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

Abstract

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.

Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

“…Seminal efforts are underway in the control of artificial quantum systems, that can be made to emulate the underlying Fermi-Hubbard models [5, 6, 7, 8,9,10,11]. 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 [12,13,14,15,16,17,18,19,20,21,22,23]. 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 [24,25].…”

“…Furthermore, scaling to similarly homogeneous but larger system sizes is not always straightforward [5,7,8,9,10,11,25]. Semiconductor quantum dots form a scalable platform that is naturally described by a Fermi-Hubbard model in the low-temperature, strong-interaction regime, when cooled down to dilution temperatures [12,13,15,14,16]. As such, pure state initialization of highly-entangled states is possible even without the use of adiabatic initialization schemes [27].…”

Electric-field-driven insulating-to-conducting transition in a mesoscopic quantum dot lattice

“…In particular, one might better understand transport in general by controlling the energy scales of importance: for quantum transport in such systems the important energies are the on-site excitation and Coulomb charging energies and the intersite tunneling matrix element. Control of these energies has been demonstrated in single lateral quantum dots connected by tunneling to leads, leading to insights into the Kondo effect [4], for example; similar insights into the Hubbard model might emerge from experiments on arrays of lateral quantum dots [5][6][7]. For classical transport modeled as charge diffusion through a tilted washboard potential, applicable to a wide variety of experimental systems [8][9][10], the energy scale is the height of the potential barrier between sites.…”

Quantum Dot Systems: a versatile platform for quantum simulations

“…The band structure effects of the previous section concern in essence single-particle physics, but this is no longer the case when interactions are relevant. A proposal for simulating interaction effects using quantum dot arrays has been made recently by Byrnes [115], focusing on the Mott metal-insulator transition (MIT): in the large tunnel coupling limit (t > U), electrons are delocalized over the whole array and ensure a large metallic conductivity, while for low tunnel coupling (t U/8), a gap opens at half-filling (1 electron per site) and splits the conducting band into two Mott-Hubbard subbands. This gap suppresses the double occupancies in the dots and halts transport by localizing the electrons.…”

“…Byrnes proposed to use undoped heterostructures [115], which would remove the dominant contribution to the disorder. We propose further to grow special heterostructures, containing a 3D gas of free electrons below the 2DEG, in order to screen the residual disorder originating from background impurities.…”