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arXiv:1204.4802 · Europhysics Letters (EPL)

Tunnelling of the 3rd kind: A test of the effective non-locality of quantum field theory

S. A. Gardiner, Holger Gies A, Joerg Jaeckel, Chris J. Wallace

Published Mar 1, 2013• 2 citations
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Abstract

Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance - provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.

DOI
10.1209/0295-5075/101/61001

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Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance - provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.
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Abstract We address a foundational question in quantum mechanics: can a particle be directly found in a classically-forbidden virtual state? We instantiate this conceptual question by investigating the traversal of electrons through a tunnel barrier, which we define in a triple quantum dot system where the occupation of the central dot is energetically avoided. The motivation behind this setup is to answer whether the central dot is occupied or not during a virtual transition when it is being explicitly monitored. We investigate this problem in two different limits of continuous measurements: the stochastic quantum diffusion and the quantum jump. We find that, even though individual trajectories differ considerably across these limits, measuring leads to a higher occupation in the central dot on average. We also find that a suitably strong measurement can significantly boost the tunneling current—an effect we call measurement-assisted tunneling . Our results demonstrate that the act of observation fundamentally reshapes tunneling dynamics, resolving the seeming paradox of detecting a particle in a classically forbidden region: weak measurements partially localize the particle, while strong measurements enforce a discontinuous either/or detection or no detection outcome.
The tunneling effect is the most popular phenomenon of quantum physics and is present in modern physical theories. Still, the most important features of this effect are already present in toy models - low dimensional quantum mechanics with high potential barriers. Even these simple systems cannot be solved analytically and approximations have to be made. Tunneling is closely related to splitting of the ground state energy which is degenerate in the classical limit. In this thesis we use two methods to estimate the energy splitting in one dimensional quantum mechanics. In semi-classical approximation the splitting is calculated in the weak coupling limit. The other approach, Tamm-Dancoff method gives very precise numerical results for finite coupling. Comparing these two approaches we are able to confirm results of the semi-classical approximation and determine range of its applicability. Several potentials are considered: anharmonic double well, cosine potential and cosine potential in periodic space with finite number of minima. We also address a non-generic problem of anharmonic triple well potential.