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Sudden quantum quenches in the presence of frustration or background synthetic gauge fields: Probing equilibrium currents of ultracold atoms in an optical lattice

Matthew Killi, Stefan Trotzky, Arun Paramekanti

Published Oct 16, 2012• 0 citations
OpenAlex

Abstract

Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states which support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

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Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Matthew Killi, Stefan Trotzky, Arun Paramekanti

Bosons and fermions, in the presence of frustration or background gauge fields, can form many-body ground states that support equilibrium charge or spin currents. Motivated by the experimental creation of frustration or synthetic gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge-invariant route to probing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge modes in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

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Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.

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Abstract The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.

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L. Fallani

I will report on very recent experiments performed at LENS with ultracold 173Yb Fermi gases in artificial gauge fields. We have engineered Raman transitions between different 173Yb nuclear spin states to synthesize an effective lattice dynamics in a finite-sized “extra dimension”, which is encoded in the internal degree of freedom of the atoms [1]. By using this innovative approach, we have realized synthetic magnetic fields for effectively-charged fermions in ladder geometries with a variable number of legs. Direct imaging of the individual legs allowed us to demonstrate the emergence of chiral edge currents and to observe edge-cyclotron orbits propagating along the edges of the system [2], thus providing a direct evidence of a fundamental feature of quantum Hall physics in condensed-matter systems. A. Celi et al., Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett. 112, 043001 (2014). M. Mancini et al., Observation of chiral edge states with neutral fermions in a synthetic Hall ribbon, preprint arXiv:1502.02495 (2015). ∗Speaker †Corresponding author: fallani@lens.unifi.it sciencesconf.org:bec2015:67564

Bulletin of the American Physical Society•Jun 12, 2015•0 citations

Edge excitations of bosonic fractional quantum Hall phases in optical lattices

Jonas A. Kjäll, Joel E. Moore

The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can support quantum Hall states, the universal edge excitations that provide the most likely experimental probe of the topological order have not been obtained. We find that the edge excitations of an interacting boson lattice model are surprisingly sensitive to interedge hybridization and edge-bulk mixing for some confining potentials. With properly chosen potentials and fluxes, the edge spectrum is surprisingly clear even for small systems with strong lattice effects such as bandwidth. Various fractional quantum Hall phases for bosons can be obtained, and the phases $\ensuremath{\nu}=1/2$ and $\ensuremath{\nu}=2/3$ have the edge spectra predicted by the chiral Luttinger liquid theory.

arXiv:1112.1800•Physical Review B•Jun 20, 2012•34 citations
Bosons and fermions, in the presence of frustration or background gauge fields, can form manybody ground states which support equilibrium 'charge' or 'spin' currents. Motivated by the experimental creation of frustration or artificial gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge invariant route to visualizing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge currents in gapped topological states, such as quantum Hall or quantum spin Hall insulators.
Bosons and fermions, in the presence of frustration or background gauge fields, can form many-body ground states that support equilibrium charge or spin currents. Motivated by the experimental creation of frustration or synthetic gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge-invariant route to probing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge modes in gapped topological states, such as quantum Hall or quantum spin Hall insulators.
Atomic bosons and fermions in an optical lattice can realize various condensed-matter states that support equilibrium current patterns in the presence of synthetic magnetic fields or non-Abelian gauge fields. As a route to probing such mass currents, we propose a nonequilibrium quantum quench of the Hamiltonian that dynamically converts the current patterns into experimentally measurable real-space density patterns. We illustrate how a specific such ``unidirectional'' quench of the optical lattice can be used to uncover bulk checkerboard and stripe current orders in lattice Bose superfluids and Fermi gases, as well as chiral edge currents in a quantum Hall state.
Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.
Abstract The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.
I will report on very recent experiments performed at LENS with ultracold 173Yb Fermi gases in artificial gauge fields. We have engineered Raman transitions between different 173Yb nuclear spin states to synthesize an effective lattice dynamics in a finite-sized “extra dimension”, which is encoded in the internal degree of freedom of the atoms [1]. By using this innovative approach, we have realized synthetic magnetic fields for effectively-charged fermions in ladder geometries with a variable number of legs. Direct imaging of the individual legs allowed us to demonstrate the emergence of chiral edge currents and to observe edge-cyclotron orbits propagating along the edges of the system [2], thus providing a direct evidence of a fundamental feature of quantum Hall physics in condensed-matter systems. A. Celi et al., Synthetic gauge fields in synthetic dimensions, Phys. Rev. Lett. 112, 043001 (2014). M. Mancini et al., Observation of chiral edge states with neutral fermions in a synthetic Hall ribbon, preprint arXiv:1502.02495 (2015). ∗Speaker †Corresponding author: fallani@lens.unifi.it sciencesconf.org:bec2015:67564
The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can support quantum Hall states, the universal edge excitations that provide the most likely experimental probe of the topological order have not been obtained. We find that the edge excitations of an interacting boson lattice model are surprisingly sensitive to interedge hybridization and edge-bulk mixing for some confining potentials. With properly chosen potentials and fluxes, the edge spectrum is surprisingly clear even for small systems with strong lattice effects such as bandwidth. Various fractional quantum Hall phases for bosons can be obtained, and the phases $\ensuremath{\nu}=1/2$ and $\ensuremath{\nu}=2/3$ have the edge spectra predicted by the chiral Luttinger liquid theory.