Optoelectronic Control of Atomic Bistability with Graphene

Mikkel Have Eriksen, Jakob E. Olsen, Christian Wolff, and Joel D. Cox

Phys. Rev. Lett. 129, 253602 – Published 16 December 2022

Abstract

We explore the emergence and active control of optical bistability in a two-level atom near a graphene sheet. Our theory incorporates self-interaction of the optically driven atom and its coupling to electromagnetic vacuum modes, both of which are sensitive to the electrically tunable interband transition threshold in graphene. We show that electro-optical bistability and hysteresis can manifest in the intensity, spectrum, and quantum statistics of the light emitted by the atom, which undergoes critical slow-down to steady state. The optically driven atom-graphene interaction constitutes a platform for active control of driven atomic systems in coherent quantum control and atomic physics.

Received 22 July 2022
Accepted 17 November 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.253602

Physics Subject Headings (PhySH)

Coherent control Nanophotonics Nonlinear optics Optical bistability Optical transient phenomena Optoelectronics Photon statistics Quantum electrodynamics Quantum information with atoms & light Spontaneous emission

Graphene

Critical exponents Lindblad equation Quantum master equation Two-level models

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsNonlinear DynamicsQuantum Information, Science & Technology

Authors & Affiliations

Mikkel Have Eriksen ¹, Jakob E. Olsen ², Christian Wolff ¹, and Joel D. Cox ^1,3,*

¹Center for Nano Optics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
²Faculty of Engineering, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
³Danish Institute for Advanced Study, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

^*cox@mci.sdu.dk

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Issue

Vol. 129, Iss. 25 — 16 December 2022

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Images

Figure 1
Optical bistability in an atom interfacing graphene. (a) Schematic illustration of a two-level atom with ground state $| 1 ⟩$ and excited state $| 2 ⟩$ placed at a distance $z$ above an extended graphene sheet encapsulated in media with dielectric permittivity $ε_{a}$ above and $ε_{b}$ below. (b) Self-interaction parameter $G$ (left vertical axis) governing the dynamics of a TLA with transition energy $ℏ ϵ = 1.0 eV$ and vacuum decay rate $Γ_{0}$ placed $z = 12 nm$ above a graphene sheet as the Fermi energy $E_{F}$ is varied, while the reflection coefficient $r$ for normal incidence (right axis) enters the effective Rabi frequency $Ω$ . (c)–(e) The steady-state TLA population difference $Z = ρ_{22} - ρ_{11}$ is plotted in red curves corresponding to time-domain simulations obtained by adiabatically sweeping (c) the external field intensity $I^{ext}$ at a distance $z = 17 nm$ , (d) the detuning $Δ_{0} = ω_{L} - ϵ$ at $z = 17 nm$ , and (e) the Fermi energy at $z = 12 nm$ , and exhibit hysteresis indicated by the arrows; black dots correspond to solutions of Eq. (9). Unless explicitly varied, the results presented in (b)–(e) correspond to parameters $ε_{a} = 1$ , $ε_{b} = 1.6$ , $I^{ext} = 10 kW / m^{2}$ , $ℏ Δ_{0} = 8 μ eV$ , and $E_{F} = 0.51 eV$ , while the TLA decay rate and transition dipole moment are $Γ_{0} \approx 0.38 {ns}^{- 1}$ and $d = 1 e \cdot nm$ , respectively, and the broadening associated with inelastic scattering in graphene is $ℏ τ^{- 1} = 0.01 eV$ .
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Figure 2
Regimes of optical bistability. (a) Regions of bistability indicated by the discriminant of Eq. (9) for various impinging light intensities $I^{ext}$ as a function of probe detuning $Δ_{0}$ and graphene-TLA distance $z$ . (b) Same as (a) but sweeping the Fermi energy $E_{F}$ at fixed detuning. (c) Normalized average radiation power as a function of $E_{F}$ for $z = 12 nm$ , corresponding to the horizontal dashed line in (b). TLA and graphene parameters are the same as those in Fig. 1 unless otherwise specified.
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Figure 3
Signatures of optical bistability in resonance fluorescence and antibunching. (a) Steady-state TLA population difference $Z$ obtained from Eq. (9) plotted as a function of the graphene Fermi energy $E_{F}$ when the TLA is $z = 12 nm$ above the graphene sheet and driven at a frequency corresponding to $Δ_{0} = 8 μ eV$ by a field of intensity $I^{ext} = 10 kW / m^{2}$ . (b) The second-order correlation function $g^{(2)} (τ)$ (left panel) and resonance fluorescence spectra (right panel) are presented as functions of delay time $τ$ and detuning $ω - ω_{L}$ , respectively, for system parameters indicated by the color-coordinated points I–IV in panel (a).
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