Beyond Spectral Homodyne Detection: Complete Quantum Measurement of Spectral Modes of Light

Spectral homodyne detection, a widely used technique for measuring quantum properties of light beams, cannot retrieve all the information needed to reconstruct the quantum state of spectral field modes. We show that full quantum state reconstruction can be achieved with the alternative measurement technique of resonator detection. We experimentally demonstrate this difference by engineering a quantum state with features that go undetected by homodyne detection but are clearly revealed by resonator detection.

Figure 1

Experimental setup. State preparation (solid green beam): An EOM displaces spectral modes, and an asymmetry resonator attenuates one of them. State detection: Either homodyne (dotted blue beam) or resonator detection (dashed red beam) is employed. A flip mirror and blocking of LO are used to choose between the two types of quantum measurement.

Figure 2

Measured expectation values of spectral quadrature observables as functions of displacement angle $\theta$. Left: Quantum state $|{\psi }_1⟩$ with a balanced energy distribution. Right: Quantum state $|{\psi }_2⟩$ with a spectral energy imbalance.

Figure 3

Measurements of spectral quantum noise produced by the balanced quantum state ${\widehat{\rho }}_r$. Top: Homodyne detection, as a function of $\phi$. Bottom: Resonator detection, as a function of $\Delta$. Solid lines (‘HD’ on top and ’RD’ on bottom) are theoretical fits to the data. Dashed line on the bottom (‘HD-like’) represents the theoretical noise curve of Eq. (10) as it would appear in resonator detection using only moments obtainable with homodyne detection.

Figure 4

Measurements of spectral quantum noise produced by the imbalanced quantum state $\widehat{\rho }$. Curves and labels follow Fig. 3.