Observation of Bose–Einstein condensation in a strong synthetic magnetic field

Abstract

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of BoseEinstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Topological states of matter are an active new frontier in physics. Topological properties at the single particle level are well understood; however, there are many open questions when strong interactions and correlations are introduced [1, 2] as in the ν = 5/2 state of the fractional quantum Hall effect [3] and in Majorana fermions [4][5][6]. For neutral ultracold atoms, new methods have been developed to create synthetic gauge fields. Forces analogous to the Lorentz force on electons are engineered either through the Coriolis force in rotating systems [7][8][9], by phase imprinting via photon recoil [10][11][12][13][14], or lattice shaking [15,16]. Much of the research with ultracold atoms has focused on the paradigmatic HarperHofstadter (HH) Hamiltonian, which describes particles in a crystal lattice subject to a strong homogeneous magnetic field [17][18][19]. For magnetic fluxes on the order of one flux quantum per lattice unit cell, the radius of the smallest possible cyclotron orbit and the lattice constant are comparable, and their competition gives rise to the celebrated fractal spectrum of Hofstadfer's butterfly whose sub-bands have non-zero Chern numbers [20] and Dirac points.So far, it has not been possible to observe the ground state of the HH Hamiltonian, which for bosonic atoms is a superfluid Bose-Einstein condensate. It is unknown whether this is due to heating associated with technical noise, non-adiabatic state preparation, or inelastic collisions. These issues are complicated, since all schemes for realizing the HH Hamiltonian use some form of temporal lattice modulation and therefore are described by a time-dependent Floquet formalism. The HH model arises after time averaging the Floquet Hamiltonian, but it is an open question to what extent finite interactions and micromotion lead to transitions between Floquet modes and therefore heating [21][22][23][24]. Bose-Einstein condensat...

Interband Heating Processes in a Periodically Driven Optical Lattice

“…This includes driving functions involving higher harmonics of the driving frequency, as they were used in the experiments described in Refs. [12,13], as well as lattices that are driven by a moving secondary lattice in order to create the Hofstadter Hamiltonian [14,15,18,19]. Furthermore, it will be crucial to understand how far such single-particle heating channels are modified in systems of interacting particles.…”

“…The concept of Floquet engineering becomes particularly relevant, when the driven system acquires properties that are qualitatively different from those of the undriven system. A prime example is the realisation of artificial magnetic fields, where driven charge-neutral atoms behave as if they had a charge coupling to an effective magnetic field [10][11][12][13][14][15][16][17][18][19].…”

Phase transition and intrinsic metric of dipolar fermions in the quantum Hall regime

“…Recently, other ways of engineering synthetic magnetic fields to realizing the FQH states have been proposed, such as the strained optical lattice 39 , optical dressing 40,41 of atoms in continuum and laser-induced tunneling in optical lattices [42][43][44][45] . It is worth mentioning that a method of direct control over the total angular moment instead of rotation frequency by using spin-flip induced insertion of angular momentum 46 was proposed recently which circumvents the prime experimental difficulties toward the realization of the quantum Hall regime in harmonically trapped gases.…”

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

“…Treating interactions in such a non-perturbative way is difficult in periodically-driven systems [5][6][7][8][9][10], which have received unprecedented attention following the realisation of dynamical localisation [11][12][13][14][15], artificial gauge fields [16][17][18][19][20][21][22], models with topological [23][24][25][26][27][28] and statedependent [29] bands, and spin-orbit coupling [30,31]. In this paper, we consider strongly-interacting periodicallydriven systems and show how the SWT can be extended to derive effective static Hamiltonians of non-equilibrium setups.…”