Artificial Gauge Fields with Ultracold Atoms in Optical Lattices

Aidelsburger, Monika

doi:10.1007/978-3-319-25829-4

Cited by 19 publications

(29 citation statements)

References 205 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us first focus on the ground band, which we assume to be non-degenerate. The eigenstates of the Hamiltonian within this band are Bloch states of the form [70]…”

Section: Data Availability Statementmentioning

confidence: 99%

Linking topological features of the Hofstadter model to optical diffraction figures

et al. 2022

View full text Add to dashboard Cite

In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogy of the robustness of transverse conductance in the Quantum Hall effect.

show abstract

“…Let us first focus on the ground band, which we assume to be non-degenerate. The eigenstates of the Hamiltonian within this band are Bloch states of the form [70]…”

Section: Data Availability Statementmentioning

confidence: 99%

Linking topological features of the Hofstadter model to optical diffraction figures

et al. 2022

View full text Add to dashboard Cite

show abstract

“…On a lattice these phases are introduced in the form of the so-called Peierls phases that a particle picks up when hopping in the lattice. Such phases allow to rewrite the tight-binding Hamiltonian of a charged particle in a magnetic field as the tight-binding Hamiltonian of a free particle where tunneling matrix elements are complex and hopping in the lattice is accompanied by the Peierls phase [78,79]. The spectrum of the Hamiltonian so obtained is the famous Hofstadter butterfly [80].…”

Section: A the Peierls Phase-factorsmentioning

confidence: 99%

Continuous-time quantum walks on planar lattices and the role of the magnetic field

2020

View full text Add to dashboard Cite

We address the dynamics of continuous-time quantum walk (CTQW) on planar 2D lattice graphs, i.e. those forming a regular tessellation of the Euclidean plane (triangular, square, and honeycomb lattice graphs). We first consider the free particle: on square and triangular lattice graphs we observe the well-known ballistic behavior, whereas on the honeycomb lattice graph we obtain a sub-ballistic one, although still faster than the classical diffusive one. We impute this difference to the different amount of coherence generated by the evolution and, in turn, to the fact that, in 2D, the square and the triangular lattices are Bravais lattices, whereas the honeycomb one is non-Bravais. From the physical point of view, this means that CTQWs are not universally characterized by the ballistic spreading. We then address the dynamics in the presence of a perpendicular uniform magnetic field and study the effects of the field by two approaches: (i) introducing the Peierls phase-factors, according to which the tunneling matrix element of the free particle becomes complex, or (ii) spatially discretizing the Hamiltonian of a spinless charged particle in the presence of a magnetic field. Either way, the dynamics of an initially localized walker is characterized by a lower spread compared to the free particle case, the larger is the field the more localized stays the walker. Remarkably, upon analyzing the dynamics by spatial discretization of the Hamiltonian (vector potential in the symmetric gauge), we obtain that the variance of the space coordinate is characterized by pseudooscillations, a reminiscence of the harmonic oscillator behind the Hamiltonian in the continuum, whose energy levels are the well-known Landau levels.

show abstract

“…Such artificial gauge fields can make the neutral ultracold atoms behave as if they were charged particles experiencing a magnetic field and were investigated experimentally and theoretically with an external lattice potential [ 11 , 12 , 13 ] or without one [ 14 , 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Lode

Dutta

Lévêque

2021

Entropy

View full text Add to dashboard Cite

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.

show abstract

Artificial Gauge Fields with Ultracold Atoms in Optical Lattices

Cited by 19 publications

References 205 publications

Linking topological features of the Hofstadter model to optical diffraction figures

Linking topological features of the Hofstadter model to optical diffraction figures

Continuous-time quantum walks on planar lattices and the role of the magnetic field

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

Contact Info

Product

Resources

About