Zero Energy Modes and Statistics of Vortices in Spinful Chiral p -Wave Superfluids (original) (raw)
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Physical Review Letters, 2008
The visualization of chiral p-wave superfluidity in Fermi gases near p-wave Feshbach resonances is theoretically examined. It is proposed that the superfluidity becomes detectable in the entire BCS-BEC regimes through (i) vortex visualization by the density depletion inside the vortex core and (ii) intrinsic angular momentum in vortex free states. It is revealed that both (i) and (ii) are closely connected with the Majorana zero energy mode of the vortex core and the edge mode, which survive until the strong coupling BCS regime is approached from the weak coupling limit and vanish in the BEC regime.
Majorana Bound State in Rotating Superfluid He3-A between Parallel Plates
Physical Review Letters, 2008
A concrete and experimentally feasible example for testing the putative Majorana zero energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid 3 He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg-Landau functional, supplemented by microscopic calculations of the Bogoliubov-de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations. PACS numbers: 67.30.he, 67.30.ht, 71.10.Pm Much attention has been focused on Majorana zeroenergy states in various research fields[1], for example, leptogenesis in cosmology in connection with the matterantimatter imbalance problem[2], the fractional quantum Hall state, chiral superconductors, and p-wave superfluids in neutral atomic gases. Of particular interest is the possible application to quantum computing, based on the fact that a pair of Majorana states is intrinsically entangled and topologically protected from external disturbance. For chiral superconductors and p-wave superfluids, the key is finding the Majorana zero energy state bound in a vortex. Its existence is guaranteed by the index theorem[1], implying in this context that in spinless chiral p-wave pairing p x ± ip y of two dimension (2D), an odd winding number vortex always possesses a Majorana state at exactly zero energy relative to the Fermi level. This state is localized at the core[3].
Physical review letters, 2007
We propose to use the recently predicted two-dimensional "weak-pairing" px + ipy superfluid state of fermionic cold atoms as a platform for topological quantum computation. In the core of a vortex, this state supports a zero-energy Majorana mode, which moves to finite energy in the corresponding topologically trivial "strong-pairing" state. By braiding vortices in the "weak-pairing" state, unitary quantum gates can be applied to the Hilbert space of Majorana zero modes. For readout of the topological qubits, we propose realistic schemes suitable for atomic superfluids.
Textures and Exotic Vortices in Neutral Fermion Superfluids
2010
There has been intense interest in various Fermion superfluids in neutral atom liquids and gases, including chiral p-wave pairing in 3 He-A phase and Feshbach-resonanced 6 Li atom gases and d-wave pairing in atom gases. It is particularly interesting to find exotic vortices and associated low-lying Fermionic excitations under rotation. Here we report on our efforts of those topics: (1) Majorana Fermion in chiral superfluids near a p-wave Feshbach resonance. (2) Possible half-quantum vortices in p-wave superfluids of trapped Fermion atom gases. (3) Stability of a halfquantum vortex in rotating superfluid 3 He-A between parallel plates. (4) Majorana bound state in rotating superfluid 3 He-A between parallel plates. (5) Non-Abelian Fractional vortex in d-wave Feshbach resonance superfluids. We will summarize some of those works in a coherent manner in order to bridge the understanding between cold atom community and superfluid 3 He community by stressing the importance of cross fertilization between them.
Vortex State in a Strongly Coupled Dilute Atomic Fermionic Superfluid
Physical Review Letters, 2003
We show that in a dilute fermionic superfluid, when the Fermions interact with an infinite scattering length, a vortex state is characterized by a strong density depletion along the vortex core. This feature can make a direct visualization of vortices in Fermionic superfluids possible.
Quantized Vorticity in Superfluid 3He-A
2000
Superfluid 3He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the order-parameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They require different experimental conditions for their creation. When the flow is applied in the superfluid state, the structure with the lowest critical velocity is formed. In 3He-A this leads to the various forms of continuous (or singularity-free) vorticity. Which particular structure is created depends on the externally applied conditions and on the global order-parameter texture.
Physica E: Low-dimensional Systems and Nanostructures, 2014
It has been widely believed that half quantum vortices are indispensable to realize topological stable Majorana zero modes and non-Abelian anyons in spinful superconductors/superfluids. Contrary to this wisdom, we here demonstrate that integer quantum vortices in spinful superconductors can host topologically stable Majorana zero modes because of the mirror symmetry. The symmetry protected Majorana fermions may exhibit non-Abelian anyon braiding.
Topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases
Physical Review A, 2012
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases under Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well-known that the system is either a Bardeen-Cooper-Schrieffer (BCS) superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zeroenergy Majorana modes. However, in the weakly interacting regime the spin-orbit coupling does not favor the spatially oscillating FFLO order parameter. As a result, it seems difficult to create an inhomogeneous topological superfluid in current cold-atom experiments.
Effective theory of chiral two-dimensional superfluids
Physical Review B, 2014
We construct, to leading orders in the momentum expansion, an effective theory of a chiral (px + ipy) two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This theory naturally incorporates the parity and timereversal violating effects such as the Hall viscosity and the edge current. The particle number current and stress tensor are computed and their linear response to electromagnetic and gravitational sources is calculated. We also consider an isolated vortex in a chiral superfluid and identify the leading chirality effect in the density depletion profile.