Strong photon antibunching in weakly nonlinear two-dimensional exciton-polaritons

Albert Ryou, David Rosser, Abhi Saxena, Taylor Fryett, and Arka Majumdar

Phys. Rev. B 97, 235307 – Published 11 June 2018

Abstract

A deterministic and scalable array of single photon nonlinearities in the solid state holds great potential for both fundamental physics and technological applications, but its realization has proved extremely challenging. Despite significant advances, leading candidates such as quantum dots and group III-V quantum wells have yet to overcome their respective bottlenecks in random positioning and weak nonlinearity. Here we consider a hybrid light-matter platform, marrying an atomically thin two-dimensional material to a photonic crystal cavity, and analyze its second-order coherence function. We identify several mechanisms for photon antibunching under different system parameters, including one characterized by large dissipation and weak nonlinearity. Finally, we show that by patterning the two-dimensional material into different sizes, we can drive our system dynamics from a coherent state into a regime of strong antibunching with second-order coherence function $g^{(2)} (0) \sim 10^{- 3}$ , opening a possible route to scalable, on-chip quantum simulations with correlated photons.

Received 6 February 2018
Revised 28 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.235307

Physics Subject Headings (PhySH)

Exciton polariton Excitons Photonics Polaritons

Nanostructures Transition metal dichalcogenides

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Albert Ryou¹, David Rosser², Abhi Saxena³, Taylor Fryett¹, and Arka Majumdar^1,2

¹Department of Electrical Engineering, University of Washington, Seattle, Washington 98195, USA
²Department of Physics, University of Washington, Seattle, Washington 98195, USA
³Department of Electrical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 97, Iss. 23 — 15 June 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Patterned 2D material-embedded cavity. (a) Schematic illustration of the proposed experimental platform. A patterned 2D-material (tungsten diselenide, ${WSe}_{2}$ ) monolayer is placed on top of a photonic crystal nanobeam cavity. The radius of the monolayer is on the order of tens of nanometers, and the cavity periodicity is 240 nm. The top view of the cavity with a simulated field profile of the fundamental mode is shown below. The calculated mode volume is about $2.5 {(λ / n)}^{3}$ . (b) Energy level diagram. The dressed states are labeled by the number of energy quanta, or Fock manifold, followed by a symbol: $| 1, - 〉$ and $| 1, + 〉$ are the first-manifold states representing the lower and upper polaritons; $| 2, e_{1} 〉$ , $| 2, e_{2} 〉$ , and $| 2, e_{3} 〉$ are the second-manifold states. The solid lines represent the eigenenergies of the Hamiltonian with nonzero nonlinearity, whereas the dotted lines represent the eigenenergies with zero nonlinearity. The arrows represent the pump laser frequency that is resonant with either $| 1, + 〉$ (blue) or $| 2, e_{3} 〉$ (red). (c) Eigenenergies as a function of the nonlinearity $U$ , calculated via exact matrix diagonalization. All parameters are normalized by the exciton-photon coupling strength $g$ .
Reuse & Permissions
Figure 2
$g^{(2)} (0)$ vs pump laser frequency for different $U$ . (a) A 2D plot of $g^{(2)} (0)$ versus pump laser frequency ( $x$ axis) relative to the exciton resonance for different values of $U$ ( $y$ axis). The color corresponds to the base-10 logarithm of $g^{(2)} (0)$ . Four strong bunching peaks (red) are observed, three of which come from the second-manifold eigenstates. The remaining bunching peak at $ω_{pump} = 0$ is due to photon-induced tunneling [7]. Also observed are three strong antibunching dips (blue): the first-manifold eigenstates (lower and upper polaritons) and a quantum-interference dip. The other parameters are $ω_{c} = ω_{e}$ and $κ = Γ = 0.01 g$ . (b) Horizontal cross sections of (a) for $U / g = 0.3$ , 0.67, and 1.5. When $U / g$ is near 2/3, the location of the quantum interference dip overlaps with that of the upper polariton at $ω_{pump} = g$ , yielding an extremely strong antibunching with $g^{(2)} (0) \sim 10^{- 7}$ .
Reuse & Permissions
Figure 3
$g^{(2)} (0)$ vs pump laser frequency for different $Γ$ and $U$ . (a)–(c) $Γ / g = 0.1$ , 0.5, and 1.0, with $U / g$ ranging from 0.1 to 0.5. The pump laser frequency is relative to the exciton resonance, and $ω_{c} = ω_{e}$ . (a) For small $Γ, g^{(2)} (0)$ resembles that in Fig. 2, with the strong quantum interference-induced antibunching appearing near $ω_{pump} = g$ . (b) For intermediate $Γ$ , the antibunching dip at $ω_{pump} = g$ becomes shallow while a new antibunching dip appears at a slightly negative $ω_{pump}$ . (c) This new antibunching dip, also due to the destructive quantum interference, can be significantly large with $g^{(2)} (0) \sim 10^{- 2}$ .
Reuse & Permissions
Figure 4
Minimum $g^{(2)} (0)$ for different $Γ$ and $U$ . A 2D plot of the minimum value of the $g^{(2)} (0)$ that appears at negative $ω_{pump}$ (see Fig. 3) versus $U$ ( $x$ axis) and $Γ$ ( $y$ axis). The color represents the base-10 logarithm of $g^{(2)} (0)$ . For a given value of $Γ$ , strong antibunching is observed for a range of $U$ . As $Γ$ increases, the optimal value of $U$ as well as its width increases. White dashed lines mark where $g^{(2)} (0) = 0.1$ . For this simulation, $κ$ is set at $0.5 g$ . The dotted appearance for strong antibunching is a numerical artifact.
Reuse & Permissions
Figure 5
$g^{(2)} (0)$ vs pump laser frequency for different $R$ . A plot of $g^{(2)} (0)$ versus pump laser frequency relative to the exciton resonance for different monolayer areas, with radius $R$ ranging from 30 to 60 nm. The strong antibunching appears for $R = 42$ nm. Inset: A plot of $g^{(2)} (τ)$ vs $τ$ for $R = 42$ nm. The rise time to unity is on the order of 1 ps.
Reuse & Permissions
Figure 6
$g^{(2)} (0)$ vs $ω_{e}$ and $ω_{c}$ . A 2D plot of $g^{(2)} (0)$ versus the exciton resonance ( $x$ axis) and the cavity resonance ( $y$ axis) relative to the pump laser frequency for monolayer radius $R = 42$ nm. The color represents the base-10 logarithm of $g^{(2)} (0)$ . As can be seen, the antibunching is robust against the change in the cavity frequency.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics