Real-time controls based on quantum measurements are powerful tools for various quantum protocols. However, their experimental realization have been limited by mode-mismatch between temporal mode of quadrature measurement and that heralded by photon detection. Here, we demonstrate real-time quadrature measurement of a single-photon wavepacket induced by a photon detection, by utilizing continuous temporal-mode-matching between homodyne detection and an exponentially rising temporal mode. Single photons in exponentially rising modes are also expected to be useful resources for interactions with other quantum systems.PACS numbers: 03.67. Lx, 42.50.Dv, 42.50.Ex, Quantum measurement is a basic requirement for various quantum protocols. In many of them, realtime acquisition of the measurement outcomes is beneficial or even required. Real-time measurement enables real-time feedback or feedforward controls of quantum systems. Measurement-based quantum computation (MBQC) [1, 2] is a typical example of such real-time usage of the measurement results, where the measurement results are fedforward to the next computational step. In addition, quantum dynamics conditioned by measurements are often referred to as quantum trajectories or quantum filters [3][4][5], and form essential parts of developing quantum control theories. Based on them, basic cases of quantum controls, e.g., suppression of noises, have been tested with a variety of systems recently [6][7][8][9].In order to put the quantum measurement-based technologies further, an important adaptation is to bridge different quantum systems or different quantum variables in the measurement system [5,10,11]. As a general problem, one may want to connect different systems as a signal and probe. Aside from the issues of connecting different systems, even when restricting us to the light field, there are two fundamental variables reflecting the waveparticle duality. One is the continuous variable (CV) field quadrature amplitudex = (â +â † )/ √ 2, and the other is the discrete variable (DV) photon numbern =â †â , wherê a andâ † denote the field annihilation and creation operators, respectively. CV-DV hybrid architectures have been identified to offer crucial advantages, ranging from deterministic and fault-tolerant MBQC [12-15] to loopholefree Bell inequality test [16]. Experimental technologies for the hybridization are also rapidly developing [17][18][19][20]; however, combining them with real-time quantumoptical controls are facing difficulties.An obstacle is a mode mismatch between CV-based homodyne detection and DV-based photon detection. To be more precise, homodyne detection is sensitive to vacuum fluctuation, while photon detection is not. Therefore, filtration of the field quadrature, i.e. integration with an appropriate weight function f (t) asX = f (t)x(t)dt is essential in order to remove irrelevant vacuum noises and obtain meaningful quadrature information matching with the field mode heralded by photon detections. At this point, quadrature measurement often fails ...
