A fast, high-order numerical method for the simulation of single-excitation states in quantum optics

Hoskins, Jeremy G.; Kaye, Jason P.; Rachh, Manas; Schotland, John C.

doi:10.48550/arxiv.2109.06956

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…This analysis therefore provides a reasonable approximation for a system of atoms and the dynamics of the atomic amplitudes can be computed in O(N 4 ) operations independent of the final time horizon T , where N is the number of atoms in the system (see Remark 4). For moderately-sized systems, say N < 1000, for example, this approach may provide a good alternative to the direct numerical solution of (5), which typically scales like O(N 2 T 2 ) even after using fast algorithms [19]. A detailed comparison of our asymptotics to the numerical solution of (5) will be presented in an forthcoming paper.…”

Section: Discussionmentioning

confidence: 99%

Analysis of single-excitation states in quantum optics

Hoskins¹,

Kaye²,

Rachh³

et al. 2021

Preprint

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In this paper we analyze the dynamics of single-excitation states, which model the scattering of a single photon from multiple two level atoms. For short times and weak atom-field couplings we show that the atomic amplitudes are given by a sum of decaying exponentials, where the decay rates and Lamb shifts are given by the poles of a certain analytic function. This result is a refinement of the "pole approximation" appearing in the standard Wigner-Weisskopf analysis of spontaneous emission. On the other hand, at large times, the atomic field decays like O(1/t 3 ) with a known constant expressed in terms of the coupling parameter and the resonant frequency of the atoms. Moreover, we show that for stronger coupling, the solutions also feature a collection of oscillatory exponentials which dominate the behavior at long times. Finally, we extend the analysis to the continuum limit in which atoms are distributed according to a given density.

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Section: Discussionmentioning

confidence: 99%

Analysis of single-excitation states in quantum optics

Hoskins¹,

Kaye²,

Rachh³

et al. 2021

Preprint

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“…The problem of efficient Volterra history integration is well known in the scientific computing literature, and several techniques have been proposed, particularly in the context of solving Volterra integral equations and computing nonlocal transparent boundary conditions. We mention fast Fourier transform (FFT)-based methods [27], methods based on sum-of-exponentials projections of the history [28][29][30][31][32][33][34][35], convolution quadrature [36,37], and hierarchical low-rank or butterfly matrix compression [22,38,39]. Of the methods mentioned above, several have been applied to the efficient numerical solution of convolutional nonlinear Volterra integral equations [27,37,38].…”

Section: Introductionmentioning

confidence: 99%

A fast time domain solver for the equilibrium Dyson equation

Kaye¹,

Strand²

2021

Preprint

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We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times, and is thus wellsuited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph, and the Sachdev-Ye-Kitaev model.

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“…The numerical solution of such a large number of coupled and time-delayed nonlinear equations in a random medium is challenging [11,12], and our methods presented in detail in [13] amortize computational cost and convergence. In this approach, the nonlinear dynamics of each emitter and the field generated by the emitters' polarization are self-consistently computed, showing a rich phenomenology of short-and long-lived excitations and synchronized oscillations.…”

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confidence: 99%

Transient dynamics of subradiance and superradiance in open optical ensembles

Lu¹,

Shanker²,

Piermarocchi³

2022

Preprint

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We introduce a computational Maxwell-Bloch framework for investigating out of equilibrium optical emitters in open cavity-less systems. To do so, we compute the pulse-induced dynamics of each emitter from fundamental light-matter interactions and self-consistently calculate their radiative coupling, including phase inhomogeneity from propagation effects. This semiclassical framework is applied to open systems of quantum dots with different density and dipolar coupling. We observe that signatures of superradiant behavior, such as directionality and faster decay, are weak for systems with extensions comparable to λ/2. In contrast, subradiant features are robust and can produce long-term population trapping effects. This computational tool enables quantitative investigations of large optical ensembles in the time domain and could be used to design new systems with enhanced superradiant and subradiant properties.

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A fast, high-order numerical method for the simulation of single-excitation states in quantum optics

Cited by 3 publications

References 29 publications

Analysis of single-excitation states in quantum optics

Analysis of single-excitation states in quantum optics

A fast time domain solver for the equilibrium Dyson equation

Transient dynamics of subradiance and superradiance in open optical ensembles

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