arXiv subjects

Indubala I. Satija

Publications and source records attributed to Indubala I. Satija.

At least 19 recordsLinked to original sources

arXiv2020

Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model

We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. The model reduces to the well-known extended Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled Kitaev chains in two respective limits. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase as the ratio of the pairing amplitude and hopping is tuned. Introducing periodic driving to the model, we observe a cascade of Floquet phases with well defined quasienergy gaps and featuring chiral Majorana edge modes at the zero- or $π$-gap, or both. Dynamical topological invariants are obtained to characterize each phase and to explain the emergence of edge modes in the anomalous phase where all the quasienergy bands have zero Chern number. Analytical solution is achieved by exploiting a generalized mirror symmetry of the model, so that the effective Hamiltonian is decomposed into that of spin-$1/2$ in magnetic field, and the loop unitary operator becomes spin rotations. We further show the dynamical invariants manifest as the Hopf linking numbers.

cond-mat.supr-con↗

arXiv2019

Nests and Chains of Hofstadter Butterflies

The \lq Hofstadter butterfly', a plot of the spectrum of an electron in a two-dimensional periodic potential with a uniform magnetic field, contains subsets which resemble small, distorted images of the entire plot. We show how the sizes of these sub-images are determined, and calculate scaling factors describing their self-similar nesting, revealing an un-expected simplicity in the fractal structure of the spectrum. We also characterise semi-infinite chains of sub-images, showing one end of the chain is a result of gap closure, and the other end is at an accumulation point.

nlin.CD↗

arXiv2018

Chiral to helical Majorana fermion transition in a $p$-wave superconductor

Chiral and helical Majorana edge modes are two archetypal gapless excitations of two-dimensional topological superconductors. They belong to superconductors from two different Altland-Zirnbauer symmetry classes characterized by $\mathbb{Z}$ and $\mathbb{Z}_2$ topological invariant respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate without symmetry breaking. Here we show that such a direct topological transition is in fact possible, provided the system possesses an additional symmetry $\mathcal{O}$ which changes the bulk topological invariant to $\mathbb{Z}\oplus \mathbb{Z}$ type. A simple model describing the proximity structure of a Chern insulator and a $p_x$-wave superconductor is proposed and solved analytically to illustrate the transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by $\mathcal{O}$-graded Chern number and hosts a pair of counter-propagating Majorana fermions. The bulk topological invariants and edge theory are worked out in detail. Implications of these results to topological quantum computing based on Majorana fermions are discussed.

cond-mat.mes-hall↗

arXiv2016

Cosine Edge Mode in a Periodically Driven Quantum System

Time-periodic (Floquet) topological phases of matter exhibit bulk-edge relationships that are more complex than static topological insulators and superconductors. Finding the edge modes unique to driven systems usually requires numerics. Here we present a minimal two-band model of Floquet topological insulators and semimetals in two dimensions where all the bulk and edge properties can be obtained analytically. It is based on the extended Harper model of quantum Hall effect at flux one half. We show that periodical driving gives rise to a series of phases characterized by a pair of integers. The model has a most striking feature: the spectrum of the edge modes is always given by a single cosine function, $ω(k_y)\propto \cos k_y$ where $k_y$ is the wave number along the edge, as if it is freely dispersing and completely decoupled from the bulk. The cosine mode is robust against the change in driving parameters and persists even to semi-metallic phases with Dirac points. The localization length of the cosine mode is found to contain an integer and in this sense quantized.

cond-mat.quant-gas↗

arXiv2015

Majorana fermions: Anholonomy of bound states

Majorana bound states appearing in 1-D $p$-wave superconductor ($\cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($\cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$\ddot{\rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $\cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition.

cond-mat.mes-hall↗

arXiv2015

Topological Map of the Hofstadter Butterfly and Van Hove Singularities

The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here we obtain simple rules to determine the Chern numbers at all scales in the butterfly fractal and lay out a very detailed topological map of the butterfly. Our study reveals the existence of a set of critical points, each corresponding to a macroscopic annihilation of orderly patterns of both the positive and the negative Cherns that appears as a fine structure in the butterfly. Such topological collapses are identified with the Van Hove singularities that exists at every band center in the butterfly landscape. We thus associate a topological character to the Van Hove anomalies. Finally, we show that this fine structure is amplified under perturbation, inducing quantum phase transitions to higher Chern states in the system.

cond-mat.other↗

arXiv2014

Floquet edge states in a harmonically driven integer quantum Hall system

Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here we shed further light on the nature of these modes by analyzing a simple type of periodic driving where the hopping along one spatial direction is modulated sinusoidally with time while the hopping along the other spatial direction is kept constant. We obtain the phase diagram for the quasienergy spectrum at flux 1/3 as the driving frequency $ω$ and the hopping anisotropy are varied. A series of topologically distinct phases with counter-propagating edge modes appear due to the harmonic driving, similar to the case of a periodically kicked system studied earlier. We analyze the time dependence of the pair of Floquet edge states localized at the same edge, and compare their Fourier components in the frequency domain. In the limit of small modulation, one of the Floquet edge mode within the pair can be viewed as the edge mode originally living in the other energy gap shifted in quasienergy by $\hbar ω$, i.e., by absorption or emission of a "photon" of frequency $ω$. Our result suggests that counter-propagating Floquet edge modes are generic features of periodically driven integer quantum Hall systems, and not tied to any particular driving protocol. It also suggests that the Floquet edge modes would remain robust to any static perturbations that do not destroy the chiral edge modes of static quantum Hall states.

cond-mat.quant-gas↗

arXiv2014

Counter-propagating edge modes and topological phases of a kicked quantum Hall system

A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.

cond-mat.quant-gas↗

arXiv2012

Noise Correlation Scalings: Revisiting the Quantum Phase Transition in Incommensurate Lattices with Hard-Core Bosons

Finite size scalings of the momentum distribution and noise correlations are performed to study Mott insulator, Bose glass, and superfluid quantum phases in hard-core bosons (HCBs) subjected to quasi-periodic disorder. The exponents of the correlation functions at the Superfluid to Bose glass (SF-BG) transition are found to be approximately one half of the ones that characterizes the superfluid phase. The derivatives of the peak intensities of the correlation functions with respect to quasiperiodic disorder are shown to diverge at the SF-BG critical point. This behavior does not occur in the corresponding free fermion system, which also exhibits an Anderson-like transition at the same critical point, and thus provides a unique experimental tool to locate the phase transition in interacting bosonic systems. We also report on the absence of primary sublattice peaks in the momentum distribution of the superfluid phase for special fillings.

cond-mat.quant-gas↗

arXiv2012

Quantum Dynamics of Solitons in Strongly Interacting Systems on Optical Lattices

Mean-field dynamics of strongly interacting bosons described by hard core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii (GP-type) where the condensate fraction remains dark and a novel non-Gross-Pitaevskii-type (non-GP-type) characterized by brightening of the condensate fraction. Here we study the effects of quantum fluctuations on these solitons using the adaptive time-dependent density matrix renormalization group method, which takes into account the effect of strong correlations. We use local observables as the density, condensate density and correlation functions as well as the entanglement entropy to characterize the stability of the initial states. We find both species of solitons to be stable under quantum evolution for a finite duration, their tolerance to quantum fluctuations being enhanced as the width of the soliton increases. We describe possible experimental realizations in atomic Bose Einstein Condensates, polarized degenerate Fermi gases, and in systems of polar molecules on optical lattices.

quant-ph↗

arXiv2012

Chern numbers hiding in time-of-flight images

We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology.

cond-mat.quant-gas↗

arXiv2011

Bright and Dark Solitons and Breathers in Strongly Repulsive Bose-Einstein Condensates

Collisional dynamics of solitary matter waves of superfluid hard core bosons, consisting of dark and bright non-linear waves as well as supersonic periodic trains, reveals remarkable richness and coherence, with the phase of the condensate playing a key role. Depending upon the condensate density and their relative velocity, two distinctive collisional types emerge: the intuitively expected repulsive collisions due to the hard core boson constraint; and, also collisions in which they "pass through" one another. In addition to confirming the soliton status of both bright and dark solitary waves, our studies reveal a variety of multi-solitons including multiple families of breathers, that can be produced and precisely controlled via quantum phase engineering.

quant-ph↗

arXiv2009

Particle-Hole Asymmetry and Brightening of Solitons in A Strongly Repulsive BEC

We study solitary wave propagation in the condensate of a system of hard-core bosons with nearest-neighbor interactions. For this strongly repulsive system, the evolution equation for the condensate order parameter of the system, obtained using spin coherent state averages is different from the usual Gross-Pitaevskii equation (GPE). The system is found to support two kinds of solitons when there is a particle-hole imbalance: a dark soliton that dies out as the velocity approaches the sound velocity, and a new type of soliton which brightens and persists all the way up to the sound velocity, transforming into a periodic wave train at supersonic speed. Analogous to the GPE soliton, the energy-momentum dispersion for both solitons is characterized by Lieb II modes.

cond-mat.quant-gas↗

arXiv2008

Phase transitions, entanglement and quantum noise interferometry in cold atoms

We show that entanglement monotones can characterize the pronounced enhancement of entanglement at a quantum phase transition if they are sensitive to long-range high order correlations. These monotones are found to develop a sharp peak at the critical point and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlations and verify that these experimentally accessible quantities indeed encode entanglement information and probe separability.

quant-ph↗

arXiv2007

Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux." A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth," a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.

cond-mat.mes-hall↗

arXiv2006

Lifshitz-like transition and enhancement of correlations in a rotating bosonic ring lattice

We study the effects of rotation on one-dimensional ultra-cold bosons confined to a ring lattice. For commensurate systems, at a critical value of the rotation frequency, an infinitesimal interatomic interaction energy opens a gap in the excitation spectrum, fragments the ground state into a macroscopic superposition of two states with different circulation and generates a sudden change in the topology of the momentum distribution. These features are reminiscent of the topological changes in the Fermi surface that occurs in the Lifshitz transition in fermionic systems. The entangled nature of the ground state induces a strong enhancement of quantum correlations and decreases the threshold for the Mott insulator transition. In contrast to the commensurate case, the incommensurate lattice is rather insensitive to rotation. Our studies demonstrate the utility of noise correlations as a tool for identifying new physics in strongly correlated systems.

cond-mat.other↗

arXiv2006

Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. Such transitions have been extensively studied for magnetic fields corresponding to Abelian gauges; they occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields, which can be realized with atoms with two pairs of degenerate internal states. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum and the minimum energy viewed as a function of momentum exhibits a step structure. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.

cond-mat.other↗

arXiv2006

Hanbury Brown-Twiss Interferometry for Fractional and Integer Mott Phases

Hanbury-Brown-Twiss interferometry (HBTI) is used to study integer and fractionally filled Mott Insulator (MI) phases in period-2 optical superlattices. In contrast to the quasimomentum distribution, this second order interferometry pattern exhibits high contrast fringes in the it insulating phases. Our detailed study of HBTI suggests that this interference pattern signals the various superfluid-insulator transitions and therefore can be used as a practical method to determine the phase diagram of the system. We find that in the presence of a confining potential the insulating phases become robust as they exist for a finite range of atom numbers. Furthermore, we show that in the trapped case the HBTI interferogram signals the formation of the MI domains and probes the shell structure of the system.

cond-mat.soft↗