Quantum transport in non-Markovian dynamically disordered photonic lattices

Ricardo Román-Ancheyta, Barış Çakmak, Roberto de J. León-Montiel, and Armando Perez-Leija

Phys. Rev. A 103, 033520 – Published 26 March 2021

Abstract

We show theoretically that the dynamics of a driven quantum harmonic oscillator subject to nondissipative noise is formally equivalent to the single-particle dynamics propagating through an experimentally feasible dynamically disordered photonic network. Using this correspondence, we find that noise-assisted energy transport occurs in this network and if the noise is Markovian or delta correlated, we can obtain an analytical solution for the maximum amount of transferred energy between all network's sites at a fixed propagation distance. Beyond the Markovian limit, we further consider two different types of non-Markovian noise and show that it is possible to have efficient energy transport for larger values of the dephasing rate.

Received 25 September 2020
Accepted 10 March 2021

DOI:https://doi.org/10.1103/PhysRevA.103.033520

Physics Subject Headings (PhySH)

Integrated optics Quantum optics

Waveguide arrays

Quantum correlations, foundations & formalism Stochastic differential equations

Atomic, Molecular & Optical

Authors & Affiliations

Ricardo Román-Ancheyta ^1,*, Barış Çakmak ², Roberto de J. León-Montiel ³, and Armando Perez-Leija^4,5

¹Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro 1, Santa María Tonantzintla, CP 72840, Puebla, Mexico
²College of Engineering and Natural Sciences, Bahçeşehir University, Beşiktaş, Istanbul 34353, Turkey
³Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Ciudad de México, Mexico
⁴Max-Born-Institut, Max-Born-Straße 2A, 12489 Berlin, Germany
⁵AG Theoretische Optik & Photonik, Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany

^*ancheyta6@gmail.com

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Vol. 103, Iss. 3 — March 2021

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Images

Figure 1
Light intensity propagation in a photonic lattice obtained by integrating Eq. (1). Light is initially launched into a single waveguide labeled as (a) and (b) $m = 0$ and (c) and (d) $m = 2$ . In (e) and (f) we show the output light intensity $I_{m} (Z) = {| E_{m} (Z) |}^{2}$ at $Z = 3 π / 2$ for the simulations presented in (b) and (d), respectively. Note that $Z \equiv C_{1} z$ is the scaled propagation distance. Here $I_{m} (Z)$ exhibits $m$ nodes, as expected from the probability distribution of the nonclassical displaced Fock states [20]. When the ramping potential is activated, $α \neq 0$ , we see Bloch-like oscillations [32] (left), where the light exhibits revivals every period $Z_{rev} = 2 π k C_{1} / α$ , with $k$ an integer [21]. We have set the ratio (a) and (c) $α / C_{1} = 1 / 2$ and (b) and (d) $α / C_{1} = 0$ , which are feasible experimental values that would allow us to implement realistic integrated photonic devices occupying few centimeter-scale footprints (see the text for more details).
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Figure 2
Light propagation in a dynamically disorder Glauber-Fock lattice. On the left we see the diagonal elements $σ_{n n}$ obtained by numerical integration of Eq. (9) describing the emerging intensity distribution in the lattice; on the right we depict the matrix elements $ρ_{n n}$ from Eq. (4). For these simulations we used the same parameters and initial conditions as for Figs. 1 and 1 but now adding white noise with a dephasing rate $Γ = 0.001$ (left) and $γ = 0.025$ (right). Due to the noise, light starts to delocalize and the effect is more prominent in the regions where complete Bloch-like oscillations would appear in the absence of noise (see Fig. 1). The vertical dashed line indicates the distance at which the light intensity is calculated.
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Figure 3
Manifestation of the noise-assisted transport phenomenon, captured by the average photon number of Eq. (18), as a function of the scaled dephasing rate $\tilde{γ} = γ / ω$ at different scaled revivals times counted by $k$ , the ratio $g / ω = 1$ , and the initial condition $m = 2$ .
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Figure 4
Noise-assisted transport phenomenon in a Glauber-Fock oscillator (lattice) as a function of the dephasing rate $γ$ under (a) Ornstein-Uhlenbeck noise and (b) power-law noise. The system was prepared initially in ground state $| 0 〉$ , i.e., $m = 0$ , $g = 1$ , $ω = 0.5$ , and $k = 1$ . For (a) $λ \to \infty$ and (b) $λ^{- 1} \to \infty$ the black solid line corresponds to the Markovian limit given by Eq. (18) and for (a) $λ^{- 1} = 10$ and (b) $λ = 10$ the red dashed line shows the behavior in the non-Markovian regime evaluating Eq. (16) at $t_{rev}$ . We obtain the red circles and black squares by integrating the master equation (11).
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