Ghost frequency-time combs: quantum coherence in classical and entangled laser beams Yanhua Shih* [1]

https://www.academia.edu/3064-979X/3/1/10.20935/AcadQuant8239 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. Materials and methods: The GFC is observed from a CW laser beam comprising 500,000 cavity modes. This laser beam is generated by an Erbium-doped fiber laser featuring a 11.7-km-long fiber ring cavity (refractive index ). The QGFC is observed from the entangled coherent state, or entangled laser beams, produced by an optical parametric oscillator (OPO), which similarly features a long fiber ring cavity and approximately half a million cavity modes. The CW laser beams, whether classical or entangled, are measured by two independent distant photodetectors. The two photodetection histories are registered and recorded by a 50 GHz multichannel digital oscilloscope. A personal computer is used to calculate the intensity-intensity correlation and the normalized second-order coherence or correlation function from the photodetection histories. Results: A sharp periodic comb-like function of maximum 50% contrast, GFC, is observed from the intensity-intensity correlation of the CW laser beam; and a similar comb-like function of 100% contrast, QGFC, is observed from the intensity-intensity correlation of the entangled coherent state, or entangled laser beams. Both classical and entangled CW laser beams produce sharp periodic comb-like correlation functions, identical to the sharp periodic pulse train generated by a mode-locked laser, except that the GFC and QGFC are functions of time delay between the two distant photodetection events, , rather than of time t. Conclusions: Building upon our recently discovered ghost frequency-time comb of 50% contrast, we proposed and theoretically analyzed a novel type of entangled coherent state, or entangled laser beams, capable of producing QGFC of 100% contrast. What are the causes of the GFC and QGFC? Classical statistical theory cannot provide a reasonable explanation. From the perspective of quantum coherence theory, observing GFC and QGFC from classical and entangled CW laser beams are entirely reasonable: 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. The above two types of superposition are consistent with the superposition principle of quantum mechanics: if there exist different yet indistinguishable alternative pathways to produce a joint-measurement event, then quantum mechanically, the probability of observing this joint-measurement event is calculated by summing the probability amplitudes of all these different yet indistinguishable alternatives. Experimental observations of GFC and QGFC may finally resolve the long-standing debate between classical statistics and quantum coherence. https://www.academia.edu/journals/academia-quantum/articles?source=journal-top-nav