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Optics and Spectroscopy

Oscillation threshold of a chain of spasers

Sergey V. Fedorov, Nikolay N. Rosanov, A. Shipulin

Published Sep 1, 2014• 0 citations
Publisher

Abstract

A model of resonance interaction of a chain of periodically spaced metal nanoparticles with a chain of quantum dots is developed. The conditions leading to oscillation in a chain of spasers in the vicinity of narrow plasmon resonances are determined. It is shown that the lowest oscillation threshold can be achieved under anomalously small values of population inversion. In this case, the range of oscillation frequency variation upon changing the resonance frequency of quantum dots can be substantially narrower that the plasmon-resonance linewidth.

DOI
10.1134/s0030400x14090070

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A model of resonance interaction of a chain of periodically spaced metal nanoparticles with a chain of quantum dots is developed. The conditions leading to oscillation in a chain of spasers in the vicinity of narrow plasmon resonances are determined. It is shown that the lowest oscillation threshold can be achieved under anomalously small values of population inversion. In this case, the range of oscillation frequency variation upon changing the resonance frequency of quantum dots can be substantially narrower that the plasmon-resonance linewidth.
Abstract The radiation spectrum of an elementary spaser (dipole nanolaser) interacting with an external low-frequency monochromatic driving field below the lasing threshold is investigated within the model approach. The mathematical model of the spaser includes (i) a plasmonic oscillatory mode of a metal nanoparticle interacting with an asymmetric single-electron two-level semiconductor quantum dot with broken spatial inversion symmetry in which inverse population is maintained by incoherent pumping and (ii) a dissipative environment interacting with both the plasmonic nanoparticle and the quantum dot. It is shown that one can effectively control the radiation spectrum of the spaser by varying the amplitude and frequency of the low-frequency field.
We consider the influence of the number of quantum dots on spaser operation. It is shown that even in the presence of only two quantum dots, the spaser behaviour is qualitatively different from that of the previously studied spaser consisting of a nanoparticle and a single quantum dot. In particular, for nonzero detuning of resonant frequencies of a nanoparticle and quantum dots, an increase in the interaction constant between quantum dots first leads to a decrease in the spasing threshold and then to its growth and even the spasing breakdown.
Theoretically predicted ''dipole lasing'', i.e., spontaneous excitation of coherent metal nano-particle dipole oscillations through interaction with a quantum-dot two-level system subject to population inversion is demonstrated. Equations for dipole lasing are the same as equations for ordinary laser, where the dipole momentum of nano-particle stands for the electromagnetic field cavity mode. Dipole lasing frequency corresponds to the localized plasmon resonance of the nano-particle. Dipole momentum of nano-particle leads to coherent dipole radiation. Optical cavity is not necessary, the size of the dipole laser can be smaller than the optical wavelength, i.e. it is dipole nano-laser. Threshold conditions and optical bistability in dipole nano-lasers are considered.
Entanglement is one of the key measures of quantum correlations present in nanophotonic systems, with promising applications in quantum optics and beyond. Previous studies have shown that the degree of entanglement between two quantum dot qubits is preserved when a metal nanoparticle is used to mediate the interactions between the qubits. In this work, we investigate long-range plasmonic mediation of qubit--qubit entanglement by studying the impact of the number of mediating metal nanoparticles on stationary concurrence. Collinear and periodically spaced metal nanoparticles that satisfy the weak-coupling approximation are considered. An effective model that enables the derivation of the mediated interactions within the framework of cavity quantum electrodynamics is employed. Under weak driving at the single particle resonance frequency, the model shows that odd-number arrays are more robust to entanglement decay. We attribute this to strong inter-qubit dissipative coupling as a result of a hybridized dipole plasmon resonating with the driving frequency in odd-number arrays. These arrays can sustain non-vanishing stationary entanglement beyond an inter-qubit spacing of one micron, opening up the possibility of independent spatial optical probing of each quantum dot.
We present a quantum theory of a spaser-based nanolaser, under the bad-cavity approximation. We find first- and second-order correlation functions g(1)(τ) and g(2)(τ) below and above the generation threshold, and obtain the average number of plasmons in the cavity. The latter is shown to be of the order of unity near the generation threshold, where the spectral line narrows considerably. In this case the coherence is preserved in a state of active atoms in contradiction to the good-cavity lasers, where the coherence is preserved in a state of photons. The damped oscillations in g(2)(τ) above the generation threshold indicate the unusual character of amplitude fluctuations of polarization and population, which become interconnected in this case. Obtained results allow to understand the fundamental principles of operation of nanolasers.
A ``dipole'' laser is proposed consisting of a nanoparticle and a two-level system with population inversion. If the threshold conditions are fulfilled, the dipole interaction between the two-level system and the nanoparticle leads to coherent oscillations in the polarization of the particles, even in the absence of an external electromagnetic field. The emitted radiation has a dipolar distribution. It does not need an optical cavity, and has a very small volume, $\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{3}$, which can be important for applications in microelectronics. Estimates of the threshold conditions are carried out for a dipole laser composed of a quantum dot and a silver nanoparticle.