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Two-dimensional lattice gauge theories with superconducting quantum circuits.

Marcos D, Widmer P, Rico E, Hafezi M, Rabl P, Wiese UJ, Zoller P - Ann Phys (N Y) (2014)

Bottom Line: Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well.We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories.The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria.

ABSTRACT

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

No MeSH data available.


Electric-field distribution for the ground state of the ring-exchange Hamiltonian (10) on a square lattice, using exact diagonalization. We have chosen open zig-zag boundaries in order to fulfil the Gauss law at each vertex. However, a charge–anticharge pair has been created at the edges by violating the Gauss law at those sites, giving rise to electric flux strings. The magnitude of the propagating electric flux is indicated on each link, and can be experimentally measured by taking snapshots of the spin distribution from an initially-prepared state.
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f000020: Electric-field distribution for the ground state of the ring-exchange Hamiltonian (10) on a square lattice, using exact diagonalization. We have chosen open zig-zag boundaries in order to fulfil the Gauss law at each vertex. However, a charge–anticharge pair has been created at the edges by violating the Gauss law at those sites, giving rise to electric flux strings. The magnitude of the propagating electric flux is indicated on each link, and can be experimentally measured by taking snapshots of the spin distribution from an initially-prepared state.

Mentions: As mentioned above, the Gauss law, , can be violated by installing a charge–anticharge pair at two lattice sites. In this situation, the electric flux flows from particle to antiparticle [see Fig. 3 for illustrative examples and Fig. 4 for an exact-diagonalization calculation], creating strings of flux whose tension and internal structure provide information about confinement: a string has an energy proportional to its length, with the string tension being the proportionality factor. In the two-dimensional QLM a string connecting two particles of charge separates into four mutually repelling strands, each carrying fractional electric flux . Similarly, a string connecting particles of charge splits into two strands.


Two-dimensional lattice gauge theories with superconducting quantum circuits.

Marcos D, Widmer P, Rico E, Hafezi M, Rabl P, Wiese UJ, Zoller P - Ann Phys (N Y) (2014)

Electric-field distribution for the ground state of the ring-exchange Hamiltonian (10) on a square lattice, using exact diagonalization. We have chosen open zig-zag boundaries in order to fulfil the Gauss law at each vertex. However, a charge–anticharge pair has been created at the edges by violating the Gauss law at those sites, giving rise to electric flux strings. The magnitude of the propagating electric flux is indicated on each link, and can be experimentally measured by taking snapshots of the spin distribution from an initially-prepared state.
© Copyright Policy - CC BY-NC-ND
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4263216&req=5

f000020: Electric-field distribution for the ground state of the ring-exchange Hamiltonian (10) on a square lattice, using exact diagonalization. We have chosen open zig-zag boundaries in order to fulfil the Gauss law at each vertex. However, a charge–anticharge pair has been created at the edges by violating the Gauss law at those sites, giving rise to electric flux strings. The magnitude of the propagating electric flux is indicated on each link, and can be experimentally measured by taking snapshots of the spin distribution from an initially-prepared state.
Mentions: As mentioned above, the Gauss law, , can be violated by installing a charge–anticharge pair at two lattice sites. In this situation, the electric flux flows from particle to antiparticle [see Fig. 3 for illustrative examples and Fig. 4 for an exact-diagonalization calculation], creating strings of flux whose tension and internal structure provide information about confinement: a string has an energy proportional to its length, with the string tension being the proportionality factor. In the two-dimensional QLM a string connecting two particles of charge separates into four mutually repelling strands, each carrying fractional electric flux . Similarly, a string connecting particles of charge splits into two strands.

Bottom Line: Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well.We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories.The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

View Article: PubMed Central - PubMed

Affiliation: Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria.

ABSTRACT

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

No MeSH data available.