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Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.

Energy-time entangled photons are critical in many quantum optical phenomena and have emerged as important elements in quantum information protocols. Entanglement in this degree of freedom often manifests itself on ultrafast timescales making it very difficult to detect, whether one employs direct or interferometric techniques, as photon-counting detectors have insufficient time resolution. Here, we implement ultrafast photon counters based on nonlinear interactions and strong femtosecond laser pulses to probe energy-time entanglement in this important regime. Using this technique and single-photon spectrometers, we characterize all the spectral and temporal correlations of two entangled photons with femtosecond resolution. This enables the witnessing of energy-time entanglement using uncertainty relations and the direct observation of nonlocal dispersion cancellation on ultrafast timescales. These techniques are essential to understand and control the energy-time degree of freedom of light for ultrafast quantum optics.The energy-time degree of freedom of non-classical light is of great interest for quantum information as it supports various encodings, including frequency bins [1], time bins [2], and broadband temporal modes [3], and is intrinsically robust for propagation through longdistance fibre links [4]. Applications which harness quantum correlations in this degree of freedom, referred to as energy-time entanglement [5], include dispersion cancellation [6,7], high-dimensional quantum key distribution [8,9], and quantum-enhanced clock synchronization [10]. In ultrafast optics and attosecond physics, the ability to measure both frequency and temporal features has led to important innovations in electric field reconstruction techniques [11,12] and pulse characterization on very short timescales, enabling advances in spectroscopy [13], laser physics [14], nonlinear optics [15], and imaging [16]. In order to characterize and control energy-time entangled photons and advance biphoton pulse shaping, similar measurement capabilities are essential in the quantum regime.Experimental signatures of entanglement can arise in correlation measurements of complementary variables [17], or through nonlocal quantum effects [5,6]. With the energy-time degree of freedom, one complementary set consists of measuring the intensity correlations as a function of the photon frequencies and as a function of their time of arrival. These have been individually realized for different photonic systems with measurements in frequency [18,19] or in time [20][21][22]. Certifying the presence of entanglement with direct measurements requires both spectral and temporal correlations, since acquiring only one remains insufficient to uniquely specify the other due to the ambiguity of the spectral phase. Depending on the platform, this can be challenging. Narrowband photons from atomic systems can be readily measured in time but are difficult to spectrally resolve [22]. THz-bandwidth photons produced in spontaneous parametric downconversion (SPDC...

We studied the dependence of dissociative ionization in H 2 on carrier-envelope phase (CEP) of few-cycle (6 fs) near-infrared laser pulses. For low-energy channels, we present the first experimental observation of the CEP dependence of combined dissociation yield (with protons emitted in both directions), as well as the highest degree of asymmetry reported to date (40%). The observed modulations in both asymmetry and combined yield could be understood in terms of interference between different n-photon dissociation pathways-n and (n + 1) photon channels for asymmetry, n and (n + 2) photon channels for yield-as suggested by the general theory of CEP effects (Roudnev and Esry 2007 Phys. Rev. Lett. 99 220406). The yield modulation is found to be π-periodic in CEP, with its phase strongly dependent on fragment kinetic energy (and reversing its sign within the studied energy range), indicating that the dissociation yield does not simply follow the CEP dependence of maximum electric field, as a naïve intuition might suggest. We also find that a positively chirped pulse can lead to a higher dissociation probability than a transformlimited pulse.

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