Low-noise optical field phase-shifting manipulated using a coherently-prepared three-level atomic medium

We propose a multifunction phase-shifting manipulator with low noise at a single-photon level, by using a three-level atomic scheme. This three-level system interacts with a strong pumping field and a weak probe field with a large detuning. Due to this large detuning, two lower states can be coherently prepared prior to the injection of the pump and probe fields. In our configuration, the duration of the pumping field is much longer than that of the probe field. By solving the Heisenberg-Langevin equations of our system under the steady state approximation, we calculate the linear susceptibility of the system and examine the quantum noise properties of the probe field in detail. We show that this scheme, which rests on the process of two-wave mixing with initial atomic coherence, exhibits many interesting properties that neither typical electromagnetically induced transparency (EIT) schemes nor active Raman gain (ARG) schemes possess. Although both EIT- and ARG-based schemes have been widely investigated in atomic medium, the direct generalizations of these schemes to the single/few photon limit prove to be more problematic. The low fidelity due to the significant probe-field attenuation in EIT medium and the large quantum noise due to the amplification of the probe field in an active Raman gain medium are the main obstacles that prohibit a high-fidelity, low-noise phase shifter from being realized in the single/few photon limit. Physically, this scheme can be viewed as a hybrid scheme in which two processes of different physical principles are allowed to interfere with each other to achieve many desired functionalities. For instance, it can be used as a lossless two-photon-broadband phase-shifter with suitable system parameters. It can also be used as an attenuator/amplifier and a total transparency with a zero phase shift. In particular, we show that by locking the pump field intensity and the two-photon detuning simultaneously a flat constant pi-phase shift can be realized with unit probe fidelity in a broad probe field frequency range. Applying the quantum regression theorem, we calculate the noise spectrum of the outgoing probe field as a large phase shift is achieved, and show that this two-photon-insensitive pi-phase shift may significantly reduce the quantum noise fluctuations associated with a Raman gain process, and have a lot of potential applications for quantum information processing and optical telecommunication. The realization of this broadband pi-phase-shift with significantly reduced quantum noise fluctuations makes this scheme attractive for the realization of low-noise phase-gate/polarization-gate at single-photon level.