Majorana Quasiparticles Protected by Z2 Angular Momentum Conservation

Abstract

We show how angular momentum conservation can stabilise a symmetry-protected quasitopological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe -spin-orbit coupling and strong inter-orbital interactions -have been experimentally realized over the last two years.PACS numbers: 37.10. Jk, 05.10.Cc, 71.10.Pm Introduction. -The past two decades have witnessed an impressive progress in understanding how to harness quantum systems supporting topological order, one of the ultimate goals being the observation of quasi-particles with non-Abelian statistics -non-Abelian anyons [1][2][3][4][5]. A pivotal role in this search has been the formulation of a model for one-dimensional (1D) p-wave superconductors [6], that supports a symmetry-protected topological phase with Majorana quasi-particles (MQPs) as edge modes. The key element for the stability of such edge modes is the presence of a Z 2 parity symmetry. At the mean-field level, this can be realized via proximityinduced superconductivity in solid-state settings [7][8][9][10][11][12], or via coupling to molecular Bose-Einsten condensates in cold atoms [13]. Remarkably, it is possible to stabilize MQPs even taking fully into account quantum fluctuations by considering canonical settings [14][15][16][17][18], where the parity symmetry emerges via, e.g., engineered pairtunneling between pairs of wires [19][20][21]. However, it is an open challenge to understand whether, in these number-conserving setups, there exist fundamental microscopic symmetries that can serve as a pristine mechanism for the realization of MQPs, that is genuinely distinct from reservoir-induced superconductivity.Here, we show how angular momentum conservation enables the realization of a symmetry-protected quasitopological phase supporting MQPs in one-dimensional number-conserving systems [22]. In particular, we show how a combination of spin-exchange interactions and crossed spin-orbit couplings in orbital Hubbard models (see Fig. 1a-b) naturally gives rise to a Z 2 spin symmetry. This symmetry serves as the enabling tool to realize (1) describes tunneling (Ht), spin-orbit-coupling (Hso), and spin-exchange processes (HW ). In cold atom settings, the spin degree of freedom is represented by different Zeeman states with nuclear spin mF , mF + 1, while the orbital degree of freedom is encoded in different electronic states, 1 S0 and 3 P0. ...

Topological Fulde-Ferrell states in alkaline-earth-metal-like atoms near an orbital Feshbach resonance

“…Note that effects of SOC under the same cross-coupling scheme have recently been considered in Ref. [22], which focuses on the charge and spin correlations in a strictly one-dimensional system and is in contrast to the pairing correlation of a quasione-dimensional system considered in this work.…”

“…Alternatively, in alkaline-earth-metal or alkaline-earth-metal-like atoms, laser-induced heating can also be drastically reduced, either by directly coupling the clock states which serve as pseudospins, or by Raman coupling two different nuclear spin states in the 1 S 0 manifold via the 3 P 1 state, whose line width is relatively narrow. Indeed, with the recent experimental realization of SOCs in alkaline-earth-metal or alkaline-earthmetal-like atoms [17][18][19][20], these systems have become the ideal platforms to study SOC physics at low temperatures [21,22].…”

“…One interesting possibility is to study the effects of synthetic spin-orbit coupling (SOC) close to an OFR [17][18][19][20][21][22]. Raman-induced synthetic SOCs in alkaline atoms have been extensively studied in recent years [23][24][25][26][27].…”

End-to-end correlations in the Kitaev chain

“…The study of edge correlations in fermion chains has been addressed from different perspectives in various contributions, some of which cited here. References [8][9][10][11], for example, focus on the analytical aspects of the problem, while references [12][13][14][15][16] survey the relation with Majorana quasiparticles in number conserving systems. Here the analysis covers the whole range of parameters and is conceptually exact, albeit with a numerical component.…”

Repulsive polarons in alkaline-earth-metal-like atoms across an orbital Feshbach resonance

“…It follows that the wealth of precision quantum control techniques, which have been developed for the purpose of quantum metrology and quantum information using the clock-state manifolds ({ 1 S 0 , 3 P 0 }), can be employed to engineer highly non-trivial manybody scenarios . Recent studies in this regard range from interaction-induced topological states [32,33], to impurity problems such as the Kondo effects [34][35][36][37][38][39] and the polaron to molecule transitions [40,41]. Naturally, the key properties of these phenomena are firmly based on the features of interactions of an OFR.…”