We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition---simultaneously inducing an effective spin-orbit interaction and magnetic field---while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as `Floquet Majorana fermions' when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.
We propose an efficient protocol for braiding atomic Majorana fermions in wire networks with AMO techniques and demonstrate its robustness against experimentally relevant errors. Based on this protocol we provide a topologically protected implementation of the Deutsch-Josza algorithm.
We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By controlling the addressing lasers, one can move, fuse and braid them. We also show that the non-Abelian braiding statistics of Majorana fermions can be demonstrated unambiguously through the construction of two braiding operations and distinguishing the resulting two output orthogonal collective spin states. A nice feature of the scheme is that the strong fluor…
We present evidence for the existence of Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by a pair hopping. Our analysis is based on the combination of a qualitative low energy approach and numerical techniques using the Density Matrix Renormalization Group. We also discuss an experimental realization of pair-hopping interactions in cold atom gases confined in optical lattices, and its possible alternative applications to quantum simulation.
We here explore Majorana Fermion states in an s-wave superfluid of cold atoms in the presence of spin-orbital coupling and an additional harmonic potential. The superfluid boundary is induced by a harmonic trap. Two locally separated Majorana Fermion states are revealed numerically based on the self-consistent Bogoliubov-de Gennes equations. The local density of states are calculated, through which the signatures of Majorana excitations may be indicated experimentally.
We propose a method to prepare Majorana pairs at the corners of imprinted defects on a two-dimensional cold atom optical lattice with $s$-wave superfluid pairing. Different from previous proposals that manipulate the effective Dirac masses, our scheme relies on the sign flip of the spin-orbit coupling at the corners, which can be tuned in experiments by adjusting the angle of incident Raman lasers. The Majorana corner pairs are found to be located at the interface between two regimes with opposite spin orbit coupling strengths in an anticlockwise direction and are robust against certain symmet…
The recent experimental realization of spin-orbit coupling (SOC) for ultra-cold atoms opens a completely new avenue for exploring new quantum matter. In experiments, the SOC is implemented simultaneously with a Zeeman field. Such spin-orbit 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 non-zero momentum Cooper pairings, in contrast …
We discuss the effects of quantum and thermal fluctuations on the Majorana edge states in a topological atomic wire coupled to a superfluid molecular gas with gapless excitations. We find that the coupling between the Majorana edge states remains exponentially decaying with the length of the wire, even at finite temperatures smaller than the energy gap for bulk excitations in the wire. This exponential dependence is controlled solely by the localization length of the Majorana states. The fluctuations, on the other hand, provide the dominant contribution to the preexponential factor, which incr…
Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which is naturally immune against microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum system from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasi-static to the fast fluctuation regime. We present detailed results for the Majorana edge correl…
We describe how microwave spectroscopy of cold fermions in quasi-1D traps can be used to detect, manipulate, and entangle exotic non-local qbits associated with "Majorana" edge modes. We present different approaches to generate the p-wave superfluidity which is responsible for these topological zero-energy edge modes. We find that the edge modes have clear signatures in the microwave spectrum, and that the line shape distinguishes between the degenerate states of a qbit encoded in these edge modes. Moreover, the microwaves rotate the system in its degenerate ground-state manifold. We use these…
We devise a number-conserving scheme for the realization of Majorana Zero Modes in an interacting fermionic ladder coupled by Aharonov-Bohm cages. The latter provide an efficient mechanism to cancel single-particle hopping by destructive interference. The crucial parity symmetry in each wire is thus encoded in the geometry of the setup, in particular, its translation invariance. A generic nearest-neighbor interaction generates the desired correlated hopping of pairs. We exhibit the presence of an extended topological region in parameter space, first in a simplified effective model via bosoniza…
Recent studies in the realization of Majorana fermion (MF) quasiparticles have focused on engineering topological superconductivity by combining conventional superconductors and spin-textured electronic materials. We propose an effective model to create unpaired MFs at a honeycomb lattice edge by generalizing a 2-dimensional topologically nontrivial Haldane model and introducing textured pairings. The core idea is to add both the spin-singlet and textured spin-triplet pairings to a pseudospin-state dependent, time-reversal symmetry (TRS) noninvariant honeycomb lattice, and to satisfy generaliz…
In this work, we consider a 3D cubic optical lattice composed of coupled 1D wires with 1D spin-orbit coupling. When the s-wave pairing is induced through Feshbach resonance, the system becomes a topological superfluid with ring nodes, which are the ring nodal degeneracies in the bulk, and supports a large number of surface Majorana zero energy modes. The large number of surface Majorana modes remain at zero energy even in the presence of disorder due to the protection from a chiral symmetry. When the chiral symmetry is broken, the system becomes a Weyl topological superfluid with Majorana arcs…
The stability conditions for the singular vortex which accompanies Majorana zero modes at the core are investigated for p-wave resonant superfluids of atomic Fermi gases. Within the Ginzburg-Landau framework we determine the stable conditions in the parameter space for the external rotation frequency and the harmonic trap frequency. There exists the narrow stable region in this parameter space for quasi-two-dimensional condensates. We also describe the detailed characterizations of the spatial structure of the order parameter in the chiral p-wave superfluids under rotation.
We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultra-cold fermions when spin-orbit, Zeeman fields and interactions are varied. We show that phases containing rings of nodes possess non-trivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase anihilate to produce bulk zero-mode Majorana fermions at phase boundaries and then become massive Dirac fermions in the gapped phase. We characteri…
Topological states of generalized dissipative Majorana wires
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高级研究所）；Research Center for Basic Sciences & Modern Technologies (RBST), Institute for Advanced Studies in Basic Science (IASBS)（基础科学与现代技术研究中心，基础科学高级研究所）
One promising avenue to study one-dimensional ($1$D) 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 $1$D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the $\mathbb{Z}_2$ fermion parity symmetry that protects them. In this Letter, we present a new mechanism to overcome this obstacle, by piercing a (syn…
In this paper, we review the recent activity of our group on the study of disorder effects on systems displaying phase coherence. These studies have focused on both the electronic transport through mesoscopic metallic spin glasses, and cold atomic gases trapped in a disordered potential.
Cold atom systems offer a great potential for the future design of new mesoscopic quantum systems with properties that are fundamentally different from semiconductor nanostructures, such as quantum dots and quantum wires with electrons. Here, we investigate the analog of a quantum wire using ultra-cold particles, and find a new scenario for the quantum transport: Attractive interactions may lead to a complete suppression of current in the low-bias range, a total current blockade. We demonstrate this effect for the example of ultra-cold quantum gases with dipolar interactions.
The recent experimental realization of 1D equal Rashba-Dresselhaus spin-orbit coupling (ERD-SOC) for cold atoms provide a disorder-free platform for the implementation and observation of Majorana fermions (MFs), similar to the well studied solid state nanowire/superconductor heterostructures. However, the corresponding 1D chains of cold atoms possess strong quantum fluctuation, which may destroy the superfluids and MFs. In this Letter, we show that such 1D topological chains with MFs may be on demand generated in a 2D non-topological optical lattice with 1D ERD-SOC by modifying local potential…
We study ensembles of fermionic cold-atom quantum wires with tunable transverse mode population and single-wire resolution. From in situ density profiles, we determine the temperature of the atomic wires in the weakly interacting limit and reconstruct the underlying potential landscape. By varying atom number and temperature, we control the occupation of the transverse modes and study the 1D-3D crossover. In the 1D limit, we observe an increase of the reduced temperature $T/T_{F}$ at nearly constant entropy per particle $S/N k_{B}$. The ability to probe individual atomic wires in situ paves th…
