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Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography

Using far field optical lithography, a single quantum dot is positioned within a pillar microcavity with a 50 nm accuracy. The lithography is performed in-situ at 10 K while measuring the quantum dot emission. Deterministic spectral and spatial matching of the cavity-dot system is achieved in a single step process and evidenced by the observation of strong Purcell effect. Deterministic coupling of two quantum dots to the same optical mode is achieved, a milestone for quantum computing.

Using far field optical lithography, a single quantum dot is positioned within a pillar microcavity with a 50 nm accuracy. The lithography is performed in-situ at 10 K while measuring the quantum dot emission. Deterministic spectral and spatial matching of the cavity-dot system is achieved in a single step process and evidenced by the observation of strong Purcell effect. Deterministic coupling of two quantum dots to the same optical mode is achieved, a milestone for quantum computing. Quantum emitters such as quantum dots [1], colloidal quantum dots [2] or single fluorescent molecule [3] are usually randomly distributed on the surface of a substrate and suffer from broad inhomogeneous distributions of their spectral lines. Although spectral identification and spatial localization of individual quantum emitters is made possible using high resolution confocal microspectroscopy, the fabrication of devices involving dots of known position and spectral characteristics remains a serious experimental challenge. An example of such device is a quantum dot (QD) which emission and location is matched to an optical microcavity mode. Such devices are desirable for high throughput and directional single photon sources [4,5,6,7] and for building blocks for quantum computing [8,9,10,11]. A deterministic and scalable fabrication method allowing choosing a single QD of given spectral characteristics to be inserted in an optical device with an accuracy of few tens of nanometers is missing. This is a prohibiting barrier to the development of solid state quantum emitter devices as well as to comprehensive fundamental investigations of solid state cavity quantum electrodynamics (CQED). Earlier CQED investigations with single QDs or nanocrystals were based on statistical approaches by which several thousands of devices were fabricated [13,14,15,16,17]. It was left to pure statistics and prohibitively long searches to get the appropriate QD at the appropriate location of the cavity as the yield was in the low 10 −3 . Lately, the need for control of the QD-cavity matching has motivated many works [18,19,20,21,22,23]. In a pioneer work, Badolato and coworkers successfully demonstrated deterministic cavity-QD coupling [12]. The spatial positioning of the QD was achieved using several technological steps (AFM, electronic lithography) each requiring an alignment accuracy of the order of ten nanometer. The spectral matching was obtained thanks to several wet-etching steps, preventing the fabrication of more than one cavity-QD device on a given sample. In this letter, we show that a far field optical lithography can be used to position a single QD in a spectrally resonant pillar microcavity with an accuracy as high as 50 nm. The lithography is performed in-situ, while measuring the QD emission in a low-temperature photoluminescence set-up. The nano-positioning is obtained by using the single QD as a probe of a focused gaussian laser beam. The cavity-QD spectral matching is achieved in the same lithography step by selecting a QD of given spectral position and making use of the non-linearity of the resist exposure process. The efficiency of the technique is shown by the observation of large controlled Purcell effect. The flexibility of our technique allows to deterministically couple for the first time, two QDs to the same optical mode, a milestone for the implementation of many quantum computing schemes.
A low density layer of InAs self assembled QDs is grown by molecular beam epitaxy and located at the center of a λ-GaAs microcavity surrounded by two Al 0.1 Ga 0.9 As/Al 0.95 Ga 0.05 As Bragg mirrors with 20 (24) pairs. The quality factor of the planar microcavity is Q=4500. The planar cavity is spin coated with a positive photoresist and inserted in a helium flow cryostat mounted on a motorized positioning system with piezoelectric actuators, providing a 20 nm accuracy. Two laser beams are focused onto the same area of the sample with a microscope objective. A red laser beam (750 nm< λ <830 nm) is used to measure the QD emission, without affecting the photoresist, while a green laser beam (λ=532 nm) is used to expose the photoresist (Fig.  1). The focusing of the two beams and their superposition is checked using a monitor camera with a x200 magnification.
The red excitation gives rise to a photoluminescence (PL) emission which is spectrally analyzed using a spectrometer and a charge coupled device camera. The QDs emission is filtered by the planar cavity mode which energy E c (θ) blueshifts with the collection angle θ [25]. As a result, QD emission within a 15 meV spectral range can be observed, corresponding to the 0.5 numerical aperture of our microscope objective. The typical PL spectrum in Fig. 1.c. shows a background emission between 1.344 eV and 1.359 eV corresponding to an emission in the cavity mode for collection angles between θ = 0 • and θ max = 30 • . The single QD exciton (X) emission appears as discrete lines. By scanning the sample position in a few micrometer range, a QD is selected. The sample position is then scanned with respect to the excitation spot with a 20 nm accuracy. The inset in Fig. 2.a. shows a mapping of the selected X emission intensity as a function of the sample position, measured below the X saturation [26]. Fig. 2.a. shows an intensity profile of the mapping along the dotted line indicated in the inset. The QD X emission presents a gaussian like intensity dependence with a width around 1µm, reflecting the laser gaussian profile. The same measurement is performed for various focusing. Fig. 2.b. shows that the QD PL intensity width is directly given by the size of the excitation spot. This observation indicates that the capture into the QD is highly efficient and diffusion outside the excitation spot negligible. Indeed Fig. 2c shows that the gaussian dependence is unchanged for excitation energy E exc between 1.5 eV and 1.6 eV and only slightly broadens for 1.65 eV . Scattering outside the excitation spot only manifests itself by a stronger signal outside the excitation spot.
Mapping the QD signal allows to determine the QD position by pointing the maximum of the QD X emission, as shown in Fig. 2.a. With a zero noise to signal ratio, we would get an accuracy limited by the QD lateral size. With the noise to signal ratio of our setup (0.4 %), moving the QD within 50 nm from the center of the excitation spot results in no measurable change in the QD signal. As a result, the QD position is pointed with a ±50 nm accuracy. This accuracy could be further improved by using sharper excitation beam profile or by monitoring a non-linear optical transition of the QD as shown in Fig. 2.e. The biexciton (XX) spatial dependence (red scatter line), is given by the square of the exciton spatial dependence (red line) [24]. When a QD of desired energy is selected and its emission intensity maximized to position the QD at the very center of the red spot, the green laser is switched on to expose the resist. The exposed area will later be used directly to define the pillar microcavity. This first step ensures the positioning of the QD at the maximum of the pillar fundamental mode.
To reach the spectral matching, one needs to adjust the pillar radius R. As shown in Fig. 3.a., the energy of the pillar fundamental mode increases as the radius decreases [27]. For the example presented in Fig. 1.c., the energy of the selected QD exciton is E X =1.350 eV and would be resonant to the fundamental mode of a pillar with R=1 µm. The key to achieve spectral matching is to expose the resist for a well chosen time. Indeed, the chemical change in the resist depends on the exposure dose in a non-linear way. Since we use a gaussian laser beam, the size of the exposed area increases with expo-sure time or laser power. The radius of the developed resist area is presented on Fig. 3.b. as a function of the exposure time for a fixed laser power. Radii ranging from below 0.5 µm to 1.5 µm are reached. Thus, to match the QD selected in Fig. 1.c., the sample is exposed for 30 s in order to obtain a 1 µm radius pillar. After exposing the resist for several QDs, the photoresist is developed, leaving circular holes centered on the selected QDs. After a lift off step, these holes define the mask to fabricate the pillar through chloride reactive ion etching. A scanning electron microscopy image of pillars of various radii designed to match QDs of various energies is presented in Fig. 3.c. Fig. 3.d. shows the obtained mode energy as a function of the target mode energy. A standard deviation as small as 0.65 meV is achieved limited by the verticality of the pillar sidewall and the accuracy of the green laser focus. Finally, Fig. 3.e. presents the quality factor Q of the pillars and their Purcell factor F p . A mean F p of 6.4 is achieved. The standard deviation of 1.4 is mainly caused by oscillations of Q predicted in [28]. Yet, obtaining homogeneous F p is not critical to achieve large scale integration of efficient single photon sources: the extraction efficiency F p /(F p + 1) is close to 1 for F p ≫ 1.
To prove the high quality of the cavity−exciton spatial matching, optical measurements are performed on the pillars. The PL spectrum of a selected QD is shown in Fig. 4.a during the lithography step (bottom). For this QD, the exposure time was chosen to obtain a pillar with R=0.85 µm (pillar 1), to match the exciton energy of 1.35 eV. The middle and upper parts of Fig. 4.a. present the PL spectra measured at 10 K and 32 K after etching. At 10 K, the X emission is greatly enhanced and the fundamental optical mode (M) of the pillar appears as a base to the X line. Spectral matching is reached at 10 K, as intended. When increasing temperature up to 32 K, the two lines become detuned [15] and well resolved. To get a better insight, PL spectra were acquired over a continuous range of temperatures from 18 K to 32 K (Fig. 4.b.). A strong increase of the QD emission is observed at resonance with the optical mode, showing the acceleration of the radiative lifetime for the X [12]. The linewidth of the optical mode out of resonance is γ c =0.89 meV (Q=1500) so that the expected Purcell factor for a QD perfectly matched to the optical mode is 8.5 [29]. To estimate the actual F P experienced by the QD, we follow the method presented in [30]. The maximum X PL signal at saturation is measured as a function of the X−cavity detuning ∆ (Fig. 4c). This maximum intensity is proportional to p sat X (∆) F P,∆ , where p sat X (∆) is the occupation probability of the QD exciton at saturation and F P,∆ is the Purcell factor depending on detuning [30]. F P is the maximum Purcell factor for the QD at exact spatial and spectral resonance with the optical mode. We take F P,∆ = FP experimental data gives F P = 9±3, close to the expected value, showing the high quality of the QD spatial matching to the optical mode. Indeed, considering an accuracy of 50 nm for the spatial positioning of the QD, we calculate that the QD is at least at 98 % of the maximum of the mode intensity. This value remains as large as 94 % for a 0.5 µm radius pillar .
We now demonstrate that our technique can be used to couple two QDs to the same optical mode in a deterministic way. During the lithography step, two QDs can be found to be close to each other both spectrally and spatially. As in the case of a single QD, our method can be used to define a resonant pillar embedding both QDs: as the QD positions are identified, the resist is exposed with the laser spot centered halfway between both QDs. This is what has been implemented for two QDs found to be located 500 nm apart and presenting exciton resonances separated by 300 µeV (Fig. 4d). Both QDs were inserted in a R=0.95 µm radius pillar (pillar 2). After etching, the emission of both QDs is slightly detuned from the pillar mode at 10 K. At 46 K, when bringing the two Xs close to resonance with the optical mode, an increase of both X emissions is observed (top spectrum). Fig. 4e. displays the temperature dependence of the emission spectra measured between 45 K and 57 K which highlight the crossing of both lines with the optical mode. For both QDs, a strong increase of the signal is observed at resonance (47 K for QD1 and 49 K for QD2), showing that both Xs experience a Purcell effect. Fig. 4.f. shows the normalized signal at saturation for both QDs, as a function of their detuning with the optical mode [31]. Both QDs present the same signal variation as a function of detuning, proving that we  Bottom : PL spectrum measured during the photolithography process at 10 K. Middle and top : PL spectra of pillar 1 (resp. pillar 2) after etching at 10 K and 32 K (resp. 46 K)(a lorentzian fit to the mode M is also shown). b: (resp. e:) PL spectra between 18 K and 32 K (resp. 44 K and 54 K) measured on pillar 1 (resp. pillar 2). c: Pillar 1: Circles : PL intensity of the X line measured at saturation as a function of detuning with the optical mode : ∆ = EM − EX . Line : fit to the data with FP = 9±3. f: Pillar 2: Squares (circles): PL intensity measured at saturation of the QD1 (QD2) X line as a function of detuning with the optical mode : ∆ 1(2) = EM − E QD1 (2) . Line : fit to the data with FP =6.5±2.5 for both QDs.
have succeeded in equally coupling two QDs to the same optical mode. The fit to the data gives F P = 6.5 ± 2.5 for both QDs. The quality factor of this pillar is Q=2350 (γ c =0.57 meV) so that the maximum F p is supposed to be 9. Since the QDs have been located 250 nm away from the centre of the pillar, their overlap to the fundamental mode is reduced to 82%, so that the expected F p is 7.3, very close to the measured value.
In conclusion, we have shown that in-situ far field optical lithography can be used to achieve both the spatial and spectral matching of a single QD with a pillar microcavity. A dozen devices have been fabricated on the same sample, within a single lithography step. Each device evidences a strong Purcell effect, showing the scalability of the technique. For the present sample, we intentionally decided to match quantum dot of various energies to show the flexibility of the spectral tuning. To go toward large scale integration of efficient single photon sources, the present technique could be automatically operated to select QDs within a narrow spectral range and fabricate arrays of cavity-QD devices at the desired wavelength. Processing higher quality factor planar cavities [32] will straightforwardly lead to scalable deterministic strong coupling regime. This technique could also be used to register many kinds of nanostructures in an easy, flexible and scalable way.
This work is partially supported by the ANR MICADOS and the SANDIE European Network. The authors thank P. Voisin and K. Karrai for fruitful discussions.