Investigations of a coherently driven semiconductor optical cavity QED system

Chip-based cavity quantum electrodynamics (QED) devices consisting of a self-assembled InAs quantum dot (QD) coupled to a high quality factor GaAs microdisk cavity are coherently probed through their optical channel using a fiber taper waveguide. We highlight one particularly important aspect of this all-fiber measurement setup, which is the accuracy to which the optical coupling level and optical losses are known relative to typical free-space excitation techniques. This allows for precise knowledge of the intracavity photon number and measurement of absolute transmitted and reflected signals. Resonant optical spectroscopy of the system under both weak and strong driving conditions are presented, which when compared with a quantum master equation model of the system allows for determination of the coherent coupling rate between QD exciton and optical cavity mode, the different levels of elastic and inelastic dephasing of the exciton state, and the position and orientation of the QD within the cavity. Pump-probe measurements are also performed in which a far off-resonant red-detuned control laser beam is introduced into the cavity. Rather than producing a measurable ac Stark shift in the exciton line of the QD, we find that this control beam induces a saturation of the resonant system response. The broad photoluminescence spectrum resulting from the presence of the control beam in the cavity points to sub-band-gap absorption in the semiconductor, and the resulting free-carrier generation, as the likely source of system saturation.

Figure 1

(Color online) Schematics of the optical fiber taper waveguide coupling approach. (a) Aluminum mount used to hold the fiber taper and position it with respect to an array of microdisk cavities. (b) Zoomed-in region of the taper-cavity coupling region.

Figure 2

(Color online) Schematic of the experimental setup used for coherent optical probing with a $1300\mathrm{nm}$ tunable laser (solid lines) and optical pumping with a $980\mathrm{nm}$ pump laser (dashed lines). Optical component acronyms: fiber polarization controller (FPC), variable optical attenuator (VOA), single-mode fiber (SMF), $1300\mathrm{nm}$ band reflected signal photodetector $\left({\mathrm{PD}}_{R-1300}\right)$, $1300\mathrm{nm}$ band transmitted signal photodetector $\left({\mathrm{PD}}_{T-1300}\right)$, and $980\mathrm{nm}$ band transmitted signal photodetector $\left({\mathrm{PD}}_{T-980}\right)$.

Figure 3

(Color online) (a) Scanning electron microscope image of a $D=2.5\text{‐}\mu \mathrm{m}$-diameter microdisk cavity. (b) Photoluminescence spectrum from a microdisk under free-space $830\mathrm{nm}$ excitation ($150\mathrm{nW}$ incident pump power) and fiber collection. Emission from the excited and ground states of the QD ensemble is present from $1100\text{to}1310\mathrm{nm}$, punctuated by regions of sharp enhanced emission due to cavity modes. For $\lambda =1285–1310\mathrm{nm}$, isolated single QD emission is seen for a fraction of devices (15 %). In this device $(D=2\mu \mathrm{m})$, the cavity mode of interest is at $\lambda =1287\mathrm{nm}$, $15\mathrm{nm}$ blue detuned of an isolated QD exciton state.

Figure 4

(Color online) (a) Normalized fiber taper transmission scan of a typical ${\mathrm{TE}}_{1,14}$ cavity mode of interest at a temperature $T=15\mathrm{K}$. The pair of resonance dips is due to surface roughness which couples and splits the clockwise and counterclockwise propagating modes of the disk. (b) ${\mathrm{TE}}_{1,m}$ cavity mode $Q$ for a number of $D=2.5\mu \mathrm{m}$ disks in the $1300\mathrm{nm}$ band (○) at $T=15\mathrm{K}$, $1400\mathrm{nm}$ band (∗) at $T=298\mathrm{K}$, and $1500\mathrm{nm}$ band (×) at $T=298\mathrm{K}$.

Figure 5

(Color online) Fiber-collected PL spectrum under pumping of a $980\mathrm{nm}$ band WGM ($5\mathrm{nW}$ input power into the fiber taper). QD states are labeled as $X_a∕X_b$ (fine-structure split neutral exciton states), $X^{-}$ (negatively charged exciton), and $X^{2-}$ (double negatively charged exciton). The inset shows a normalized transmission scan of the cavity mode at $\lambda =1297.5\mathrm{nm}$. Sample $\text{temperature}=15\mathrm{K}$.

Figure 6

SEM images of microdisk cavities (a) after initial device fabrication, (b) after two steps of ${\mathrm{H}}_2{\mathrm{O}}_2∕{\mathrm{C}}_6{\mathrm{H}}_8{\mathrm{O}}_7$ etching, and (c) after 14 steps of ${\mathrm{H}}_2{\mathrm{O}}_2∕{\mathrm{C}}_6{\mathrm{H}}_8{\mathrm{O}}_7$ etching.

Figure 7

(Color online) (a) and (b) Transmitted and (c) and (d) reflected spectra from the cavity as a function of laser-QD detuning $\left(\Delta {\lambda }_{\mathrm{la}}\right)$ and cavity-QD detuning $\left(\Delta {\lambda }_{\mathrm{ca}}\right)$, under weak driving by the probe beam $(n_{\mathrm{cav}}⪡1)$ at $15\mathrm{K}$. Spectra are normalized to unity. The top plots (a) and (c) show a series of individual spectra, while the bottom plots (b) and (d) show a compilation of this data as an image plot.

Figure 8

(Color online) (a) Normalized (to unity) reflected spectra from the cavity as a function of laser-QD detuning $\left(\Delta {\lambda }_{\mathrm{la}}\right)$ and cavity-QD detuning $\left(\Delta {\lambda }_{\mathrm{ca}}\right)$. Normalized reflected (b) and transmitted (c) spectra over a zoomed-in region [dashed box region of (a)], where the cavity mode dispersively couples to the $X_b$ state.

Figure 9

(Color online) Normalized (to unity) transmitted [(a) and (b)] and reflected [(c) and (d)] spectra from the cavity as a function of dropped power into the cavity $\left(P_{\mathrm{d}}\right)$ at the cavity-QD detuning level marked “i” in Figs. 7a, 7c. Here, the spectra are plotted as a function of $\Delta {\lambda }_l$, the detuning from the short-wavelength resonance peak or dip. (e) Normalized transmission contrast $\left(\Delta T\right)$ vs $P_{\mathrm{d}}$ and average intracavity photon number $\left(n_{\mathrm{cav}}\right)$, taken at the dashed-line spectral position shown in (a).

Figure 10

(Color online) Illustration of the processes considered in modeling the microdisk-QD system.

Figure 11

(Color online) (a) Reflection spectrum from the QD-microdisk system near resonance [position (i) in Fig. 7c] under weak driving. The solid red line is the measured reflected power normalized to input power; the dashed blue line is a QME model of the system using the parameters listed in Table . (b)–(d) Experimental data (red solid line) and model plots (dashed lines) for variations of the parameters listed in Table as follows: (b) $\xi =\{0,0.25,0.5,0.75,1\}\pi$ corresponding to dotted green, dashed blue, dash-dotted cyan, dotted purple, and dashed black lines, respectively, (c) ${\gamma }_{\perp }∕2\pi =({\gamma }_{\parallel }∕2)∕2\pi =(1∕2{\tau }_{\mathrm{sp}})∕2\pi =0.08\mathrm{GHz}$, and (d) ${\gamma }_{\perp }∕2\pi =({\gamma }_{\parallel }∕2+{\gamma }_p)∕2\pi =(1∕2{\tau }_{\mathrm{sp}}+{\gamma }_p)∕2\pi =0.97\mathrm{GHz}$.

Figure 12

(Color online) (a) Experimental data and (b) theoretical model of the normalized (to input power) reflected spectrum as a function of dropped power into the cavity $\left(P_{\mathrm{d}}\right)$ at the cavity-QD detuning level marked “i” in Fig. 7c. Here, the spectra are plotted as a function of $\Delta {\lambda }_l$, the detuning from the short-wavelength resonance peak or dip. (c) Mode splitting (circles) and peak reflection value (diamonds) as a fuction of $P_{\mathrm{d}}$ and $n_{\mathrm{cav}}$. Theoretical predictions are shown as dashed lines.

Figure 13

(Color online) (a) Normalized (to unity) transmission spectrum for the cavity studied in Sec. 5, for a detuning from the QD of $\Delta {\lambda }_{\mathrm{ca}}=-100\mathrm{pm}$. (b) Image plot of the transmitted spectra as a function of laser-QD detuning $\left(\Delta {\lambda }_{\mathrm{la}}\right)$ and cavity-QD detuning $\left(\Delta {\lambda }_{\mathrm{ca}}\right)$. (c) Series of transmission spectra for a zoomed-in region of $\Delta {\lambda }_{\mathrm{ca}}$. Sample $\text{temperature}=8\mathrm{K}$.

Figure 14

(Color online) (a) Image plot showing multiple unaveraged transmission spectra, all acquired under the same experimental conditions, for the device studied in Fig. 13 close to resonance $\Delta {\lambda }_{\mathrm{ca}}=0$. (b) Plot of scan 15 from (a), shown as a light-colored line, along with the average of all scans from (a), shown as a dark colored line. (c) Plot of the ensemble-averaged root-mean-square deviation between the single scan and averaged transmission data.

Figure 15

(Color online) (a) Schematic of the experimental setup and procedure used in pump-probe measurements. Acronyms for optical components are single-mode fiber (SMF), fiber polarization controller (FPC), variable optical attenuator (VOA), bandpass filter (BPF), tunable bandpass filter (TBPF), short-pass filter (SPF), photodetector for the $1300\mathrm{nm}$ band probe beam transmission $\left(\mathrm{P}{\mathrm{D}}_{T-1300}\right)$, and photodetector for the $1400\mathrm{nm}$ band ac Stark control beam transmission $\left(\mathrm{P}{\mathrm{D}}_{T-1400}\right)$. (b) Transmission scans of the (left) on-resonance cavity-QD system under weak driving $(n_{\mathrm{cav}}\approx 5\times {10}^{-3})$ and (right) $1488\mathrm{nm}$ ac Stark shift pump beam WGM. (c) Resonant transmission versus on-resonance probe power. Image plot of the normalized (to unity) transmission as a function of probe laser-QD detuning $\left(\Delta {\lambda }_{\mathrm{la}}\right)$ and probe beam strength [dropped power into the cavity $\left(P_{\mathrm{d}}\right)$ on the left axis and average intracavity photon number $\left(n_{\mathrm{cav}}\right)$ on the right axis], for the device studied in Fig. 13, at a cavity-QD detuning close to resonance $\Delta {\lambda }_{\mathrm{ca}}\approx 0$. (d) Resonant transmission versus ac Stark pump power. Image plot of the normalized (to unity) transmission spectrum as a function of probe laser-QD detuning $\left(\Delta {\lambda }_{\mathrm{la}}\right)$ and pump beam strength [dropped $1488\mathrm{nm}$ ac Stark pump beam power into the cavity $\left(P_{\mathrm{d},\text{pump}}\right)$ on the left axis and average intracavity pump photon number $\left(n_{\mathrm{cav},\text{pump}}\right)$ on the right axis], at a cavity-QD detuning close to resonance $\Delta {\lambda }_{\mathrm{ca}}\approx 0$.

Figure 16

(Color online) Comparison of the two saturation mechanisms discussed for the device studied in Fig. 13. The blue circles plot the scaled transmission contrast $\Delta T$ against $n_{\mathrm{cav}}$, where only a probe beam is applied. The red squares plot $\Delta T$ against $n_{\mathrm{cav},\text{pump}}$, where the probe power is fixed at $n_{\mathrm{cav}}\approx 0.005$ and the pump power is varied. The ordinate axis is scaled such that the range of transmission contrast is between the minimum and maximum measured values for each experiment. The unscaled values of $\Delta T_{\min }$ $\left(\Delta T_{\max }\right)$ are 0.22 (0.53) for the probe beam only measurement, and 0.26 (0.48) for the pump-probe measurement.

Figure 17

(Color online) (a) Integrated emission $\left(I\right)$ into the $1293–1296\mathrm{nm}$ wavelength region as a function of $P_{\mathrm{d},\text{pump}}$ and $n_{\mathrm{cav},\text{pump}}$. A least-squares fit assuming $I\propto {\left(P_{\mathrm{d},\text{pump}}\right)}^x$ yields $x\approx 1.5$. The inset shows the data plotted on a logarithmic scale. (b) Emission spectrum over a broad wavelength range for $P_{\mathrm{d},\text{pump}}=10\mu \mathrm{W}$.