arXiv subjects

Rahul Trivedi

Publications and source records attributed to Rahul Trivedi.

At least 55 records · Page 3Linked to original sources

arXiv2022

Few-particle scattering from localized quantum systems in spatially structured bosonic baths

Understanding dynamics of localized quantum systems embedded in engineered bosonic environments is a central problem in quantum optics and open quantum system theory. We present a formalism for studying few-particle scattering from a localized quantum system interacting with an bosonic bath described by an inhomogeneous wave-equation. In particular, we provide exact relationships between the quantum scattering matrix of this interacting system and frequency domain solutions of the inhomogeneous wave-equation thus providing access to the spatial distribution of the scattered few-particle wave-packet. The formalism developed in this paper paves the way to computationally understanding the impact of structured media on the scattering properties of localized quantum systems embedded in them without simplifying assumptions on the physics of the structured media.

quant-ph↗

arXiv2022

Simulation of large-area metasurfaces with a distributed transition matrix method

Inverse design of large-area metasurfaces can potentially exploit the full parameter space that such devices offer and achieve highly efficient multifunctional flat optical elements. However, since practically useful flat optics elements are large in the linear dimension, an accurate simulation of their scattering properties is challenging. Here, we demonstrate a method to compute accurate simulations and gradients of large-area metasurfaces. Our approach relies on two key ingredients - a simulation distribution strategy that allows a linear reduction in the simulation time with number of compute (GPU) nodes and an efficient single-node computation using the Transition-matrix (T-matrix) method. We demonstrate ability to perform a distributed simulation of large-area, while accurately accounting for scatterer-scatterer interactions significantly beyond the locally periodic approximation, and efficiently compute gradients with respect to the metasurface design parameters. This scalable and accurate metasurface simulation method opens the door to gradient-based optimization of full large-area metasurfaces.

physics.optics↗

arXiv2022

Superradiance in dynamically modulated Tavis-Cumming model with spectral disorder

Superradiance is the enhanced emission of photons from quantum emitters collectively coupling to the same optical mode. However, disorder in the resonant frequencies of the quantum emitters can perturb this effect. In this paper, we study the interplay between superradiance and spectral disorder in a dynamically modulated Tavis-Cummings model. Through numerical simulations and analytical calculations, we show that the effective cooperativity of the superradiant mode, which is always formed over an extensive number of emitters, can be multiplicatively enhanced with a quantum control protocol modulating the resonant frequency of the optical mode. Our results are relevant to experimental demonstration of superradiant effects in solid-state quantum optical systems, wherein the spectral disorder is a significant technological impediment towards achieving photon-mediated emitter-emitter couplings.

quant-ph↗

arXiv2021

Convergence guarantees for discrete mode approximations to non-Markovian quantum baths

Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.

quant-ph↗

arXiv2021

Gradient descent globally solves average-case non-resonant physical design problems

Optimization problems occurring in a wide variety of physical design problems, including but not limited to optical engineering, quantum control, structural engineering, involve minimization of a simple cost function of the state of the system (e.g. the optical fields, the quantum state) while being constrained by the physics of the system. The physics constraints often makes such problems non-convex and thus only locally solvable, leaving open the question of finding the globally optimal design. In this paper, I consider design problems whose physics is described by bi-affine equality constraints, and show that under assumptions on the stability of these constraints and the physical system being non-resonant, gradient descent globally solves a typical physical design problem. The key technical contributions of this paper are (i) outline a criteria that ensure the convergence of gradient descent to an approximate global optima in the limit of large problem sizes, and (ii) use random matrix theory to outline ensembles of physically motivated problems which, on an average, satisfy this convergence criteria.

math.OC↗

arXiv2021

Augmenting On-Chip Microresonator through Photonic Inverse Design

Recent advances in the design and fabrication of on-chip optical microresonators has greatly expanded their applications in photonics, enabling metrology, communications, and on-chip lasers. Designs for these applications require fine control of dispersion, bandwidth and high optical quality factors. Co-engineering these figures of merit remains a significant technological challenge due to design strategies being largely limited to analytical tuning of cross-sectional geometry. Here, we show that photonic inverse-design facilitates and expands the functionality of on-chip microresonators; theoretically and experimentally demonstrating flexible dispersion engineering, quality factor beyond 2 million on the silicon-on-insulator platform with single mode operation, and selective wavelength-band operation.

physics.optics↗

arXiv2021

Control design for inhomogeneous broadening compensation in single-photon transducers

A transducer of single photons between microwave and optical frequencies can be used to realize quantum communication over optical fiber links between distant superconducting quantum computers. A promising scalable approach to constructing such a transducer is to use ensembles of quantum emitters interacting simultaneously with electromagnetic fields at optical and microwave frequencies. However, inhomogeneous broadening in the transition frequencies of the emitters can be detrimental to this collective action. In this article, we utilise a gradient-based optimization strategy to design the temporal shape of the laser field driving the transduction system to mitigate the effects of inhomogeneous broadening. We study the improvement of transduction efficiencies as a function of inhomogeneous broadening in different single-emitter cooperativity regimes and correlate it with a restoration of superradiance effects in the emitter ensembles. Furthermore, to assess the optimality of our pulse designs, we provide certifiable bounds on the design problem and compare them to the achieved performance.

quant-ph↗

arXiv2021

Quantum optics of soliton microcombs

Soliton microcombs -- phase-locked microcavity frequency combs -- have become the foundation of several classical technologies in integrated photonics, including spectroscopy, LiDAR, and optical computing. Despite the predicted multimode entanglement across the comb, experimental study of the quantum optics of the soliton microcomb has been elusive. In this work, we use second-order photon correlations to study the underlying quantum processes of soliton microcombs in an integrated silicon carbide microresonator. We show that a stable temporal lattice of solitons can isolate a multimode below-threshold Gaussian state from any admixture of coherent light, and predict that all-to-all entanglement can be realized for the state. Our work opens a pathway toward a soliton-based multimode quantum resource.

physics.optics↗

arXiv2021

Quantum algorithms for powering stable Hermitian matrices

Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations, simulation of discrete-time Markov chains, or discovering the spectral properties of matrices with iterative methods. In this paper, we investigate the possibility of speeding up matrix powering of sparse stable Hermitian matrices on a quantum computer. We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms -- (i) an adaption of quantum-walk based fast forwarding algorithm (ii) an algorithm based on Hamiltonian simulation. Furthermore, by mapping the N-bit parity determination problem to a matrix powering problem, we provide no-go theorems that limit the quantum speedups achievable in powering non-Hermitian matrices.

quant-ph↗

arXiv2020

Optimal two-photon excitation of bound states in non-Markovian waveguide QED

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave-packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave-packets that can excite a given superposition of these bound states. As specific examples, we study bound state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

quant-ph↗

arXiv2020

Spectrally reconfigurable quantum emitters enabled by optimized fast modulation

The ability to shape photon emission facilitates strong photon-mediated interactions between disparate physical systems, thereby enabling applications in quantum information processing, simulation and communication. Spectral control in solid state platforms such as color centers, rare earth ions, and quantum dots is particularly attractive for realizing such applications on-chip. Here we propose the use of frequency-modulated optical transitions for spectral engineering of single photon emission. Using a scattering-matrix formalism, we find that a two-level system, when modulated faster than its optical lifetime, can be treated as a single-photon source with a widely reconfigurable photon spectrum that is amenable to standard numerical optimization techniques. To enable the experimental demonstration of this spectral control scheme, we investigate the Stark tuning properties of the silicon vacancy in silicon carbide, a color center with promise for optical quantum information processing technologies. We find that the silicon vacancy possesses excellent spectral stability and tuning characteristics, allowing us to probe its fast modulation regime, observe the theoretically-predicted two-photon correlations, and demonstrate spectral engineering. Our results suggest that frequency modulation is a powerful technique for the generation of new light states with unprecedented control over the spectral and temporal properties of single photons.

quant-ph↗

arXiv2020

The crux of using the cascaded emission of a 3-level quantum ladder system to generate indistinguishable photons

We investigate the degree of indistinguishability of cascaded photons emitted from a 3-level quantum ladder system; in our case the biexciton-exciton cascade of semiconductor quantum dots. For the 3-level quantum ladder system we theoretically demonstrate that the indistinguishability is inherently limited for both emitted photons and determined by the ratio of the lifetimes of the excited and intermediate states. We experimentally confirm this finding by comparing the quantum interference visibility of non-cascaded emission and cascaded emission from the same semiconductor quantum dot. Quantum optical simulations produce very good agreement with the measurements and allow to explore a large parameter space. Based on our model, we propose photonic structures to optimize the lifetime ratio and overcome the limited indistinguishability of cascaded photon emission from a 3-level quantum ladder system.

cond-mat.mes-hall↗

arXiv2020

Data-driven acceleration of Photonic Simulations

Designing modern photonic devices often involves traversing a large parameter space via an optimization procedure, gradient based or otherwise, and typically results in the designer performing electromagnetic simulations of correlated devices. In this paper, we present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwell's equations using two machine learning models (principal component analysis and a convolutional neural network) trained on simulations of correlated devices. These data-driven models are trained to predict a subspace within which the solution of the frequency-domain Maxwell's equations lie. This subspace can then be used for augmenting the Krylov subspace generated during the GMRES iterations. By training the proposed models on a dataset of grating wavelength-splitting devices, we show an order of magnitude reduction ($\sim 10 - 50$) in the number of GMRES iterations required for solving frequency-domain Maxwell's equations.

physics.comp-ph↗

arXiv2020

Analytic and geometric properties of scattering from periodically modulated quantum-optical systems

We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first order contribution to the transmission or equal-time N-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature i.e. it only depends on the Hamiltonian trajectory and not on the precise nature of the modulation being applied.

quant-ph↗

arXiv2020

Fundamental bounds for scattering from absorptionless electromagnetic structures

The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic device design, it is unclear whether the performance of resulting designs is close to that of the best possible design. This question remains unsettled for absorptionless electromagnetic devices since the absence of material loss makes it difficult to provide provable bounds on their scattering properties. We resolve this problem by providing non-trivial lower bounds on performance metrics that are convex functions of the scattered fields. Our bounding procedure relies on accounting for a constraint on the electric fields inside the device, which can be provably constructed for devices with small footprints or low dielectric constrast. We illustrate our bounding procedure by studying limits on the scattering cross-sections of dielectric and metallic particles in the absence of material losses.

physics.optics↗

arXiv2019

Point-coupling Hamiltonian for frequency-independent linear optical devices

We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering matrix, and show that an application of the quantum scattering matrix on an input state is equivalent to applying the inverse of classical scattering matrix on the annihilation operators describing the optical modes. We show how to construct the point-coupling Hamiltonian corresponding to a general linear optical device described by a classical scattering matrix, and provide examples of Hamiltonians for some commonly used linear optical devices. Finally, in order to demonstrate the practical utility of the point-coupling Hamiltonian, we use it to rigorously formulate a matrix-product-state based simulation for time-delayed feedback systems wherein the feedback is provided by a linear optical device described by a scattering matrix as opposed to a hard boundary condition (e.g. a mirror with less than unity reflectivity).

quant-ph↗

arXiv2019

Photon blockade in weakly-driven cavity QED systems with many emitters

We use the scattering matrix formalism to analyze photon blockade in coherently-driven CQED systems with a weak drive. By approximating the weak coherent drive by an input single- and two-photon Fock state, we reduce the computational complexity of the transmission and the two-photon correlation function from exponential to polynomial in the number of emitters. This enables us to easily analyze cavity-based systems containing $\sim$50 quantum emitters with modest computational resources. Using this approach we study the coherence statistics of polaritonic photon blockade while increasing the number of emitters for resonant and detuned multi-emitter CQED systems --- we find that increasing the number of emitters worsens photon blockade in resonant systems, and improves it in detuned systems. We also analyze the impact of inhomogeneous broadening in the emitter frequencies on both polaritonic and subradiant photon blockade through this system.

quant-ph↗

arXiv2019

Generation of non-classical light using semiconductor quantum dots

Sources of non-classical light are of paramount importance for future applications in quantum science and technology such as quantum communication, quantum computation and simulation, quantum sensing and quantum metrology. In this review we discuss the fundamentals and recent progress in the generation of single photons, entangled photon pairs and photonic cluster states using semiconductor quantum dots. Specific fundamentals which are discussed are a detailed quantum description of light, properties of semiconductor quantum dots and light-matter interactions. This includes a framework for the dynamic modelling of non-classical light generation and two-photon interference. Recent progress will be discussed in the generation of non-classical light for off-chip applications as well as implementations for scalable on-chip integration.

quant-ph↗