Single quantum-dot Purcell factor and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>factor in a photonic crystal waveguide

Rao, V. S. C. Manga; Hughes, Stephen

doi:10.1103/physrevb.75.205437

Cited by 216 publications

(66 citation statements)

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“…Apart from the direct visualization of the Andersonlocalized spatial profiles, knowledge of the actual eigenmodes and of their detailed Bloch-mode components can give insight into the mechanisms of slow-light propagation, 25,27,[41][42][43][44] radiation, 6,28,29 and disorder-induced [5][6][7][8][9][10][11][12][13][14][15][16] losses. When modeling systems with coupled photonic and electronic degrees of freedom, such as quantum dots embedded in cavities or guides 19,[45][46][47][48][49][50][51][52][53] or PHC polaritons, 31,54 it is most natural to start with the eigenstates of both coupled subsystems, especially within a fully quantum mechanical treatment where second quantization of electromagnetic modes is needed. If the linear response function is known, then eigenmodes can be obtained by finding the poles of its analytical continuation on the complex frequency plane.…”

Section: Introductionmentioning

confidence: 99%

“…25,27 Slow light in particular can be exploited to enhance the coupling of light to the electronic states of embedded quantum dots, for applications as single-photon emitters. 19,[45][46][47][48][49][50][51][52][53] In this context in particular, knowing the actual eigenmodes of the electromagnetic field is crucial for modeling their coupling to electronic states. 55 Otherwise, the method should also be useful to model the states of a disordered two-dimensional PHC at the edges of the band gap.…”

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confidence: 99%

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Electromagnetic modes of a disordered photonic crystal

Savona

2011

Phys. Rev. B

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We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on the basis of Bloch modes of the corresponding periodic structure, and the resulting eigenvalue problem is diagonalized on a truncated basis including a finite number of Bloch bands. The Bloch-mode expansion is very effective for modeling modes of very extended disordered structures in a given frequency range, as only spectrally close bands must be included in the basis set. The convergence can be easily verified by repeating the diagonalization for an increased band set. As illustrations, we apply the method to the W1 line-defect waveguide and to the L3 coupled-cavity waveguide, both based on a photonic crystal slab with a triangular lattice of circular holes. We compute and characterize the eigenfrequencies, spatial field profiles, and radiation loss rates of the localized modes induced by disorder. For the W1 waveguide, we demonstrate that radiation losses, at the bottom of the spatially even guided band, are determined by a small hybridization with Bloch modes of the spatially odd band, induced by disorder in spite of their frequency separation. The Bloch-mode expansion method has a very broad range of applications: It can be also used to accurately compute the modes of structures with systematic modulations of the periodic dielectric constant, as in several designs of high-Q cavities.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Electromagnetic modes of a disordered photonic crystal

Savona

2011

Phys. Rev. B

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“…Strong confinement of light using photonic or plasmonic structures has found applications ranging from the enhanced efficiency of light emitters [3][4][5][6], optical modulation [7,8], and molecule sensing [9] to energy harvesting [10,11]. In particular, localized surface-plasmon polaritons (LSPPs) supported by metallic nanoparticles are capable of trapping light even when the particle sizes are much smaller than the natural resonance wavelengths, giving rise to strong electromagnetic field confinement [12][13][14].…”

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confidence: 99%

Electrodynamical Light Trapping Using Whispering-Gallery Resonances in Hyperbolic Cavities

Salandrino

et al. 2014

Phys. Rev. X

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We theoretically study spherical cavities composed of hyperbolic metamaterials with indefinite permittivity tensors. Such cavities are capable of electrodynamically confining fields with deep subwavelength cavity sizes. The supported resonant modes are analogous to the whispering-gallery modes found in dielectric microcavities with much larger physical sizes. Because of the nature of electrodynamical confinement, these hyperbolic metamaterial cavities exhibit quality factors higher than predicted in the electrostatic limit. In addition, confining electromagnetic fields into the small cavities results in an extremely high photonic local density of states. DOI: 10.1103/PhysRevX.4.021015 Subject Areas: Optics, PlasmonicsManipulating electromagnetic waves with engineered structures leads to strongly modified light-matter interactions, which in turn affect various interesting phenomena in areas such as quantum optics [1] and nonlinear light generation [2]. Strong confinement of light using photonic or plasmonic structures has found applications ranging from the enhanced efficiency of light emitters [3][4][5][6], optical modulation [7,8], and molecule sensing [9] to energy harvesting [10,11]. In particular, localized surface-plasmon polaritons (LSPPs) supported by metallic nanoparticles are capable of trapping light even when the particle sizes are much smaller than the natural resonance wavelengths, giving rise to strong electromagnetic field confinement [12][13][14]. Such confined resonant modes are described as electrostatic resonances, in which case light is mostly stored in the form of electric energy [15]. Although one can, in principle, achieve ultrasmall mode volume by using LSPP resonators, the electrostatic nature of such resonators limits the quality factor of the resonances because induced displacement currents inside metals generate intrinsic Ohmic loss.On the other hand, microcavities and photonic crystals confine light in an electrodynamical manner, in which case half of the stored energy is electric energy and the other is magnetic energy. Unlike LSPP resonators, these cavities have little Ohmic loss associated with the constituting materials. By using microspheres and toroids, the whispering-gallery modes (WGMs) exhibit quality factors as high as 10 9 [16,17]. Nevertheless, the physical size of such a cavity is typically much larger than the wavelength, i.e., D ≫ λ=n, where D is the cavity size, λ is the natural resonance wavelength, and n is the optical index of the material. Large cavity size, in general, limits the achievable local field enhancement.Indefinite media, also known as hyperbolic metamaterials (HMMs), exhibit unusual hyperbolic dispersion because of anisotropic permittivity of opposite signs along different directions [18]. Microcavities made of HMMs have been shown to support Fabry-Perot-type resonances with effective refractive indices as high as 17.4 [19]. Such hyperbolic cavities exhibit deep subwavelength confinement of electromagnetic waves due to the large effective indices. In...

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“…While single photons are routinely produced in different experimental setups [6], e.g., by using natural or artificial atoms coupled to cavities or waveguides [7][8][9][10][11][12], single-mode multiphoton states are much harder to generate [13]. Current methods are limited by either exponentially small success probabilities or low fidelities.…”

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confidence: 99%

“…DOI: 10.1103/PhysRevLett.118.213601 On-demand generation of optical propagating photons is at the basis of many applications in quantum information science, including multipartite teleportation [1], quantum repeaters [2], cryptography [3,4], and metrology [5]. While single photons are routinely produced in different experimental setups [6], e.g., by using natural or artificial atoms coupled to cavities or waveguides [7][8][9][10][11][12], single-mode multiphoton states are much harder to generate [13]. Current methods are limited by either exponentially small success probabilities or low fidelities.…”

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confidence: 99%

Efficient Multiphoton Generation in Waveguide Quantum Electrodynamics

et al. 2017

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Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a longstanding goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling. DOI: 10.1103/PhysRevLett.118.213601 On-demand generation of optical propagating photons is at the basis of many applications in quantum information science, including multipartite teleportation [1], quantum repeaters [2], cryptography [3,4], and metrology [5]. While single photons are routinely produced in different experimental setups [6], e.g., by using natural or artificial atoms coupled to cavities or waveguides [7][8][9][10][11][12], single-mode multiphoton states are much harder to generate [13]. Current methods are limited by either exponentially small success probabilities or low fidelities. The enhancement of light-matter interactions provided by quantum nanophotonics opens up new avenues to create high-fidelity multiphoton states. For example, m quantum emitters can be strongly coupled to structured waveguides, which show large Purcell factors, P 1D , so that m atomic excitations can be mapped to a waveguide mode with an error (or infidelity, I m ) scaling as m=P 1D . However, the resulting state is not a single mode, but a complex entangled state of several modes [14], so that it cannot be directly used for quantum information purposes. Single-mode multiphoton states can be created by storing m collective excitations in N ≫ m atoms, which are then mapped to a photonic state of the waveguide. While the latter process can be achieved with very low infidelity, scaling as m 2 =ðNP 1D Þ [14,15], present schemes for the first part scale like I m ∝ m= ffiffiffiffiffiffiffiffi P 1D p [14], as they still do not fully exploit the strong coupling to the waveguide nor collective effects. This ultimately limits the fidelity of the whole procedure.In this work we show how to overcome this limitation with new schemes for the heralded generation of m collective excitations in N ≫ m atoms coupled to a waveguide. The idea is to use the atoms to both create the excitations one by one, and to herald the success of the process. In this way, arbitrarily sma...

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Single quantum-dot Purcell factor andβfactor in a photonic crystal waveguide

Cited by 216 publications

References 53 publications

Electromagnetic modes of a disordered photonic crystal

Electromagnetic modes of a disordered photonic crystal

Electrodynamical Light Trapping Using Whispering-Gallery Resonances in Hyperbolic Cavities

Efficient Multiphoton Generation in Waveguide Quantum Electrodynamics

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