Quantum uncertainty: ΔxΔp experimental evaluation and direct visualization

The time evolution of a quantum particle’s product of uncertainties in position and momentum is calculated when it is coupled with an external source. We have used a simple toy model where the particle is subject to a harmonic potential and coupled with an equivalent harmonic oscillator via a linear term. It is found that the long-time-averaged product is an increasing function of the coupling strength. It diverges when one of the eigenmodes of the coupled system goes soft, with the singular term twice of that for the stationary state. Generally, there is a jump of finite size for this quantity when a small coupling is turned on, compared to the uncoupled case. Similar behaviors have also been found for the von Neumann entanglement entropy, which is calculated exactly using a covariance matrix formalism. We find that the mode-interference plays an important role in the main features of this work.

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Quantum uncertainty: ΔxΔp experimental evaluation and direct visualization

Cited by 2 publications

References 24 publications

On the experimental verification of the uncertainty principle of position and momentum

On the experimental verification of the uncertainty principle of position and momentum

Effects of coupling with a quantum oscillator on time-evolution of uncertainties of a quantum particle and entanglement entropy

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