Tuning the photon statistics of a strongly coupled nanophotonic system

We investigate the dynamics of single- and multiphoton emission from detuned strongly coupled systems based on the quantum-dot–photonic-crystal resonator platform. Transmitting light through such systems can generate a range of nonclassical states of light with tunable photon counting statistics due to the nonlinear ladder of hybridized light-matter states. By controlling the detuning between emitter and resonator, the transmission can be tuned to strongly enhance either single- or two-photon emission processes. Despite the strongly dissipative nature of these systems, we find that by utilizing a self-homodyne interference technique combined with frequency filtering we are able to find a strong two-photon component of the emission in the multiphoton regime. In order to explain our correlation measurements, we propose rate equation models that capture the dominant processes of emission in both the single- and multiphoton regimes. These models are then supported by quantum-optical simulations that fully capture the frequency filtering of emission from our solid-state system.

Figure 1

Strongly coupled QD-cavity system: (a) Spectra of the strongly coupled QD–photonic crystal cavity system detected in cross-polarized reflectivity measurements, exhibiting an anticrossing—the signature of strong coupling. The QD resonance is tuned through the cavity resonance by changing the sample temperature. (b) Calculated energy level structure of the first two rungs of a strongly coupled Jaynes-Cummings system. Each rung $n$ consists of an upper polariton and a lower polariton $\mathrm{UP}n$ and $\mathrm{LP}n$, respectively. (c) Measured degree of second-order coherence as a function of the laser detuning for a QD-cavity detuning of $\mathrm{\Delta }=3g$. The polaritonic frequencies are indicated by solid black lines, the bare cavity frequency a dashed red line, and the bare QD frequency by a dotted blue line.

Figure 2

Photon-blockade regime: (a) Spectrum of the strongly coupled system at $\mathrm{\Delta }=3.5g$ and resonant excitation of UP1 with a 25 ps long pulse. (b) Illustration of the JC ladder. The excitation laser is resonant with UP1 (depicted with a solid blue upward arrow) but not resonant with higher climbs up the ladder. Following excitation of UP1, possible recombination channels are from UP1 to the ground state (solid blue downward arrow) or from LP1 to the ground state (dashed red arrow) via a phonon-assisted population transfer from UP1 to LP1 (curved orange arrow). (c)–(f) Correlation measurement of the (c) unfiltered signal, revealing $g_D^{\left(2\right)}\left(0\right)=0.263\pm 0.008$, (d) filtered emission from UP1 [indicated in blue on the left in (a)], revealing $g_D^{\left(2\right)}\left(0\right)=0.162\pm 0.016$, (e) filtered emission from LP1 [indicated in red on the right in (a)], revealing $g_D^{\left(2\right)}\left(0\right)=0.063\pm 0.010$, and (f) cross-correlation between UP1 and LP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.079\pm 0.018$.

Figure 3

Photon-induced tunneling regime: (a) Spectrum of the strongly coupled system at $\mathrm{\Delta }=5.2g$ for exciting UP2 with a 25 ps long pulse (gray circles) fitted with a quantum optical model with (solid black line) and without SHS (gray dashed line). (b) Illustration of the JC ladder. The resonant two-photon excitation of UP2 is depicted with two solid green arrows. The most likely relaxation channels are from UP2 to UP1 (upper dashed red arrow), from UP1 to the ground state (solid blue arrow), or from LP1 to the ground state (lower dashed red arrow) via a phonon-assisted population transfer from UP1 to LP1 (curved orange arrow). Correlation measurements of (c) the unfiltered signal, revealing $g_D^{\left(2\right)}\left(0\right)=1.174\pm 0.022$, (d) the filtered emission UP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.332\pm 0.028$, and (e) the emission from the transitions from UP2 to UP1 and from LP1 to the ground state, revealing $g_D^{\left(2\right)}\left(0\right)=1.490\pm 0.034$. (f) Simulated pulsewise second-order coherence versus the position of the frequency filter and taking into account the experimental parameters (laser pulse approximately tuned to two-photon resonance). The dotted blue (dashed red) line represents the frequency of UP1 (LP1) and black circles represent measured values.

Figure 4

Photon-blockade regime: (a) Spectrum of the strongly coupled system at $\mathrm{\Delta }=3.5g$ and resonant excitation of UP1 with an 80 ps long pulse. The emission from UP1 is illustrated in blue on the left and the emission from LP1 in red on the right. (b) Illustration of the JC ladder. The excitation laser is resonant with UP1 (depicted with a solid blue upward arrow) but not resonant with higher climbs up the ladder. Following excitation of UP1, possible recombination channels are from UP1 to the ground state (solid blue downward arrow) or from LP1 to the ground state (dashed red arrow) via a phonon-assisted population transfer from UP1 to LP1 (curved orange arrow). (c)–(f) Correlation measurement of the (c) unfiltered signal, revealing $g_D^{\left(2\right)}\left(0\right)=0.330\pm 0.003$, (d) filtered emission from UP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.227\pm 0.008$, (e) filtered emission from LP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.284\pm 0.011$, and (f) cross-correlation between UP1 and LP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.405\pm 0.005$.

Figure 5

Photon-induced tunneling regime: (a) Spectrum of the strongly coupled system at $\mathrm{\Delta }=2.9g$ for exciting UP2 with an 80 ps long pulse. (b) Illustration of the JC ladder. The resonant two-photon excitation of UP2 is depicted with two solid green arrows. The most likely recombination channels are from UP2 to UP1 (upper dashed red arrow), from UP1 to the ground state (solid blue arrow), or from LP1 to the ground state (lower dashed red arrow) via a phonon-assisted population transfer from UP1 to LP1 (curved orange arrow). Correlation measurements of (c) the unfiltered signal, revealing $g_D^{\left(2\right)}\left(0\right)=1.560\pm 0.005$, (d) the filtered emission UP1, revealing $g_D^{\left(2\right)}\left(0\right)=0.324\pm 0.013$, and (e) the emission from the transitions from UP2 to UP1 and from LP1 to the ground state, revealing $g_D^{\left(2\right)}\left(0\right)=2.091\pm 0.021$.

Figure 6

Rate equation model: Spectrum of the strongly coupled system at (a) $\mathrm{\Delta }=3.5g$ for exciting UP1 with a 25 ps long pulse and (b) $\mathrm{\Delta }=5.2g$ for exciting UP2 with a 25 ps long pulse. The data (gray circles) are fitted with a function built of Lorentzian and Gaussian line shapes (solid black line). The Lorentzian at UP1 (LP1) frequency is shown as a dotted blue (dashed red) line. Calculated time-resolved population of (c) UP1 (dotted blue line) and LP1 (dashed red line) in the photon blockade and (d) UP1 (dotted blue line), LP1 (dashed red line), UP2 (dot-dashed green line), and LP2 (solid orange line) in the photon-induced tunneling regime. Integrated photoluminescence intensity at the frequency of UP1 (dotted blue line) and LP1 (dashed red line) in (e) the photon blockade and (f) the photon-induced-tunneling regime.