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arXiv:1512.06096

Phase coherent resonator detection as a complete quantum measurement of the two-mode spectral quantum state of light

F. A. S. Barbosa, A. S. Coelho, K. N. Cassemiro, M. Martinelli, P. Nussenzveig, Alessandro S. Villar

Published Dec 18, 2015• 0 citations
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Abstract

The introduction of phase coherence in the detection of quantum noise of light yields a pure quantum measurement of spectral modes. We theoretically show that such coherent quantum measurement performed with the technique of resonator detection (RD) is able to access any direction in the two-mode phase space of spectral sidebands under appropriate conditions, thus furnishing a complete measurement of the four-dimensional Wigner function. We obtain a realistic measurement operator for coherent RD by including the effects of imperfect resonator mode matching in our analysis. Moreover, we experimentally demonstrate the realization of phase coherent RD to characterize a two-mode displaced quantum state.

DOI
10.48550/arxiv.1512.06096

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The introduction of phase coherence in the detection of quantum noise of light yields a pure quantum measurement of spectral modes. We theoretically show that such coherent quantum measurement performed with the technique of resonator detection (RD) is able to access any direction in the two-mode phase space of spectral sidebands under appropriate conditions, thus furnishing a complete measurement of the four-dimensional Wigner function. We obtain a realistic measurement operator for coherent RD by including the effects of imperfect resonator mode matching in our analysis. Moreover, we experimentally demonstrate the realization of phase coherent RD to characterize a two-mode displaced quantum state.
The quantum noise in photocurrent fluctuations usually gives incomplete information about the quantum state of spectral sideband modes of bright light beams involved in the detection. Each frequency component of the noise spectrum corresponds to two sideband modes symmetrically located around the bright optical field. In the case of the usual homodyne detection, it limits the ability to recover discriminated information of each mode involved. We theoretically show that complete reconstruction of the two-mode quantum state can be obtained by using phase-locked (coherent) resonator detection, even for non-Gaussian states. We experimentally demonstrate the technique by measuring a two-mode displaced coherent state.
We revisit the problem of quantum state reconstruction of light beams from the photocurrent quantum noise. As is well known, but often overlooked, two longitudinal field modes contribute to each spectral component of the photocurrent (sideband modes). We show that spectral homodyne detection is intrinsically incapable of providing all the information needed for the full reconstruction of the two-mode spectral quantum state. Such a limitation is overcome by the technique of resonator detection. A detailed theoretical description and comparison of both methods is presented, as well as an experiment to measure the six-mode quantum state of pump-signal-idler beams of an optical parametric oscillator above the oscillation threshold.
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.
Summary form only given.We show experimentally the reconstructions of Wigner functions for the output states of a laser. These states have classical Wigner functions with Gaussian cross-sections. In order to investigate the spectral properties of the output states, we normalize the Wigner functions in the inverse Radon transform algorithm to a coherent state. In this way, we are able to compare the full spectrum of Wigner functions obtained with different detection frequencies, paying particular attention to Wigner functions near the laser relaxation oscillation. The same normalized Wigner function is also used to measure squeezed optical states from an optical parametric oscillator. When large modulation is introduced to the laser beam, a dc component is introduced in the Wigner function. We show that Wigner functions of incoherent superposition states can be reconstructed using this modulation technique. In some cases, fluctuations can be large enough to produce highly non-Gaussian Wigner functions. We provide examples of such cases and show that optical homodyne tomography can provide essentially new information not detectable with standard quadrature variance measurements. Furthermore, we demonstrate that single sideband analysis used to date will sometimes no longer suffice in the analysis of such optical states. We include the higher order sideband correlations experimentally and discuss the necessity of these higher order sidebands for measuring non-Gaussian quantum states, e.g. Schrodinger's cat and Fock states.