Disorder and flat-band physics in a transmon kagome lattice
Heikkinen, Elina (2024-06-03)
E. Heikkinen
03.06.2024
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202406034162
https://urn.fi/URN:NBN:fi:oulu-202406034162
Tiivistelmä
Arrays of superconducting transmon devices have arisen as a promising platform for quantum information science and quantum simulations. A chain of capacitively coupled transmons is known to naturally realize the attractive Bose-Hubbard model, with the transmon devices representing lattice sites and their excitations being thought of as bosons in the lattice. In this thesis, the model is generalized to the two-dimensional case and applied to the kagome lattice, which is known for its exotic physical properties.
The Bose-Hubbard Hamiltonian is studied here for truncated kagome lattices containing 12, 18, and 27 transmons and either one or six bosonic excitations, using typical parameter values present in realistic arrays. Both periodic and nonperiodic single-boson systems are considered, whereas the lattices with six bosons are only investigated in the case of regular boundaries without periodic boundary conditions. The systems are analyzed numerically via the exact diagonalization method.
In a kagome lattice with a single boson, the model is reduced to the tight-binding model, and the energy band structure can be solved analytically. The lowest band is found to be flat, which is related to localized single-particle states and various novel physical phenomena. The analytical results are compared to the numerically computed eigenenergies of small kagome lattice sections. Lattices with periodic boundary conditions are discovered to agree with the analytical energies, while nonperiodic lattices are different with fewer flat-band energies.
In the interacting many-body system of six bosons, the focus of this work is on highly excited transmon states, or equivalently multiple bosons occupying a single lattice site. The numerical results show that an eigenstate belonging to the lowest energy band is either a localized state with all the bosons in the same lattice site, or a superposition of these states. As a result of the finite size of the kagome lattice, the lowest energies are dependent on the neighborhood of the lattice site or sites featured in each corresponding eigenstate.
The finite size of the smallest kagome lattice also influences the dynamics of a state with all the six bosons initially localized on the same lattice site. The stack of bosons will remain in sites located for example at the corners of the lattice, but the stack exhibits slow collective hopping between equivalent neighboring sites. The limitations set by the small manufacturing imperfections inherent to real transmon arrays are also discussed, and the effects that this disorder may have on the energies, states, and dynamics of the system are examined.
The Bose-Hubbard Hamiltonian is studied here for truncated kagome lattices containing 12, 18, and 27 transmons and either one or six bosonic excitations, using typical parameter values present in realistic arrays. Both periodic and nonperiodic single-boson systems are considered, whereas the lattices with six bosons are only investigated in the case of regular boundaries without periodic boundary conditions. The systems are analyzed numerically via the exact diagonalization method.
In a kagome lattice with a single boson, the model is reduced to the tight-binding model, and the energy band structure can be solved analytically. The lowest band is found to be flat, which is related to localized single-particle states and various novel physical phenomena. The analytical results are compared to the numerically computed eigenenergies of small kagome lattice sections. Lattices with periodic boundary conditions are discovered to agree with the analytical energies, while nonperiodic lattices are different with fewer flat-band energies.
In the interacting many-body system of six bosons, the focus of this work is on highly excited transmon states, or equivalently multiple bosons occupying a single lattice site. The numerical results show that an eigenstate belonging to the lowest energy band is either a localized state with all the bosons in the same lattice site, or a superposition of these states. As a result of the finite size of the kagome lattice, the lowest energies are dependent on the neighborhood of the lattice site or sites featured in each corresponding eigenstate.
The finite size of the smallest kagome lattice also influences the dynamics of a state with all the six bosons initially localized on the same lattice site. The stack of bosons will remain in sites located for example at the corners of the lattice, but the stack exhibits slow collective hopping between equivalent neighboring sites. The limitations set by the small manufacturing imperfections inherent to real transmon arrays are also discussed, and the effects that this disorder may have on the energies, states, and dynamics of the system are examined.
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