Local-oscillator-agnostic squeezing detection

Abstract

We address the problem of measuring nonclassicality in continuous-variable bosonic systems without having access to a known reference signal. To this end, we construct broader classes of criteria for nonclassicality which allow us to investigate quantum phenomena regardless of the quantumness of selected subsystems. Such witnesses are based on the notion of partial normal ordering. This approach is applied to balanced homodyne detection using arbitrary, potentially nonclassical local oscillator states, yet only revealing the probed signal's quantumness. Our framework is compared to standard techniques, and the robustness and advanced sensitivity of our approach is shown. Therefore, a widely applicable framework, well-suited for applications in quantum metrology and quantum information, is derived to assess the quantum features of a photonic system when a well-defined coherent laser as a reference state is not available in the physical domain under study.

Figures (3)

• Figure 1: Balanced homodyne detection. The SI and the here arbitrary LO interfere on a $50/50$ beam splitter. Both outputs are measured with photodetectors, whose difference defines the observable $\hat{L}$. The LO's phase $\theta$ may be controlled.
• Figure 2: Partially normally ordered $\left\langle{\stackrel{A}{:}}(\Delta\hat{L})^2{\stackrel{A}{:}}\right\rangle$ (solid, black) and fully normally ordered $\left\langle: (\Delta\hat{L})^2 :\right\rangle$ (dashed, gray) field fluctuations as a function of the phase parameter $\theta$. Here, the LO is a squeezed-vacuum state ($3\,\mathrm{dB}$), and a classical coherent state (mean photon number of one) is taken as the SI. The full normal ordering becomes negative not because of a nonclassical SI but because of the nonclassical LO, yielding a false-positive squeezing indicator for the SI when the LO's properties are not known. Our method based on partial normal ordering, however, correctly shows that no nonclassicality is in the SI.
• Figure 3: Noise parameter $\mathcal{N}$ [Eq. \ref{['eq:NoiseParameter']}] as a function of the LO intensity $\langle\hat{b}^\dag\hat{b}\rangle$ (logarithmic scale) for the common coherent-state LO (dashed, gray) and a squeezed-vacuum LO (solid, black). The nonclassical SI ($3\,\mathrm{dB}$ squeezing) yields a negative value $\mathcal{N}<0$, thus demonstrates noise suppression below the shot-noise limit (at $\mathcal{N}=0$). A coherent LO laser underperforms, requiring a high intensity and approaching the highest sensitivity (also $3\,\mathrm{dB}$) from above. A squeezed LO outperforms the coherent one, including an optimal noise reduction at a finite squeezing value (again $3\,\mathrm{dB} \rightarrow \langle\hat{b}^\dag \hat{b}\rangle\approx0.124$).