Enhanced optical Stark shifts in a single quantum dot embedded in an H1 photonic crystal nanocavity

Photonic crystal (PhC) nanocavities embedded with semiconductor quantum dots (QDs) are one of the most promising platforms for studying cavity quantum electrodynamics (QED)¹⁾ and for developing solid-state classical and quantum information processing devices at optical frequencies. The strong optical confinement of PhC nanocavities both in time and space facilitates strong interactions between QD excitons and cavity photons,^2,3) providing a basis for developing low-power all-optical switches^4,5) and photonic quantum gates.⁶⁾ A robust approach to developing such devices is to use the enhanced optical Stark effect in the nanocavity,^5,7–12) which shifts the resonant frequencies of QD excitons under the irradiation of laser light. When applying the Stark shift to a coupled QD-cavity system in resonance, its optical transmission spectrum can be largely modified, thereby functioning as an optical switch upon external laser irradiation.⁵⁾ Moreover, the optical Stark shift occurs instantaneously and its amount can be controlled precisely, simply by tuning the laser power. These excellent properties have also enabled studies of ultrafast dynamics in QD cavity QED systems¹²⁾ and the generation of entangled photons.⁸⁾

In order to further exploit the optical Stark effect for the above-mentioned applications, it is essential to obtain a larger shift with a lower irradiated laser power. The Stark shift per irradiated laser power is proportional to ηQ/V, where η is the coupling efficiency of the external laser to the cavity mode, Q is the cavity Q factor, and V is the cavity mode volume. The latter two factors, i.e., Q/V, determine the Stark shift per intracavity photon under a given QD-cavity energy detuning condition. PhC nanocavities are known to be suitable for increasing Q/V and have indeed enabled a large Stark shift on the order of ten µeV with a few tens of intracavity photons.⁷⁾ Nevertheless, further improvement of the optical confinement of the nanocavities, i.e., increasing Q/V, is required for realizing optical devices operating in or close to the quantum regime. Moreover, little attention has been paid to improving η in order to maximize the Stark effect. A low η leads to wasting a large portion of the irradiated laser power, which not only degrades the energy efficiency in device applications, but also increases optical noise in actual experiments.

In this Letter, we demonstrate large optical Stark shifts in an H1-type point-defect photonic crystal nanocavity, which is designed to simultaneously possess a large η, a high Q, and a small V.¹³⁾ We observed an enhanced Stark shift of 70 µeV under the irradiation of a continuous wave (CW) laser with a power of 450 nW, which is roughly 2 orders of magnitude lower than that in the previous reports.⁷⁾ We found that a large shift occurs with only four intracavity photons on average, demonstrating that the H1 PhC nanocavity is a useful platform for developing ultralow-power quantum/classical optical devices using QD-based cavity QED.

Figure 1(a) shows a schematic of our H1-type PhC nanocavity. The point defect cavity is defined by a missing air hole in a triangular PhC lattice (lattice constant, a, of 260 nm) on a 130-nm-thick GaAs slab (refractive index n = 3.46). We modified the positions and sizes of air holes near the defect along the Γ–K direction, so as to increase Q and η.¹³⁾ We preserve the C₆ rotation symmetry of the design, such that the cavity supports doubly degenerated cavity modes, which are important for various cavity QED applications.^14,15) The first and third nearest neighbor air holes are shifted by Δ₁ = 0.12a and Δ₃ = −0.25a, respectively. In our previous study,¹³⁾ we found that the negative shift of the third air hole, Δ₃, is a key to increasing ηQ in the design. The radii of the air holes (r) are defined to be 0.3a, while the first and second nearest neighbor holes are shrunk to be $r'_{1} = 0.24a$ and $r'_{2} = 0.27a$, respectively. These modifications result in a Q factor of 61,000 and a small mode volume V of 0.47(λ/n)³ for the fundamental doubly degenerated dipole cavity modes resonating at a wavelength (λ) of 940 nm, calculated using a finite difference time domain algorithm. The two fundamental modes are cross-polarized with a large field overlap, such that the simultaneous coupling of an individual QD to both modes is possible. Figure 1(b) shows a calculated far-field profile of one of the fundamental modes. 35% of the far field is distributed within a numerical aperture (NA) of 0.65. The ratio of the field in the NA is roughly three times higher than that in the design without the shift in Δ₃, which will lead to an improvement in η.¹⁶⁾ All these properties are suitable for increasing ηQ/V for achieving a larger Stark shift with a lower laser power.

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We fabricated the designed cavity into a 130-nm-thick GaAs slab containing a layer of InAs QD with an areal density of 10⁹ cm⁻², using standard semiconductor nanofabrication processes. We set the fabricated sample into a temperature-controlled liquid-helium-flow cryostat (cooled to 4 K) and investigated its optical properties by using a micro-photoluminescence (PL) measurement setup. The optical carrier injection into the sample was performed using a CW titanium:sapphire laser oscillating at 800 nm. We also irradiated another laser light onto the sample using a tunable CW external-cavity diode laser (ECDL) to study the optical Stark effect. The two laser sources are merged by a beam splitter in the optical path and were focused onto the sample surface by an objective lens with a NA of 0.65. The PL signal from the sample was collected using the same objective lens and guided to a spectrometer (resolution ∼20 µeV) equipped with a liquid-nitrogen-cooled Si camera detector. We employed linear polarizers in order to suppress optical noise due to ECDL backreflection from the sample surface.

First, we investigated coupling properties between a single QD and the two fundamental cavity modes in a fabricated sample. Figure 2(a) shows a PL spectrum of the sample solely pumped with the carrier injection laser with a power of 300 nW. We observed two peaks from the dipole cavity modes (labeled C1 and C2) and a single QD. The Q factors are estimated to be 25,000 (cavity decay rate κ = 51 µeV) for the C1 mode and 28,000 (κ = 47 µeV) for the C2 mode. The observed mode splitting in the spectrum and the degraded Q factors compared with the numerical calculations are considered to arise from fabrication imperfections. Figure 2(b) shows a color map of spectra measured with various cavity resonant frequencies with respect to the QD emission peak. The cavity-mode frequencies were tuned by the gas condensation technique.¹⁷⁾ At the two crossing points of the QD with the C1 and C2 modes, clear anticrossings were observed, suggesting that the QD is in a strong coupling regime with both cavity modes. We deduced the coupling constant g ($\propto \sqrt{V}$) between the QD and the C1 (C2) mode to be 109 µeV (126 µeV). These large g values were made possible by the small V and are among the highest values ever reported for InAs QDs in PhC nanocavities.^18–21)

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Then, we irradiated the ECDL light onto the sample and investigated its effects on the QD emission spectrum. For this measurement, we detuned the C1 mode to −0.8 nm from the QD and scanned the ECDL around the C1 resonance while continuing the optical carrier injection. The power of the ECDL, P_inc, was fixed at 560 nW (measured before the objective lens) and its polarization was set almost parallel to the C1 mode for better coupling between the external laser and the cavity. The PL spectra obtained by scanning the ECDL wavelength are summarized in Fig. 3(a). A clear redshift of the QD emission peak can be seen as the laser wavelength is tuned to the C1 mode resonance, suggesting the occurrence of the Stark effect. The shift of the QD peak position was well reproduced by a numerical calculation based on a quantum master equation, as shown by the blue solid line in Fig. 3(a). The simulation model was based on a two-level system coupled to two orthogonal cavity modes.

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Next, we investigated the ECDL power (P_inc) dependence of the QD resonance shift under the condition that the ECDL is tuned to the C1 mode resonance, which is detuned by −0.92 nm from the QD. The carrier injection condition was the same as in the prior experiments. Measured QD emission spectra are shown in Fig. 3(b). We observed a gradual redshift with increasing laser power, together with a broadening of the QD emission linewidth. We fitted the QD spectra with a Lorentzian peak function and found a linear linewidth broadening with respect to the ECDL power. This behavior coincides well with that predicted for the optical Stark effect reported in the literature.⁷⁾ We also studied the ECDL power dependence under another experimental condition that the C1 mode is detuned by +0.55 nm from the investigated QD peak while the ECDL is tuned to the C1 resonance. The measured spectra are shown in Fig. 3(c). In this case, we observed a gradual blue shift of the QD emission peak when increasing the ECDL power. The observed flip of the direction of the shift when changing the sign of laser detuning is also characteristic of the optical Stark effect. These experiments reveal that the observed QD shifts are caused by the optical Stark effect, excluding the possibility of other origins, such as sample heating.

Finally, we discuss the Stark shift per irradiated ECDL power as well as that per intracavity photon. Figure 4 is a plot of the Stark shift measured in the individual QD peak as a function of ECDL power under three different experimental conditions. Conditions (i) and (ii) correspond to the situations shown in Figs. 3(b) and 3(c), respectively. Under another condition (iii), the C2 mode is detuned +1.05 nm from the QD, while the ECDL is resonantly irradiated to the C2 mode aligned with the direction of laser polarization. Even under this condition using another cavity mode, we observed large optical Stark shifts with low irradiated powers. Meanwhile, the largest slope of 155 µeV/µW was obtained for condition (i); the value of this slope is roughly two orders of magnitude larger than that reported in the literature.⁷⁾ Moreover, the linear slope can be compared with a cavity QED model of the optical Stark shift,¹⁾ δ = 2n_cav(g²/κΔ), where Δ is the QD-cavity energy detuning and n_cav is the intracavity photon number, which is equal to ηP_inc/E_cav (E_cav is the energy of the single intracavity photon). Here, we neglected the influence of dephasing, which exists in the QD and is enhanced by the carrier injection, which was kept weak so as to minimize the disturbance to the system. Using this equation and the experimentally extracted values of g, κ, Δ, δ, and P_inc, we can deduce η to be 2.2%. We also estimated that the intracavity photon number at the ECDL power for the maximum Stark shift (δ = 70 µeV) was only 4, suggesting the possibility of ultralow energy per bit optical switching as well as photonic quantum gate applications. One peculiar observation in Fig. 4 is the larger Stark shifts under condition (i) than those under condition (ii) despite the larger Δ in (i). We consider this to be due to poor alignment when performing the measurements under condition (ii), confirming the importance of laser-cavity field overlap for efficiently inducing the optical Stark effect. In particular, we assume that the main cause of the alignment drift is the change in the objective lens focus, which could largely modify the optical coupling between the focused laser field and the nanocavity mode that is confined close to the diffraction limit. A similar discussion could be applicable for the measurements under condition (iii), in which we observed a lower slope of the shift despite using the C2 mode, which has a larger coupling constant with the QD than that of the C1 mode. These discrepancies in the alignment during the optical measurements should be suppressed to enable the correct experimental evaluation of η in the future. These analyses also suggest that the very large slopes of the Stark shift currently observed could be further improved by additional refinement of the optical setup, such as ECDL laser field shaping.

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In conclusion, we demonstrated a large optical Stark effect in a single QD coupled to an H1 PhC nanocavity, which was designed to simultaneously support a high Q factor, small V, and high η. We observed a large Stark shift of 70 µeV under an extremely low excitation laser power of 450 nW, which is roughly two orders of magnitude lower than those in the previous reports. The large shift was sustained by only four intracavity photons on average, paving the way for the development of ultralow-power quantum and classical optical devices.

Acknowledgments