liquid parameters are taken from a phenomenological energy density functional (SLy4) which correctly reproduces the equation of state of neutron matter. At low density, we find screening, i.e., pairing is reduced, while at higher densities, we find anti-screening, i.e., pairing is enhanced. This enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We discuss in detail the critical temperature $T_c$ in the limit of low densities and show that the suppression of $T_c$ predicted by Gor'kov and Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$ interaction is scaled with the Fermi momentum. We also discuss the effect of non-condensed pairs on the density dependence of $T_c$ in the framework of the Nozières-Schmitt-Rink theory.

nucl-th↗

arXiv2018

Involutions of rank 2 Higgs bundle moduli spaces

We consider the moduli space of rank 2 Higgs bundles with fixed determinant over a smooth projective curve X of genus 2 over the complex numbers, and study involutions defined by tensoring the vector bundle with an element $α$ of order 2 in the Jacobian of the curve, combined with multiplication of the Higgs field by $\pm 1$. We describe the fixed points of these involutions in terms of the Prym variety of the covering of $X$ defined by $α$, and give an interpretation in terms of the moduli space of representations of the fundamental group.

math.AG↗