Loss-insensitive quantum noise reduction in a Raman amplifier with coherent feedback

Abstract

A quantum amplifier usually adds extra noise inevitably through coupling to internal degrees of freedom while amplifying the signal. The introduction of quantum correlations can effectively suppress this extra noise. In this work, we utilize the established quantum correlation between the Stokes field and atomic spin waves in the Raman amplification process to feedback a portion of the Stokes field into the amplifier. This leads to a reduction in quantum noise that is independent of the feedback loss at high gain. A maximum of 6 dB noise reduction is observed. The single-path feedback amplifier is found to be sensitive to the feedback phase, a property that expands its potential for applications in quantum precision measurement, and the general concept can be extended to integrated optics and fiber optic systems.

Figures (5)

• Figure 1: Conceptual schematic for a Raman amplifier with single-path feedback. The Raman amplifier, labeled with its gain $G$ and $g$ which satisfy the relation $G^2-g^2=1$, amplifies the input signal field and couples the amplified field $\hat{a}_{out}$ into the feedback loop, which feeds back to the amplifier’s input as $\hat{a}_{in}$; a beam splitter with transmittance $T$ then splits the output field, routing a portion $\hat{b}_{out}$ to a photodetector (PD) that is combined with a local oscillator (LO) for noise measurement, while the remaining field continues in the feedback path. The orange closed loop forms the feedback channel, which introduces additional vacuum noise $\hat{c}_0$ via loss and adjusts the phase of the feedback loop using a piezoelectric transducer. $\hat{b}_0$ represents the additional vacuum noise introduced by the feedback loop. The green lines denote the input $\hat{S}_{in}$ and output $\hat{S}_{out}$ at the idler port of the Raman amplifier, which corresponds to the non-propagating atomic state.
• Figure 2: Schematic of the coherent feedback Raman amplifier setup based on a $\mathrm{Rb^{87}}$ atomic ensemble. A pump field (W) propagates through the atomic ensemble, driving the Raman interaction by optically pumping atoms from the ground state $|g\rangle$ to the excited state $|e\rangle$. This process generates a Stokes field ($S$) via stimulated Raman scattering, as atoms relax from $|e\rangle$ to a metastable state $|m\rangle$ and coherently excite a spin wave($\hat{S}_{a}$) within the ensemble. A portion of the Stokes output field is directed into a coherent feedback loop via a polarization beam splitter (PBS) and mirror (M1). The feedback loop includes an attenuator (L) to control feedback loss, and a combination of a half-wave plate (HWP) and PBS that sets the signal transmissivity (T). The field is then retroreflected as the feedback Stokes field ($S^\prime$) back into the atomic ensemble via a piezo-electric transducer (PZT) mounted on mirror (M2) for phase scanning. A local oscillator (LO) is combined with the output field at a beam splitter (BS) for homodyne detection (HD). Unwanted light is routed to a beam dump (BD).
• Figure 3: Noise reduction of a Raman amplifier (a) Quantum noise level of the output as the feedback phase is scanned. The vacuum or shot noise level is -73.6 dB (b) Noise reduction ratio as a function of the quantum gain $G_{qn}$ of Raman amplifier without feedback. The solid curve is a fit to Eq.(\ref{['R2']}).
• Figure 4: Noise reduction as a function of feedback parameters with theoretical fitting (a) Measured noise reduction as a function of feedback loss $L$, with the solid red curve representing a theoretical fit from Eq. \ref{['R']}. (b) Measured noise reduction as a function of beam splitter transmittance $T$, with the solid red curve representing a theoretical fit from Eq. \ref{['R']}.
• Figure 5: Observed single-path feedback amplifier sensitive to feedback phase. Interference fringes, represented by red data points with a blue sinusoidal fitting curve, are measured at the output of RA as a function of phase scan (gray). The black curve corresponds to the background intensity level.