Reconstruction of SU(1,1) States

Abstract

We show how group symmetries can be used to reconstruct quantum states. In our scheme for SU(1,1) states, the input field passes through a non-degenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode. The density matrix in the Fock basis is retrieved from the measured data by least squares method after singular value decomposition of the design matrix. Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered.

8 pages, 5 figures, submitted to PRA

References in corpus (5)

• Wigner functions, squeezing properties and slow decoherence of atomic Schrodinger cats
• Radon transform and pattern functions in quantum tomography
• Self-homodyne tomography of a twin-beam state
• Quantum State Reconstruction of a Bose-Einstein Condensate
• Measuring the Cyclotron State of a Trapped Electron

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• Unitary relation for the time-dependent SU(1,1) systems
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Operational definition of quantum correlations of light
• Sharply tunable group velocity in alkali vapors using a single low-power control field
• Permutation symmetry for the tomographic probability distribution of a system of identical particles