arXiv subjects

R. Ganesh

Publications and source records attributed to R. Ganesh.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scattering off a junction

Scattering off a potential is a fundamental problem in quantum physics. It has been studied extensively with amplitudes derived for various potentials. In this article, we explore a setting with no potentials, where scattering occurs off a junction where many wires meet. We study this problem using a tight-binding discretization of a star graph geometry -- one incoming wire and $M$ outgoing wires intersecting at a point. When an incoming wave scatters, one part is reflected along the same wire while the rest is transmitted along the others. Remarkably, the reflectance increases monotonically with $M$, i.e., the greater the number of outgoing channels, the more the particle bounces back. In the $M \rightarrow \infty$ limit, the wave is entirely reflected back along the incoming wire. We rationalize this observation by establishing a quantitative mapping between a junction and an on-site potential. To each junction, we assign an equivalent potential that produces the same reflectance. As the number of wires ($M$) increases, the equivalent potential also increases. A recent article by one of us has drawn an equivalence between junctions and potentials from the point of view of bound state formation. Our results here show that the same equivalence also holds for scattering amplitudes. We verify our analytic results by simulating wavepacket motion through a junction. We extend the wavepacket approach to two dimensions where analytic solutions cannot be found. An incoming wave travels on a sheet and scatters off a point where many sheets intersect. Unlike in 1D, the equivalent potential is momentum-dependent. Nevertheless, for any given momentum, the equivalent potential grows monotonically with the number of intersecting sheets. Our findings can be tested in ultracold atom setups and semiconductor structures.

cond-mat.quant-gas↗

arXiv2023

Spreading entanglement through pairwise exchange interactions

The spread of entanglement is a problem of great interest. It is particularly relevant to quantum state synthesis, where an initial direct-product state is sought to be converted into a highly entangled target state. In devices based on pairwise exchange interactions, such a process can be carried out and optimized in various ways. As a benchmark problem, we consider the task of spreading one excitation among $N$ two-level atoms or qubits. Starting from an initial state where one qubit is excited, we seek a target state where all qubits have the same excitation-amplitude -- a generalized-W state. This target is to be reached by suitably chosen pairwise exchange interactions. For example, we may have a a setup where any pair of qubits can be brought into proximity for a controllable period of time. We describe three protocols that accomplish this task, each with $N-1$ tightly-constrained steps. In the first, one atom acts as a flying qubit that sequentially interacts with all others. In the second, qubits interact pairwise in sequential order. In these two cases, the required interaction times follow a pattern with an elegant geometric interpretation. They correspond to angles within the spiral of Theodorus -- a construction known for more than two millennia. The third protocol follows a divide-and-conquer approach -- dividing equally between two qubits at each step. For large $N$, the flying-qubit protocol yields a total interaction time that scales as $\sqrt{N}$, while the sequential approach scales linearly with $ N$. For the divide-and-conquer approach, the time has a lower bound that scales as $\log N$. With any such protocol, we show that the phase differences in the final state cannot be independently controlled. For instance, a W-state (where all phases are equal) cannot be generated by pairwise exchange.

quant-ph↗

arXiv2022

Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets

The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration space of this problem is $SO(3)$, the space of all rotations in three dimensions. This is a topological space with two types of closed loops: trivial loops that can be adiabatically shrunk to a point and non-trivial loops that cannot. In the traditional formulation of the problem, stationary states are periodic over both types of closed loops. However, periodicity conditions may change if Berry phases are introduced. We argue that time-reversal-symmetry allows for only one new possibility -- a Berry phase of $π$ attached to all non-trivial loops. We derive the corresponding stationary states by exploiting the connection between $SO(3)$ and $SU(2)$ spaces. The solutions are anti-periodic over any non-trivial loop, i.e., stationary states reverse sign under a $2π$ rotation about any axis. Remarkably, this framework is realized in the low-energy physics of certain quantum magnets. The magnets must satisfy the following conditions: (a) the classical ground states are unpolarized, carrying no net magnetization, (b) the set of classical ground states is indexed by $SO(3)$, and (c) the product $N\times S$ is a half-integer, where $N$ is the number of spins and $S$ is the spin quantum number. We demonstrate this result in a family of Heisenberg antiferromagnets defined on polygons with an odd number of vertices. At each vertex, we have a spin-$S$ moment that is coupled to its nearest neighbours. In the classical limit, these magnets have coplanar ground states. Their quantum spectra, at low energies, correspond to `spherical top' and `symmetric top' rigid rotors. For integer values of $S$, we recover traditional rigid rotor spectra. With half-integer-$S$, we obtain rotor spectra with a Berry phase of $π$.

cond-mat.str-el↗

arXiv2022

Quantum dimer model on fullerenes: resonance, scarring and confinement

The earliest known examples of quantum superposition were found in organic chemistry -- in molecules that `resonate' among multiple arrangements of $π$-bonds. Small molecules such as benzene resonate among a few bond arrangements. In contrast, a large system that stretches over a macroscopic lattice may resonate among an extensive number of configurations. This is analogous to a quantum spin liquid as described by Anderson's resonating valence bond (RVB) picture. In this article, we study the intermediate case of somewhat large molecules, the C$_{20}$ and C$_{60}$ fullerenes. We build a minimal description in terms of quantum dimer models, allowing for local resonance processes and repulsion between proximate $π$-bonds. This allows us to characterize ground-states, e.g., with C$_{60}$ forming a superposition of 5828 dimer covers. Despite the large number of contributing dimer covers, the ground state shows strong dimer-dimer correlations. Going beyond the ground state, the full spectrum of C$_{60}$ shows many interesting features. Its Hilbert space is bipartite, leading to spectral reflection symmetry. It has a large number of protected zero-energy states. In addition, the spectrum contains many scar-like states, corresponding to localized dimer-rearrangement-dynamics. Resonance dynamics in QDMs can manifest in the behaviour of defects, potentially binding defects via an effective attractive interaction. To test this notion, we introduce pairs of vacancies at all possible separations. Resonance energy reaches its lowest value when the vacancies are closest to one another. This suggests confinement of monomers, albeit within a finite cluster. We discuss qualitative pictures for understanding bonding in fullerenes and draw connections with results from quantum chemistry.

cond-mat.str-el↗

arXiv2021

Disorder-induced currents as signatures of chiral superconductivity

Chiral superconductors are expected to carry a spontaneous, chiral and perpetual current along the sample edge. However, despite the availability of several candidate materials, such a current has not been observed in experiments. In this article, we suggest an alternative probe in the form of impurity-induced chiral currents. We first demonstrate that a single non-magnetic impurity induces an encircling chiral current. Its direction depends on the chirality of the order parameter and the sign of the impurity potential. Building on this observation, we consider the case of multiple impurities, e.g., realized as adatoms deposited on the surface of a candidate chiral superconductor. We contrast the response that is obtained in two cases: (a) when the impurities are all identical in sign and (b) when the impurities have mixed positive and negative signs. The former leads to coherent currents within the sample, arising from the fusion of individual current loops. The latter produces loops of random chirality that lead to incoherent local currents. These two scenarios can be distinguished by measuring the induced magnetic field using recent probes such as diamond NV centres. We argue that impurity-induced currents may be easier to observe than edge currents, as they can be tuned by varying impurity strength and concentration. We demonstrate these results using a toy model for $p_x \pm i p_y$ superconductivity on a square lattice. We develop an improved scheme for Bogoliubov deGennes (BdG) simulations where both the order parameter as well as the magnetic field are determined self-consistently.

cond-mat.supr-con↗

arXiv2021

State selection in frustrated magnets

Magnets with frustration often show accidental degeneracies, characterized by a large classical ground-state space (CGSS). Quantum fluctuations may `select' one of these ground states -- a phenomenon labeled `order by (quantum) disorder' in literature. In this article, we examine the mechanism(s) by which such state selection takes place. We argue that a magnet, at low energies, maps to a particle moving on the CGSS. State selection corresponds to localization of the particle at a certain point on this space. We distinguish two mechanisms that can bring about localization. In the first, quantum fluctuations generate a potential on the CGSS. If the potential has a deep enough minimum, then the particle localizes in its vicinity. We denote this as `order by potential' (ObP). In the second scenario, the particle localizes at a self-intersection point due to bound-state formation -- a consequence of geometry and quantum interference. Following recent studies by the present authors, we denote this scenario as `order by singularity' (ObS). We place our discussion within the context of the one-dimensional spin-$S$ Kitaev model. We map out its CGSS which grows systematically with increasing system size. It resembles a network where the number of nodes increases exponentially. In addition, the number of wires that cross at each node also grows exponentially. This self-intersecting structure leads to ObS, with the low-energy physics determined by a small subset of the CGSS, consisting of `Cartesian' states. A contrasting picture emerges when an additional XY antiferromagnetic coupling is introduced. The CGSS simplifies dramatically, taking the form of a circle. Spin-wave fluctuations generate a potential on this space, giving rise to state selection by ObP under certain conditions. Apart from contrasting ObS and ObP, we discuss the possibility of ObS in macroscopic magnets.

cond-mat.str-el↗

arXiv2020

Collective excitations in vortices and vortex lattices

Emergent lattices at mesoscopic length scales have evoked interest in several recent contexts, e.g., in crystalline arrangements of skyrmions. It is a challenging task to determine their collective excitations as the unit cells are large and can contain complex textures. We address this issue in the oldest known example of an emergent mesoscopic lattice, the vortex lattice in a superfluid. We show that a tight binding approach can successfully describe collective modes. We begin with a single isolated vortex in a two dimensional system. With suitable pinning mechanims, the low energy excitations take the form of localized pairing fluctuations. They can be viewed as wave-like disturbances that propagate around the vortex centre, in the azimuthal direction. In particular, the lowest energy excitations are gyrotropic and breathing modes. The former corresponds to circular motion of the eye of the vortex, while the latter represents an oscillation between sharper and broader vortex profiles. These modes are `bosonic' analogues of atomic orbitals with the vortex profile playing the role of the nuclear potential. Moving to a sparse vortex lattice with well separated vortices, the single-vortex excitations provide a convenient basis for finding normal modes. We derive an analogue of Bloch's theorem in this context, revealing a non-trivial phase contribution arising from the orbital field. We set up a tight binding prescription and use it to explicitly determine the band structure of excitations about a square vortex lattice. Our results can be tested in ultracold atomic gases with synthetic magnetic fields.

cond-mat.supr-con↗

arXiv2020

Excitonic collective modes in Weyl semi-metals

Weyl semi-metals are three dimensional generalizations of graphene with point-like Fermi surfaces. Their linear electronic dispersion leads to a window in the particle-hole excitation spectrum which allows for undamped propagation of collective excitations. We argue that interactions in Weyl semi-metals generically lead to well-defined exciton modes. However, using a minimal model for interactions, we show that the exciton binding energy is exponentially small for weak interactions. This is due to effective two-dimensional character in the space of particle-hole pairs that are available for bound state formation. This is ultimately a consequence of linear electronic dispersion in three dimensions. Nevertheless, intermediate interaction strengths can lead to sharp spin-carrying excitonic resonances. We demonstrate this in a model Weyl semi-metal with broken time-reversal symmetry and Hubbard interactions, using GRPA (generalized random phase approximation) analysis. Excitons in Weyl semi-metals have evoked interest as their condensation could lead to an axionic charge density wave order. However, we find that the leading instability corresponds to intra-valley spin density wave order which shifts the Weyl points without opening a gap. Our results suggest interesting directions for experimental studies of three dimensional Dirac systems.

cond-mat.str-el↗

arXiv2020

Characteristics of a Plasma Source with adjustable multi-pole line cusp geometry

Two magnetic configurations of Multi-cusp Plasma Device (MPD) have been explored to obtain high quiescence level, large uniform plasma region with nearly flat mean density and temperature profiles. In particular, properties of plasma in a six-pole six magnet (SPSM) and twelve pole six magnets (TPSM) cusp configurations are rigorously compared and reported here. It is found that more uniform plasma with nearly flat profiles is found in TPSM along with increased quiescence level. Findings are verified across various magnetic field strengths for both configurations.

physics.plasm-ph↗

arXiv2020

Finite $β$ Effects on Short Wavelength Ion Temperature Gradient Modes

The electromagnetic effect is studied on the short wavelength branch of the ion temperature gradient mode in the linear regime for the first time using a global gyrokinetic model. The short wavelength ion temperature gradient mode growth rate is found to be reduced in the presence of electromagnetic perturbations at finite plasma $β$. The effect on real frequency is found to be weak. The threshold value of $η_i$ is found to increase for the mode as the magnitude of $β$ is increased. The global mode structure of the short wavelength branch of the ion temperature gradient mode is compared with the conventional branch. The magnetic character of the mode, measured as the ratio of mode average square values of electromagnetic potential to electrostatic potential, is found to increase with increasing values of the plasma $β$. The mixing length estimate for flux shows that the maximum contribution still comes from the long wavelengths modes. The magnitude of the flux decreases with increasing $β$.

physics.plasm-ph↗

arXiv2020

Order by singularity in Kitaev clusters

The Kitaev model is a beautiful example of frustrated interactions giving rise to deep and unexpected phenomena. In particular, its classical version has remarkable properties stemming from exponentially large ground state degeneracy. Here, we present a study of magnetic clusters with spin-$S$ moments coupled by Kitaev interactions. We focus on two cluster geometries -- the Kitaev square and the Kitaev tetrahedron -- that allow us to explicitly enumerate all classical ground states. In both cases, the classical ground state space (CGSS) is large and self-intersecting, with non-manifold character. The Kitaev square has a CGSS of four intersecting circles that can be embedded in four dimensions. The tetrahedron CGSS consists of eight spheres embedded in six dimensions. In the semi-classical large-$S$ limit, we argue for effective low energy descriptions in terms of a single particle moving on these non-manifold spaces. Remarkably, at low energies, the particle is tied down in bound states formed around singularities at self-intersection points. In the language of spins, the low energy physics is determined by a distinct set of states that lies well below other eigenstates. These correspond to `Cartesian' states, a special class of classical ground states that are constructed from dimer covers of the underlying lattice. They completely determine the low energy physics despite being a small subset of the classical ground state space. This provides an example of order by singularity, where state selection becomes stronger upon approaching the classical limit.

cond-mat.str-el↗

arXiv2020

The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting

Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be directly tuned. In previous studies by the current authors, it has been suggested that the Hubbard model maps to an $SO(3)$ non-linear sigma model, where the phase competition becomes manifest. In this article, we rigorously demonstrate this mapping and use it to study thermal disordering of a supersolid. Starting with the attractive Hubbard model in the presence of an orbital field, we take the limit of strong coupling where a pseudospin description emerges. The in-plane pseudospin components represent superconducting pairing while the out-of-plane component encodes charge density wave order. We obtain an effective spin-$1/2$ Hamiltonian with ferromagnetic in-plane couplings and antiferromagnetic z-z couplings. In addition, the orbital field gives rise to a textured Dzyaloshinskii-Moriya interaction that has the same periodicity as the magnetic unit cell. In order to examine the nature of ordering in this spin model, we consider it in the classical limit. We assume slowly varying fields, leading to the $SO(3)$ non-linear sigma model description. As an application of these ideas, we study the nature of ordering using simulated annealing and classical Monte Carlo simulations. The ground state represents a supersolid with coexisting superconductivity and charge order. It can be viewed as a `meron crystal', a regular arrangement of superconducting vortices with charge-ordered cores. The coherent overlap of core regions gives rise to coherent long-ranged charge order. As the temperature is raised, this charge order is lost via a sharp phase transition in the Ising universality class.

cond-mat.supr-con↗

arXiv2019

Observation of neutrals carrying ion-acoustic wave momentum in partially ionized plasma

An experimental study of Ion Acoustic (IA) wave propagation is performed to investigate the effect of neutral density for argon plasma in an unmagnetized linear plasma device. The neutral density is varied by changing the neutral pressure, which in turn allows the change in ion-neutral, and electron-neutral collision mean free path. The collisions of plasma species with neutrals are found to modify the IA wave characteristics such as the wave amplitude, velocity, and propagation length. Unlike the earlier reported work where neutrals tend to heavily damp IA wave in the frequency regime ω<ν_in (where ω is ion-acoustic mode frequency and ν_in is ion-neutral collision frequency), the experimental study of IA wave presented in this paper suggests that the collisions support the wave to propagate for longer distances as the neutral pressure increases. A simple analytical model is shown to qualitatively support the experimental findings.

physics.plasm-ph↗

arXiv2019

Isothermal Equation of State of Three Dimensional Yukawa Gas

Molecular Dynamics (MD) simulation is carried out to examine the effect of particle confinement on the pressure of 3D Yukawa gas. Confinement effects are taken into account by using perfectly reflecting boundary condition in MD simulations. An equation of state relating pressure to number density is obtained. The results of the MD simulations show that in weak coupling regime pressure of confined Yukawa gas is much bigger than the kinetic pressure and scales quadratically with number density. Results are compared with earlier theories and experiments which show quadratic scaling of dust pressure with density.

physics.plasm-ph↗

arXiv2019

Effective theories for quantum spin clusters: Geometric phases and state selection by singularity

Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum spin clusters where every pair of spins is connected by an $XY$ antiferromagnetic bond. The dimer with two spin-$S$ spins provides the simplest example, it maps to a quantum particle on a ring ($S^1$). The trimer is more complex, equivalent to a particle that lives on two disjoint rings ($S^1\otimes \mathbb{Z}_2$). It has an additional subtlety for half-integer $S$ values, wherein both rings must be threaded by $π$-fluxes to obtain a satisfactory mapping. This is a consequence of the geometric phase incurred by spins. For both the dimer and the trimer, the effective theory can be seen from a path-integral-based derivation. This approach cannot be extended to the quadrumer which has a non-manifold ground state space, consisting of three tori that touch pairwise along lines. In order to understand the dynamics of a particle in this space, we develop a tight-binding model with this connectivity. Remarkably, this successfully reproduces the low-energy spectrum of the quadrumer. For half-integer spins, a geometric phase emerges which can be mapped to two $π$-flux tubes that reside in the space between the tori. The non-manifold character of the space leads to a remarkable effect - the dynamics at low energies is not ergodic as the particle is localized around singular lines of the ground state space. The low-energy spectrum consists of an extensive number of bound states formed around singularities. Physically, this manifests as an order-by-disorder-like preference for collinear ground states. However, unlike order-by-disorder, this `order by singularity' persists even in the classical limit. We discuss consequences for field theoretic studies of magnets.

cond-mat.str-el↗

arXiv2019

Skyrmion-like textures in superconductors with competing order

Vortex cores in a superconductor can develop structure and manifest competing orders. In strong magnetic fields, the inter-vortex distance can become short enough for vortex cores to overlap, giving rise to long ranged textures. We show that spin orbit coupling (SOC) can modify the interaction between vortex cores to give rise to undulating competing order fields. We illustrate this using the SO(3) theory of competing orders, wherein superconductivity and a scalar order form a three-component vector field. We consider a spherical surface with a radial magnetic flux that creates two vortices. We find stationary solutions where both vortex cores develop competing order in (a) the same sense, and (b) opposite senses. The latter represents a topologically stable vector configuration analogous to a single skyrmion. Its free energy is lowered when SOC is introduced, making it the ground state beyond a threshold SOC strength. We study this physics on the two dimensional plane using the attractive Hubbard model with Rashba SOC. Here, charge density wave (CDW) order competes with superconductivity. We find phases with long ranged, but spatially modulated, CDW order where the average CDW moment vanishes. In a wide range of parameters, CDW loses its rigidity as SOC lowers the energy cost for domain wall formation. We discuss consequences for systems such as the cuprates where charge order develops without a sharp diffraction peak.

cond-mat.supr-con↗

arXiv2018

Experimental observation of drift wave turbulence in an inhomogeneous six-pole cusp magnetic field of MPD

This paper presents a detailed study on the controlled experimental observation of drift wave instabilities in an inhomogeneous Six pole cusp magnetic field generated by an in-house developed Multi-pole line cusp magnetic field device (MPD) [Patel et al. Rev. Sci. Instrum., 44, 726 (2018)]. The device is composed of six axially symmetric cusps and non-cusp (in between two consecutive magnets) regions. The observed instability has been investigated in one of these non-cusp regions by controlling the radial plasma density gradient with changing pole magnetic field which is a unique feature of this device. It has been observed that the frequency of the instability changes explicitly with the density gradient. Moreover the scale length of plasma parameters, frequency spectrum, cross-correlation function, and fluctuation level of plasma densities has been measured in order to identify the instability. The cross field drift velocity due to fluctuation in plasma parameters have been measured from the wave number- frequency S (kz, ω) spectrum and verified with the theoretical values obtained from density scale length formula. Further from the S (kz, ω) spectrum it has been found that the drift velocity alternates the sign in the consecutive non-cusp regions.

physics.plasm-ph↗

arXiv2018

Vortex core ordering in Abrikosov lattices

Vortex lattices, arising from repulsive inter-vortex interactions, are a canonical example of emergent phenomena. Recent studies on the cuprates have drawn attention to the appearance of competing correlations within vortex cores. This gives internal structure to each vortex and changes the nature of inter-vortex interactions, especially at short range. This can have significant consequences for vortex lattices wherein vortices are in close proximity to one another. We consider the attractive Hubbard model, a prototypical model for phase competition, with checkerboard charge density wave order appearing in vortex cores. We use next-nearest-neighbour hopping, $t'$, to tune the strength of competing order in the core. Using Bogoliubov deGennes mean field simulations, we study the variation in quasiparticle gap, superfluid stiffness and shear stiffness, as the core order is tuned. The presence of competing order allows for a new defect: domain walls that separate regions with different types of charge order overlying the vortex-laden superfluid background. We find the energy cost of such domain walls. Our results indicate a stable intermediate supersolid region with coexisting superfluid and charge orders. At one end, this phase is unstable to melting of the vortex lattice into a purely charge ordered state, possibly via an intervening liquid-like state. At the other end, charge order becomes incoherent due to domain formation while superconducting order persists.

cond-mat.supr-con↗