Ultrafast Photon-Photon Interaction in a Strongly Coupled Quantum Dot-Cavity System

We study dynamics of the interaction between two weak light beams mediated by a strongly coupled quantum dot–photonic crystal cavity system. First, we perform all-optical switching of a weak continuous-wave signal with a pulsed control beam, and then perform switching between two weak pulsed beams (40 ps pulses). Our results show that the quantum dot–nanocavity system enables fast, controllable optical switching at the single-photon level.

Figure 1

(a) Scanning electron micrograph of the photonic crystal cavity. (b) In the experiment, a combination of pulsed control laser (frequency ${\omega }_c$), nonresonant pulsed or continuous-wave pump laser at ${\omega }_e$ above the QD exciton line, and pulsed or continuous-wave signal laser (${\omega }_s$) is employed. The cavity is backed by a distributed Bragg reflector, effectively creating a single-sided cavity [4]. A cross-polarized confocal microscope configuration reduces the laser background that is reflected from the sample without coupling to the cavity, which is polarized at 45° to the incident laser polarization. The measurement is effectively a transmission measurement from the horizontal (H) into the vertical (V) polarization. (c) Anticrossing observed in the PL as the QD single exciton (X) is temperature tuned through the cavity. The QD is pumped through higher-order excited states by optical excitation at ${\omega }_e$ corresponding to a wavelength of ${\lambda }_e=878\mathrm{nm}$. (d) The transmitted intensity of a broadband light source (in the cross-polarized setup) shows the mode splitting of the strongly coupled QD-cavity system (this signal is resolved on a spectrometer). (e) PL lifetime $\sim 17\mathrm{ps}$ when the QD is tuned into the cavity and pulsed excitation is at wavelength ${\lambda }_e=878\mathrm{nm}$. The emission that is expected theoretically, based on the system parameters in (d) and a 10-ps relaxation time into the single exciton state, is shown in the solid line.

Figure 2

All-optical switching of the CW signal beam by a pulsed control beam through the strongly coupled QD/cavity system. (a) Cavity transmission when the signal and control are tuned to the cavity, which is resonant with the QD (panel 1). The transmitted cavity output is normalized with respect to the maximum cavity transmission. As the signal and control input powers are increased (panels 2 and 3), the QD saturates and results in a net-positive nonlinear transmission. For the three panels, the CW signal powers are 12, 168, and 240 nW, respectively; the pulsed control powers are 0.2, 1.6, and 3.8 nW, respectively (all measured before the objective lens). (b) Plots of the theoretically estimated intracavity photon number $⟨a^{†}a⟩$, which gives the transmission by $T=2\kappa ⟨a^{†}a⟩$. We plot the calculated intracavity photon number for the control beam intracavity photon number $n(c)$, signal and control $n(s+c)$, and the differential photon number $\Delta n=n(s+c)-n(s)-n(c)$.

Figure 3

All-optical switching between two weak laser pulses interacting via a strongly coupled QD-cavity system. (a) Time-delay setup for producing pulses at a separation of $\Delta t$. (b) Simulated interaction of two laser pulses, represented by the instantaneous intracavity photon number $⟨a^{†}a⟩$ as a function of the time delay $\Delta t$ between the two 40 ps long Gaussian pulses. Curves are calculated for a set of different rates of pure QD dephasing [13], ${\gamma }_d$, which causes a reduction of the transmission dips before and after the peak. Pure dephasing also causes a blurring of the spectral normal mode splitting [13], which in turn raises the transmission for increasing ${\gamma }_d$. (c) Pump-power dependence of the cavity transmission for coincident pulses repeating at 80 MHz. Different curves correspond to the average power of each of the pulses used in the experiment (averaged over 13 ns, the pulse repetition period). (d) Signal observed when the cavity-QD system is probed with two 40 ps long pulses as a function of their delay. When the two pulses have a temporal overlap inside the cavity (i.e., delay approaches zero), the QD saturates and the overall cavity transmission increases. The power in the single of the two pulses corresponds roughly to the 3.4 nW trace in (c). Best agreement is found with the theoretical plot for a pure dephasing rate ${\gamma }_d/2\pi \sim 5\mathrm{GHz}$ (the solid red line).