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Academia quantum.

Ghost frequency-time combs: quantum coherence in classical and entangled laser beams

Yanhua H. Shih

Published Mar 31, 2026• 0 citations
Publisher

Abstract

Introduction: Proceeding from the recently discovered ghost frequency-time comb (GFC) of 50% contrast found through intensity-intensity correlation measurements of multi-cavity-mode continues-wave (CW) laser beams, this report further extends this analysis to a novel type of entangled coherent state, or entangled laser beams, capable of producing GFC of 100% contrast, described as the “quantum ghost frequency-time comb” (QGFC). Despite being in continuous-wave operation, both classical and entangled laser beams produce sharp periodic comb-like correlation functions. Why is there a “nonlocal” and periodic correlation between the two distant locally and independently measured CW laser beams? Can the GFC and QGFC phenomena be interpreted as correlations between statistical intensity fluctuations? For the QGFC specifically, this question becomes particularly acute: How do “zero-coincidences” occur in the measurement of CW laser beams? Why do “zero-coincidences” occur periodically? This report address these questions. Although both GFC and QGFC are observed, or more precisely, calculated from locally measured intensity fluctuations, the 50% contrast GFC is caused by an incoherent superposition of quantum probability amplitudes of all possible randomly paired cavity modes, while the 100% contrast QGFC is caused by a coherent superposition of quantum probability amplitudes of all possible entangled pairs of cavity-modes, where these amplitudes contribute to a nonlocal joint photodetection event. Experimental observations of GFC and QGFC may finally resolve the long-standing debate between classical statistics and quantum coherence. Besides their fundamental significance, bright GFC and QGFC make important contributions to the fields of nonlocal positioning, time transfer and precision spectroscopy. High-brightness entangled laser beams may also open up new applications that might not be realizable by using entangled photon pairs at the single-photon level.

DOI
10.20935/acadquant8239

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arXiv:0805.1166•May 7, 2008•1 citation
Introduction: Proceeding from the recently discovered ghost frequency-time comb (GFC) of 50% contrast found through intensity-intensity correlation measurements of multi-cavity-mode continues-wave (CW) laser beams, this report further extends this analysis to a novel type of entangled coherent state, or entangled laser beams, capable of producing GFC of 100% contrast, described as the “quantum ghost frequency-time comb” (QGFC). Despite being in continuous-wave operation, both classical and entangled laser beams produce sharp periodic comb-like correlation functions. Why is there a “nonlocal” and periodic correlation between the two distant locally and independently measured CW laser beams? Can the GFC and QGFC phenomena be interpreted as correlations between statistical intensity fluctuations? For the QGFC specifically, this question becomes particularly acute: How do “zero-coincidences” occur in the measurement of CW laser beams? Why do “zero-coincidences” occur periodically? This report address these questions. Although both GFC and QGFC are observed, or more precisely, calculated from locally measured intensity fluctuations, the 50% contrast GFC is caused by an incoherent superposition of quantum probability amplitudes of all possible randomly paired cavity modes, while the 100% contrast QGFC is caused by a coherent superposition of quantum probability amplitudes of all possible entangled pairs of cavity-modes, where these amplitudes contribute to a nonlocal joint photodetection event. Experimental observations of GFC and QGFC may finally resolve the long-standing debate between classical statistics and quantum coherence. Besides their fundamental significance, bright GFC and QGFC make important contributions to the fields of nonlocal positioning, time transfer and precision spectroscopy. High-brightness entangled laser beams may also open up new applications that might not be realizable by using entangled photon pairs at the single-photon level.
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.
We report an experimental demonstration of a time transfer and distant clock synchronization scheme based on what we have labeled as a ghost frequency comb, observed from the nonlocal correlation measurements of a laser beam. Unlike a conventional frequency comb, the laser beam used in this work does not consist of a pulse train but instead it is in a continuous-wave operation. The laser beam, consisting of half a million longitudinal cavity modes from a fiber ring laser, is split into two beams, each sent to a distant observer. In their local measurements, both observers observe constant intensity with no pulse structure present. Surprisingly, a pulse train of comb-like, ultra-narrow peaks is observed from their nonlocal correlation function measurement. This observation makes an important contribution to the field of precision spectroscopy, as we show in optical correlation-based nonlocal timing and positioning.
How macroscopic definite outcomes and nonlocal correlations emerge from entangled superpositions across spacelike-separated regions without superluminal action or {\it ad hoc} wavefunction collapse remains a defining open question in the foundations of quantum mechanics. Here, we resolve this century-long paradox within \textit{linear} relativistic quantum electrodynamics by developing an open-system and measurement-defined framework realized in dual, spacelike-separated nonlinear crystals driven synchronously by a multi-mode optical frequency comb and seeded by an ultra-narrow coherent laser. Expanding the transverse electromagnetic vector potential into discrete single-photon frequency-comb supermodes, we show that tracing out the unmeasured continuous-wave idler field yields an exact spatial dephasing Lindblad master equation whose decoherence rate is governed by the non-orthogonal state overlap of single-photon-added coherent states. Connecting this open-system map to free-vector-space quotient measurement theory, we demonstrate that single-particle interference arises from the geometric projection of the composite state onto detector-defined conditional cosets rather than remote collapse, establishing strict operational equivalence across pump, seed, and signal phase scans. The resulting wave-particle-entanglement triality equality P2+E2+V2=1P^2 + E^2 + V^2 = 1P2+E2+V2=1 is saturated across the complete parameter space, while the atomic-clock-referenced comb structure anchors continuous-variable time-frequency displacement stabilizers directly at the hardware layer. Our work unifies induced coherence, Bohr's complementarity, and quotient measurement theory, providing a microscopic pathway toward fault-tolerant bosonic quantum information processing.
The measurement and manipulation of coherent optical fields have been transformed by the optical frequency comb. Today, the optical frequency comb grants measurements precise enough to count individual cycles of light as well as the generation of nearly any coherent electromagnetic field from the ultraviolet through the infrared. These capabilities have enabled the most precise realizations and comparisons of time, precision spectroscopy over broad bandwidths, and the ability to convert stable signals between optical and microwave fields–seamlessly connecting the entire electromagnetic spectrum from hertz (100 ) to petahertz (1015). These applications involve the interference of a frequency comb with another coherent light source, such as another frequency comb or a single-frequency continuous-wave laser. However, coherent light represents only one type of light. The vast majority of light emanates from “black bodies” such as stars, which is in a thermal state as opposed to a coherent state, and carries profound information about the universe and humanity’s place within it. Other types of light defy classical electromagnetism and are known as non-classical or quantum light. Such quantum light may play central roles in quantum communication, quantum computation, and quantum-enhanced metrology. In this thesis, the use of the optical frequency comb in the interferometric measurement of thermal and quantum light is investigated, with a focus on assessing fundamental limits to the sensitivity of such measurements. In order to measure thermal light, a technique called dual-comb correlation spectroscopy is explored. This technique entails heterodyne measurement of the field of thermal light and subsequent correlation of the field in time. This process reveals the spectrum of thermal light at high resolution and across broad bandwidths. New theoretical work uncovers previously unknown fundamental limits on sensitivity when measuring realistically weak thermal light. Experimental investigation verifies this scaling and is accompanied by a demonstration of spectroscopy at the equivalent power spectral density of our Sun, realizing a greater than 1000-fold sensitivity increase over past demonstrations of this technique. These insights pave the way for expansion of this technique to comb-based spatial correlation of thermal fields. This advancement would allow for extended baseline synthetic aperture hyperspectral imaging throughout the optical spectrum, facilitating novel and profound observations of the universe. The use of frequency combs for the measurement of quantum light is also investigated. This scenario breaks typical quantum optics assumptions, such as large, mode-matched local oscillators, and necessitates new quantum measurement operators. Such measurement operators are derived, which not only describe homodyne measurements on any quantum state of light with a frequency comb local oscillator, but also indicate that the shot noise limit generally reached in comb-based measurements of coherent light (such as in continuous-wave laser heterodyne and dual-comb spectroscopy) does not correspond to the quadrature or coherent state-overlap description standard in quantum optics. Efforts to experimentally reach this “standard” quantum limit demonstrate a significant improvement in the signal-to-noise ratio over the conventional comb-based shot noise limit, paving the way for lower-power portable optical clocks and quantum-enhanced frequencycomb metrology.
Frequency combs are multimode photonic systems that underlie countless precision sensing and metrology applications. Since their invention over two decades ago, numerous efforts have pushed frequency combs to broader bandwidths and more stable operation. More recently, quantum squeezing and entanglement have been explored in single frequency comb systems for quantum advantages in sensing and signal multiplexing. However, the production of quantum light across multiple frequency combs remains unexplored. In this work, we theoretically explore a mechanism that generates a series of nonlinearly coupled frequency combs through cascaded three-wave upconversion and downconversion processes mediated by a single idler comb. We show how this system generates inter- and intracomb two-mode squeezing and entanglement spanning a very large spectral range, from ultraviolet to mid-IR frequencies. Finally, we show how this system can be engineered to produce on-demand multimode quantum light through covariance matrix optimization. Our findings could enable tunable broadband ghost spectroscopy protocols, squeezing-enhanced pump-probe measurements, and broadband entanglement between spectrally-multiplexed quanta of information.
One of the most surprising consequences of quantum mechanics is the nonlocal multi-particle interference observable in joint-detection of distant particle-detectors. Ghost imaging is one of such phenomena. Two types of ghost imaging have been experimentally demonstrated since 1995. Type-one ghost imaging uses entangled photon pairs as the light source. The nonlocal point-to-point image-forming correlation is the result of a constructive-destructive superposition among a large number of biphoton amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of producing a joint-detction event between distant photodetectors. Type-two ghost imaging uses chaotic-thermal light. The type-two image-forming correlation is the result of interferences between paired two-photon amplitudes, corresponding to two different yet indistinguishable alternative ways of triggering a join-detection event by two independent photons. A great deal of confusion about ghost imaging comes from "ghost shadow". Similar to x-ray photography, a ghost shadow can be made in coincidences by "blocking-partial blocking-unblocking" of either co-rotating laser beams or classically correlated "speckles". "Ghost shadow" is indeed a classical phenomenon. The physics of ghost imaging, however, is fundamentally different. This article is aimed at exploring the nonlocal two-photon interference nature of ghost imaging.