{"id":116369,"date":"2025-05-20T06:27:22","date_gmt":"2025-05-20T06:27:22","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/116369\/"},"modified":"2025-05-20T06:27:22","modified_gmt":"2025-05-20T06:27:22","slug":"cavity-quantum-electrodynamics-with-moire-photonic-crystal-nanocavity","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/116369\/","title":{"rendered":"Cavity quantum electrodynamics with moir\u00e9 photonic crystal nanocavity"},"content":{"rendered":"

Design and optimization of moir\u00e9 superlattice structures<\/p>\n

The MPhC superlattice is composed of two layers of photonic crystals twisted at a specific angle. As the twist angle decreases, the size of the unit cell of the superlattice increases37<\/a>. However, the field distribution of fundamental modes remains essentially the same37<\/a>. The Q\/V ratio of fundamental modes of the MPhC nanocavity increases sharply as the twist angle decreases. It is worth noting that an MPhC nanocavity with Q factor exceeding 1 million has been demonstrated recently at a small twist angle42<\/a>. A smaller twist angle results in a higher Q factor, but the resonance wavelength of MPhC nanocavity redshifts. It requires smaller lattice constants and airhole radii for resonance with QDs, which makes the device more difficult to fabricate. Generally, a trade-off must be made between fabrication feasibility, the twist angle, and the number of moir\u00e9 layers. To match the photoluminescence (PL) of the QDs, we designed the MPhC superlattice with a twist angle of 6.01\u00b0, as shown in Fig.\u00a01<\/a>a. The design principle of MPhC nanocavities is discussed in Supplementary Note\u00a01<\/a>. The fabricated moir\u00e9 superlattices are finite in size, resulting in different surrounding environments for each unit cell. Therefore, the superlattice is divided into four types of nanocavities with different spatial equivalence, which are marked in red (A), black (B), blue (C), and gray (D) in Fig.\u00a01<\/a>a, respectively. Figure\u00a01<\/a>b depicts the band structure of the twisted nanocavity calculated by the time-domain finite-difference method where the lattice constant of the single-layer photonic crystal a is 302\u2009nm, the radius of the airhole r (0.238a) is 72\u2009nm. The red dots in the bandgap show the band of orthogonal degenerate fundamental (1st) modes. Other higher-order (2nd, 3rd) modes also appear in the bandgap. Figure\u00a01<\/a>c shows the spectrum of the nanocavity obtained from the simulation, where P1 are the orthogonal degenerate fundamental modes, and P2-P4 are the higher-order modes. The corresponding field distributions as well as Q, V are shown in Fig.\u00a01<\/a>d. The fundamental modes have both high Q and ultra-low V. Although the higher-order modes have high Q but a relatively larger V, therefore, we take advantage of the fundamental modes to study CQED. Figure\u00a01<\/a>e shows the Q and V of the four different types of cavities from the same moir\u00e9 superlattice structure. The Q of fundamental modes from cavities A and B are higher than those from cavities C and D, while their V do not show a big difference, ~0.35(\u03bb\/n)3.<\/p>\n

Fig. 1: Structure and cavity mode properties of MPhC superlattices.<\/b>\"figure<\/a><\/p>\n

a<\/b> Schematic of the MPhC superlattice. A, B, C, and D represent different types of cavities marked in different colors. b<\/b> Band structure of the twisted nanocavity with a lattice constant of a\u2009=\u2009302\u2009nm and radius of r\u2009=\u200972\u2009nm. c<\/b> The spectrum of different cavity modes labeled by P1\u2013P4 of the nanocavity obtained from the simulation. d<\/b> The corresponding field distributions, Q and V of different modes corresponding to (c<\/b>), where Px and Py are the orthogonal degenerate fundamental modes. e<\/b> The theoretical Q and theoretical V of fundamental modes for different types of nanocavities.<\/p>\n

To observe the effective coupling of QDs with MPhC nanocavities experimentally, we optimize the Q and the effective area of the fundamental modes, focusing on cavity A. The effective area is defined as the region within GaAs where the electric field strength exceeds half of the maximum field strength. The Q and the effective area are optimized by tuning the lattice constants a and simultaneously fixing the hole radius r of the single-layer photonic crystal slab, which means the filling ratio is changed, as shown in Fig.\u00a02<\/a>a, b. In Fig.\u00a02<\/a>a, the black and red lines represent the theoretical V and Q of the fundamental modes for different a values. With r fixed at 72\u2009nm, the Q increases as a increases, while V remains ~0.39(\u03bb\/n)3. When a\u2009=\u2009314\u2009nm, the Q of the fundamental modes can reach 105. In Fig.\u00a02<\/a>b, the effective area increases from 11,500\u2009nm2 to 15,500\u2009nm2 as a increases, with an improvement of ~35% for the Px fundamental mode. Figure\u00a02<\/a>c, d shows the mode profile of the effective area for the Px mode when a is 298\u2009nm and 314\u2009nm, respectively. The effective area of the Px mode is noticeably larger for a\u2009=\u2009314\u2009nm compared to a\u2009=\u2009298\u2009nm, thereby enabling a larger possibility to achieve QD-cavity coupling. The optimization for Py mode is described in Supplementary Note\u00a02<\/a>. Optimizing the effective area of MPhC nanocavity is a major direction for the future. Our work offers valuable insights for other researchers to develop applications based on these high Q\/V nanocavities. The increase in effective area also allows the position of the QDs to be further away from the GaAs\/vacuum interface. Therefore, fewer QDs will be affected by detrimental factors such as surface charge fluctuations55<\/a>.<\/p>\n

Fig. 2: Optimization of fundamental modes in moir\u00e9 nanocavities.<\/b>\"figure<\/a><\/p>\n

a<\/b> The theoretical Q and V of fundamental modes for different a. b<\/b> The effecitve area of Px fundamental mode with different a. c<\/b>, d<\/b> The cavity mode profile of effective area (blue) of Px fundamental mode when a is 298\u2009nm and 314\u2009nm with r\u2009=\u200972\u2009nm.<\/p>\n

PL spectroscopy of moir\u00e9 nanocavities<\/p>\n

Figure\u00a03<\/a>a shows the scanning electron microscope (SEM) image of a MPhC nanocavity. The photonic crystal slab with a thickness of 150\u2009nm sandwiches a single-layer of InGaAs QDs in the center, which functions as quantum emitters at near-infrared wavelengths. The structure fabrication process is shown in Supplementary Note\u00a03<\/a>. To investigate the coupling between single QDs and nanocavities, the density of QDs is required to be low enough, which is less than 10\u2009\u03bcm\u22122 in this work. The moir\u00e9 nanocavities are mounted in a liquid helium flow cryostat for the confocal micro-PL measurement. QDs and MPhC nanocavity modes are excited by a 532\u2009nm continuous-wave laser. Even when the cavity mode is detuned from the QDs, photons in the cavity mode are generated by the emission from the ensemble of QDs with the assistance of phonons56<\/a>,57<\/a>. The PL signals are detected by a charged-coupled device camera with a spectral resolution of 60\u2009\u03bceV. The collected PL spectrum from cavity A with a\u2009=\u2009310\u2009nm, r\u2009=\u200972\u2009nm, and \u03b4d\u2009=\u20094\u2009nm is shown in Fig.\u00a03<\/a>b. Px and Py are the split fundamental modes, and P2, P3, and P4 are the higher-order modes, as shown in Fig.\u00a01<\/a>c.<\/p>\n

Fig. 3: Characterization of MPhC nanocavities.<\/b>\"figure<\/a><\/p>\n

a<\/b> SEM image of a MPhC superlattice structure. b<\/b> The collected PL spectrum from cavity A with a\u2009=\u2009310\u2009nm, r\u2009=\u200972\u2009nm, and \u03b4d\u2009=\u20094\u2009nm. The inset shows the polarization diagram of fundamental modes. c<\/b> Average experimental Q of two split peaks from different types of nanocavities of the superlattice structure, where error bars represent the mean deviation. d<\/b> The experimental PL spectra from different cavities in the same superlattice structure. The spectra are shifted for clarity.<\/p>\n

The wavefunctions of the fundamental modes are localized in the center of the nanocavity, spatially separated from the fundamental modes of the surrounding cavities, which ensures independent collection of PL for different types of MPhC nanocavities. The polarization diagram of Px and Py modes is shown in the inset of Fig.\u00a03<\/a>b. The pair of fundamental modes is linearly polarized and orthogonal to each other37<\/a>,38<\/a>,51<\/a>. The two peaks are theoretically degenerate, but the degeneracy is lifted because the fabricated circular air holes are not ideal with the C6 symmetry breaking, which is also verified by the numerical simulation, as shown in Supplementary Note\u00a04<\/a>.<\/p>\n

Figure\u00a03<\/a>c shows Q of Px and Py peaks from different spatial types of nanocavities in the moir\u00e9 superlattice structure. In the experiment, the Qs of two peaks from cavity A and cavity B are similar and twice higher than those from cavity C and D. The collected PL spectra from different cells in the MPhC superlattice structure are shown in Fig.\u00a03<\/a>d. The spectra of the nanocavities exhibit similar PL peak profiles, but the mode wavelengths of each nanocavity differ, suggesting the existence of slight local differences while maintaining the global bilayer twisted lattice coupling effect.<\/p>\n

The schematic diagram of the outermost layer of the nanocavity structure is shown in Fig.\u00a04<\/a>a. Due to the C6 symmetry of the nanocavity structure, there are three different types of adjacent airhole pairs with spacings labeled as D1, D2, and D3. The outermost air holes of the nanocavity are close to each other due to the rotation configuration of the bilayer photonic crystal. The retained GaAs is not enough to support the entire bilayer twisted photonic crystal structure, making it challenging to fabricate suspended MPhC nanocavities successfully37<\/a>,42<\/a>. To solve the problems, two methods are used to optimize the MPhC structures. One method is to tune the lattice constant of the single-layer photonic crystal, as shown in Fig.\u00a04<\/a>b. Another method is to reduce the relative distance between each pair of air holes in the outermost layer while maintaining the C6 symmetry, as shown in Fig.\u00a04<\/a>c. As the lattice constant a increases from 298\u2009nm to 314\u2009nm or the displacement distance \u03b4d increases from 0\u2009nm to 16\u2009nm, the retained GaAs material marked by the red box in Fig.\u00a04<\/a>b, c increases, so that the outermost layer has more GaAs material to support the entire structure. The experimental results from MPhC superlattice structures with different superlattice period numbers are presented in Supplementary Note\u00a05<\/a>.<\/p>\n

Fig. 4: MPhC nanocavity structure and fundamental mode characteristics with different a and \u03b4d.<\/b>\"figure<\/a><\/p>\n

a<\/b> The schematic diagram of the outermost layer of the nanocavity structure. b<\/b> Enlarged SEM images of the outermost layer of the nanocavity structure for different a of the fabricated photonic crystal structures, where the scale bar is 0.4\u2009\u03bcm. c<\/b> Enlarged SEM images of the outermost layer of the nanocavity structure with different displacement distances \u03b4d, where the scale bar is 0.4\u2009\u03bcm. d<\/b>, e<\/b> Average wavelengths of two split fundamental modes for different a and \u03b4d, where error bars represent the mean deviation. f<\/b>, g<\/b> Average Qs of two split fundamental modes for different a and \u03b4d, where error bars represent the mean deviation. All the structures here have air holes with r\u2009=\u200972\u2009nm for the single-layer lattice.<\/p>\n

The wavelength and Q fitted through the Lorentz line shape of Px concerning a and \u03b4d are shown in Fig.\u00a04<\/a>d, f. As a increases, the cavity central wavelength is redshifted, and the Q increases. Take an example, with \u03b4d\u2009=\u20090, when a increases from 298\u2009nm to 314\u2009nm, the wavelength is redshifted from 968\u2009nm to 1022\u2009nm, and Q improves from 800 to 1700. As \u03b4d increases, the wavelength is blue-shifted. The relation between Q and \u03b4d varies according to the lattice constant. When a is small, Q improves as \u03b4d increases, e.g., when a\u2009=\u2009298\u2009nm, Q improves from 810 to 1300 as \u03b4d increases from 0\u2009nm to 16\u2009nm. When a is large, the increase in Q is not obvious as \u03b4d increases. When a\u2009=\u2009314\u2009nm, \u03b4d\u2009=\u200916\u2009nm, Q can reach ~2000. The results for Py mode with a and \u03b4d are similar to those of Px, as shown in Fig.\u00a04<\/a>e, g. The simulation results and experimental PL spectra of MPhC nanocavities with varying \u03b4d are shown in Supplementary Note\u00a07<\/a>. We have also investigated the wavelength fluctuations of different MPhC nanocavities of the same cavity type in one superlattice. The mode fluctuations of the fundamental modes are ~6\u2009nm (Supplementary Note\u00a06<\/a>), which is similar to the fluctuation range of robust topological corner states13<\/a>.<\/p>\n

Purcell enhancement of single quantum dots<\/p>\n

To investigate the interaction between single QD and the nanocavity, we use a low-excitation power of 15\u2009\u03bcW to pump the sample so that the QDs and the cavity appear simultaneously on the PL spectrum. Figure\u00a05<\/a>a shows the PL spectra of the QD crossing the nanocavity fundamental mode by varying the temperature. Figure\u00a05<\/a>b shows the Lorentz fitting results of the area intensity of the QD in Fig.\u00a05<\/a>a. As the QD-cavity mode detuning \u0394E changes from negative to positive, the area intensity of the QD PL first increases and then decreases. The asymmetry in the QD emission intensity with respect to the QD-cavity mode detuning is the result of ramping up of nonradiative losses, such as the Auger effect and phonon emission58<\/a>,59<\/a>. When \u0394E is \u22121.15\u2009meV, the area intensity of QD is ~1.8. When the QD is in resonance with the cavity mode, the area intensity of QD is ~15.1, indicating the Purcell enhancement for weak coupling between the QD and the cavity. The fitted intensities and wavelength variations with temperature of the QDs corresponding to the spectra in Fig.\u00a05<\/a>a are presented in Supplementary Note\u00a08<\/a>. We can see that the area intensity of the QD is enhanced by a factor of ~8.4 when the QD is in resonance with the nanocavity mode. Other typical PL spectra of QDs and MPhC cavity modes at different detunings are presented in Supplementary Note\u00a09<\/a>.<\/p>\n

Fig. 5: Purcell effect and single-photon emission characteristics of single QDs coupled to MPhC nanocavities.<\/b>\"figure<\/a><\/p>\n

a<\/b> PL spectra of the QD as it is tuned across the MPhC nanocavity with a\u2009=\u2009310\u2009nm and \u03b4d\u2009=\u200916\u2009nm by changing the measurement temperature. b<\/b> The fitted intensity of the QDs corresponding to the spectra in (a<\/b>), where \u0394E is the QD-cavity mode detuning energy. c<\/b> The decay curves of QDs in bulk material, non-resonance, and resonance with the cavity and the IRF of system. d<\/b> The statistical analysis of the lifetimes for QDs in bulk, in resonance, and non-resonance with MPhC nanocavities. The black line is the average lifetime of QDs in bulk. e<\/b> Second-order correlation measurement of single photons emitted by the QD in bulk (left) and the QD coupled with MPhC nanocavities (right).<\/p>\n

To further confirm the Purcell enhancement factor, we implemented time-resolved PL spectroscopy for QDs in different conditions. Figure\u00a05<\/a>c shows the raw fluorescence decay data for QDs under different conditions. The black dots show the typical decay curve of a QD in bulk material (\u03c4Bulk\u2009=\u2009906\u2009\u00b1\u2009150\u2009ps). The red dots correspond to the decay curve of the QD that is nonresonant with the MPhC cavity mode (\u03c4Non\u2009=\u20092500\u2009\u00b1\u20099\u2009ps). The blue dots correspond to the decay curve of QD in resonance with the cavity (\u03c4In\u2009=\u2009282\u2009\u00b1\u20097.7\u2009ps). To confirm that the observed variation in the QD spontaneous emission rate is primarily due to the coupling with the nanocavity as the temperature changes, a control experiment is presented in Supplementary Note\u00a011<\/a>. The lifetime decay curve of the QD in resonance with the MPhC nanocavity mode exhibits the biexponential decay behavior, where the fast decay component of the decay curves is caused by the Purcell enhancement60<\/a> and the slow decay component might be due to QD refilling by carriers captured from charge centers and surrounding excitonic bath61<\/a>. The decay rate of the QD in resonance with the cavity exhibits an enhancement with a factor of three compared to the QD in the bulk material, which is limited by the instrument response function (IRF) of the system (\u03c4IRF\u2009=\u2009288\u2009\u00b1\u20098.0\u2009ps, gray dots). Since the lifetime of the QD in resonance with the cavity modes is close to the IRF of the system, it is difficult to obtain convincing results by deconvolution. To show the potential of our system for future applications62<\/a>, we calculate the theoretical Purcell factor using both experimental Q and theoretical Q. When the dipole is located >50\u2009nm from the edge of the center hole, the calculated Purcell factor ranges from 50 to 233 when using the experimental Q. More details are shown in Supplementary Note\u00a010<\/a>.<\/p>\n

To further explore the CQED effect, we have conducted a statistical analysis of the lifetimes of multiple QDs in different conditions, as shown in Fig.\u00a05<\/a>d.The black line denotes the fitted average lifetime value (~906\u2009ps) of the QD lifetimes in the bulk material (~140 QDs). The red dots represent the lifetime statistics for QDs embedded in the MPhC superlattice structures, which are not resonant with the cavity mode. In this case, the spontaneous emission from the QDs is suppressed due to the presence of the photonic bandgap of the MPhC superlattice structures, resulting in a longer lifetime compared to the QDs in bulk material. The blue dots represent the lifetime statistics of QDs in resonance with the cavity mode. We observed that the spontaneous emission rates are either suppressed or enhanced for QDs, depending on their interaction with the bandgap or the cavity mode, respectively. Some of the lifetime measurement results are presented in Supplementary Note\u00a012<\/a>, including those for Purcell-enhanced QDs (Supplementary Fig.\u00a013<\/a>) and radiation-suppressed QDs (Supplementary Fig.\u00a014<\/a>). The observed Purcell effect in experiments is further discussed in Supplementary Note\u00a013<\/a>. We have evaluated the quantum efficiency by assuming the value of the nonradiative decay rate from 0.01\u2009\u03bceV to 0.1\u2009\u03bceV63<\/a>. The corresponding efficiency without (with) Purcell effect ranges from 0.9397 (0.9930) to 0.9939 (0.9993) in Supplementary Note\u00a014<\/a>. This result suggests the Purcell factor is high enough for a range of applications, such as single-photon sources and low-threshold lasers.<\/p>\n

Finally, we performed second-order correlation (g2)\u00a0measurement to demonstrate the enhanced single-photon emission by coupling the QD with the MPhC nanocavity. Left panel in Fig.\u00a05<\/a>e is the g2 of the bulk QD, exhibiting a g2(0) of 0.65 before deconvolution. In contrast, right in Fig.\u00a05<\/a>e shows the g2 of the QD resonant to the cavity mode. The linewidth of the fitted curve is narrower than that of the QD in bulk, where the linewidth reflects the lifetime of exciton emission. The value of g2(0)\u2009=\u20090.28\u2009\u00b1\u20090.10 is obtained, which confirms the single-photon emission from the QD and the improvement of single-photon emission by the MPhC nanocavity. We emphasize that the time-resolved spectroscopy in Fig.\u00a05<\/a> is limited by the convolution of IRF. The actual Purcell factor could be higher, and the actual g2(0) should be smaller than the values extracted from the raw spectra. Nonetheless, the comparison between the QDs in different conditions clearly demonstrates the Purcell effect from the cavity-QD coupling.<\/p>\n","protected":false},"excerpt":{"rendered":"Design and optimization of moir\u00e9 superlattice structures The MPhC superlattice is composed of two layers of photonic crystals…\n","protected":false},"author":2,"featured_media":116370,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[3965,3966,74,15191,70,15579,16,15],"class_list":{"0":"post-116369","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-humanities-and-social-sciences","9":"tag-multidisciplinary","10":"tag-physics","11":"tag-quantum-optics","12":"tag-science","13":"tag-single-photons-and-quantum-effects","14":"tag-uk","15":"tag-united-kingdom"},"share_on_mastodon":{"url":"","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/116369","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=116369"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/116369\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/116370"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=116369"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=116369"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=116369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}