Four-Channel Franson Interferometer

• The paper demonstrates a four-channel Franson interferometer that measures energy–time entanglement via dual unbalanced Michelson interferometers and four detector outputs.
• Methodology combines spectral separation, active phase stabilization, and time-correlated single-photon counting to analyze the quantum dot biexciton–exciton cascade.
• Results reveal phase-dependent two-photon interference with visibilities up to 64% within an 80 ps window, highlighting paths for improving Bell-violation thresholds.

Searching arXiv for the cited paper and closely related Franson-interferometer/energy-time entanglement work to ground the article. {"^^^^^^^^8query8 (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^^^^^", "^^^^^^^^8max_results8 ^^^^8max_results8^^^^} {"^^^^^^^^8query8 interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^^^^^", "^^^^^^^^8max_results8 ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8^^^^} {"^^^^^^^^8query8 entanglement from a monolithically integrated quantum dot on silicon^^^^^^^^8\8 "^^^^^^^^8max_results8 ^^^^8max_results8^^^^} A four-channel Franson interferometer is an energy–time entanglement measurement architecture in which two unbalanced interferometers analyze the two photons of a correlated pair and all output ports are monitored, yielding four coincidence channels. In the implementation reported in "Energy-time entanglement from a monolithically integrated quantum dot on silicon" (&&&^^^^8query8^^^^&&&), the device is used to characterize the biexciton–exciton (PRESERVED_PLACEHOLDER_^^^^8query8^^^^–PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^) cascade emitted by a single InGaAs/GaAs quantum dot monolithically grown on a silicon substrate under continuous-wave two-photon excitation. The reported system combines spectral separation of the PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^ and PRESERVED_PLACEHOLDER_^^^^8query8^^^^ photons, two unbalanced Michelson interferometers with independently controlled phases, active phase stabilization, and four-channel superconducting nanowire single-photon detection. Within that configuration, phase-dependent two-photon interference with visibilities up to PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ for an 8^^^^8query8^^^^ ps integration window is observed, with the experiment explicitly framed as an energy–time entanglement measurement approaching, but not exceeding, the Bell-violation threshold (&&&^^^^8query8^^^^&&&).

^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^. Definition and operating principle

In the reported experiment, the four-channel Franson interferometer is built to probe the energy–time correlations of the PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^–PRESERVED_PLACEHOLDER_^^^^8query8^^^^ cascade from a single quantum dot on silicon (&&&^^^^8query8^^^^&&&). The source emits biexciton and exciton photons at approximately 9^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv88^^^^.^^^^8\8query8^^^^ nm and 9^^^^8max_results8query8^^^^.^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8query8^^^^ nm, respectively, and these are separated by a fiber-coupled transmission spectrometer before entering distinct analysis paths. One interferometer is assigned to the PRESERVED_PLACEHOLDER_^^^^8\8^^^^ photon, identified as the idler, and the other to the ${\rm X}$ photon, identified as the signal.

The Franson configuration operates by introducing, for each photon, a choice between a short path and a long path. In the post-selected coincidence basis, only the short–short and long–long alternatives contribute to the central interference peak. The experiment states that, under this Franson post-selection, the two-photon state reduces to the time-bin-entangled form

$$|\psi_{\rm F}\rangle = \frac{1}{\sqrt{2}}\left(|S_sS_i\rangle + e^{\,i(\phi_s+\phi_i)}|L_sL_i\rangle\right),$$

where PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8^^^^ and PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^ are the signal and idler interferometer phases, respectively (&&&^^^^8query8^^^^&&&).

A common point of confusion is the meaning of “four-channel.” In this implementation, the term does not denote four interferometers. It denotes four detector outputs generated by two interferometers, each having two output ports. Those outputs are monitored by four superconducting nanowire single-photon detectors (SNSPDs): CH^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^ and CH^^^^8max_results8^^^^ for the signal/PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8max_results8^^^^ outputs, and CH^^^^8query8^^^^ and CH^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ for the idler/PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8^^^^ outputs (&&&^^^^8query8^^^^&&&).

^^^^8max_results8^^^^. Optical architecture

The optical design consists of excitation, spectral separation, two unbalanced Michelson interferometers, and a co-propagating stabilization path (&&&^^^^8query8^^^^&&&). Each interferometer begins with a ^^^^8max_results8query8^^^^/^^^^8max_results8query8^^^^ non-polarizing beamsplitter. Two retroreflectors define a short arm PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ of approximately ^^^^8query8^^^^.^^^^8max_results8^^^^ cm and a long arm PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8max_results8^^^^ of approximately ^^^^8max_results8max_results8^^^^ cm, giving a path-length difference PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8^^^^ cm and a temporal delay PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8\8^^^^ ns.

One long-arm mirror is mounted on a micrometer translation stage for coarse matching, while each short-arm mirror is mounted on a piezoelectric actuator for fine phase control. The two independently controlled phases are denoted PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer88^^^^ for the signal/PRESERVED_PLACEHOLDER_^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^9 interferometer and PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^ for the idler/PRESERVED_PLACEHOLDER_^^^^8max_results8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^ interferometer (&&&^^^^8query8^^^^&&&). This separation between coarse path matching and fine nm-scale phase tuning is central to obtaining stable interference fringes over extended measurement times.

The reported stabilization strategy uses a narrow-linewidth continuous-wave diode laser that is fiber-split into both interferometers. First-order interference fringes from this reference field are detected on two silicon SPADs, time-tagged, and used as inputs to two independent PID loops. Those loops lock PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^ and PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^ to better than a few tens of nanometers over hours (&&&^^^^8query8^^^^&&&). The use of self-aligned retroreflectors is specifically identified as reducing sensitivity to beam pointing, which is a technical feature of the interferometer rather than of the source.

The core optical parameters reported for the interferometer are summarized below.

Parameter	Reported value
Short arm length	PRESERVED_PLACEHOLDER_^^^^8max_results8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ cm
Long arm length	PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^ cm
Path imbalance	PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^ cm
Temporal delay	PRESERVED_PLACEHOLDER_^^^^8max_results8\8^^^^ ns
Detector timing jitter	PRESERVED_PLACEHOLDER_^^^^8max_results88^^^^ ps

These values are significant because the Franson geometry requires separation of the noninterfering short–long and long–short events from the interfering short–short and long–long events while retaining overlap of the latter within the source coherence constraints (&&&^^^^8query8^^^^&&&).

^^^^8query8^^^^. State description and coincidence theory

The experiment formulates the PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^9–PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ cascade in the time domain as a two-photon state

PRESERVED_PLACEHOLDER_^^^^8query8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^

where PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^ is the joint spectral amplitude (&&&^^^^8query8^^^^&&&). This representation identifies the emitted pair as spectrally correlated prior to interferometric analysis.

For the post-selected central peak, the coincidence probability for signal detector PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ and idler detector PRESERVED_PLACEHOLDER_^^^^8query8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ is written as

PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^

where PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ is the overall count rate, PRESERVED_PLACEHOLDER_^^^^8query8\8^^^^ is the two-photon interference visibility for that detector pair, and PRESERVED_PLACEHOLDER_^^^^8query88^^^^ is a fixed phase offset determined by the number of reflections (&&&^^^^8query8^^^^&&&). The appearance of PRESERVED_PLACEHOLDER_^^^^8query8^^^^9 rather than a single interferometer phase is the characteristic Franson signature: interference is encoded in the sum of the two local phases.

Visibility is defined, for each channel pair PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8query8^^^^, by

PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^

with PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8max_results8^^^^ and PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8query8^^^^ obtained from fitted extrema of the sinusoidal fringe in PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ (&&&^^^^8query8^^^^&&&). In the reported experiment, the four coincidence combinations are CH^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8max_results8^^^^CH^^^^8query8^^^^, CH^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8query8^^^^CH^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^, CH^^^^8max_results8^^^^PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8\8^^^^CH^^^^8query8^^^^, and CH^^^^8max_results8^^^^PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv88^^^^CH^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^.

The article also gives the CHSH relation

PRESERVED_PLACEHOLDER_^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^9

and, for perfect sinusoidal correlations of visibility PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^,

PRESERVED_PLACEHOLDER_^^^^8max_results8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^

Accordingly, Bell violation requires

PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^

This threshold is central to the interpretation of the reported results: the measured visibilities indicate non-classical two-photon interference, but the reported average 8^^^^8query8^^^^ ps-window visibility remains below the nominal Bell-violation threshold (&&&^^^^8query8^^^^&&&).

^^^^8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^. Four-channel detection topology and post-selection

After recombination, each interferometer provides two output ports, and all four are fiber-coupled to SNSPDs (&&&^^^^8query8^^^^&&&). The four detectors are therefore not redundant monitors of a single fringe; they define the complete two-output-by-two-output coincidence topology of the apparatus. All four SNSPD channels feed a Time-Correlated Single-Photon Counting (TCSPC) module. The system efficiency is given as approximately 8^^^^8max_results8^^^^%, and the combined timing jitter is approximately ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8query8^^^^ ps (&&&^^^^8query8^^^^&&&).

Coincidence histograms are recorded between every signal output and every idler output. The resulting four pairwise combinations permit independent visibility extraction for each channel pair. The experiment records coincidences in 8^^^^8query8^^^^ ps bins, and temporal post-selection windows PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^ are varied from 8^^^^8query8^^^^ ps up to ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8query8query8^^^^ ps around the central short–short plus long–long peak (&&&^^^^8query8^^^^&&&).

This post-selection strategy is essential to the Franson method as implemented here. The central peak contains the interfering short–short and long–long contributions, whereas the short–long and long–short events are temporally displaced by the interferometer delay PRESERVED_PLACEHOLDER_^^^^8max_results8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ ns (&&&^^^^8query8^^^^&&&). The width of the accepted temporal window directly affects the measured visibility by trading off count rate against contamination from residual noninterfering background.

A plausible implication is that the four-channel design provides a direct way to diagnose channel-dependent imbalances. The paper explicitly notes that optimized ^^^^8max_results8query8^^^^/^^^^8max_results8query8^^^^ beamsplitters could minimize channel imbalance and PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^ errors (&&&^^^^8query8^^^^&&&), indicating that the individual channel visibilities are not expected to be identical in practice.

^^^^8max_results8^^^^. Source dynamics and measured performance

The interferometer performance is linked in the paper to the intrinsic dynamics of the quantum dot source (&&&^^^^8query8^^^^&&&). Under off-resonant pulsed excitation, the radiative lifetimes are reported as

• PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^ ps
• PRESERVED_PLACEHOLDER_^^^^8max_results8\8^^^^ ps

Under two-photon excitation at PRESERVED_PLACEHOLDER_^^^^8max_results88^^^^, the optical coherence times measured with a Michelson interferometer are reported as

• PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^9 ps
• PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ ps

These values place the source in a regime where pure dephasing is present, as the paper explicitly notes through the condition PRESERVED_PLACEHOLDER_^^^^8query8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^ (&&&^^^^8query8^^^^&&&). That relation is used in the article not as an abstract coherence criterion, but as a direct explanation for degraded two-photon coherence.

The measured visibilities depend strongly on the temporal integration window. For the narrow 8^^^^8query8^^^^ ps window, the average visibility is reported as

PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^

For the broad ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8query8query8^^^^ ps window, the maximal channel result is

PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^

while another channel gives

PRESERVED_PLACEHOLDER_^^^^8query8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^

The mean visibility at PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^ ps is reported as PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ (&&&^^^^8query8^^^^&&&).

The paper attributes the reduction in PRESERVED_PLACEHOLDER_^^^^8query8\8^^^^ with increasing PRESERVED_PLACEHOLDER_^^^^8query88^^^^ to residual noninterfering background, specifically blinking and long-time bunching, and states that this reduction persists even after background subtraction (&&&^^^^8query8^^^^&&&). A common misconception would be to equate a large post-selection window with a more complete estimate of entanglement quality. In the reported system, wider windows increase background admixture and therefore reduce the observed interference contrast.

^^^^8query8^^^^. Constraints, interpretation, and projected improvements

The reported four-channel Franson interferometer is presented as demonstrating “clear energy–time entanglement from a QD on silicon” while also identifying the main reasons the observed visibility remains below the Bell threshold (&&&^^^^8query8^^^^&&&). The constraints are technical rather than conceptual.

First, finite detector timing jitter of approximately ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8query8^^^^ ps imposes a compromise between time resolution and count rate (&&&^^^^8query8^^^^&&&). Narrow windows better isolate the most coherent part of the central peak, but they reduce the number of accepted coincidences. Second, the radiative lifetimes of hundreds of picoseconds impose an upper bound on PRESERVED_PLACEHOLDER_^^^^8query8^^^^9: the paper states that if the delay becomes too large, the short–short and long–long wave packets no longer overlap (&&&^^^^8query8^^^^&&&). Third, pure dephasing, residual re-excitation, and blinking further degrade two-photon coherence.

The article identifies several potential improvements: reducing PRESERVED_PLACEHOLDER_^^^^8\8query8^^^^ to better match the approximately ^^^^8query8query8query8^^^^ ps and ^^^^8query8query8query8^^^^ ps lifetimes while still isolating the short–long and long–short peaks; using optimized ^^^^8max_results8query8^^^^/^^^^8max_results8query8^^^^ beamsplitters to minimize channel imbalance; enhancing photon coherence via the Purcell effect or lower excitation power to suppress excitation-induced dephasing; and implementing narrower spectral filtering or active suppression of blinking to cut background (&&&^^^^8query8^^^^&&&). It further states that, with these improvements, one expects PRESERVED_PLACEHOLDER_^^^^8\8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8^^^^–PRESERVED_PLACEHOLDER_^^^^8\8max_results8^^^^, which would be sufficient for Bell violation because PRESERVED_PLACEHOLDER_^^^^8\8query8^^^^ is required (&&&^^^^8query8^^^^&&&).

This outlook defines the significance of the four-channel Franson interferometer in the reported setting. It is not merely a diagnostic for fringe visibility; it is an architecture for assessing whether a monolithically integrated III–V-on-silicon quantum dot can serve as a deterministic source of energy–time entangled photon pairs in scalable quantum photonic technologies (&&&^^^^8query8^^^^&&&). The reported visibilities therefore occupy an intermediate position: they are high enough to establish non-classical phase-dependent two-photon interference, but not yet high enough to constitute a Bell-inequality violation under the stated CHSH criterion.

^^^^8\8^^^^. Position within quantum photonics on silicon

Within the specific scope of the reported work, the four-channel Franson interferometer functions as the entanglement-analysis stage for a monolithically integrated III–V-on-silicon emitter platform (&&&^^^^8query8^^^^&&&). The paper frames scalable quantum photonic technologies as requiring deterministic entangled-photon sources compatible with established semiconductor manufacturing platforms, and it identifies integration of self-assembled III–V quantum dots with silicon-based architectures as a central challenge (&&&^^^^8query8^^^^&&&). The interferometer is therefore part of a broader effort to verify that such integrated emitters preserve the coherence needed for non-classical photonic correlations.

The experiment also situates the interferometer within a coherent-control program for the source itself. Under coherent two-photon excitation, the biexciton–exciton cascade is reported to exhibit coherent control evidenced by Rabi oscillations and dressed-state formation (&&&^^^^8query8^^^^&&&). In that context, the Franson measurement probes not only photon-pair generation but the phase coherence of the cascade after integration onto silicon.

A plausible implication is that the four-channel format is particularly useful for integrated-source studies because it exposes channel-resolved imperfections that would be obscured in a reduced-output measurement. In the reported system, this includes detector-pair-dependent visibilities and reflection-induced phase offsets PRESERVED_PLACEHOLDER_^^^^8\8Franson interferometer quantum dot energy-time entanglement silicon quantum dot Franson arXiv8^^^^ (&&&^^^^8query8^^^^&&&). For that reason, the apparatus serves both as an entanglement verifier and as a metrological tool for diagnosing the interplay among source coherence, interferometer imbalance, and detection asymmetry.

Taken together, the reported implementation defines the four-channel Franson interferometer as a phase-stabilized, dual-Michelson, four-detector analysis system for energy–time entanglement in the PRESERVED_PLACEHOLDER_^^^^8\8max_results8^^^^–PRESERVED_PLACEHOLDER_^^^^8\8query8^^^^ cascade of a monolithically integrated quantum dot on silicon. Its principal result is the observation of phase-dependent two-photon interference with visibilities up to PRESERVED_PLACEHOLDER_^^^^8\8\8^^^^ for an 8^^^^8query8^^^^ ps integration window and PRESERVED_PLACEHOLDER_^^^^8\88^^^^ for the strongest channel at ^^^^8arXiv (Hohn et al., 30 Jun 2026) Energy-time entanglement from a monolithically integrated quantum dot on silicon Franson interferometer8query8query8query8^^^^ ps, establishing energy–time entanglement while delineating the technical conditions required to surpass the approximately ^^^^8\8query8^^^^.^^^^8\8 Bell-violation threshold (&&&^^^^8query8^^^^&&&).