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Majorana quasiparticles in ultracold one-dimensional gases

Iemini F., Mazza L., Fallani L., Zoller P., Fazio R., Dalmonte M.

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

In this Proceedings we report some recent results on Majorana quasi-particles published in Phys. Rev. Lett. 118, 200404 (2017). We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological 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.

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In this Proceedings we report some recent results on Majorana quasi-particles published in Phys. Rev. Lett. 118, 200404 (2017). We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological 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.
We show how angular momentum conservation can stabilize a symmetry-protected quasitopological phase of matter supporting Majorana quasiparticles 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 interorbital interactions-have been experimentally realized over the last two years.
One promising avenue to study one-dimensional (1D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a 1D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes [C. V. Kraus et al., Phys. Rev. Lett. 111, 173004 (2013)]. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the Z2{\mathbb{Z}}_{2}Z2​ fermion-parity symmetry that protects them. In this Rapid Communication, we present a mechanism to overcome this obstacle, by piercing a (synthetic) magnetic $\ensuremath{\pi}$ flux through each plaquette of the Fermi ladder. Using bosonization, we show that in this case there exists an exact leg-interchange symmetry that is robust to interchain hopping, and acts as fermion parity at long wavelengths. We utilize density matrix renormalization group and exact diagonalization to verify that the resulting model exhibits Majorana boundary modes up to large single-particle tunnelings, comparable to the intrachain hopping strength. Our work highlights the unusual impacts of different topologically trivial band structures on these interaction-driven topological phases, and identifies a distinct route to stabilizing Majorana boundary modes in 1D fermionic ladders.
We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation and the absence of a single particle gap. Majorana zero modes are localized to the interface between a topological region in the middle of the trap and trivial regions at its wings. Unlike the realization of a topological superconductor in proximity coupled nano-wires, the Majorana modes do not carry a quantum number associated with the total fermion parity. Instead, the topological degeneracy is protected by an emergent Z2Z_2Z2​ symmetry present only at low energies. We discuss the experimental implications of the novel zero modes, as manifest for example in the response to modulation of a local potential near the position of the Majorana bound states. For the range of interaction strength corresponding to Luttinger parameter 121212, on the other hand the zero-mode can be detected as a sharp low frequency response at an energy which generically scales with system size as 1/LK/21/L^{K/2}1/LK/2 and is therefore parametrically separated from the phonons.
The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue for exploring new quantum matters. In experiments, the SO coupling is implemented simultaneously with a Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with nonzero center-of-mass momentum Cooper pairings, in contrast to the zero center-of-mass momentum pairings in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in SO-coupled Fermi gases in the presence of a large out-of-plane Zeeman field. In this paper, we address this question by studying the mean-field quantum phases of 1D (quasi-1D) SO-coupled fermionic cold-atom optical lattices.
The remarkable properties and potential applications of Majorana fermions have led to considerable efforts in recent years to realize topological matters that host these excitations. For a number conserving system, there have been a few proposals, using either coupled chain models or a multi-component system with spin–orbit coupling (SOC), to create number fluctuation of fermion pairs in achieving Majorana fermions. In this work, we show that Majorana edge states can occur in a spinless Fermi gas in 1D lattices with tunable p -wave interaction. This is facilitated by the conversion between a pair of (open-channel) fermions and a (close channel) boson, thereby allowing the number fluctuation of fermion pairs in a single chain. This scheme requires neither SOC nor a multi-chain setup and can be implemented easily. Using the density-matrix-renormalization-group method, we have identified the Majorana phase in a wide range of parameter regimes as well as its associated phase transitions. The topological nature of the Majorana phase manifests itself in a strong edge–edge correlation in an open chain that is robust against disorder, as well as in a non-trivial winding number in the bulk generated by using twisted boundary condition. It is also shown that the Majorana phase in this system can be stable against atom losses due to few-body collisions on the same site, and can be easily identified from the fermion momentum distribution. These results pave the way for probing the intriguing Majorana physics in a simple and stable cold atoms system.
We study Majorana fermions (MFs) in quasi-one dimensional (quasi-1D) and higher-dimensional fermionic optical lattices with a strictly 1D spin-orbit coupling, which has already been realized in cold atom experiments. We show that when the superfluid order parameters are homogeneous and are enforced to be identical along different chains, there are multiple MFs at each end with or without an experimentally tunable in-plane Zeeman field Vy{V}_{y}Vy​. For Vy=0{V}_{y}=0Vy​=0 the multiple MFs are topologically protected by a chiral symmetry; however, for ${V}_{y}\ensuremath{\ne}0$ the existence of multiple MFs is related to the peculiar spectrum properties of the system despite the broken chiral symmetry. In the generalization to higher dimensions, the multiple MFs form a zero-energy flat band. Furthermore, when the superfluid order parameters are solved self-consistently, the multiple MFs are usually destroyed because of the inhomogeneous order parameters of either Bardeen-Cooper-Schrieffer (Vy=0{V}_{y}=0Vy​=0) type or Fulde-Ferrell (${V}_{y}\ensuremath{\ne}0$) type. Our results are useful to guide the experimentalists on searching for MFs in ultracold spin-orbit coupled fermionic superfluids.