Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

Tokman, M. D.; Long, Zhongqu; Almutairi, Sultan; Wang, Yongrui; Vdovin, Valery; Belkin, Mikhail; Belyanin, Alexey

doi:10.1063/1.5044539

Cited by 17 publications

(17 citation statements)

References 41 publications

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“…For given commutation relations of the two operators: [ĝ 1 , ĝ2 ] = C, where C is a constant, correct Langevin sources should ensure the conservation of commutation relations at any moment of time, despite the presence of the relaxation operator in Eq. (A1); see [28][29][30].…”

Section: Noise Correlatormentioning

confidence: 99%

Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

Tokman¹,

Erukhimova²,

Wang³

et al. 2020

Preprint

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We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tri-state entanglement are realized near the parametric resonances in a coupled system. The model includes decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg-Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables, and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

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Section: Noise Correlatormentioning

confidence: 99%

Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

Tokman¹,

Erukhimova²,

Wang³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

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“…For given commutation relations of the two operators, [ g 1 , g 2 ] C, where C is a constant, correct Langevin sources should ensure the conservation of commutation relations at any moment of time, despite the presence of the relaxation operator in Eq. (A1), see [34,43,44]. The group of terms i ℏ [ H, g] + R( g) can often be written as follows:…”

Section: From Heisenberg-langevin Equations To the Stochastic Equatiomentioning

confidence: 99%

Generation and dynamics of entangled fermion–photon–phonon states in nanocavities

et al. 2020

Self Cite

View full text Add to dashboard Cite

We develop the analytic theory describing the formation and evolution of entangled quantum states for a fermionic quantum emitter coupled simultaneously to a quantized electromagnetic field in a nanocavity and quantized phonon or mechanical vibrational modes. The theory is applicable to a broad range of cavity quantum optomechanics problems and emerging research on plasmonic nanocavities coupled to single molecules and other quantum emitters. The optimal conditions for a tripartite entanglement are realized near the parametric resonances in a coupled system. The model includes dissipation and decoherence effects due to coupling of the fermion, photon, and phonon subsystems to their dissipative reservoirs within the stochastic evolution approach, which is derived from the Heisenberg–Langevin formalism. Our theory provides analytic expressions for the time evolution of the quantum state and observables and the emission spectra. The limit of a classical acoustic pumping and the interplay between parametric and standard one-photon resonances are analyzed.

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“…Phase matched SPDC restricts both the choice of non-linear materials and the available states the daughter photons can occupy. This has prompted the search for SPDC where phase matching is absent [9][10][11][12]. Here we register over 1000 photon pairs per second generated in a micrometer-sized SPDC source continuously pumped at a moderate power.…”

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confidence: 99%

Microscale Generation of Entangled Photons without Momentum Conservation

Okoth¹,

Cavanna²,

Santiago-Cruz³

et al. 2019

Phys. Rev. Lett.

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Spontaneousparametric down-conversion (SPDC) is a well-developed tool to produce entangled photons for practical applications, such as quantum imaging [1][2][3], quantum key distribution [4,5] and quantum metrology [6,7], as well as for tests of quantum mechanics [8]. So far, SPDC sources have exclusively been used in the phase matched regime: when the emitted daughter photons conserve the momentum of the pump photon. Phase matched SPDC restricts both the choice of non-linear materials and the available states the daughter photons can occupy. This has prompted the search for SPDC where phase matching is absent [9][10][11][12]. Here we register over 1000 photon pairs per second generated in a micrometer-sized SPDC source continuously pumped at a moderate power. This is both the smallest SPDC source reported to date and, due to the relaxed phase matching, an entirely new type of two-photon radiation. Reducing the interaction length and localizing the position of the daughter photons creation leads to a huge uncertainty in their momentum. The uncertain momentum mismatch leads to a frequency-angular spectrum an order of magnitude broader than that of phase matched SPDC. This results in record breaking spatio-temporal correlation widths and huge entanglement. We believe that similar sources can be realized on thinner platforms, not only compounding the aforementioned effects, but also allowing easy integrability on optical chips.For SPDC, the probability of a pump photon, with momentum k p (wavevector k p ), to decay into two daughter photons, signal and idler with momenta k s,i (wavevectors k s,i ), strongly depends on the momentum (wavevector) mismatch ∆k ≡ k s + k i − k p . The allowed mismatch forms an uncertainty relation with the volume over which the non-linear interaction takes place. Its component parallel to the pump, or longitudinal mismatch ∆k || , is restricted by the inverse length of the nonlinear material. The component perpendicular to the pump, or transverse mismatch ∆k ⊥ , is restricted by the inverse non-linear interaction area, which is generally given by the Gaussian profile of the pump beam.In a phase-matched process, ∆k || = 0, the longitu-dinal momentum of the pump photon is conserved by the daughter photons. However, this is a special case and is only satisfied in a few non-linear materials with the appropriate electronic and optical properties. More generally ∆k || = 0, causing pairs to be generated in or out of phase with respect to pairs generated earlier in the non-linear material. The relative phase difference depends on the non-linear interaction length, L. If L is equal to an odd multiple of the so called coherence length, L c = π ∆k || [13], the interference between the emitted pairs is fully constructive leading to a local maximum in the emission probability. At L < L c , the pairs are always generated in phase. Moreover, with small length L, the allowed longitudinal mismatch can be very large, which leads to a very broad spectrum of emitted photons, both in frequency and in angle. F...

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Purcell enhancement of the parametric down-conversion in two-dimensional nonlinear materials

Cited by 17 publications

References 41 publications

Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

Generation and dynamics of entangled fermion-photon-phonon states in nanocavities

Generation and dynamics of entangled fermion–photon–phonon states in nanocavities

Microscale Generation of Entangled Photons without Momentum Conservation

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