Interference of quantum beats in Hong–Ou–Mandel interferometry

Jing Qiu; Jun-Heng Shi; Yong-Sheng Zhang; Shen-Sheng Han; You-Zhen Gui

doi:10.1364/PRJ.3.000082

Journals >Photonics Research >Volume 3 >Issue 3 >Page 82 > Article

Photonics Research
Vol. 3, Issue 3, 82 (2015)

Interference of quantum beats in Hong–Ou–Mandel interferometry

Jing Qiu¹, Jun-Heng Shi¹, Yong-Sheng Zhang^2、3、*, Shen-Sheng Han¹, and You-Zhen Gui^1、4、*

Author Affiliations

¹Key Laboratory for Quantum Optics and Center for Cold Atom Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Lab of Quantum Information, University of Science and Technology of China, Hefei 230026, China

³e-mail: yshzhang@ustc.edu.cn

⁴e-mail: yzgui@siom.ac.cn

show less

DOI: 10.1364/PRJ.3.000082 Cite this Article Set citation alerts

Jing Qiu, Jun-Heng Shi, Yong-Sheng Zhang, Shen-Sheng Han, You-Zhen Gui. Interference of quantum beats in Hong–Ou–Mandel interferometry[J]. Photonics Research, 2015, 3(3): 82 Copy Citation Text

EndNote(RIS)

BibTex

Plain Text

show less

Abstract

Quantum beats can be produced in fourth-order interference such as in a Hong–Ou–Mandel (HOM) interferometer by using photons with different frequencies. Here we present theoretically the appearance of interference of quantum beats when the HOM interferometer is combined with a Franson-type interferometer. This combination can make the interference effect of photons with different colors take place not only within the coherence time of downconverted fields but also in the region beyond that. We expect that it can provide a new method in quantum metrology, as it can realize the measurement of time intervals in three scales.

Keywords

Coherent optical effects Photon statistics Quantum detectors

| ψ 〉 = \int d ω_{s} d ω_{i} Φ (ω_{s}, ω_{i}) {\hat{a}}_{s}^{†} (ω_{s}) {\hat{a}}_{i}^{†} (ω_{i}) | 0 〉,

(1)

View in Article

\exp (- i ω_{s} τ_{1}) [1 + \exp (- i ω_{s} τ_{2})] [1 + \exp (- i ω_{i} τ_{2})],

(2)

View in Article

| ψ 〉 = \int d ω_{s} d ω_{i} Φ (ω_{s}, ω_{i}) \exp (- i ω_{s} τ_{1}) [1 + \exp (- i ω_{s} τ_{2})] [1 + \exp (- i ω_{i} τ_{2})] {\hat{a}}_{s}^{†} (ω_{s}) {\hat{a}}_{i}^{†} (ω_{i}) | 0 〉 .

(3)

View in Article

{\hat{E}}_{1}^{(+)} (t_{1}) = \int d ω_{1} {\hat{a}}_{1} (ω_{1}) g_{1} (ω_{1}) \exp (- i ω_{1} t_{1}),

(4)

View in Article

{\hat{E}}_{2}^{(+)} (t_{2}) = \int d ω_{2} {\hat{a}}_{2} (ω_{2}) g_{2} (ω_{2}) \exp (- i ω_{2} t_{2}),

(5)

View in Article

〈 0 | {\hat{E}}_{1}^{(+)} (t_{1}) {\hat{E}}_{2}^{(+)} (t_{2}) | ψ 〉 = 〈 0 | \int d ω_{s} d ω_{i} d ω_{1} d ω_{2} Φ (ω_{s}, ω_{i}) g_{1} (ω_{1}) g_{2} (ω_{2}) \times \exp (- i ω_{1} t_{1}) \exp (- i ω_{2} t_{2}) \exp (- i ω_{s} τ_{1}) \times [1 + \exp (- i ω_{s} τ_{2})] [1 + \exp (- i ω_{i} τ_{2})] \times {\hat{a}}_{1} (ω_{1}) {\hat{a}}_{2} (ω_{2}) {\hat{a}}_{s}^{†} (ω_{s}) {\hat{a}}_{i}^{†} (ω_{i}) | 0 〉 .

(6)

View in Article

R (τ_{1}, τ_{2}) = \int d t_{1} d t_{2} G^{(2)} (t_{1}, t_{2}) = \int d t_{1} d t_{2} {| 〈 0 | {\hat{E}}_{1}^{(+)} (t_{1}) {\hat{E}}_{2}^{(+)} (t_{2}) | ψ 〉 |}^{2} = \int d ω_{s} d ω_{i} {Φ (ω_{s}, ω_{i}) Φ^{*} (ω_{s}, ω_{i}) - Φ (ω_{s}, ω_{i}) \times Φ^{*} (ω_{i}, ω_{s}) \exp [- i (ω_{s} - ω_{i}) τ_{1}]} [\cos (ω_{s} τ_{2}) + 1] \times [\cos (ω_{i} τ_{2}) + 1] {\exp [- \frac{{(ω_{s} - ω_{a})}^{2}}{σ^{2}}] \exp [- \frac{{(ω_{i} - ω_{b})}^{2}}{σ^{2}}] + \exp [- \frac{{(ω_{i} - ω_{a})}^{2}}{σ^{2}}] \times \exp [- \frac{{(ω_{s} - ω_{b})}^{2}}{σ^{2}}]} .

(7)

View in Article

R (τ_{1}, τ_{2}) = \int d t_{1} d t_{2} G^{(2)} (t_{1}, t_{2}) = \int d t_{1} d t_{2} {| 〈 0 | {\hat{E}}_{1}^{(+)} (t_{1}) {\hat{E}}_{2}^{(+)} (t_{2}) | ψ 〉 |}^{2} = \int d ω {{| f (ω) |}^{2} + {| f (- ω) |}^{2} - [f (ω) f^{*} (- ω) \times \exp (- 2 i ω τ_{1}) + c.c.]} [\cos ((ω_{0} + ω) τ_{2}) + 1] \times [\cos ((ω_{0} - ω) τ_{2}) + 1] {\exp [- \frac{{(ω_{0} + ω - ω_{a})}^{2}}{σ^{2}}] \exp [- \frac{{(ω_{0} - ω - ω_{b})}^{2}}{σ^{2}}] + \exp [- \frac{{(ω_{0} - ω - ω_{a})}^{2}}{σ^{2}}] \exp [- \frac{{(ω_{0} + ω - ω_{b})}^{2}}{σ^{2}}]} .

(8)

View in Article

R (τ_{1}, τ_{2}) = 1 - \exp (- \frac{σ^{2} τ_{1}^{2}}{2}) \cos [(ω_{a} - ω_{b}) τ_{1}] - \frac{1}{2} \exp [- \frac{σ^{2} {(τ_{1} - τ_{2})}^{2}}{2}] \cos [(ω_{a} - ω_{b}) (τ_{1} - τ_{2})] - \frac{1}{2} \exp [- \frac{σ^{2} {(τ_{1} + τ_{2})}^{2}}{2}] \cos [(ω_{a} - ω_{b}) (τ_{1} + τ_{2})] .

(9)

View in Article

Jing Qiu, Jun-Heng Shi, Yong-Sheng Zhang, Shen-Sheng Han, You-Zhen Gui. Interference of quantum beats in Hong–Ou–Mandel interferometry[J]. Photonics Research, 2015, 3(3): 82

Download Citation

EndNote(RIS)

BibTex

Plain Text

Set citation alerts for the article

Tools

Set citation alerts for the article

Save the article for my favorites

Paper Information