Abstract
The phenomenon of ultrastrong light-matter interaction of a two-dimensional electron gas within a lumped element electronic circuit resonator is explored. The gas is coupled through the oscillating electric field of the capacitor, and in the limit of very small capacitor volumes, the total number of electrons of the system can be reduced to only a few. One of the peculiar features of our quantum mechanical system is that its Hamiltonian evolves from the fermionic Rabi model to the bosonic Hopfield model for light-matter coupling as the number of electrons is increased. We show that the Dicke states, introduced to describe the atomic super-radiance, are the natural base to describe the crossover between the two models. Furthermore, we illustrate how the ultrastrong coupling regime in the system and the associated antiresonant terms of the quantum Hamiltonian have a fundamentally different impact in the fermionic and bosonic cases. In the intermediate regime, our system behaves like a multilevel quantum bit with nonharmonic energy spacing, owing to the particle-particle interactions. Such a system can be inserted into a technological semiconductor platform, thus opening interesting perspectives for electronic devices where the readout of quantum electrodynamical properties is obtained via the measure of a DC current.
- Received 19 March 2014
DOI:https://doi.org/10.1103/PhysRevX.4.041031
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Published by the American Physical Society
Popular Summary
The nanometer scale of today’s electronic circuits enables the realization of devices relying on a few electrons only, entirely governed by the laws of quantum mechanics. Thanks to the use of metallic resonators, quanta of light can also be squeezed into dimensions that are much smaller than their wavelengths. We have derived a formalism to describe the interaction occurring between the electric field of an oscillating electromagnetic circuit and the electrons confined within its capacitor. Of particular interest is the so-called “strong-coupling regime” in which the energy exchange between the electric field and the electrons is reversible, thus giving rise to coherent quantum phenomena, exploitable for new functionalities. Such devices can surely be realized at THz frequencies, where strong light-matter interactions have already been demonstrated.
The volume of the capacitor of our model quantum circuit can be varied in order to change the total number of electrons from approximately 100,000 down to 1 while keeping the same electronic density. This fact allows us to understand the strong light-matter coupling regime in two completely different limits. For one electron only, our system behaves similarly to a single atom interacting with electromagnetic radiation; when many electrons participate in the interaction, we recover a situation typical of condensed-matter physics but characterized by the presence of collective (plasmonic) electron excitations. In the intermediate regime of a few electrons only, the transition energies depend on the number of excitations because of the strong dipole-dipole interactions, similarly to the photon blockade phenomenon with Rydberg atoms.
Atomic physics and condensed matter are thus directly linked through our formalism. The proposed solid-state architecture would thus enable the implementation of a basic element for multistage quantum logic.
