Magnetism in Strongly Interacting One-Dimensional Quantum Mixtures

Abstract

We consider two species of bosons in one dimension near the Tonks-Girardeau limit of infinite interactions. For the case of equal masses and equal intraspecies interactions, the system can be mapped to a S = 1/2 XXZ Heisenberg spin chain, thus allowing one to access different magnetic phases. Using a powerful ansatz developed for the two-component Fermi system, we elucidate the evolution from few to many particles for the experimentally relevant case of an external harmonic confinement. In the few-body limit, we already find clear evidence of both ferromagnetic and antiferromagnetic spin correlations as the ratio of intraspecies and interspecies interactions is varied. Furthermore, we observe the rapid emergence of symmetry-broken magnetic ground states as the particle number is increased. We therefore demonstrate that systems containing only a few bosons are an ideal setting in which to realize the highly sought-after itinerant ferromagnetic phase.Quantum magnetism is ubiquitous in nature and plays a central role in important phenomena such as hightemperature superconductivity [1]. Furthermore, it underpins the technological advances in data storage [2], and it promises a new generation of spintronic devices, where the spin of the electron rather than its charge is used to transfer information. However, despite its ubiquity, magnetic phenomena are often difficult to characterise and treat theoretically; for instance, itinerant ferromagnetism of delocalized fermions requires strong interactions and is thus not completely understood [3].One can gain insight into magnetic phases by considering cleaner, more idealised versions of the phenomena. In particular, an important question is whether or not ferromagnetism can exist without an underlying lattice [4]. This possibility was investigated experimentally in atomic Fermi gases [5,6], but the system proved to be unstable towards fermion pairing rather than magnetism. More recently, it has been proposed that itinerant ferromagnetism can be realised in a strongly interacting one-dimensional (1D) Fermi gas [7]. However, in this case, one cannot access the ferromagnetic phase without explicitly breaking the spin symmetry with an external field [8], and this potentially complicates the observation of ferromagnetism.In this Letter, we show that both itinerant ferromagnetism and antiferromagnetism can be investigated with a 1D two-component mixture of bosons [9]. For the case of equal masses and equal intraspecies interactions (g ↑↑ = g ↓↓ ), the Bose-Bose mixture may be regarded as a pseudo-spin S = 1/2 system, and it can be mapped to a 1D spin chain in the limit of strong interactions [10,11]. In particular, for infinite intraspecies interactions, the system is formally equivalent to a 1D Fermi gas. However, in contrast to the Fermi case, one can break the SU (2) symmetry and access different magnetic phases by varying the ratio of intraspecies and interspecies interactions (see Fig. 1 We consider two species of bosons in one dimension near the Tonks-Girardeau limit of i...

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

“…This mechanism appears to be very general and it is present always whenever fermions of different mass are being considered. We believe that our results may shed some light on the quantum magnetism [43][44][45][46][47][48][49][50] and the role of mass imbalance in spatial separation of the density profiles [51,52].…”

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

“…Indeed, in the lowenergy regime, the κ internal degrees of freedom (interacting via highly-symmetric terms) can be mapped onto an effective SU (κ) spin chain subjected to a Sutherland Hamiltonian [8,9], which reduces to the most traditional SU (2) Heisenberg model in the case of two components [10][11][12]. Such systems are therefore currently at the focus of an intense experimental [7,13,14] and theoretical [15][16][17][18] activity. Inevitably, a compelling question arises about probing the magnetic-like properties of these gases, via experimental techniques as elementary as possible, besides in-situ spin-resolved imaging of the cloud.…”

Interaction-induced Bloch oscillation in a harmonically trapped and fermionized quantum gas in one dimension

“…In this way, various spin-chain Hamiltonians can be constructed in response to different external perturbations, including interactions, gauge fields and trapping potentials, which have been used to address and engineer novel spin spirals and magnetic orders in 1D systems [12][13][14][15][16][17][18][19][20][21][22][23][24]. Experimentally, an anti-ferromagnetic spin chain has been recently confirmed in a small cluster of 1D trapped fermions [25].…”

“…Following this idea one can construct various spin chain models as studied in the literature [12][13][14][15][16][17][18][19][20][21][22][23][24].…”