Cascaded cold atomic ensembles in a diamond configuration as a spectrally entangled multiphoton source

H. H. Jen

Phys. Rev. A 95, 043840 – Published 25 April 2017

Abstract

We theoretically investigate the spectral entanglement of a multiphoton source generated from the cascade emissions in cascaded cold atomic ensembles. This photon source is highly directional, which is guaranteed under the four-wave mixing condition, and is also highly frequency correlated due to finite driving pulse durations and superradiant decay constants. We utilize Schmidt decomposition to study the bipartite entanglement of the biphoton states projected from the multiphoton ones. This entropy of entanglement can be manipulated by controlling the driving parameters and superradiant decay rates. Moreover, the projected biphoton states in the cascaded scheme can have larger entanglement than the one produced from only one atomic ensemble, which results from larger capacity in multipartite entanglement. This cascaded scheme enables a multiphoton source useful in quantum-information processing. It also allows for potential applications in multimode quantum communication and spectral shaping of high-dimensional continuous frequency entanglement.

Received 25 January 2017

DOI:https://doi.org/10.1103/PhysRevA.95.043840

Physics Subject Headings (PhySH)

Entanglement manipulation Quantum communication Quantum information processing with continuous variables Quantum information with atoms & light Quantum optics Single- and few-photon ionization & excitation Spontaneous emission Superradiance & subradiance

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

H. H. Jen^*

Institute of Physics, Academia Sinica, Taipei 11529, Taiwan

^*sappyjen@gmail.com

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Issue

Vol. 95, Iss. 4 — April 2017

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Images

Figure 1
Proposed multiphoton source from the cascade emissions in the cascaded scheme with a diamond-type atomic configuration. In the inset of (a) the signal and idler photon pair ${\hat{a}}_{s, i}^{†}$ is created by two pump fields $Ω_{a, b}$ with single- and two-photon detunings $Δ_{1, 2}$ , driving the atomic ensembles (AEs). For demonstration we plot (a) three- and (b) four-photon generations in the cascaded scheme. In (a) ${\hat{a}}_{i}^{†}$ is sent to ${AE}^{'}$ along with a pump field $Ω_{b}$ , and then is converted into a pair of photons ${\hat{a}}_{s^{'}}^{†}$ and ${\hat{a}}_{i^{'}}^{†}$ . The excitation and photon emission angles are denoted as $θ_{a, b, s, i}$ with respect to the long axis of AE. In (b) ${\hat{a}}_{i}^{†}$ and ${\hat{a}}_{i^{'}}^{†}$ are sent sequentially to ${AE}^{'}$ and ${AE}^{''}$ , interacting with pump fields $Ω_{b}$ , and then effectively are converted into three photons ${\hat{a}}_{s^{'}}^{†}, {\hat{a}}_{s^{''}}^{†}$ , and ${\hat{a}}_{i^{''}}^{†}$ . $| Ψ 〉$ are the effective multiphoton states in the cascaded scheme.
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Figure 2
First ten Schmidt eigenvalues $λ_{n}$ of the projected spectral distributions $| f_{3, B 1} |$ . The spectral ranges for both signal and idler photons are postselected to $\pm 200 Γ_{3}$ throughout all figures where we also set $Γ_{3}^{N} = 5 Γ_{3}$ and $τ_{a} = τ_{b} = 0.25 Γ_{3}^{- 1}$ without loss of generality. The insets (a) and (b) are projected spectral distributions with $Δ ω_{s} = 0$ and $Δ ω_{(s^{'})} = 0$ , respectively, with corresponding Schmidt eigenvalues ( $□$ and $\circ$ ).
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Figure 3
First ten Schmidt eigenvalues $λ_{n}$ of the projected spectral distributions $| f_{3, B 2} |$ . The parameters are the same as in Fig. 2 while the insets (a) and (b) are projected spectral distributions with $Δ ω_{i (s^{'})} = 0$ and corresponding Schmidt eigenvalues ( $□$ and $\circ$ , respectively).
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Figure 4
First ten Schmidt eigenvalues $λ_{n}$ of the projected spectral distributions $| f_{3, B 1} |$ with different decay constants $Γ_{3}^{N}$ and $Γ_{3}^{N^{'}}$ . The parameters are the same as in Fig. 2 while the insets (a) and (b) are projected spectral distributions as in Fig. 2 with $Γ_{3}^{N} / Γ_{3} = 1 (5)$ and $Γ_{3}^{N^{'}} / Γ_{3} = 5 (1)$ , respectively. Corresponding Schmidt eigenvalues are denoted by $□$ and $\circ$ .
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Figure 5
Three-dimensional isosurface plots for projected spectral distributions $| f_{4, C 1} |$ with annihilated photon (a) ${\hat{a}}_{s}$ or (b) ${\hat{a}}_{i^{''}}$ . The isosurface plots are chosen for respectively projected and normalized $| f_{4, C 1} | = 0.3$ where they show tilted and axial spectral distributions in (a) and (b), respectively.
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Figure 6
First ten Schmidt eigenvalues $λ_{n}$ and two mode functions of the projected spectral distributions $| f_{4, B 3} |$ with annihilated photons ${\hat{a}}_{s^{'}}$ and ${\hat{a}}_{s^{''}}$ . The parameters are the same as in Fig. 2. (a) $λ_{n}$ shows an abrupt decrease in logarithmic scale, indicating an extremely low entropy of entanglement. (b) Two idler mode probability densities (solid and dashed for the first and the second modes) in $Δ ω_{i^{'}}$ and $Δ ω_{i^{''}}$ , respectively.
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