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Frontiers in Optics

Schrödinger kittens and higher-order Fock states : generation and detection of propagating light fields with negative Wigner functions

Alexei Ourjoumtsev, Aurélien Dantan, Rosa Tualle-Brouri, Philippe Grangier

Published Jan 1, 2006• 0 citations
Publisher

Abstract

We describe recent progress in the experimental realization of propagating light fields with observed negative Wigner functions, measured by pulsed homodyne quantum tomography. This includes in particular Schrödinger cat states with small amplitudes ("Schrödinger kittens") [1], and n=2 Fock states [2]. Quantum information applications of such states will be discussed, such as loophole-free tests of Bell's inequalities [3].

DOI
10.1364/ls.2006.ltud2

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"Schrödinger Kittens" and other quantum states of light with negative Wigner functions

Alexei Ourjoumtsev

•Jan 1, 2007•0 citations
We describe recent progress in the experimental realization of propagating light fields with observed negative Wigner functions, measured by pulsed homodyne quantum tomography. This includes in particular Schrödinger cat states with small amplitudes ("Schrödinger kittens") [1], and n=2 Fock states [2]. Quantum information applications of such states will be discussed, such as loophole-free tests of Bell's inequalities [3].
We present a detailed experimental analysis of a free-propagating light pulse prepared in a "Schrödinger kitten" state, which is defined as a quantum superposition of "classical" coherent states with small amplitudes. This kitten state is generated by subtracting one photon from a squeezed vacuum beam, and it clearly presents a negative Wigner function. The predicted influence of the experimental parameters is in excellent agreement with the experimental results. The amplitude of the coherent states can be amplified to transform our "Schrödinger kittens" into bigger Schrödinger cats, providing an essential tool for quantum information processing.
A "Schrödinger cat" state of free-propagating light can be defined as a quantum superposition of well separated coherent states. 1, 2 We demonstrated, theoretically and experimentally, a protocol which allows to generate arbitrarily large squeezed Schrödinger cat states, using a homodyne detection and photon number states as resources. We implemented this protocol experimentally with light pulses containing two photons, producing a squeezed Schrödinger cat state with a negative Wigner function. This state clearly presents several quantum phase-space interference fringes between the "dead" and "alive" components, and it is large enough to become useful for experimental tests of quantum theory and quantum information processing.
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.