Hannover 2003 – scientific programme

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Q: Quantenoptik

Q 52: Quanteneffekte 3

Q 52.7: Talk

Friday, March 28, 2003, 15:30–15:45, F107

A complete hierarchy of observable conditions for nonclassicality of quantum states — •Thomas Richter and Werner Vogel — AG Quantenoptik, Universitaet Rostock

Necessary and sufficient conditions are derived that completely characterize the nonclassicality of quantum states of the harmonic oscillator. Making use of a theorem by Bochner we derive an infinite hierarchy of conditions for the characteristic function of the quantum state. The full hierarchy of conditions is completely equivalent to the failure of the Glauber-Sudarshan P-function to be a probability density. The reformulated version of the P-function criterion is directly related to measurable quantities that can be observed in phase-sensitive measurements such as homodyne detection. It generalizes a previously proposed criterion for nonclassicality [1] that has already been applied in experiments [2]. Examples of phase-insensitive nonclassical quantum states are considered. [1] W. Vogel, Phys. Rev. Lett. 84, 1849 (2000).

[2] A. Lvovsky and J.H. Shapiro, Phys. Rev. A 65, 033830 (2002).