Coherence squeezing in optical interference

Abstract

We introduce the concept of optical coherence squeezing in double-slit interference. We construct Hermitian operators that characterize the coherence at the slits, leading to coherence uncertainty relations and a corresponding squeezing condition. We also analyze states exhibiting such squeezing and show its manifestations in the uncertainty of the magnitudes and positions of the intensity fringes. Our work identifies coherence as a fundamental degree of freedom for squeezing, complementing phase, amplitude, and polarization, which could benefit quantum-enhanced interferometry.

Figures (6)

• Figure 1: Illustration of the G space. (a) Normalized interference Poincaré sphere with the state vector $\mathbf{g}$, intensity distinguishability $D$, and fringe visibility $V$. (b) Representation of a two-mode coherent state $\ket{\alpha}_1\!\ket{\beta}_2$. The sphere has an average radius of $G_0$. The uncertainties of the G parameters are equal, as depicted by the uniform uncertainty cloud (red).
• Figure 2: G-space representations of bright quadrature-squeezed states. In both cases, a projection of the uncertainty volume is presented in the $G_2G_3$ plane. In (a) the magnitude $|G_2+\mathrm{i}G_3|$ is squeezed, while in (b) the squeezing occurs in the phase $\arg(G_2+\mathrm{i}G_3)$.
• Figure 3: Intensity fluctuations $\Delta I$ from Eqs. (\ref{['coherent']})--(\ref{['phase-squeezed']}) over a fringe-pattern period in terms of the wave number $k$ and path difference $\Delta r$ for selected squeeze parameter values $q$: (a)$0.15$, (b)$0.4$, (c) $0.6$, and (d)$0.8$. The dotted red, blue dashed, and green solid curves correspond to the coherent, amplitude-squeezed, and phase-squeezed states, respectively. We set $K=1$ and $\bar{n}=10^{15}$ in Eqs. (\ref{['coherent']})--(\ref{['phase-squeezed']}).
• Figure 4: Visualization of the fluctuating intensity fringe patterns based on Eqs. (\ref{['intensity']})--(\ref{['phase-squeezed']}) in terms of the wave number $k$ and path difference $\Delta r$. The red, blue, and green fringes correspond to the coherent, amplitude-squeezed, and phase-squeezed states, respectively. To highlight the differences at the extrema, we have separated the curves vertically and included insets. The yellow lines show the regions where the intensity may reach zero due quantum uncertainty.
• Figure 5: Single-photon interference when $c_1=c_2=1/\sqrt{2}$. (a) Intensity fringe pattern $I\pm \Delta I/2$ obtained from Eq. (\ref{['intensity-single-photon']}) for $K=1$ in terms of the wave number $k$ and path difference $\Delta r$. The yellow bars indicate locations at which the uncertainty area touches the horizontal axis. (b) Corresponding G-space representation. The uncertainty in the radial direction ($G_2$) vanishes, yet the uncertainty in $G_1$ and $G_3$ remains. The latter causes the phase $\arg(G_2+\mathrm{i}G_3)$ to exhibit uncertainty, as depicted by the red disc.