Researching | Nonreciprocal unconventional photon blockade in a spinning optomechanical system

Journals >Photonics Research >Volume 7 >Issue 6 >Page 630 > Article

Photonics Research
Vol. 7, Issue 6, 630 (2019)

Nonreciprocal unconventional photon blockade in a spinning optomechanical system

Baijun Li¹, Ran Huang¹, Xunwei Xu², Adam Miranowicz^3,4,5, and Hui Jing^1,6

Author Affiliations

¹Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China

²Department of Applied Physics, East China Jiaotong University, Nanchang 330013, China

³Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan

⁴Faculty of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland

⁵e-mail: miran@amu.edu.pl

⁶e-mail: jinghui73@gmail.com

show less

DOI: 10.1364/PRJ.7.000630 Cite this Article Set citation alerts

Baijun Li, Ran Huang, Xunwei Xu, Adam Miranowicz, Hui Jing, "Nonreciprocal unconventional photon blockade in a spinning optomechanical system," Photonics Res. 7, 630 (2019) Copy Citation Text

show less

Abstract

We propose how to achieve quantum nonreciprocity via unconventional photon blockade (UPB) in a compound device consisting of an optical harmonic resonator and a spinning optomechanical resonator. We show that, even with very weak single-photon nonlinearity, nonreciprocal UPB can emerge in this system, i.e., strong photon antibunching can emerge only by driving the device from one side but not from the other side. This nonreciprocity results from the Fizeau drag, leading to different splitting of the resonance frequencies for the optical counter-circulating modes. Such quantum nonreciprocal devices can be particularly useful in achieving back-action-free quantum sensing or chiral photonic communications.

Δ_{F} = \pm \frac{n r Ω ω_{R}}{c} (1 - \frac{1}{n^{2}} - \frac{λ}{n} \frac{d n}{d λ}) = \pm η Ω,

(1)

View in Article

H = ℏ Δ_{L} a_{L}^{†} a_{L} + ℏ (Δ_{R} + Δ_{F}) a_{R}^{†} a_{R} + ℏ ω_{m} b^{†} b + ℏ J (a_{L}^{†} a_{R} + a_{R}^{†} a_{L}) + ℏ g a_{R}^{†} a_{R} (b^{†} + b) + i ℏ ϵ_{d} (a_{L}^{†} - a_{L}),

(2)

View in Article

\frac{d}{d t} q = ω_{m} p, \frac{d}{d t} p = - ω_{m} q - g_{b} a_{R}^{†} a_{R} - \frac{γ_{m}}{2} p + ξ, \frac{d}{d t} a_{L} = - (\frac{κ_{L}}{2} + i Δ_{L}) a_{L} - i J a_{R} + ϵ_{d} + \sqrt{κ_{L}} a_{L, in}, \frac{d}{d t} a_{R} = - (\frac{κ_{R}}{2} + i Δ_{R}^{'}) a_{R} - i J a_{L} - i g_{b} q a_{R} + \sqrt{κ_{L}} a_{R, in},

(3)

View in Article

⟨ ξ (t) ξ (t^{'}) ⟩ = \frac{1}{2 π} \int d ω e^{- i ω (t - t^{'})} Γ_{m} (ω),

(4)

View in Article

Γ_{m} (ω) = \frac{ω γ_{m}}{2 ω_{m}} [1 + \coth (\frac{ℏ ω}{2 k_{B} T})],

(5)

View in Article

⟨ a_{K, in}^{†} (t) a_{K, in} (t^{'}) ⟩ = 0, ⟨ a_{K, in} (t) a_{K, in}^{†} (t^{'}) ⟩ = δ (t - t^{'}),

(6)

View in Article

\frac{d}{d t} δ q = ω_{m} δ p, \frac{d}{d t} δ p = - ω_{m} δ q - g_{b} (β^{*} δ a_{R} + β δ a_{R}^{†}) - \frac{γ_{m}}{2} δ p + ξ, \frac{d}{d t} δ a_{L} = - (\frac{κ_{L}}{2} + i Δ_{L}) δ a_{L} - i J δ a_{R} + \sqrt{κ_{L}} a_{L, in}, \frac{d}{d t} δ a_{R} = - (\frac{κ_{R}}{2} + i Δ_{R}^{'}) δ a_{R} - i J δ a_{L} - i g_{b} q_{s} δ a_{R} - i g_{b} β δ q + \sqrt{κ_{R}} a_{R, in} .

(7)

View in Article

δ a_{L} (ω) = E (ω) a_{L, in} (ω) + F (ω) a_{L, in}^{†} (ω) + G (ω) a_{R, in} (ω) + H (ω) a_{R, in}^{†} (ω) + Q (ω) ξ (ω),

(8)

View in Article

E (ω) = \sqrt{κ_{L}} \frac{A_{1} (ω)}{A_{5} (ω)}, F (ω) = - \sqrt{κ_{L}} \frac{A_{2} (ω)}{A_{5} (ω)}, G (ω) = \sqrt{κ_{R}} \frac{A_{3} (ω)}{A_{5} (ω)}, H (ω) = - \sqrt{κ_{R}} \frac{A_{4} (ω)}{A_{5} (ω)}, Q (ω) = - i \frac{g_{b} χ (ω)}{ω_{m} A_{5} (ω)} [β A_{3} (ω) + β^{*} A_{4} (ω)],

(9)

View in Article

A_{1} (ω) = [{(\frac{κ_{R}}{2} + i ω)}^{2} + Δ_{R}^{'' 2}] V_{1}^{-} (ω) - g_{b}^{4} {| β |}^{4} {[\frac{χ (ω)}{ω_{m}}]}^{2} V_{1}^{-} (ω) + J^{2} V_{2}^{+}, A_{2} (ω) = - i J^{2} g_{b}^{2} β^{2} \frac{χ (ω)}{ω_{m}}, A_{3} (ω) = - i J V_{1}^{-} (ω) V_{2}^{-} - i J^{3}, A_{4} (ω) = - J g_{b}^{2} β^{2} \frac{χ (ω)}{ω_{m}} V_{1}^{-} (ω), A_{5} (ω) = V_{1}^{+} A_{1} (ω) + i J A_{3} (ω),

(10)

View in Article

Δ_{R}^{''} = Δ_{R}^{'} + g_{b} q_{s} - g_{b}^{2} {| β |}^{2} χ (ω), χ (ω) = ω_{m}^{2} / (ω_{m}^{2} - ω^{2} + \frac{i ω γ_{m}}{2}), V_{1}^{\pm} (ω) = \frac{κ_{L}}{2} \pm i (Δ_{L} - ω), V_{2}^{\pm} (ω) = \frac{κ_{R}}{2} \pm i (Δ_{R} - ω) .

(11)

View in Article

g_{L}^{(2)} (0) = \frac{{| α |}^{4} + 4 {| α |}^{2} R_{1} + 2 Re [α^{* 2} R_{2}] + R_{3}}{{({| α |}^{2} + R_{1})}^{2}},

(12)

View in Article

⟨ δ a_{L}^{\pm} (t) δ a_{L} (t) ⟩ = \frac{1}{2 π} \int_{- \infty}^{+ \infty} X_{a_{L}^{\pm} a_{L}} d ω,

(13)

View in Article

δ a_{L}^{+} (t) = δ a_{L}^{†} (t), δ a_{L}^{-} (t) = δ a_{L} (t), and X_{a_{L}^{†} a_{L}} = {| Q (- ω) |}^{2} Γ_{m} (- ω) + {| F (- ω) |}^{2} + {| H (- ω) |}^{2}, X_{a_{L} a_{L}} = Q (ω) Q (- ω) Γ_{m} (- ω) + E (ω) F (- ω) + G (ω) H (- ω) .

(14)

View in Article

\dot{ρ} = \frac{1}{i ℏ} [H, ρ] + \frac{κ_{L}}{2} L [a_{L}] (ρ) + \frac{κ_{R}}{2} L [a_{R}] (ρ) + \frac{γ_{m}}{2} ({\bar{n}}_{m} + 1) L [b] (ρ) + \frac{γ_{m}}{2} {\bar{n}}_{m} L [b^{†}] (ρ),

(15)

View in Article

| φ ⟩ = C_{00} | 0, 0 ⟩ + C_{10} | 1, 0 ⟩ + C_{01} | 0, 1 ⟩ + C_{20} | 2, 0 ⟩ + C_{11} | 1, 1 ⟩ + C_{02} | 0, 2 ⟩,

(16)

View in Article

Δ_{opt} \approx \frac{- a_{3} + sgn (E) \sqrt{λ_{1}} - \sqrt{λ_{2}}}{4 a_{4}}, g_{opt} = \sqrt{- \frac{ω_{m} [Δ_{opt} (4 Δ_{opt}^{2} + 5 κ^{2}) + Δ_{F} λ_{3}]}{2 (2 J^{2} - κ^{2}) + 2 Δ_{F} λ_{4}}},

(17)

View in Article

Figures&Tables (6)

References (101)

Copy Citation Text

Baijun Li, Ran Huang, Xunwei Xu, Adam Miranowicz, Hui Jing, "Nonreciprocal unconventional photon blockade in a spinning optomechanical system," Photonics Res. 7, 630 (2019)

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address