Quantum state tomography of ultrafast optical pulses at telecom wavelength by broadband balanced homodyne detection

The efficient transfer of a quantum state from photons to matter qubits in order to momentarily store information has become a central problem in quantum information processing. A quantum memory turns out to be an essential tool to achieve advanced technologies such as quantum networks, quantum repeaters, deterministic single photon sources or linear optics quantum computers. The realization of a quantum interface has been investigated in various forms, among which one can find solid-state atomic ensembles, color centers in crystal lattices, cold atomic gases, optical phonons in diamond and many others. Here we focus on a broadband quantum interface for high repetition rate (76 MHz) ultrafast optical pulses (250 fs) at telecommunication wavelength (1530 nm) based on the photon echo process occurring in semiconductor quantum dots. We evaluated the quantum state of photonic qubits in order to characterize the impact of the storage on the transmitted signal. Homodyne traces corresponding to projections of the Wigner function of the signal on rotated quadrature components were obtained using broadband balanced homodyne detection, i.e. mixing the ultrafast optical pulses to analyze with a high repetition rate pulsed local oscillator. The reconstruction of the Wigner function from the homodyne traces was performed using three algorithms: The inverse Radon transform, the minimax adaptive reconstruction and the maximum likelihood estimation. The three methods lead to similar results, concluding that for an input pulse in a coherent state, the reemitted photon echo is also in a coherent state.