arXiv subjects

Rajesh K. Malla

Publications and source records attributed to Rajesh K. Malla.

At least 19 recordsLinked to original sources

arXiv2025

Noise-Assisted Feedback Control of Open Quantum Systems for Ground State Properties

Intrinsic noise in pre-fault-tolerant quantum devices poses a major challenge to the reliable realization of unitary dynamics in quantum algorithms and simulations. To address this, we present a method for simulating open quantum system dynamics on a quantum computer, including negative dissipation rates in the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. Our approach lies beyond the standard Markovian approximation, enabling the controlled study of non-Markovian processes within a quantum simulation framework. Using this method, we develop a quantum algorithm for calculating ground-state properties that exploits feedback-controlled, noise-assisted dynamics. In this scheme, Lyapunov-based feedback steers the system toward a target virtual state under engineered noise conditions. This framework offers a promising strategy for harnessing current quantum hardware and advancing robust control protocols based on open system dynamics.

quant-ph↗

arXiv2025

Competing Bosonic Reactions: Insight from Exactly Solvable Time-Dependent Models

We discuss the progress on exactly solvable multistate Landau-Zener models from a perspective of their application to competing reactions of particle creation from a false vacuum. Such models generally predict that, even with identical initial conditions, and for nearly the same other particle parameters, a quantum coherent evolution results in a final particle distribution with significant asymmetry. We use an exact solution of the driven bosonic Tavis-Cummings model for two reaction pathways in order to quantify this effect, reveal a corresponding phase transition, and identify its universality class.

quant-ph↗

arXiv2024

Detecting Multipartite Entanglement Patterns using Single Particle Green's Functions

We present a protocol for detecting multipartite entanglement in itinerant many-body electronic systems using single particle Green's functions. To achieve this, we first establish a connection between the quantum Fisher information (QFI) and single particle Green's functions by constructing a set of witness operators built out of single electron creation and destruction operators in a doubled system. This set of witness operators is indexed by a momenta $k$. We compute the QFI for these witness operators and show that for thermal ensembles it can be expressed as an auto-convolution of the single particle spectral function. We then apply our framework to a one-dimensional fermionic system to showcase its effectiveness in detecting entanglement in itinerant electron models. We observe that the detected entanglement level is sensitive to the wave vector associated with witness operator. Our protocol will permit detecting entanglement in many-body systems using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, two spectroscopies that measure the single particle Green's function. It offers the prospect of the experimental detection of entanglement through spectroscopies beyond the established route of measuring the dynamical spin response.

quant-ph↗

arXiv2024

Feedback-based Quantum Algorithm Inspired by Counterdiabatic Driving

In recent quantum algorithmic developments, a feedback-based approach has shown promise for preparing quantum many-body system ground states and solving combinatorial optimization problems. This method utilizes quantum Lyapunov control to iteratively construct quantum circuits. Here, we propose a substantial enhancement by implementing a protocol that uses ideas from quantum Lyapunov control and the counterdiabatic driving protocol, a key concept from quantum adiabaticity. Our approach introduces an additional control field inspired by counterdiabatic driving. We apply our algorithm to prepare ground states in one-dimensional quantum Ising spin chains. Comprehensive simulations demonstrate a remarkable acceleration in population transfer to low-energy states within a significantly reduced time frame compared to conventional feedback-based quantum algorithms. This acceleration translates to a reduced quantum circuit depth, a critical metric for potential quantum computer implementation. We validate our algorithm on the IBM cloud computer, highlighting its efficacy in expediting quantum computations for many-body systems and combinatorial optimization problems.

quant-ph↗

arXiv2023

Quantum dynamics of non-Hermitian many-body Landau-Zener systems

We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multi-state Landau-Zener models. The non-hermiticity is due to the anti-Hermitian couplings between the diabatic levels. We find that there exists a new conservation law, unique to this class of models, that describes the simultaneous growth of the unnormalized wavefunctions. These models have practical applications in Bose-Einstein condensates, and they can describe the dynamics of multi-species bosonic systems. The conservation law relates to a pair-production mechanism that explains the dissociation of diatomic molecules into atoms. We provide a general framework for both solvable and semiclassically solvable non-Hermitian Landau-Zener models. Our findings will open new avenues for a number of diverse emergent phenomena in explicitly time-dependent non-Hermitian quantum systems.

quant-ph↗

arXiv2022

Nonadiabatic dissociation of molecular Bose-Einstein condensates: competition between chemical reactions

We provide a framework to solve generic models describing the dissociation of multiple molecular Bose-Einstein condensates in a nonadiabatic regime. The competition between individual chemical reactions can lead to non-trivial dependence on critical components such as path interference and symmetries, thus, affecting the final distribution of atomic population. We find an analytical solution for an illustrative example model involving four atomic modes. When the system parameters satisfy $CPT$ symmetry, where $C$ is charge conjugation, $P$ is parity, and $T$ is time-reversal symmetry, our solution predicts a population imbalance between atomic modes that is exponentially sensitive to system parameters. However, a weakly broken symmetry alters the population in each atomic mode and can reverse the population imbalance. Our solution also demonstrates a strong quantum correlation between atomic modes that leads to the spontaneous production of atoms in a multi-mode squeezed state. Moreover, in our framework, a time-dependent non-Hermitian quantum mechanics naturally manifests which can alternatively be realized experimentally in photonic systems.

quant-ph↗

arXiv2022

Ultrafast Nonequilibrium Dynamics in Two-dimensional Quantum Spin-Hall Materials

We develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin-Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to non-adiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for identifying topological invariants in two-dimensional quantum spin-Hall solid state systems.

cond-mat.mes-hall↗

arXiv2022

Landau-Zener transition between two levels coupled to continuum

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, {\em i}, to survive the transition and to remain in the first level, depends exponentially on the square of the tunnel matrix element between the two levels. This result remains valid when the second level, {\em f}, is broadened due to e.g. coupling to continuum [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. If the level, {\em i}, is also coupled to continuum, albeit much weaker than the level {\em f}, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level {\em i} after crossing {\em f} is {\em enhanced} due to the coupling to continuum. This, as shown in the present paper, is the result of a second-order process, which is an {\em additional coupling between the levels}. The underlying mechanism of this additional coupling is virtual tunneling from {\em i} into continuum followed by tunneling back into {\em f}.

cond-mat.mes-hall↗

arXiv2022

Effect of decay of the final states on the probabilities of the Landau-Zener transitions in multistate non-integrable models

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interference of the virtual paths, it can be argued that the independence of the broadening persists, we focus on non-integrable models involving interference. For a simple four-state model, which allows an analytical treatment, we demonstrate that the decay of the excited states affects the survival probability provided that {\em the widths of the final states are different}.

cond-mat.mes-hall↗

arXiv2022

Coherent reaction between molecular and atomic Bose-Einstein condensates: integrable model

We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a nonexponential dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate. We find that the emerging phase can have a thermalized energy distribution with the temperature defined by the rate of the transition. This phase, however, has strong purely quantum correlations.

quant-ph↗

arXiv2021

Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators

The recent observations of nonlinear Hall effect in time-reversal symmetry protected systems and on the surface of three-dimensional topological insulators due to an in-plane magnetic field have attracted immense experimental and theoretical investigations in two-dimensional transition metal dichalcogenides and Weyl semimetals. The origin of this type of second order effect has been attributed to the emergence of a Berry curvature dipole, which requires a low-symmetry environment. Here, we propose a mechanism for generating such a second order nonlinear Hall effect in Kane-Mele two-dimensional topological insulators due to spatial and time reversal symmetry breaking in the presence of Zeeman and Rashba couplings. By actively tuning the energy gaps with external electromagnetic fields we also demonstrate that the nonlinear Hall effect shows remarkable signatures of topological phase transitions existing in the considered two-dimensional systems.

cond-mat.mes-hall↗

arXiv2021

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these signatures manifest in the nonlinear Kerr effect and in third-harmonic generation processes. We show that the resonant nonlinear spectral response of topological fermions can be traced to specific Dirac cones in these materials, enabling characterization of topological invariants in any phase by detecting the cross-polarized component of the electromagnetic field. By shedding light on the unique processes involved in harmonic generation via topological phenomena our findings open an encouraging path towards the development of novel nonlinear systems based on two-dimensional semiconductors of the graphene family.

cond-mat.mes-hall↗

arXiv2021

Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly-looking models belong to different topological classes.

cond-mat.mes-hall↗

arXiv2019

High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts

In the presence of spin-orbit coupling two branches of the energy spectrum of 2D electrons get shifted in the momentum space. Application of in-plane magnetic field causes the splitting of the branches in energy. When both, spin-orbit coupling and Zeeman splitting are present, the branches of energy spectrum cross at certain energy. Near this energy, the Landau quantization becomes peculiar since semiclassical trajectories, corresponding to individual branches, get coupled. We study this coupling as a function of proximity to the topological transition. Remarkably, the dependence on the proximity is strongly asymmetric reflecting the specifics of the behavior of the trajectories near the crossing. Equally remarkable, on one side of the transition, the magnitude of coupling is an oscillating function of this proximity. These oscillations can be interpreted in terms of the St{ü}ckelberg interference. Scaling of characteristic detuning with magnetic length is also unusual. This unusual behavior cannot be captured by simply linearizing the Fermi contours near the crossing point.

cond-mat.mes-hall↗

arXiv2018

Interaction-induced long-time tail of a nonlinear ac absorption in a localized system: a relay-race mechanism

In conventional solid-state electron systems with localized states the ac absorption is linear since the inelastic widths of the energy levels exceeds the drive amplitude. The situation is different in the systems of cold atoms in which phonons are absent. Then even a weak drive leads to saturation of the ac absorption within resonant pairs, so that the population of levels oscillates with the Rabi frequency. We demonstrate that, in the presence of weak dipole-dipole interactions, the response of the system acquires a long-time component which oscillates with frequency much smaller than the Rabi frequency. The underlying mechanism of this long-time behavior is that the fields created in the course of the Rabi oscillations serve as resonant drive for the second-generation Rabi oscillations in pairs with level spacings close to the Rabi frequency. The frequency of the second-generation oscillations is of the order of interaction strength. As these oscillations develop, they can initiate the next-generation Rabi oscillations, and so on. Formation of the second-generation oscillations is facilitated by the non-diagonal component of the dipole-dipole interaction tensor.

cond-mat.dis-nn↗

arXiv2018

Shape of the zeroth Landau level in graphene with non-diagonal disorder

Non-diagonal (bond) disorder in graphene broadens Landau levels (LLs) in the same way as random potential. The exception is the zeroth LL, $n=0$, which is robust to the bond disorder, since it does not mix different $n=0$ states within a given valley. The mechanism of broadening of the $n=0$ LL is the inter-valley scattering. Several numerical simulations of graphene with bond disorder had established that $n=0$ LL is not only anomalously narrow but also that its shape is very peculiar with three maxima, one at zero energy, $E=0$, and two others at finite energies $\pm E$. We study theoretically the structure of the states in $n=0$ LL in the presence of bond disorder. Adopting the assumption that the bond disorder is strongly anisotropic, namely, that one type of bonds is perturbed much stronger than other two, allowed us to get an analytic expression for the density of states which agrees with numerical simulations remarkably well. On the qualitative level, our key finding is that delocalization of $E=0$ state has a dramatic back effect on the density of states near $E=0$. The origin of this unusual behavior is the strong correlation of eigenstates in different valleys.

cond-mat.dis-nn↗

arXiv2018

Effective tunnel conductance and effective ac conductivity of randomly strained graphene

We consider a single-layer graphene with high ripples, so that the pseudo-magnetic fields due to these ripples are strong. If the magnetic length corresponding to a typical pseudo-magnetic field is smaller than the ripple size, the resulting Landau levels are local. Then the effective properties of the macroscopic sample can be calculated by averaging the local properties over the distribution of ripples. We find that this averaging does not wash out the Landau quantization completely. Average density of states (DOS) contains a feature (inflection point) at energy corresponding to the first Landau level in a {\em typical} field. Moreover, the frequency dependence of the ac conductivity %while the average ac conductivity contains a maximum at a frequency corresponding to the first Landau level in a typical field. This nontrivial behavior of the effective characteristics of randomly strained graphene is a consequence of non-equidistance of the Landau levels in the Dirac spectrum.

cond-mat.mes-hall↗

arXiv2018

Resonant reflection of interacting electrons from an impurity in a quantum wire: interplay of Zeeman and spin-orbit effects

A single-channel quantum wire with two well-separated Zeeman subbands and in the presence of a weak spin-orbit coupling is considered. An impurity level which is split off the upper subband is degenerate with the continuum of the lower subband. We show that, when the Fermi level lies in the vicinity of the impurity level, the transport is completely blocked. This is the manifestation of the effect of resonant reflection and can be viewed as resonant tunneling between left-moving and right-moving electrons via the impurity level. We incorporate electron-electron interactions and study their effect on the shape of the resonant-reflection profile. This profile becomes a two-peak structure, where one peak is caused by resonant reflection itself, while the origin of the other peak is reflection from the Friedel oscillations of the electron density surrounding the impurity.

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