Architecture dependence of photon antibunching in cavity quantum electrodynamics

Matthew Bradford and Jung-Tsung Shen

Phys. Rev. A 92, 023810 – Published 10 August 2015

Abstract

We investigate numerically the architecture dependence of the characteristics of antibunched photons generated in cavity quantum electrodynamic systems. We show that the quality of antibunching [the smallness of the second-order intensity correlation function at zero time $g^{(2)} (0)$ ] and the generation efficiency significantly depend on the configurations: the arrangements of single-mode optical cavities and waveguides. We found that for certain class of architecture, when the Jaynes-Cummings system (the atom-cavity system) couples to two terminated waveguides, there exists a fundamental tradeoff between high transmission and low $g^{(2)} (0)$ , and is sensitive to dissipation. We further show that optimal antibunching can be achieved in two alternative cavity quantum electrodynamic configurations operating in the dissipatively weak coupling regime such that the two-photon transmission can be two orders of magnitude higher for the same $g^{(2)} (0)$ .

Received 27 August 2014

DOI:https://doi.org/10.1103/PhysRevA.92.023810

Authors & Affiliations

Matthew Bradford and Jung-Tsung Shen^*

Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA

^*jushen@wustl.edu

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Vol. 92, Iss. 2 — August 2015

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Figure 1
Cavity QED circuits exhibiting photon blockade for the transmission field. (a) Inline geometry with a JC system placed between two terminated waveguides. (b) Side-coupled geometry with a JC system coupled to a single waveguide. (c) $T$ geometry with a generalized JC system coupled to two terminated waveguides. For all configurations, $Γ$ represents the cavity-waveguide coupling strength (i.e., halfwidth of the cavity linewidth); $g$ represents the atom-cavity coupling strength; the intercavity coupling strength for the $T$ geometry is given by $ξ$ . All coupling strengths have the unit of frequency. $ω_{a}$ is the angular transition frequency of the two-level atom, and $ω_{c}$ is the resonant frequency of the cavities. The on-resonance case (that is, $ω_{a} = ω_{c}$ ) is considered throughout. Each waveguide has a single transverse mode for each operating frequency.
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Figure 2
Energy-level diagrams, operating schemes, and single-photon transmission spectra for the JC and generalized JC systems. (a) Top: JC level scheme is shown up to the second manifold, with single-photon operating frequencies $ω_{i} = ω_{c} - g$ for the inline (blue arrows) and $ω_{s} = ω_{c}$ for the side-coupled (green arrows) geometries. Each $n$ -photon manifold has two energy levels. Bottom: single-photon transmission spectrum for inline (with $Γ / g = 0.15$ ) and side-coupled (with $Γ / g = 1.75$ ) geometries with arrows indicating single-photon operating frequency [41]. (b) Top: generalized JC level scheme is shown up to the second manifold, with single-photon operating frequency $ω_{T} = ω_{c}$ for the $T$ geometry (red arrows). Each $n$ -photon manifold has $2 n + 1$ energy levels. Bottom: single-photon transmission spectrum for the $T$ geometry with $Γ / g = 1.4$ and $ξ / g = 1.9$ . Each energy level is broadened (gray color) when coupled to the waveguide.
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Figure 3
Probability density plot for two-photon transport in cQED circuits. (a) Inline geometry $(Γ / g = 0.15)$ . (b) Side-coupled geometry $(Γ / g = 1.75)$ . (c) $T$ geometry $(Γ / g = 1.4, ξ / g = 1.9)$ . In each plot, the two-photon input state at $t = 0$ is shown as a disk in the third quadrant. For the output state, the part in the first quadrant corresponds to both photons transmitted; the part in the third quadrant corresponds to both photons reflected; and the parts in the second and fourth quadrants correspond to one photon transmitted and one reflected. The input state is made transparent to visually distinguish it from the output. Simulation parameters correspond to $g x_{0} / v = - 70, g σ / v = 15$ for all cases.
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Figure 4
Performance plots of the cQED circuits. (a) Semilog plot of $g^{(2)} (0)$ . (b) Two-photon transmission $P_{t t}$ . (c) $g^{(2)} (0)$ versus $Γ / g$ and $ξ / g$ for the $T$ geometry. (d) $P_{t t}$ versus $Γ / g$ and $ξ / g$ for the $T$ geometry. For all cases, $g σ / v = 15$ . The white dashed line in (c) and (d) denotes the valley relation.
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Figure 5
Effects of cavity and atomic dissipations. (a) Inline and side-coupled geometries. Parentheses in the legend denote (circuit type, $γ_{c} / g, γ_{a} / g$ ). (b) $T$ geometry. Parentheses in the legend denote ( $ξ / g, γ_{c} / g, γ_{a} / g$ ). Dissipation equal to $0.1 g$ corresponds to or is larger than many current experimental conditions [19, 21, 22, 23]).
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Figure 6
Regular and folded coordinates for describing different cavity QED geometries. (a) Folded coordinates to describe inline and $T$ geometries, wherein photons are reflected unless they interact with the cavity. (b) Regular, left-right coordinates to describe side-coupled geometry, wherein photons continue to propagate unimpeded unless they interact with the cavity.
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