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Quantum simulation of Fermi-Hubbard models in semiconductor quantum dot arrays

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 Added by Tim Byrnes
 Publication date 2007
  fields Physics
and research's language is English




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We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of quantum dots defined in a semiconductor two-dimensional electron gas system. Bands with energies above the lowest energy band are used to form the Hubbard model, which allows for an experimentally simpler realization of the device. We find that depending on average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a d-wave superconducting phase should be observable using current fabrication technologies.



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Interacting fermions on a lattice can develop strong quantum correlations, which lie at the heart of the classical intractability of many exotic phases of matter. Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical pure-state initialisation and readily adhere to an engineerable Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder inherent to solid state has made attempts at emulating Fermi-Hubbard physics on solid-state platforms few and far between. Here, we show that for gate-defined quantum dots, this disorder can be suppressed in a controlled manner. Novel insights and a newly developed semi-automated and scalable toolbox allow us to homogeneously and independently dial in the electron filling and nearest-neighbour tunnel coupling. Bringing these ideas and tools to fruition, we realize the first detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here show how quantum dots can be used to investigate the physics of ever more complex many-body states.
We investigate pump-induced exciton inversion in a quantum-dot cavity system with continuous wave drive. Using a polaron-based master equation, we demonstrate excited-state populations above 0.9 for an InAs dot at a phonon bath temperature of 4K. In an exciton-driven system, the dominant mechanism is incoherent excitation from the phonon bath. For cavity driving, the mechanism is phonon-mediated switching between ground- and excited-state branches of the ladder of photon states, as quantum trajectory simulations clearly show. The exciton inversion as a function of detuning is found to be qualitatively different for exciton and cavity driving, primarily due to cavity filtering. The master equation approach allows us to include important radiative and non-radiative decay processes on the zero phonon line, provides a clear underlying dynamic in terms of photon and phonon scattering, and admits simple analytical approximations that help to explain the physics.
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