arXiv subjects

E. A. Muljarov

Publications and source records attributed to E. A. Muljarov.

At least 19 recordsLinked to original sources

arXiv2026

Optimization of path-integral tensor-multiplication schemes in open quantum systems

Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits the applicability when applied to systems with long memory times. Here we provide a general optimization of tensor multiplication schemes for systems with pair correlations and finite memory times. This optimization effectively reduces the tensor sizes by using a matrix representation of tensors combined with singular value decomposition to filter out negligible contributions. This approach dramatically reduces both computational time and memory usage of the traditional tensor-multiplication schemes. While more memory-efficient representations exist, this approach enables a consistent extrapolation scheme for the rapid estimation of the exact value. As a demonstration, we apply it to the Trotter decomposition with linked cluster expansion technique, and use it to investigate a quantum dot-microcavity system at large coupling strengths. We also apply the optimization in a case where the memory time is very long -- specifically in a system containing two spatially separated quantum dots in a common phonon bath.

quant-ph↗

arXiv2025

Rigorous theory of coupled resonators

We demonstrate the general failure of the famous concept of tight binding and mode hybridization underlying modern theories of coupled open resonators. In spite of sophisticated examples in the literature, successfully illustrating these theories, the latter fail to describe any planar systems. This includes the simplest possible case of two dielectric slabs placed next to each other or separated by a distance, which is straightforward for verification, due to its analytical solvability. We present a rigorous theory capable of calculating correctly the eigenmodes of arbitrary three-dimensional dispersive coupled resonators in terms of their individual modes, providing insight into the proper mode hybridization and formation of bonding and antibonding supermodes. Planar optical resonators, such as coupled slabs and Bragg-mirror microcavities, are used for illustrative purposes as they allow precise and reliable verification of the theory.

physics.optics↗

arXiv2024

Controlling dephasing of coupled qubits via shared-bath coherence

The interaction of a quantum system with its environment limits its coherence time. This, in particular, restricts the utility of qubits in quantum information processing applications. In this paper, we show that the decoherence of a coupled qubit system can be minimized, or even eliminated, by exploiting the quantum coherence of the bath itself. We investigate the dephasing in a system of two spatially separated, electronically decoupled qubits, with direct or mediated coupling, interacting with a shared bath. For illustration, we treat Förster or cavity-mediated coupling between semiconductor quantum dots interacting with acoustic phonons. Using the rigorous method of Trotter's decomposition with cumulant expansion, we demonstrate a reduction in the dephasing rates at specific distances between the dots. The control of dephasing with distance is a coherent effect of the shared bath and is absent for independent baths. It can be understood in terms of phonon-assisted transitions between the entangled qubit states of the coupled system.

cond-mat.mes-hall↗

arXiv2024

Exceptional Bound States in the Continuum

Bound states in the continuum (BICs) and exceptional points (EPs) are unique singularities of non-Hermitian systems. BICs demonstrate enhancement of the electromagnetic field at the nanoscale, while EPs exhibit high sensitivity to small perturbations. Here, we demonstrate that several BICs can be merged into one EP, forming an EP-BIC. The resulting state inherits properties from both BICs and EP, namely, it does not radiate and shows extremely high sensitivity to perturbations. We validate the developed theory with numerical simulations and demonstrate the formation of second and third-order EP-BICs in stacked dielectric metasurfaces. We also show that the losses of the resulting leaky resonances exhibit an anomalous behavior when the unit cell is broken, which differs from the asymptotics commonly attributed to BICs.

physics.optics↗

arXiv2023

Impact of the phonon environment on the nonlinear quantum-dot-cavity QED. I. Path-integral approach

We demonstrate a strong influence of the phonon environment on the coherent dynamics of the quantum dot (QD)-cavity system in the quantum strong coupling regime. This regime is implemented in the nonlinear QD-cavity QED and can be reliably measured by heterodyne spectral interferometry. We present a semi-analytic asymptotically exact path integral-based approach to the nonlinear optical response of this system, which includes two key ingredients: Trotter's decomposition and linked-cluster expansion. Applied to the four-wave-mixing optical polarization, this approach provides access to different excitation and measurement channels, as well as to higher-order optical nonlinearities and quantum correlators. Furthermore, it allows us to extract useful analytic approximations and analyze the nonlinear optical response in terms of quantum transitions between phonon-dressed states of the anharmonic Jaynes-Cummings (JC) ladder. Being well described by these approximations at low temperatures and small exciton-cavity coupling, the exact solution deviates from them for stronger couplings and higher temperatures, demonstrating remarkable non-Markovian effects, spectral asymmetry, and strong phonon renormalization of the JC ladder.

cond-mat.mes-hall↗

arXiv2023

Impact of the phonon environment on the nonlinear quantum-dot cavity QED. II. Analytical approach

The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.

cond-mat.mes-hall↗

arXiv2022

Varying the medium surrounding an optical resonator: An efficient and rigorous way to calculate its spectral changes

Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications. Computationally, it presents, however, a fundamental challenge owing to the nature of the eigenstates of an open system lacking completeness outside it. We solve this challenge by making a linear transformation of Maxwell's equations which maps perturbations of the surrounding medium onto effective perturbations within the system where the resonant states are complete. By treating such perturbations with the rigorous resonant state expansion, we find the modified modes of the system for arbitrary perturbations of the medium with any required accuracy. Numerically efficient single and few mode approximations are shown to be precise in practically important cases of, respectively, plasmonic nanoparticles and dielectric micro resonators.

physics.optics↗

arXiv2021

Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism

The scattering of electromagnetic waves by resonant systems is determined by the excitation of quasinormal modes (QNMs), i.e., the eigenmodes of the system. This Review addresses three fundamental concepts in relation with the representation of the scattered field as a superposition of the excited QNMs: normalization, orthogonality, and completeness. Orthogonality and normalization enable a straightforward assessment of the QNM excitation strength for any incident wave. Completeness guaranties that the scattered field can be faithfully expanded into the QNM basis. These concepts are non-trivial for non-conservative (non-Hermitian) systems and have driven many theoretical developments since initial studies in the 70's. Yet, owing to recent achievements, they are not easily grasped from the extensive and scattered literature, especially for newcomers in the field. After recalling fundamental results obtained in early studies on the completeness of the QNM basis for simple resonant systems, we review recent achievements and debates on the normalization, clarify under which circumstances the QNM basis is complete, and highlight the concept of QNM regularization with complex coordinate transform.

quant-ph↗

arXiv2021

Influence of disorder on a Bragg microcavity

Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair slabs (composing the mirrors) and the cavity, and calculate the resonant energy and linewidth of each disordered microcavity exactly, comparing the results with the resonant-state expansion for a large basis set and within its first and second orders of perturbation theory. We show that random shifts of interfaces cause a growth of the inhomogeneous broadening of the fundamental mode that is proportional to the magnitude of disorder. Simultaneously, the quality factor of the microcavity decreases inversely proportional to the square of the magnitude of disorder. We also find that first-order perturbation theory works very accurately up to a reasonably large disorder magnitude, especially for calculating the resonance energy, which allows us to derive qualitatively the scaling of the microcavity properties with disorder strength.

cond-mat.dis-nn↗

arXiv2020

Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion

A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the Green's function are derived using the Mittag-Leffler theorem, and their convergence to the exact solution is analyzed, allowing us to select optimal representations. Based on them, more efficient versions of the resonant-state expansion (RSE) are formulated, with a particular focus on the static mode contribution, including versions of the RSE with a complete elimination of static modes. These general versions of the RSE, applicable to non-spherical optical systems, are verified and illustrated on exactly solvable examples of a dielectric sphere in vacuum with perturbations of its size and refractive index, demonstrating the same level of convergence to the exact solution for both transverse electric and transverse magnetic polarizations.

physics.optics↗

arXiv2020

Phonon-induced dephasing in quantum dot-cavity QED: Limitations of the polaron master equation

A semiconductor quantum dot (QD) embedded within an optical microcavity is a system of fundamental importance within quantum information processing. The optimization of quantum coherence is crucial in such applications, requiring an in-depth understanding of the relevant decoherence mechanisms. We provide herein a critical review of prevalent theoretical treatments of the QD-cavity system coupled to longitudinal acoustic phonons, comparing predictions against a recently obtained exact solution. Within this review we consider a range of temperatures and exciton-cavity coupling strengths. Predictions of the polaron Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equations, as well as a variation of the former adapted for adiabatic continuous wave excitation (CWE), are compared against an asymptotically exact solution based upon Trotter's decomposition (TD) theorem. The NZ and TCL implementations, which apply a polaron transformation to the Hamiltonian and subsequently treat the exciton-cavity coupling to second order, do not offer a significant improvement accuracy relative to the polaron transformation alone. The CWE adaptation provides a marked improvement, capturing the broadband features of the absorption spectrum (not present in NZ and TCL implementations). We attribute this difference to the effect of the Markov approximation, and particularly its unsuitability in pulsed excitation regime. Even the CWE adaptation, however, breaks down in the regime of high temperature ($50K$) and strong exciton-cavity coupling ($g \gtrsim 0.2$ meV). The TD solution is of comparable computational complexity to the above-mentioned master equation approaches, yet remains accurate at higher temperatures and across a broad range of exciton-cavity coupling strengths (at least up to $g=1.5$ meV).

cond-mat.mes-hall↗

arXiv2019

Phonon-Induced Dephasing in Quantum Dot-Cavity QED

We present a semi-analytic and asymptotically exact solution to the problem of phonon-induced decoherence in a quantum dot-microcavity system. Particular emphasis is placed on the linear polarization and optical absorption, but the approach presented herein may be straightforwardly adapted to address any elements of the exciton-cavity density matrix. At its core, the approach combines Trotter's decomposition theorem with the linked cluster expansion. The effects of the exciton-cavity and exciton-phonon couplings are taken into account on equal footing, thereby providing access to regimes of comparable polaron and polariton timescales. We show that the optical decoherence is realized by real phonon-assisted transitions between different polariton states of the quantum dot-cavity system, and that the polariton line broadening is well-described by Fermi's golden rule in the polariton frame. We also provide purely analytic approximations which accurately describe the system dynamics in the limit of longer polariton timescales.

cond-mat.mes-hall↗

arXiv2019

Resonant-state expansion applied to three-dimensional open optical systems: A complete set of static modes

We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to correctly describe the static electric field of a charge redistribution within the optical system due to a perturbation of the permittivity. We demonstrate the convergence of the RSE towards the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated in [Doost {\it et al.}, Phys. Rev. A {\bf 90}, 013834 (2014)], where only a single static mode per each angular momentum was introduced, and show that using a complete set of static modes leads to a small, though non-negligible correction of the RSE result, improving the agreement with finite-element simulations. As another example of applying the RSE with a complete set of static modes, we calculate the resonant states of a dielectric cylinder, also comparing the result with a finite-element simulation.

physics.optics↗

arXiv2019

Resonant state expansion applied to one-dimensional quantum systems

The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in various potentials approximated by combinations of Dirac delta functions. The resonant state expansion is first verified for a triple quantum well system, showing convergence to the available analytic solution as the number of resonant states in the basis increases. The method is then applied to multiple quantum well and barrier structures, including finite periodic systems. Results are compared with the eigenstates in triple quantum wells and infinite periodic potentials, revealing the nature of the resonant states in the studied systems.

quant-ph↗

arXiv2019

Terahertz emitters based on microcavity dipolaritons

We propose the use of dipolaritons -- quantum well excitons with large dipole moment, coupled to a planar microcavity -- for generating terahertz (THz) radiation. This is achieved by exciting the system with two THz detuned lasers that leads to dipole moment oscillations of the exciton polariton at the detuning frequency, thus generating a THz emission. We have optimized the structural parameters of a system with microcavity embedded AlGaAs double quantum wells and shown that the THz emission intensity is maximized if the laser frequencies both match different dipolariton states. The influence of the electronic tunnel coupling between the wells on the frequency and intensity of the THz radiation is also investigated, demonstrating a trade-off between the polariton dipole moment and the Rabi splitting.

cond-mat.mes-hall↗

arXiv2019

99% beta factor and directional coupling of quantum dots to fast light in photonic crystal waveguides determined by hyperspectral imaging

Spontaneous emission from excitonic transitions in InAs/GaAs quantum dots embedded in photonic crystal waveguides at 5K into non-guided and guided modes is determined by direct hyperspectral imaging. This enables measurement of the absolute coupling efficiency into the guided modes, the beta-factor, directly, without assumptions on decay rates used previously. Notably, we found beta-factors above 90% over a wide spectral range of 40meV in the fast light regime, reaching a maximum of (99 $\pm$ 1)%. We measure the directional emission of the circularly polarized transitions in a magnetic field into counter-propagating guided modes, to deduce the mode circularity at the quantum dot sites. We find that points of high directionality, up to 97%, correlate with a reduced beta-factor, consistent with their positions away from the mode field antinode. By comparison with calibrated finite-difference time-domain simulations, we use the emission energy, mode circularity and beta-factor to estimate the quantum dot position inside the photonic crystal waveguide unit cell.

cond-mat.mes-hall↗

arXiv2018

Resonant-state expansion of three-dimensional open optical systems: Light scattering

A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross-sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is based on the expansion of the Green's function into the resonant states of the system. These can be calculated by any means, including the popular finite element and finite-difference time-domain methods. However, using the resonant-state expansion with a spherically-symmetric analytical basis, such as that of a homogeneous sphere, allows to determine a complete set of the resonant states of the system within a given frequency range. Furthermore, it enables to take full advantage of the expansion of the field outside the system into vector spherical harmonics, resulting in simple analytic expressions. We verify and illustrate the developed approach on an example of a dielectric sphere in vacuum, which has an exact analytic solution known as Mie scattering.

physics.optics↗

arXiv2018

How to calculate the pole expansion of the optical scattering matrix from the resonant states

We present a formulation for the pole expansion of the scattering matrix of open optical resonators, in which the pole contributions are expressed solely in terms of the resonant states, their wavenumbers, and their electromagnetic fields. Particularly, our approach provides an accurate description of the optical scattering matrix without the requirement of a fit for the pole contributions or the restriction to geometries or systems with low Ohmic losses. Hence, it is possible to derive the analytic dependence of the scattering matrix on the wavenumber with low computational effort, which allows for avoiding the artificial frequency discretization of conventional frequency-domain solvers of Maxwell's equations and for finding the optical far- and near-field response based on the physically meaningfull resonant states. This is demonstrated for three test systems, including a chiral arrangement of nanoantennas, for which we calculate the absorption and the circular dichroism.

physics.optics↗