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Frontiers in Optics

Mode-locked two-photon entangled states

Y. J. Lu, R. L. Campbell, Z. Y. Ou

Published Jan 1, 2003• 0 citations
Publisher

Abstract

When the modes of a laser are locked in phase, the output field becomes pulses with equal time intervals. Similarly, a mode-locked two-photon state consists of N frequency-conjugate photon pairs in superposition, which provides the mechanism for phase locking of the different frequency components. The quantum state has the following form:

DOI
10.1364/fio.2003.waa6

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When the modes of a laser are locked in phase, the output field becomes pulses with equal time intervals. Similarly, a mode-locked two-photon state consists of N frequency-conjugate photon pairs in superposition, which provides the mechanism for phase locking of the different frequency components. The quantum state has the following form:
With the recently introduced particle interpretation of the double-slit experiment for light fields [Phys. Rev. Lett. 134, 13360 (2025)], all related interference phenomena can be reinterpreted in terms of light particle states that either couple (bright) or do not couple (dark) with detectors. Here, we apply this approach to multimode pulsed lasers, unifying the description of their generation inside optical cavities and propagation outside them, now relying solely on quantum mechanics, i.e., without invoking wave superposition to explain pulse shaping. Specifically, we demonstrate that multimode interference presents a dominance of particle dark states over the bright ones and mode-locked pulsed lasers consist of a continuous photon beam, with photons forming bright states during pulses and dark states in between. Additionally, we analyze mode-locked pulsed lasers, showing that the theoretical bright-to-dark state ratio matches the experimental pulse-to-interval duration ratio.
We have constructed a mode-locked optical parametric oscillator (OPO), synchronously pumped by the second harmonic of a continuously mode-locked Nd:YAG laser and based on type II phase matching in a KTP crystal. The two subharmonics (signal and idler waves) are nearly degenerate in frequency but are distinct orthogonal polarization states, and the oscillator is thus a nondegenerate OPO. Above threshold, the intensities of the signal and idler output beams should be highly correlated, as recently demonstrated for a similar single-frequency OPO.1 Ideally, the quantum noise on the corresponding photocurrent difference signal is completely suppressed for frequencies that are small compared to the OPO cavity bandwidth. Since this configuration produces intense light beams with potentially very good noise suppression, it is an important prototype for possible applications, e.g., to spectroscopy. Initial results with our OPO show an excess uncorrelated polarization noise, possibly due to depolarized light scattering in the KTP crystal. When the OPO cavity is stabilized with the signal and idler degenerate in frequency, they can be mixed to form a superposition by manipulating their polarization. When the oscillator is pumped below threshold, a pulsed squeezed vacuum state is produced in two such mixtures.2 When the polarizations are mixed inside the OPO cavity by a Faraday rotator, the backaction evasion necessary for a quantum nondemolition (QND) measurement of one of the field quadratures of an externally injected beam is obtained.3 The pulsed local oscillator used in observing the squeezing or QND effects is derived from the fundamental output of the pump laser. Progress in implementing these experiments with our mode-locked OPO is described as well as possible applications to time-domain measurements with noise below the shot-noise limit.
Shih (2026) reported the observation of ghost frequency-time combs (GFC, 50% contrast) from continuous-wave laser beams, and theoretically predicted quantum ghost frequency-time combs (QGFC, 100% contrast) from entangled coherent states, concluding that classical statistical theory cannot explain the phenomena and that quantum coherence theory — specifically non-local superposition of probability amplitudes — is required. This paper demonstrates that the GFC and QGFC are fully consistent with the Conjugate Photonic Model (CPM) without invoking either vacuum agents or non-local wave-function collapse. In the CPM, each photon is a rotating dipole with internal phase . The GFC emerges from the local beating between the internal phases of randomly paired dipoles across the two detectors — the same mechanism responsible for photonic trimers and mode-locking. The QGFC emerges from the phase synchrony imposed by the energy conservation condition — the macroscopic analogue of the Pi-Cosmic Generating Function . The Path provides fixed propagation conditions (, , ) with no internal structure to act as vacuum agent. The "non-locality" of GFC is resolved: the correlation is local in the phase of each dipole, propagated deterministically through the closed Energy–Path system to the two detectors.