Finite-time quantum-to-classical transition for a Schroedinger-cat state

Abstract

The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum to classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial definition have well defined physical meaning and allow a deeper understanding of the quantum to classical transition. Our analysis shows that, for most nonclassicality measures, the Schrödinger cat dies after a finite time. Moreover, our results challenge the prevailing idea that more macroscopic states are more susceptible to decoherence in the sense that the transition from quantum to classical occurs faster. Since nonclassicality is prerequisite for entanglement generation our results also bridge the gap between decoherence, which appears to be only asymptotic, and entanglement, which may show a sudden death. In fact, whereas the loss of coherences still remains asymptotic, we have shown that the transition from quantum to classical can indeed occur at a finite time.

9+epsilon pages, 4 figures, published version. Originally submitted as "Sudden death of the Schroedinger cat", a bit too cool for APS policy :-)

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• Collapse and revival of quantum coherence for a harmonic oscillator interacting with a classical fluctuating environment
• Overcoming decoherence of cat-states formed in a cavity using squeezed-state inputs
• Creation, storage and retrieval of an optomechanical cat state
• Q-functions as models of physical reality
• Gaussification through decoherence
• Quantum backflow effect and nonclassicality
• Generating the Schrodinger cat state in a nanomechanical resonator coupled to a charge qubit
• Quantum to classical transition induced by gravitational time dilation
• Quantum speed of evolution in a Markovian bosonic environment
• Steady Schrödinger cat state of a driven Ising chain
• Non-classicality tests and entanglement witnesses for macroscopic mechanical superposition states
• Detecting quantum non-Gaussianity of noisy Schrödinger cat states