Tuning excitation can change photon number coherence in quantum dots

The work by Hagen, Bracht, Bozzio, Cygorek, Reiter, Walther, and Axt shows that the “Swing-UP of quantum EmitteR population” (SUPER) scheme can significantly decrease the PNC of the emitted photon, compared to resonant excitation. The team’s calculations reveal a laser-induced Stark shift effectively disconnects the quantum dot from the cavity during excitation, accounting for environmental effects like phonons and radiative losses.

SUPER Scheme Reduces Photon Number Coherence in Quantum Dots

Calculations by Paul C. A. This shift effectively isolates the quantum dot from the surrounding cavity during excitation, resulting in a measurable reduction in photon number coherence compared to traditional resonant excitation methods. The findings, published in a recent study, have implications for the development of secure quantum communication protocols. These sources, often using quantum dots embedded within photonic microcavities, require precise control over emitted photon characteristics to ensure secure data transmission.

The team’s work demonstrates that the SUPER scheme, while often implemented to enhance single photon source properties, can paradoxically diminish this important characteristic. This decoupling is not a theoretical artifact. The calculations explicitly incorporate environmental factors like phonons and radiative losses, reflecting a realistic model of the system. The mechanism behind this reduction stems from the Stark shift induced by the laser pulses used in the SUPER scheme.

When applied to a quantum dot within a cavity, this shift temporarily detunes the quantum dot from the cavity’s resonant frequency, preventing efficient emission of photons into the cavity. This contrasts sharply with resonant excitation, where photons are readily emitted and outcoupled from the cavity. The researchers modeled this process using a density matrix formulation, tracking the coherences between vacuum and single-photon states, specifically, the coherence between the zero- and one-photon states, which dominates photon number coherence in single-photon sources.

This discovery offers a novel approach to scrambling photon number coherence, a technique used to enhance security in quantum cryptographic protocols. Existing methods, such as discrete phase modulation and laser gain switching, are known to have potential security vulnerabilities.

The SUPER scheme, by naturally reducing photon number coherence through the Stark shift, presents an alternative strategy that circumvents these known loopholes. “This provides an interesting alternative to standard PNC scrambling methods used in quantum cryptography,” the researchers write, highlighting the potential for improved security. The study’s model incorporates a quantum dot, a quantized microcavity, and accounts for both radiative and cavity losses, demonstrating a sophisticated approach to simulating the complex interactions within the system.

The team’s calculations show that under SUPER excitation, the Stark shift effectively prohibits photon emission from the quantum dot into the cavity, directly impacting the observed photon number coherence. This effect is visually represented in their schematic diagrams, illustrating the difference in photon behavior between resonant excitation and the SUPER scheme.

Researchers at Universität Bayreuth, TU Dortmund, and the University of Vienna show that the “Swing-UP of quantum EmitteR population” (SUPER) scheme can significantly decrease the PNC of the emitted photon, compared to resonant excitation. The findings emphasise the importance of carefully considering all aspects of excitation schemes, even those intended to improve performance, to ensure the highest levels of security and efficiency.

Stark Shift Decouples Quantum Dot from Cavity During SUPER Excitation

This decoupling prevents photon emission into the cavity while the excitation lasers are active, a key distinction from resonant excitation methods. Calculations reveal the Stark shift’s impact extends beyond simply reducing PNC. It fundamentally alters the timing of photon emission. Under resonant excitation, photons are emitted into the cavity during the excitation phase, contributing to a larger photonic coherence. Conversely, the SUPER scheme delays emission until after the laser pulse concludes, preventing substantial coherence buildup within the cavity itself.

This temporal shift is directly linked to the off-resonant nature of the SUPER scheme and the resulting Stark shift’s influence on the quantum dot’s energy levels. The study’s model accounts for environmental effects, including phonons and radiative losses, to accurately represent this behavior. The observed decoupling manifests in the electronic and cavity Fock state occupations.

Photon Number Coherence Measurement via Hong-Ou-Mandel Interference

This level of detail moves beyond idealized theoretical models by incorporating elements that typically degrade performance in physical devices, offering a more robust assessment of the findings. The method for quantifying photon number coherence relies on Hong-Ou-Mandel interference, where a photon from the source is combined with a delayed photon from the same origin, triggered by an earlier pulse. The resulting intensity at the output ports of the beamsplitter is predicted to be $N_{c,d}$ = ρ_(11)(1 ± |${\rho }_{01}$|^2/ρ_(11) cos(φ^a-φ^b), a formula used to assess the degree of coherence between the vacuum and single-photon states.

A state is considered pure when the equality |${\rho }_{01}$|^2 = ${\rho }_{00}{\rho }_{11}$ holds, indicating a strong, well-defined quantum state, while any deviation signifies a mixed state with reduced coherence. This measurement technique provides a means to characterize the quality of single photon emission, a critical factor for secure quantum communication.

The study’s approach to analyzing the quantum dot-cavity system involves constructing a reduced density matrix, ${\rho }_{Sn}^{\text{S^′n^′}}$, which describes the system’s evolution, tracing out both phononic and quantum dot degrees of freedom to isolate the cavity’s behavior. This process yields information about the occupations of both the quantum dot and the cavity, represented by ${\rho }_{XX}$ and ${\rho }_{nn}$ respectively, alongside electronic and photonic coherences, ${\rho }_{GX}$ and ${\rho }_{nm}$.

By examining these parameters, researchers can gain insight into how the SUPER excitation scheme affects the coherence properties of the emitted photons, and how that differs from resonant excitation. The team’s calculations provide a detailed picture of the quantum state evolution, allowing for a precise assessment of photon number coherence.

QD-Cavity System Model Includes Phonons and Radiative Losses

The research team’s model details a quantum dot coupled to a quantized microcavity, accounting for energy dissipation through both radiative decay and interactions with phonons. The team employed a reduced density matrix, denoted as ${\rho }_{Sn}^{\text{S^′n^′}}$, to describe the quantum dot-cavity system, tracing out the influence of phonons to simplify the model while retaining accuracy.

The calculations reveal that the SUPER scheme achieves lower PNC values while maintaining a comparable degree of tunability to resonant excitation, allowing for flexibility in optimizing single photon sources. The model’s inclusion of phonons is important, as these vibrations within the crystal lattice of the quantum dot can influence the coherence of the emitted photons.

By fully accounting for these environmental effects, the researchers demonstrate the robustness and practical relevance of their findings. “We showed for a QD-cavity model including the effect of phonons that the SUPER scheme can produce single photons with significantly smaller PNC than a resonant pulse of equal duration could, while still allowing a large degree of tunability by variation of the second pulse area,” the paper concludes. The ability to manipulate PNC through the SUPER scheme offers a novel approach to tailoring single photon sources for specific quantum communication applications.

Optimized SUPER Parameters for Brightness and Low PNC

This approach allows for comparable tunability while simultaneously achieving lower PNC values, offering a distinct advantage for certain quantum cryptographic protocols. The laser envelopes employed were Gaussian, with pulse durations σ chosen to be identical for both pulses, and the team varied only the second pulse area, ${\Theta }_2$, to observe its effect on the system’s coherences. Integrated occupations and coherences were then analyzed, revealing Rabi-like behavior and a clear impact on both the quantum dot and cavity photons.

This careful manipulation of excitation parameters demonstrates a level of control over the system’s quantum state beyond that offered by simple resonant excitation. This means that the emission of photons into the cavity is delayed until after the laser pulses have passed, effectively suppressing the buildup of photonic coherence within the cavity itself.

Unlike resonant excitation, where photonic coherence builds up during the pulse, SUPER ensures that this coherence remains minimal, leading to a significantly lower PNC. The calculations account for the fact that a perfectly excited quantum dot, as described by Eq. (6) in the paper, would theoretically produce no PNC whatsoever, and the SUPER scheme approaches this ideal scenario. the use of short laser pulses with SUPER excitation triggers an additional incoherent mechanism mediated by phonons, further decreasing PNC, though at a slight cost to brightness.

This phonon-mediated process, arising from vibrations within the quantum dot’s crystal lattice, contributes to the overall suppression of coherence, demonstrating the importance of considering environmental effects in these calculations. The team found that at the end of the laser driving, SUPER leaves only a small electronic coherence in the quantum dot, which is then converted into a correspondingly small PNC.

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