Unconventional phases of attractive Fermi gases in synthetic Hall ribbons

Abstract

An innovative way to produce quantum Hall ribbons in a cold atomic system is to use M hyperfine states of atoms in a one-dimensional optical lattice to mimic an additional "synthetic dimension." A notable aspect here is that the SU(M) symmetric interaction between atoms manifests as "infinite ranged" along the synthetic dimension. We study the many-body physics of fermions with SU(M) symmetric attractive interactions in this system using a combination of analytical field theoretic and numerical density-matrix renormalization-group methods. We uncover the rich ground-state phase diagram of the system, including unconventional phases such as squished baryon fluids, shedding light on many-body physics in low dimensions. Remarkably, changing the parameters entails interesting crossovers and transition; e.g., we show that increasing the magnetic field (that produces the Hall effect) converts a "ferrometallic" state at low fields to a "squished baryon superfluid" (with algebraic pairing correlations) at high fields. We also show that this system provides a unique opportunity to study quantum phase separation in a multiflavor ultracold fermionic system.

Measuring Chern numbers in Hofstadter strips

“…Other studies have considered using them to engineer topological quantum walks [26,27,51], study the properties of quantum systems on triangular and hexagonal lattices [52,53], realize Weyl semimetals [54], simulate 4D models [37] -in particular 4D quantum Hall phenomena [55,56,57] -or lattices with complex topologies [58]. Finally, these systems open a very promising route to the study of many-body phenomena, especially in topological systems [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73].…”

Experimental Band Structure Spectroscopy along the Synthetic Dimension

“…The synthetic frequency dimension platform that we have experimentally demonstrated here, along with the band structure measurement technique, is ripe for probing systems beyond 1D [10-12, 26, 50, 51]. For example, 2D quantum Hall phenomena such as one-way edge states [8,9,52] and synthetic Hall ribbons [5,15,53,54] could be observed in extensions of our system, with the added benefit of frequency conversion from transport along the synthetic dimension. Even within 1D, there have been proposals to realize unique photon transport phenomena using dynamically modulated cavities, which could be implemented in a reconfigurable fashion in our platform [24,55].…”

“…Recently, there has been significant interest in creating analogous periodic systems not in real space but in synthetic space, allowing one to explore higher-dimensional physics with a structure of fewer physical dimensions [2][3][4][5][6][7][8][9][10][11][12]. Synthetic dimensions are internal degrees of freedom of a system that can be configured into a lattice, for example the hyperfine spin states in cold atoms [4][5][6][13][14][15][16][17], the orbital angular momentum of photons [7,[18][19][20], or the modes at different frequencies of optical ring resonators [8,9]. These systems are again characterized by a band structure in synthetic space, but an experimental demonstration of directly measuring this band structure is lacking.In this work we provide the first direct experimental demonstration of a band structure in the synthetic dimension.…”

Spin-gap spectroscopy in a bosonic flux ladder

“…Theoretical studies have highlighted the presence of fractional charge excitations and predicted a host of novel phases of matter (such as charge-, bond-and density-waves or orbital antiferromagnets) leading to a more complex phenomenology than V-M competition in the bosonic case [47][48][49]. Triggered by interest in the quantum Hall effect, analogues of the chiral modes which characterize both integer and fractional phases have been discussed [24,34,42,[50][51][52][53][54][55].…”