Ultra-Strong Light-Matter Coupling in Deeply Subwavelength Thz LC Resonators
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This is a repository copy of Ultra-Strong Light-Matter Coupling in Deeply Subwavelength THz LC Resonators. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/146109/ Version: Accepted Version Article: Jeannin, M, Mariotti Nesurini, G, Suffit, S et al. (7 more authors) (2019) Ultra-Strong Light-Matter Coupling in Deeply Subwavelength THz LC Resonators. ACS Photonics, 6 (5). pp. 1207-1215. ISSN 2330-4022 https://doi.org/10.1021/acsphotonics.8b01778 ©2019 American Chemical Society This is an author produced version of a paper published in ACS Photonics. Uploaded in accordance with the publisher's self-archiving policy. Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. 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Linfield, Carlo Sirtori, and Yanko Todorov ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01778 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 3, 2019 Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. 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Page 1 of 25 ACS Photonics 1 2 3 4 5 6 7 8 Ultra-Strong Light-Matter Coupling in Deeply 9 10 11 Subwavelength THz LC resonators 12 13 14 , 15 Mathieu Jeannin,∗ † Giacomo Mariotti Nesurini,† Stéphan Suffit,† Djamal 16 17 18 Gacemi,† Angela Vasanelli,† Lianhe Li,‡ Alexander Giles Davies,‡ Edmund 19 20 Linfield,‡ Carlo Sirtori,† and Yanko Todorov† 21 22 23 Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, Sorbonne 24 † 25 Paris Cité, CNRS-UMR 7162, 75013 Paris, France 26 27 School of Electronic and Electrical Engineering, University of Leeds, LS2 9JT Leeds, 28 ‡ 29 United Kingdom 30 31 32 E-mail: [email protected] 33 34 35 Abstract 36 37 38 The ultra-strong light-matter coupling regime has been demonstrated in a novel 39 40 three-dimensional inductor-capacitor (LC) circuit resonator, embedding a semiconduc- 41 tor two-dimensional electron gas in the capacitive part. The fundamental resonance of 42 43 the LC circuit interacts with the intersubband plasmon excitation of the electron gas 44 45 at ωc = 3.3 THz with a normalized coupling strength 2ΩR/ωc = 0.27. Light matter 46 47 interaction is driven by the quasi-static electric field in the capacitors, and takes place 48 = 10−6 3 49 in a highly subwavelength effective volume Veff λ0 . This enables the observation 50 3 51 of the ultra-strong light-matter coupling with 2.4 10 electrons only. Notably, our × 52 53 fabrication protocol can be applied to the integration of a semiconductor region into 54 55 arbitrary nano-engineered three dimensional meta-atoms. This circuit architecture can 56 be considered the building block of metamaterials for ultra-low dark current detectors. 57 58 59 1 60 ACS Paragon Plus Environment ACS Photonics Page 2 of 25 1 2 3 Keywords 4 5 6 Intersubband Transitions, Strong Coupling, Plasmons, Terahertz 7 8 Metamaterials were introduced to enable new electromagnetic properties of matter which 9 10 are not naturally found in nature. Celebrated examples of such achievements are, for in- 11 12 stance, negative refraction1 and artificial magnetism.2 The unit cells of metamaterials are ar- 13 14 tificially designed meta-atoms that have dimensions ideally much smaller than the wavelength 15 16 3 of interest λ0. Such meta-atoms act as high frequency inductor-capacitor (LC) resonators 17 18 3 which sustain a resonance close to λ0 √LC. The resonant behaviour, occurring into highly 19 ∝ 20 subwavelength volumes, generates high electromagnetic field intensities which, as pointed out 21 22 by the seminal paper of Pendry et al.,2 are crucial to implement artificial electromagnetic 23 24 properties of a macroscopic ensemble of meta-atoms. Moreover, the ability to control and 25 26 enhance the electromagnetic field at the nanoscale is beneficial for optoelectronic devices, 27 28 such as nano-lasers4 electromagnetic sensors5–7 and detectors.8–12 For instance, metamate- 29 30 rial architectures have lead to a substantial decrease of the thermally excited dark current 31 32 in quantum infrared detectors, resulting in higher temperature operation.11,12 33 34 The LC circuit can be seen as a quantum harmonic oscillator sustaining vacuum electric 35 36 1/2 field fluctuations that scale as 1/V , where Veff is the effective volume of the capacitive 37 eff 38 parts.13 For an emitter/absorber inserted between the capacitor plates, the light-matter 39 40 interaction is proportional to 1/V 1/2, and thus strongly enhanced. Fundamental electro- 41 eff 42 dynamical phenomena, such as the Purcell effect14 and strong light-matter coupling regime15 43 44 can therefore be observed. In the strong coupling regime, energy is reversibly exchanged be- 45 46 tween the matter excitation and the electromagnetic resonator at the Rabi frequency ΩR. 47 48 This results in an energy splitting of the circuit resonance into two polaritons states sepa- 49 50 rated by 2~ΩR. The regime of strong coupling has been observed in many physical systems 51 52 which have been reviewed e.g. in Refs. 16–18, and some specific realizations with metama- 53 54 terial resonators were achieved in the sub-THz,19 THz20–22 and the Mid-IR23–25 part of the 55 56 spectrum. In these systems, the highly subwavelength interaction volumes combined with 57 58 59 2 60 ACS Paragon Plus Environment Page 3 of 25 ACS Photonics 1 2 3 the collective effect of N identical electronic transitions result into high coupling constants 4 e 5 1/2 Ω (N /Veff ) , and allow reaching the ultra-strong coupling regime where the Rabi split- 6 R ∝ e 7 ting becomes of the same order of magnitude as the frequency of the material excitation 8 9 26 ω˜, 2Ω /ω˜ 1. Since there is virtually no lower limit for the interaction volume Veff in 10 R ≈ 11 LC resonators, the fascinating regime of ultra-strong coupling can be realized in structures 12 13 having few electrons only.27,28 In such limit, the effective bosonization procedure employed 14 15 to describe the properties of the two-dimensional electron gas breaks down, and one can in- 16 17 vestigate the unique regime where the few electrons in the system have to be exactly treated 18 19 as fermions.27 20 21 Recently, the ultra-strong coupling regime with a small number of electrons has been 22 23 experimentally observed by coupling transitions between Landau levels in a two dimensional 24 25 electron gas under a high magnetic field and nanogap complementary bow-tie antennas, with 26 27 a record low number of 80 electrons.28 Those studies were performed in the sub-THz part of 28 29 the spectrum (300GHz) using resonators based on a planar geometry. Here, we demonstrate 30 31 a three-dimensional metamaterial architecture that has the potential to go beyond this limit 32 33 in the THz range (3THz), without the need for a magnetic field. Our metamaterial allows 34 35 confining the electric field in all directions of space into nanoscale volumes, on the order of 36 37 −6 3 Veff = 10 λ . The resonance of the structure is coupled to an intersubband (ISB) transition 38 0 39 of high density electron gas in the ground state of semiconductor quantum wells (QWs). 40 41 A relative Rabi frequency of 2ΩR/ω˜ = 0.27 is attained with a record low overall number 42 43 3 of electrons Ne 10 for intersubband systems.