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Physica Scripta

A Gallery of Quantum States: Tomography of Nonclassical Light

J. Mlynek, Gerd Breitenbach, and S. Schiller

Published Jan 1, 1998• 2 citations
Publisher

Abstract

The complete family of squeezed states of a continuous-wave mode pair of the electromagnetic field was generated and analyzed by tomographical methods. Wigner functions, photon number distributions, density matrices, and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub- and super-Poissonian photon statistics, and bifurcations of the phase distribution were observed.

DOI
10.1238/physica.topical.076a00098

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The complete family of squeezed states of a continuous-wave mode pair of the electromagnetic field was generated and analyzed by tomographical methods. Wigner functions, photon number distributions, density matrices, and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub- and super-Poissonian photon statistics, and bifurcations of the phase distribution were observed.
States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.
Displaced Fock states of the electromagnetic field have been synthesized by overlapping the pulsed optical single-photon Fock state ∣1〉|1〉∣1〉 with coherent states on a high-reflection beam splitter and completely characterized by means of quantum homodyne tomography. The reconstruction reveals nonclassical properties of displaced Fock states, such as negativity of the Wigner function and photon number oscillations. To our knowledge, this is the first time complete tomographic reconstruction has been performed on a highly nonclassical optical state.
We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.
Abstract We present a theoretical study on the generation and nonclassical properties of hybrid squeezed states (HSS), a class of engineered quantum states with enhanced quantum features. Using a modified beam splitter-Kerr medium scheme, we construct superpositions of squeezed vacuum and two-photon-added squeezed states, providing a flexible framework to generate and control hybrid quantum states. Nonclassicality is analysed via Mandel's QQQ parameter, photon number distributions, probability distribution functions, and Wigner functions, revealing sub-Poissonian statistics, oscillatory photon distributions, and significant Wigner negativity. Phase-sensitivity analysis within a Mach-Zehnder interferometric framework demonstrates that HSS outperform conventional squeezed and photon-added squeezed states, achieving measurement precisions that exceed the standard quantum limit and approach the Heisenberg limit under optimal parameters. These results establish hybrid squeezed states as a powerful resource for quantum metrology, communication, and optical interferometry.