Numerical Analysis of Photon Absorption of Gate-defined Quantum Dots Embedded in Asymmetric Bull's-eye Optical Cavities

arXiv:2304.05038 · physics.optics, cond-mat.mes-hall, physics.app-ph · Submitted 2023-04-11 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Numerical Analysis of Photon Absorption of Gate-defined Quantum Dots Embedded in Asymmetric Bull's-eye Optical Cavities".

Mira: The gist:

Kai: First, who's behind it and why it matters.

Title and authors: Kai: We started by looking at the title of this paper "Numerical Analysis of Photon Absorption of Gate-defined Quantum Dots Embedded in Asymmetric Bull’s-eye Optical Cavities" and the authors, Sangmin Ji and Satoshi Iwamoto.

Mira: The title tells us right away that they are numerically analyzing how photons get absorbed when a quantum dot is put inside an asymmetric bull's-eye cavity structure.

Lev: So what does that mean in practical terms for someone working on superconducting qubits or embedded QDs? What’s the big picture here?

Kai: It means we’re looking at how to make the coupling of light into a quantum dot more efficient, regardless of which way the light is pointing.

Mira: They are addressing that polarization dependence problem directly by showing that they can achieve this improvement without having to rely on specific polarization orientations for the light.

Lev: So it’s about making our interfaces more robust, less sensitive to how we orient the laser or photon source, which is a huge win for network systems.

Kai: They also mention that they are building on previous work where they showed this could improve absorption efficiency by a factor of more than four hundred with just the air-bridge bull's-eye cavity thirty-three <ref:2304.05038#pg2,by a factor of more than 400>.

Mira: So this isn't entirely new territory; they’re showing how to go further than what was already demonstrated in those earlier studies.

Lev: What’s the main thing this paper adds on top of that previous work?

Kai: This study numerically demonstrates that you can get a further sixteen times improvement in efficiency by just tweaking the distance of the substrate from the semiconductor slab where they form the bull's-eye structure.

Mira: That simple physical change—moving that substrate—is what unlocks this extra gain, and it points us toward a new lever for design.

Lev: So, we’re seeing a simple geometric adjustment leading to a significant performance increase in absorption efficiency for these embedded quantum systems.

Kai: It's about finding that specific geometry where the coupling dynamics get optimized for better photon capture.

Mira: This sets up the next part of our discussion about what that asymmetry actually does physically.

The paper's summary: Kai: So, let’s look at what the paper actually summarizes in this "Numerical Analysis of Photon Absorption of Gate-defined Quantum Dots Embedded in Asymmetric Bull’s-eye Optical Cavities".

Mira: They summarize that they used a specific cavity setup with a one hundred sixty-five nm thick semiconductor slab, which includes a fifteen nm thick GaAs quantum well and a GaAs substrate separated by Tgap distance.

Lev: So, what are the key parameters they are using to describe this system? What’s the technical setup?

Kai: The cavity is an air-bridge bull’s-eye cavity made of a six-period circular Bragg grating surrounding a circular cavity with diameter Ac equals a, and two straight channels crossing in the center.

Mira: And they use four gold metal lines, each thirty-six nm wide and forty nm thick as electrodes to define the structure <ref:2304.05038#pg2>.

Lev: And what’s the main goal of this modeling? What are they calculating specifically?

Kai: They are using temporal coupled-mode theory to get an analytical expression for the absorption efficiency of the quantum dot at its resonant wavelength lambda zero.

Mira: That expression involves SQD over Seff times eta far M, where Seff is an effective mode area defined by integrating UE(x, y) over x and y.

Lev: And then they define M as a rate matching between the QW and the GaAs substrate, which is given by four gamma abs gamma t (gamma t plus gamma b plus gamma abs) to the power of two.

Kai: That term M represents how well those different material components are matching up in terms of their decay rates.

Mira: The key finding they summarize is that the absorption efficiency oscillates with a period around half of the resonant wavelength, Tgap over lambda zero being about zero point five.

The paper's improvements: Kai: Now we get to the actual results and how these numbers compare to what they calculated directly.

Mira: They found that there's a nice agreement between their analytical expression and the direct calculations, which proves the analytical expression they discussed earlier is valid.

Lev: So what’s the most important quantitative result they report? What’s the efficiency gain?

Kai: At Tgap over lambda zero equal to zero point four where their in-phase condition is satisfied, the absorption efficiency of the QD at lambda zero is about sixteen times higher than it was for a cavity without a substrate <ref:2304.05038#pg3>.

Mira: That sixteen times enhancement is what they highlight when comparing the case with a substrate against the free-standing cavity.

Lev: So what's driving that big jump? What factors are they pointing to as the dominant drivers?

Kai: They clarify that upward directionality, Φ equals gamma t over gamma rad, plays a dominant role in this improvement.

Mira: The presence of the substrate acts like a partial mirror that reflects light and modifies the vertical coupling constant of the cavity.

Lev: So it’s not just one thing; it’s both how light couples vertically and how much of that reflected light overlaps with our excitation beam that matters.

Kai: They also show that the far-field spatial overlap, eta far, is favored by the substrate presence too.

Conclusion: Mira: So to wrap up this discussion on "Numerical Analysis of Photon Absorption of Gate-defined Quantum Dots Embedded in Asymmetric Bull’s-eye Optical Cavities".

Kai: The main implication is that substrate-induced asymmetry can improve absorption in a simple way by simply adjusting the distance between the substrate and the semiconductor slab.

Mira: They clearly show that this method works because of upward-preferred coupling and the narrow far-field emission pattern realized by that asymmetry.

Lev: So, for real hardware, what's our final word on applying these findings?

Kai: It suggests a simple design change can boost collection efficiency for photons emitted from a gated defined QD, which is useful for improving photon collection efficiency.

Mira: We also found that this substrate effect is applicable to other host materials of solid-state qubits, like bulk single-crystal diamonds.

Lev: I think the key here is that we need to realize that this asymmetry in cavity design can be a simple tool for boosting absorption performance across different qubit platforms.

Kai: We’ll move on next time, so keep an eye out for more papers from the arXiv.

SANGMIN JI, SATOSHI IWAMOTO

Institute of Industrial Science, the University of Tokyo · Research Center for Advanced Science and Technology, The University of Tokyo

physics.optics, cond-mat.mes-hall, physics.app-ph

Submitted: 2023-04-11

Updated: 2023-04-11

DOI: 10.1364/OPTCON.492718

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: The gist: The study numerically demonstrates that a further 1.6 times improvement in efficiency is possible by simply adjusting the distance of the substrate from the semiconductor slab where the

Key concepts

Bull's-eye cavity: This is a specific optical cavity structure designed with a circular Bragg grating surrounding a central circular cavity and two straight channels. It is used here to create an asymmetric environment that supports doubly degenerate modes, which are necessary for achieving polarization-independent light interaction.
Upward-preferred coupling ($\Phi$): This concept describes the directionality of light coupling within the system, defined as the ratio of transverse coupling constant ($\gamma_t$) to radial radiation constant ($\gamma_{rad}$). The substrate introduces this preference, meaning it favors light coupling in one specific vertical direction, which is crucial for enhancing absorption.
Rate matching ($M$): Rate matching refers to how well the cavity's internal decay rate matches the external coupling rates. In this context, $M$ quantifies how effectively the substrate modifies these rates. The analysis showed that improvements in $M$, rather than changes in other factors, are the primary drivers for increasing absorption efficiency.
Far-field spatial overlap ($\eta_{far}$): This term measures how well the spatial profile of the light mode inside the cavity overlaps with a Gaussian beam used to excite it. The presence of a substrate is shown to favor this overlap, meaning it helps concentrate the light more effectively into the QD, thereby boosting overall absorption efficiency.

Terminology

Entanglement — 5× in this paper · explained in 4 episodes
Fidelity — 2× in this paper · explained in 2 episodes
Momentum transfer — 2× in this paper · explained in 2 episodes
Papers — 1× in this paper · explained in 3 episodes
Quantum sensing — 1× in this paper · explained in 2 episodes
Superconducting Qubits — 1× in this paper · explained in 2 episodes

Summary

The gist: The study numerically demonstrates that a further 1.6 times improvement in efficiency is possible by simply adjusting the distance of the substrate from the semiconductor slab where the bull’s-eye structure is formed, clarifying that upward-preferred coupling and narrow far-field emission pattern realized by substrate-induced asymmetry enable this improvement

Model and cavity characteristics

The researchers considered a cavity structure involving a 165-nm-thick semiconductor slab comprising a 15-nm-thick GaAs QW (TQW = 15 nm, z = 0 at the center of the QW layer) and a GaAs substrate which is Tgap apart from the slab. The cavity structure used was an air-bridge bull’s-eye cavity comprised of a six-period circular Bragg grating surrounding a circular cavity with diameter Ac = a, with two straight channels crossing the center providing space for gate formation and enabling the air-bridge structure. The electrodes consisted of four gold metal lines, which were 36 nm wide and 40 nm thick. The C4v symmetry of the entire structure guarantees that the cavity supports doubly degenerate modes, which are essential for achieving a polarization-independent response.

Analytical expression for absorption enhancement

The analytical expression derived using temporal coupled-mode theory shows that the absorption efficiency of the QD in a cavity at the resonant wavelength of λ0 is obtained as ηabsQD (λ0) = SQD/Seff ηfarM (1). The effective mode area Seff represents an effective mode area of the cavity mode defined as Seff = ∫z=0 UE(x, y)dxdy (2). The term M represents a rate matching (Q matching) between QW x y (a) + 0 - + 0 - w z GaAs substrate. This rate matching is given by M = 4gammaabsgammat(gammat + gammab + gammaabs)2 (4).

Results and discussion on substrate effect

The results based on Eq. (1) and from direct calculations show a nice agreement, which demonstrates the validity of the analytical expression discussed in 2.2. The absorption efficiency oscillates with a period of approximately half of the resonant wavelength (Tgap/λ0 0.5). The in-phase (out-of-phase) conditions are almost satisfied at around Tgap/λ0 = 0.4 (Tgap/λ0 = 0.65). At Tgap/λ0 = 0.4, where the in-phase condition is satisfied, ηabsQD (λ) is 1.6 times higher than that for the cavity without substrate.

Dominant factors affecting absorption enhancement

The analysis of each factor determining the absorption efficiency clarified that the upward directionality, Φ = gammat/gammarad, plays a dominant role in the improvement. The presence of substrate acts as a partial mirror that reflects light, thereby modifying the vertical coupling constant of the cavity. Furthermore, the far-field spatial overlap between the cavity mode and the incident Gaussian beam, ηfar, is also favored by the presence of substrate. The improvement in M is shown to be the primary important where the higher efficiency ηabsQD (λ0) is obtained compared to the free-standing cavity.

Conclusion

The substrate-induced asymmetry can improve absorption in a simple manner. The analysis of each factor determining the absorption efficiency clarified that the upward directionality, Φ = gammat/gammarad, plays a dominant role in the improvement. We also found that the far-field spatial overlap between the cavity mode and the incident Gaussian beam, ηfar, is also favored by the presence of substrate. The substrate-induced asymmetry can improve absorption in a simple manner. This simple method would be useful for improving the collection efficiency of photons emitted from a gatedefined QD [44]. We would also emphasize that this substrate effect is applicable to other host materials of solid-state qubits, such as bulk single-crystal diamonds [45].

Table 1 Summary

Table 1 summarizes the values of SQD/Seff, ηfar, and M that contribute to the largest and smallest absorption efficiencies. The absorption efficiency at Tgap/λ0 = 0.4, ηabsQD (λ0) = 0.0195, is approximately 1.64 times enhanced than that of the free-standing situation (ηabsQD (λ0) = 0.0119), where M and ηfar show an improvement of around 50% and 10%, respectively. These results confirm again that the improvement in M dominates the improvement in absorption efficiency. The reduction in SQD/Seff is less than 1%. At Tgap/λ0 = 0.65, ηabsQD (λ0) is 0.0042, which is 0.35 times of ηabsQD (λ0) for no substrate case. The reductions of M and ηfar are responsible for the efficiency drop. A proper cavity design can improve M and ηfar to further improve the absorption efficiency. Achieving Qrad close to Qabs allows M to be close to the maximally achievable Φ.

Future directions

Field-based design methods [42,43] can be applied to precisely design the emission profile. For bull’s-eye cavities, a simpler approach is to control the divergence of the emission profile by adjusting the size of the circular cavity. By increasing the cavity size, a narrower far-field emission pattern can be obtained. However, because a large cavity also causes a decrease in SQD/Seff, a proper optimization that considers the trade-off between M × ηfar and SQD/Seff is required in the future<ref:2304.

Improvements for AI systems

Polarization-Independent Photon-Spin Conversion: The improved system can achieve Improving the photon–spin conversion efficiency without polarization dependence by utilizing substrate-induced asymmetry to realize a further 1.6 times improvement in efficiency.
Enhanced Quantum Interface Efficiency: The AI system, when applied to quantum network simulation or device design, can optimize gate-defined quantum dot embedding by adjusting the distance of the substrate from the semiconductor slab where the bull’s-eye structure is formed to maximize absorption efficiency.
Directional Coupling Optimization: The system can exploit upward-preferred coupling and narrow far-field emission pattern realized by substrate-induced asymmetry to enhance photon absorption, suggesting a method for engineering directional coupling induced by out-of-plane asymmetry in the cavity.

Abstract

Improving the photon-spin conversion efficiency without polarization dependence is a major challenge in realizing quantum interfaces gate-defined quantum dots (QDs) for polarization-encoded photonic quantum network systems. Previously, we reported the design of an air-bridge bull's-eye cavity that enhances the photon absorption efficiency of an embedded gate-defined QD regardless of the photon polarization. Here, we numerically demonstrate that a further 1.6 times improvement in efficiency is possible by simply adjusting the distance of the substrate from the semiconductor slab where the bull's-eye structure is formed. Our analysis clarifies that the upward-preferred coupling and narrow far-field emission pattern realized by substrate-induced asymmetry enable the improvement.