Tunable passive squeezing of squeezed light through unbalanced double homodyne detection

TL;DR

The paper shows that double homodyne detection can be engineered to perform a tunable squeezing operation on the measured quantum state by deliberately unbalancing the input beamsplitter, enabling direct sampling of the squeezed Q function with strength controlled by the reflectivity. Using a polarization-based implementation, the authors realize and characterize a multimode squeezed vacuum from a SPOPO, demonstrating continuous control over the deformation of the phase-space Q function from phase-squeezed to amplitude-squeezed regimes and even unsqueezing to a thermal-like state. The work provides both a theoretical framework and experimental validation for POVM engineering in quantum optics, offering a resource-efficient alternative to full tomography and enabling on-line state processing and applications in metrology and non-Gaussianity certification. The approach integrates state manipulation into the measurement device, highlighting potential for rapid, direct-state characterization in scalable quantum technologies.

Abstract

The full characterization of quantum states of light is a central task in quantum optics and information science. Double homodyne detection provides a powerful method for the direct measurement of the Husimi Q quasi-probability distribution, offering a complete state representation in a simple experimental setting and a limited time frame. Here, we demonstrate that double homodyne detection can serve as more than a passive measurement apparatus. By intentionally unbalancing the input beamsplitter that splits the quantum signal, we show that the detection scheme itself performs an effective squeezing or anti-squeezing transformation on the state being measured. The resulting measurement directly samples the Q function of the input state as if it were acted upon by a squeezing operator whose strength is a tunable experimental parameter : the beamsplitter's reflectivity. We experimentally realize this technique using a robust polarization-encoded double homodyne detection to characterize a squeezed vacuum state. Our results demonstrate the controlled deformation of the measured Q function's phase-space distribution, confirming that unbalanced double homodyne detection is a versatile tool for simultaneous quantum state manipulation and characterization.

Figures (6)

• Figure 1: Principle of operation of double homodyne detection. A signal state $\hat{\rho}_s$ is mixed with a vacuum field into the input beamsplitter BS${^*}$ with reflectivity $R$. The two output fields are measured by two homodyne detectors HD1 and HD2 (green rectangles) with a phase reference given by two local oscillator (LO) with a relative phase of $\pi/2$. The two HDs thus sample orthogonal quadratures $\hat{q}_1$ and $\hat{p}_2$ of the input signal state with a precision limited by the Heisenberg uncertainty principle.
• Figure 2: Scheme of the experimental double homodyne detection setup based on polarization, where the input beamsplitter BS${^*}$ of Fig. \ref{['F1']} is substituted by a polarization beam splitter. A half-wave plate in the path of the signal beam is added to control the unbalancing and the local oscillator is prepared in circular polarization mode.
• Figure 3: Scheme of the experimental setup. The initial beam is split in two parts. The first part is used for the generation of the state. A SPOPO cavity is pumped by an up-converted pump beam, resulting in a multimode squeezed vacuum at the output. The second part is used for the local oscillator of the DHD, where we can chose the mode of the LO using a pulse shaper.
• Figure 4: Experimental Q function of a squeezed state reconstructed with $N_p=5\times 10^4$ samples. The black lines represent the contours of the fit by a two-dimensional Gaussian. The fitted values give a squeezing and antisqueezing levels of -1.25 dB and 2.6 dB, respectively.
• Figure 5: Experimental Q function of a squeezed state for different values of R reconstructed with $N_p=5\times 10^4$ samples. Values of R above 0.5 squeeze the state in the amplitude quadrature $q_1$ whereas values of R below 0.5 along phase quadrature $p_2$ in turn.