Observation of chiral currents with ultracold atoms in bosonic ladders

Abstract

We report on the observation of the Meissner effect in bosonic flux ladders of ultracold atoms. Using artificial gauge fields induced by laser-assisted tunneling, we realize arrays of decoupled ladder systems that are exposed to a uniform magnetic field. By suddenly decoupling the ladders and projecting into isolated double wells, we are able to measure the currents on each side of the ladder. For large coupling strengths along the rungs of the ladder, we find a saturated maximum chiral current corresponding to a full screening of the artificial magnetic field. For lower coupling strengths, the chiral current decreases in good agreement with expectations of a vortex lattice phase. Our work marks the first realization of a low-dimensional Meissner effect and, furthermore, it opens the path to exploring interacting particles in low dimensions exposed to a uniform magnetic field.The Meissner effect is the hallmark signature of a superconductor exposed to a magnetic field [1,2]. For a type-II superconductor, full screening of the applied external field occurs up to a critical field H c1 . Such a screening is the result of circular surface currents on the superconductor that generate an opposite field, canceling the applied field. The superconductor thus acts as a perfect diamagnet in the Meissner phase. For larger field strengths H > H c1 , however, the superconductor is not able to fully screen the applied field and an Abrikosov vortex lattice phase is formed in the system. In lowdimensional quantum systems it has been a longstanding challenge to probe analogue ideas and to investigate the interplay of orbital magnetic field effects and interactions. While a single one-dimensional system does not allow for any orbital magnetic field effects, a ladder system is the simplest extension where these are permitted [3][4][5][6][7][8].Here we report on the realization of such bosonic ladders for ultracold atoms exposed to a uniform artificial magnetic field created by laser-assisted tunneling [9][10][11][12][13][14][15][16][17]. Previously, such ladders have been discussed in the context of Josephson-junction arrays [3,[18][19][20][21] and more recently also for ultracold atoms exposed to an artificial gauge field [6][7][8]. In our experiment we can measure the probability current on either leg of the ladders and, in addition, observe the momentum distribution of the system after time-of-flight expansion. Rather than varying the external field strength, we determine the response of the system as a function of the ratio of transverse rung coupling K to coupling along the legs of the ladder J (see Fig. 1). In full analogy to the type-II superconductor, we find evidence for a Meissner phase with maximum chiral currents that screen the applied field. Below a critical coupling strength (K/J) c we find a decreasing chiral current, in good agreement with theoretical expectations for a vortex phase with only partial screening. b a y x J Ke ilφ d y d x l l+1 1 E (J) 0 4 -4 q (π/d y ) 0 -1 K/J 0 1 2 3 (K/J) C L R FIG. 1. Experimental...

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

“…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 condensation has been achieved in staggered flux configurations [15,25] and in small ladder systems [26,27] further highlighting its noted absence in the uniform field configuration.In this article, we report the first observation of BoseEinstein condensation in Hofstadter's butterfly. The presence of a superfluid state in the HH lattice allows us to analyze the symmetry of the periodic wavefunction by self-diffraction of coherent matter waves during ballistic expansion -analogous to a von Laue x-ray diffraction pattern, which reveals the symmetry of a lattice.…”

“…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 condensation has been achieved in staggered flux configurations [15,25] and in small ladder systems [26,27] further highlighting its noted absence in the uniform field configuration.…”

Ultracold Fermions in a Cavity-Induced Artificial Magnetic Field

“…The resulting geometry is an array of decoupled ladder structures ( Fig. 1) [8]. The atoms can tunnel along the leg direction of the ladder.…”

“…Such artificial magnetic fields have been used in quantum gases confined to optical lattices to realize two showcase models of topologically insulating phases, the Hofstadter model in two-dimensions [4][5][6][7] or on a ladder geometry [8] and the Haldane model [9].…”

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.…”