Nanoscale Coherent Light Source

Raphael Holzinger, David Plankensteiner, Laurin Ostermann, and Helmut Ritsch

Phys. Rev. Lett. 124, 253603 – Published 26 June 2020

Abstract

A laser is composed of an optical resonator and a gain medium. When stimulated emission dominates mirror losses, the emitted light becomes coherent. We propose a new class of coherent light sources based on wavelength sized regular structures of quantum emitters whose eigenmodes form high- $Q$ resonators. Incoherent pumping of few atoms induces light emission with spatial and temporal coherence. We show that an atomic nanoring with a single gain atom at the center behaves like a thresholdless laser, featuring a narrow linewidth. Symmetric subradiant excitations provide optimal operating conditions.

Received 23 March 2020
Accepted 8 June 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.253603

Physics Subject Headings (PhySH)

Atom lasers Lasing without inversion Quantum description of light-matter interaction Spontaneous emission

Atomic, Molecular & Optical

Authors & Affiliations

Raphael Holzinger ^*, David Plankensteiner, Laurin Ostermann, and Helmut Ritsch

Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, A-6020 Innsbruck, Austria

^*raphael.holzinger@uibk.ac.at

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Issue

Vol. 124, Iss. 25 — 26 June 2020

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Images

Figure 1
Coherent light emission from a partially pumped atomic array. (a) A ring of atoms with an additional atom in its center incoherently pumped with a rate $ν$ . (b) The atoms decay at a spontaneous decay rate $Γ_{0}$ and are collectively coupled to the center atom with dispersive coupling $Ω_{p}$ and dissipative coupling $Γ_{p}$ , respectively. In turn, the ring atoms have couplings $Ω_{i j}$ and $Γ_{i j}$ among each other. The symmetric excitation exhibits a collective decay rate $Γ_{coll}$ . (c) The field intensity generated in the steady state according to Eq. (3) for a ring of $N = 11$ atoms in the $x z$ plane with $y = 2.5 λ_{0}$ , $d = λ_{0} / 5$ , and $ν = 0.1 Γ_{0}$ . (d) The field intensity in the $x y$ plane with $z = 2.5 λ_{0}$ .
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Figure 2
Dissipative system dynamics. (a) Time evolution of the eigenstates of the Hamiltonian from Eq. (1) for $N = 5$ ring atoms with an interatomic distance $d = λ_{0} / 2$ and an incoherent pump rate $ν = Γ_{0} / 2$ starting from the ground state (GS). The state $| Ψ_{1, 2} ⟩$ features a large contribution from the symmetric state of the ring atoms $| ψ_{sym} ⟩$ and shows significantly higher populations than all other excited eigenstates (gray lines) at all times. (b) Stationary population of the eigenstates for different pump rates. We can see that, even for large pump rates $ν > Γ_{0}$ , the symmetric single-excitation states dominate.
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Figure 3
Super- and subradiance of the symmetric state. The decay rate of the symmetric state $Γ_{sym}$ as a function of the atom number in the ring and their interatomic distance. The white dots highlight specific interatomic distances where the decay of the symmetric state is the smallest (subradiant).
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Figure 4
Coupling of the central gain atom to the outer ring. (a) The dissipative coupling $Γ_{p}$ between the central atom and the ring atoms as a function of the atom number $N$ and the interatomic distance $d$ . One can see that it becomes negligible at the points where $| ψ_{sym} ⟩$ is subradiant (white dots). (b) Cooperativity $C$ for different distances and atom numbers. The cooperativity is large when $d \to 0$ due to the divergent behavior of $Ω_{p}$ , or when $Γ_{sym}$ is small.
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Figure 5
Intensity and statistics of the emitted light. (a) Steady-state second-order correlation as a function of the ring atom number and atom spacing. For each atom number $N$ there are specific interatomic distances $d$ where the emitted light changes from thermal-like light emission (red), passing over regions of Poissonian statistics (white), to sub-Poissonian properties (blue). (b) The radiated intensity $I_{out}$ for the same parameter region. Where $g^{(2)} (0) = 1$ the intensity is maximal, regardless of the atom number. (c) The spectral linewidth $Δ ν$ for the same parameters. It reduces to well below $Γ_{0}$ . The pump rate was $ν = 0.1 Γ_{0}$ . As before, the white dots indicate subradiance of the symmetric state.
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Figure 6
Thresholdless coherent light emission. (a) $I_{out}$ as a function of the pump rate $ν$ for $N = 5$ , $d = λ_{0} / 2$ exhibiting a maximum from $ν \approx 4 Γ_{0}$ onwards. (b) A zoom in to the weak pump region shows the immediate onset of the intensity $I_{out}$ at small $ν$ . (c) The second-order correlation $g^{(2)} (0)$ in steady state is 1 for finite, but small $ν$ . (d) The radiative linewidth $Δ ν$ (blue) in the steady state stays well below the pump broadened linewidth $Γ_{0} + ν$ of a single emitter (gray), and approaches the decay rate $Γ_{sym}$ of the symmetric state (yellow, dashed line).
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