Interferometry using discrete energy levels in nuclear, atomic or molecular systems is the foundation for a wide range of physical phenomena and enables powerful techniques such as nuclear magnetic resonance, electron spin resonance, Ramsey-based spectroscopy and laser/maser technology. It also plays a unique role in quantum information processing as qubits are realized as energy superposition states of single quantum systems. Here, we demonstrate quantum interference of different energy states of single quanta of light in full analogy to energy levels of atoms or nuclear spins and implement a Ramsey interferometer with single photons. We experimentally generate energy superposition states of a single photon and manipulate them with unitary transformations to realize arbitrary projective measurements, which allows for the realization a high-visibility single-photon Ramsey interferometer. Our approach opens the path for frequency-encoded photonic qubits in quantum information processing and quantum communication.
Main Text:The two-state model represents the most fundamental quantum system and can be applied to a wide variety of physical systems. Ramsey interferometry, magnetic resonance imaging, and electron-spin resonance spectroscopy are governed by similar 2-level system dynamics, which involves molecular-atomic levels, nuclear spin, and electronic spin, respectively. The coupling between energy levels is achieved using electromagnetic fields, which can be tailored at will and allows for many advanced techniques such as adiabatic elimination and stimulated Raman adiabatic passage in higher dimensional atomic system, or spin locking in NMR. Quantum interference involving systems in superposition of different energies is at the heart of fundamental and applied physics. For example, quantum coherence has been highly useful in increasing the accuracy of time measurement from the first idea of using NMR suggested by Rabi in 1945 (1) to the first atomic clock relying on the Ramsey interferometry (2,3), which has been recently extended by using trapped single ions (4). In addition, Ramsey interferometry on single Rydberg atoms has allowed the nondestructive measurement of the number of photon in a cavity (5) and single spin manipulation using the same techniques constitutes one of the most promising routes towards quantum processing (6-8). Matter-wave interferometers using collective energy levels of atoms in a BEC have also been demonstrated (9) and used to measure gravity down to record breaking precision (10). Nevertheless, a fundamental quantum system that has not been extensively studied in the context of discrete 2-level energy systems (i.e. frequency) is the single photon. Translating those studies to photonics system can be implemented by controlling light with light using nonlinear optics. For classical light the analogy between atomic/molecular optics and nonlinear optics is well known (11) and there are various cases where the complex dynamics of light propagation in a nonlinear medium can be si...