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Photonics Research
Vol. 1, Issue 1, 16 (2013)

High-order sideband optical properties of a DNA–quantum dot hybrid system [Invited]

Yang Li and Kadi Zhu^*

Author Affiliations

Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China

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DOI: 10.1364/PRJ.1.000016 Cite this Article Set citation alerts

Yang Li, Kadi Zhu. High-order sideband optical properties of a DNA–quantum dot hybrid system [Invited][J]. Photonics Research, 2013, 1(1): 16 Copy Citation Text

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Abstract

High-order sideband nonlinear optical properties in a DNA–quantum dot coupled system are investigated theoretically here. In this paper, we demonstrate the significant enhancement of the third- and fifth-order optical nonlinear properties of the system by applying the pump-probe technique with pump-exciton detuning tuned to zero. It is shown clearly that these phenomena cannot occur without the DNA–quantum dot coupling, implying some potential applications like DNA detection. We can also obtain and tune the significantly amplified sideband beams at frequencies ωp 2ωD. This research could provide people a deeper insight into the nonlinear optical behaviors in coupled DNA–quantum dot systems.

Keywords

Optical nonlinearities in organic materials Quantum optics

H = ℏ Δ_{p} s_{z} + \sum_{i = 1}^{n} (\frac{p_{i}^{2}}{2 m_{i}} + \frac{1}{2} m_{i} ω_{i}^{2} q_{i}^{2}) - ℏ Ω_{p} (s^{+} + s^{-}) + ℏ ϑ s_{z} - μ [E_{s} s^{+} \exp (- i δ t) + E_{s}^{*} s^{-} \exp (i δ t)],

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\frac{d s_{z}}{d t} = - Γ_{1} (s_{z} + 1 / 2) + i Ω_{p} (s^{+} - s^{-}) + \frac{i μ E_{s} \exp (- i δ t)}{ℏ} s^{+} - \frac{i μ E_{s}^{*} \exp (i δ t)}{ℏ} s^{-},

(2)

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\frac{d s^{-}}{d t} = - (i Δ_{p} + i ϑ + Γ_{2}) s^{-} - 2 i Ω_{p} s_{z} - \frac{2 i μ E_{s} \exp (- i δ t)}{ℏ} s_{z} + F_{n},

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\frac{d^{2} ϑ}{d t^{2}} + \frac{d ϑ}{τ_{D} d t} + ω_{D}^{2} ϑ = - λ ω_{D}^{2} s_{z} + ξ_{n},

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〈 ξ^{+} (t) ξ (t^{'}) 〉 = \frac{1}{τ_{D} ω_{D}} \int \frac{ω + ω \coth (\frac{ℏ ω}{2 k_{B} T})}{2 π e^{i ω (t - t^{'})}} d ω .

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s_{0} = \frac{2 i Ω_{p} s_{z 0}}{i λ s_{z 0} - Γ_{2} - i Δ_{p}}, ϑ_{0} = - λ s_{z 0},

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\frac{1}{2} Γ_{1} Γ_{2}^{2} + \frac{1}{2} Γ_{1} Δ_{p}^{2} = (- Γ_{1} λ^{2}) s_{z 0}^{3} + (\frac{- Γ_{1} λ^{2}}{2} + 2 Γ_{1} λ Δ_{p}) s_{z 0}^{2} + (- Γ_{1} Δ_{p}^{2} - Γ_{1} Γ_{2}^{2} + Γ_{1} λ Δ_{p} - 4 Γ_{2} Ω_{p}^{2}) s_{z 0} .

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〈 \dot{δ} s_{z} 〉 = i Ω_{p} (〈 δ s^{- *} 〉 - 〈 δ s^{-} 〉) - Γ_{1} 〈 δ s_{z} 〉 + \frac{i μ E_{s} \exp (- i δ t)}{ℏ} (s_{0}^{*} + 〈 δ s^{- *} 〉) - \frac{i μ E_{s}^{*} \exp (i δ t)}{ℏ} (s_{0} + 〈 δ s^{-} 〉),

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〈 \dot{δ} s^{-} 〉 = - (i Δ_{p} + Γ_{2}) 〈 δ s^{-} 〉 - 2 i Ω_{p} 〈 δ s_{z} 〉 - i (ϑ_{0} 〈 δ s^{-} 〉 + 〈 δ ϑ 〉 s_{0} + 〈 δ s^{-} 〉 〈 δ ϑ 〉) - \frac{2 i μ E_{s} \exp (- i δ t)}{ℏ} (s_{z 0} + 〈 δ s_{z} 〉),

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〈 \ddot{δ} ϑ 〉 + \frac{〈 \dot{δ} ϑ 〉}{τ_{D}} + ω_{D}^{2} 〈 δ ϑ 〉 = - λ ω_{D}^{2} 〈 δ s_{z} 〉 .

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s_{- 2} = M_{-} s_{z - 2} + A_{-},

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s_{+ 2} = M_{+} s_{z + 2} + A_{+} + M_{0} s_{z +} E_{s},

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χ {(ω_{p} - 2 ω_{s})}_{eff}^{(3)} = \frac{N μ^{2} s_{+ 2}}{3 ε_{0} ℏ Ω_{p} E_{s}^{2}} = Σ_{3} χ^{(3)},

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χ {(- 3 ω_{p} + 2 ω_{s})}_{eff}^{(5)} = \frac{N μ^{4} s_{- 2}}{5 ε_{0} ℏ^{3} Ω_{p}^{3} E_{s}^{* 2}} = Σ_{5} χ^{(5)},

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P_{all} = N μ 〈 δ s^{-} 〉 = ε_{0} \sum_{j = 1} ε_{j} E_{j} = \sum_{j = 1} P_{j},

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\frac{- ζ_{3}}{100} = \frac{Im (P_{ω_{p} - 2 ω_{s}}) ω_{e g} z}{2 c ε_{0} | E_{s} |} = \frac{N μ Im (s_{+ 2}) ω_{e g} z}{2 c ε_{0} | E_{s} |},

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\frac{- ζ_{5}}{100} = \frac{Im (P_{- 3 ω_{p} + 2 ω_{s}}) ω_{e g} z}{2 c ε_{0} | E_{s} |} = \frac{N μ Im (s_{- 2}) ω_{e g} z}{2 c ε_{0} | E_{s} |},

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E_{o} = E_{i} \exp (- Im (ε) ω z / 2 c),

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E_{o} \approx E_{i} (1 - Im (ε) ω z / 2 c) .

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References (41)

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Yang Li, Kadi Zhu. High-order sideband optical properties of a DNA–quantum dot hybrid system [Invited][J]. Photonics Research, 2013, 1(1): 16

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