We experimentally demonstrate the generation of multi-photon Fock states with up to three photons in well-defined spatial-temporal modes synchronized with a classical clock. The states are characterized using quantum optical homodyne tomography to ensure mode selectivity. The three-photon Fock states are probabilistically generated by pulsed spontaneous parametric down conversion at a rate of one per second, enabling complete characterization in 12 hours.

Improved measurement techniques are central to technological development and foundational scientific exploration. Quantum physics relies on detectors sensitive to non-classical features of systems, enabling precise tests of physical laws and quantum-enhanced technologies including precision measurement and secure communications. Accurate detector response calibration for quantum-scale inputs is key to future research and development in these cognate areas. To address this requirement, quantum detector tomography has been recently introduced. However, this technique becomes increasingly challenging as the complexity of the detector response and input space grow in a number of measurement outcomes and required probe states, leading to further demands on experiments and data analysis. Here we present an experimental implementation of a versatile, alternative characterization technique to address many-outcome quantum detectors that limits the input calibration region and does not involve numerical post processing. To demonstrate the applicability of this approach, the calibrated detector is subsequently used to estimate non-classical photon number states.

Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.

Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entanglement of the two output modes. A conditional projective measurement onto a single photon state at one output mode heralds the success of the process. This operation, which implements a measurement-induced nonlinearity, is capable of suppressing particular photon-number probability amplitudes of an arbitrary quantum state. We employ coherent-state process tomography to determine the precise operation realized in our experiment, which is mathematically represented by a process tensor. To identify the key sources of experimental imperfection, we develop a realistic model of the process and identify three main contributions that significantly hamper its efficacy. The experimentally reconstructed process tensor is compared with the model, yielding a fidelity better than 0.95. This enables us to identify three key challenges to overcome in realizing a filter with optimal performance-namely the single-photon nature of the auxiliary state, high mode overlap of the optical fields involved, and the need for photon-number-resolving detection when heralding. The results show that the filter does indeed exhibit a non-linear response as a function of input photon number and preserves the phase relation between Fock layers of the output state, providing promise for future applications.

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