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arXiv:1204.5184 · Physical Review A

Use of quantum quenches to probe the equilibrium current patterns of ultracold atoms in an optical lattice

Matthew Killi, Arun Paramekanti

Published Jun 27, 2012• 28 citations
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Abstract

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.

DOI
10.1103/physreva.85.061606

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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.
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.
Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarized fermions is prepared along with a Bose–Einstein condensate in a shallow three-dimensional optical lattice. After a quench that suppresses tunnelling between lattice sites for both the fermions and the bosons, we observe long-lived coherent oscillations in the fermionic momentum distribution, with a period that is determined solely by the Fermi–Bose interaction energy. Our results show that coherent quench dynamics can serve as a sensitive probe for correlations in delocalized fermionic quantum states and for quantum metrology. In ultracold quantum gases, coherent nonequilibrium dynamics has been observed for bosons, but remained elusive in fermionic systems. Here, Will et al. demonstrate coherent quench dynamics in a hybrid quantum system composed of a metallic state of fermionic atoms and a Bose–Einstein condensate.
We propose an analog quantum simulation of chiral magnetic dynamics using ultracold atoms in an optical superlattice. The massive Schwinger model in the zero gauge coupling limit maps onto the Rice-Mele model, with the fermion mass and topological angle encoded in the superlattice parameters. We study the real-time dynamics of the vector current following two quench protocols that drive continuous chirality injection and chirality relaxation. Simulations with realistic superlattice parameters and experimental noise demonstrates clear mass dependence of the current dynamics in both protocols, robust against experimental imperfections. The vector current may be directly measurable via single-bond-resolved detection, establishing cold atom superlattices as a viable platform for probing non-equilibrium chiral phenomena.
We calculate the time-of-flight patterns of strongly interacting bosons confined in a two-dimensional square lattice in the presence of an artificial magnetic field, using a quantum rotor model that is inherently combined with the Bogoliubov approach. We consider various geometries of the magnetic flux, which are expected to be realizable, or have already been implemented in experimental settings. The flexibility of the method allowed us to study cases where the artificial magnetic field is uniform or staggered or forms a checkerboard configuration. The effects of additional temporal modulation of the optical potential that results from application of Raman lasers driving particle transitions between lattice sites are also included. The time-of-flight patterns presented may serve as a verification of the chosen gauge in experiments, but also provide important hints on unconventional, nonzero-momentum condensates, or the possibility of observing graphenelike physics resulting from the occurrence of Dirac cones in artificial magnetic fields in systems of ultracold bosons in optical lattices. Also, we elucidate the differences between the effects of magnetic fields in solids and of artificial magnetic fields in optical lattices, which can be controlled on a much higher level, leading to effects not possible in condensed matter physics.
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.