Quantum logic and imaging with photons

In this talk, we will discuss two different problems viz., conditional phase gate with photonic qubits and quantum imaging with undetected photons.
The primary motivation for the first problem on phase gate is to explore all optical systems for quantum logical operations. This will involve an investigation of quantum nonlinear optical schemes based on three- and four-wave mixing processes to see which ones would and would not be useful for the construction of a phase gate at the single-photon level. The main emphasis, here, will be to develop a conceptual framework through Hamiltonian models to understand the necessary conditions to achieve a conditional phase shift. Following this, we will take the positive results from these models and apply them to a realistic atomic system to explore the possibility of physical realization of a conditional phase gate in the lab. We will discuss the interaction of single-photon pulses with an ensemble of N-type atoms, and look at the “giant Kerr” effect in electromagnetically induced transparency to understand the nature of atom-photon interaction and how the phase gets built in such a system. Furthermore, we will understand how the bandwidth gets restricted naturally in such an atomic system.
The second problem, i.e., Quantum imaging with undetected photons (QIUP), is a novel interferometric technique in which the light that illuminates the object is not detected. The image is constructed from the single-photon interference pattern of the photon that never interacted with the object. QIUP exploits quantum indistinguishability by path identity and the imaging in this technique is enabled by the spatial correlations between the twin photons. We will discuss the process of imaging in both near- and far-field configurations along with their resolution limit.