Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session G36: Topological Phases and Majorana Fermions in Cold Atoms |
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Sponsoring Units: DAMOP Chair: Nigel Cooper, University of Cambridge Room: 211 |
Tuesday, March 3, 2015 11:15AM - 11:27AM |
G36.00001: Topological States in a One-Dimensional Fermi Gas with Attractive Interactions Jonathan Ruhman, Erez Berg, Ehud Altman We show that a single one-dimensional 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. Topological ground state degeneracy is associated with interfaces between two distinct phases that naturally form in the harmonic confining potential due to the spatial variations of the chemical potential. We find that backscattering by impurities, or simply by the interfaces themselves, effects a splitting in the topological degeneracy which generally scales as $1/L^{K/2}$, where $L$ is the size of the system and $K$ is the Luttinger parameter. However, when the interfaces are sufficiently smooth, as in the case of a harmonic confining potential, the splitting becomes exponentially small in the system size. We also discuss the experimental implications of the novel ground state degeneracy, as manifest for example in the response to simple dipole modulations of the harmonic trap potential. [Preview Abstract] |
Tuesday, March 3, 2015 11:27AM - 11:39AM |
G36.00002: One-dimensional topological chains in two-dimensional non-topological optical lattices Lei Jiang, Chuanwei Zhang Majorana fermions appear near the topological phase boundary. In 2D, Majorana fermions are found when vortices, which stand for topological defects, are formed in topological superfluids. Due to the complications to generate 2D topological superfluids in experiments, Majorana fermions are not easily achievable in 2D systems. In our work, we show, by imprinting 1D local potentials in a finite 2D system, we can realize a 1D topological chain on demand even in originally non-topological 2D systems. A pair of zero-energy Majorana fermions can be stable in this system and exist at the ends of the topological chain. We also demonstrate the possibility to arrange an array of Majorana fermions by separating topological chains with non-topological ones. Similar results can be obtained in 3D optical lattices. Compared with strictly 1D systems, quantum fluctuations are strongly suppressed in such high dimensional optical lattices. Because all requirements of our model are within the reach of current experiments, our proposed scheme may provide an experimental feasible platform for observing Majorana states in 2D ultra-cold atom optical lattices. [Preview Abstract] |
Tuesday, March 3, 2015 11:39AM - 11:51AM |
G36.00003: Dynamical detection of a topological phase transition in one-dimensional spin-orbit-coupled Fermi gases F. Setiawan, Krishnendu Sengupta, Ian Spielman, Jay Sau We theoretically study the dynamics of topological phase transition in one-dimensional (1D) spin-orbit coupled (SOC) Fermi gases with attractive interaction as a means of detecting the phase transition. The transition from conventional (trivial) superfluid to topological superfluid phase happens as the intensity of the Raman lasers (Zeeman field) is ramped above the critical value. To minimize effect of heating, we propose to ramp from a conventional superfluid phase through the topological phase transition and back. We calculate the momentum distribution of the atoms after the ramp by solving the time-dependent Bogoliubov-de Gennes (BdG) equations self-consistently with the initial state of the Fermi gas being the thermal state. We show that the phase transition can be detected by measuring the scaling of the momentum distribution with the ramp rate. [Preview Abstract] |
Tuesday, March 3, 2015 11:51AM - 12:03PM |
G36.00004: Distribution functions and probes of far-from-equilibrium topological matter Yunxiang Liao, Matthew Foster We investigate radio-frequency (RF) spectroscopy and superconductor-normal metal tunneling as probes of out-of-equilibrium topological systems. As an example, we study a 2D p$+$ip superfluid following an instantaneous quench of the coupling strength [Foster et al. PRB 2013, PRL 2014]. The long-time asymptotic order parameter of this system can be constant or time-periodic. In both cases, the post-quench Cooper pairs each occupy a linear combination of two states, with coefficients determined by the distribution function. In strong quenches where the order parameter is periodic, the bases are two Floquet states with opposite quasi-energy. We derive expressions for the RF and tunneling spectra for these post-quench states, examining both average values and harmonics. While the distribution function strongly affects the RF signal, it disappears from the tunneling spectrum. We show that the bulk RF signal obtained by occupying the lower Floquet band is dramatically different from that of the post-quench states. This is intimately related to the difference between the topology of the state, which cannot change under closed evolution, versus the topology of the non-equilibrium excitation spectrum. We also look for signatures of Majorana edge states in systems with an edge. We compute the local RF signal, which depends upon the non-equilibrium excitation spectrum of bulk and edge states as well as their occupation. [Preview Abstract] |
Tuesday, March 3, 2015 12:03PM - 12:15PM |
G36.00005: Fractional Angular Momentum in Cold-Atom Systems Yuhe Zhang, Sreejith Ganesh Jaya, Nathan D Gemelke, Jainendra K Jain The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically\footnote{Zhang et al., PRL 113, 160404.} that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall (FQH) state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect. We extend our work to investigate the quasiholes in 5/2 FQH state which are believed to obey non-Abelian statistics. We will study the effect of non-Abelian statistics for test particles binding quasiholes in a Moore-Read Pfaffian state, which is produced for bosons subject to a three-body contact interaction, and also for bosons with two-body contact interaction. [Preview Abstract] |
Tuesday, March 3, 2015 12:15PM - 12:27PM |
G36.00006: Rotational properties of two-component Bose gases in the lowest Landau level Marius Meyer, Ganesh Jaya Sreejith, Susanne Viefers We study the rotational (yrast) spectra of dilute two-component atomic Bose gases in the low angular momentum regime, assuming equal interspecies and intraspecies interaction. Our analysis employs the composite fermion (CF) approach including a pseudospin degree of freedom. While the CF approach is not {\it a priori} expected to work well in this angular momentum regime, we show that composite fermion diagonalization gives remarkably accurate approximations to low energy states in the spectra. For angular momenta $0 < L < M$ (where $N$ and $M$ denote the numbers of particles of the two species, and $M \geq N$), we find that the CF states span the full Hilbert space and provide a convenient set of basis states which, by construction, are eigenstates of the symmetries of the Hamiltonian. Within this CF basis, we identify a subset of the basis states with the lowest $\Lambda$-level kinetic energy. Diagonalization within this significally smaller subspace constitutes a major computational simplification and provides very close approximations to ground states and a number of low-lying states within each pseudospin and angular momentum channel. [Preview Abstract] |
Tuesday, March 3, 2015 12:27PM - 12:39PM |
G36.00007: Probing Fractional Quantum Hall Physics with Rotating Bose Gases Louis Jacome, Jianshi Zhao, Nate Gemelke Rapidly rotating and repulsively interacting Bose gases are expected to exhibit character reminiscent of the fractional quantum Hall effect (FQH) in two-dimensional electron gases. Such states are expected to possess excitations with fractionalized braid statistics, although no convincing measurement of this behavior has yet been made in either system. In this talk, we describe progress toward realizing FQH physics using cold Rb-87 atoms confined to an optical lattice with rotating lattice sites. The inclusion of high resolution optical microscopy to perform occupancy-resolved detection expands on previous measurements, and promises new avenues to directly interrogate novel behavior including pair-correlation and braiding statistics as proposed recently [1]. Finally, we discuss new emergent phenomena in chains of tunnel-coupled FQH droplets, including the existence of a novel class of insulating and superfluid states which exhibit local fractional Hall character, and dissipationless transport phenomena governed by new topological invariants. [1]Fractional Angular Momentum in Cold-Atom Systems, Yuhe Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, PRL 113, 160404 (2014) [Preview Abstract] |
Tuesday, March 3, 2015 12:39PM - 12:51PM |
G36.00008: Emergent Fermi Sea in A System of Interacting Bosons Yinghai Wu, Jainendra Jain An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The bosons each bind a single vortex as a result of the repulsive interaction, and these fermionic bound states, namely composite fermions, form a spin-singlet Fermi sea. [Preview Abstract] |
Tuesday, March 3, 2015 12:51PM - 1:03PM |
G36.00009: Few-body treatment of the quantum Hall system Chris Greene, Kevin Daily, Rachel Wooten The quantum Hall system is perhaps the simplest real physical system to exhibit complicated, highly-correlated quantum behavior\footnote{D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. \textbf{48}, 1559 (1982)}. Our initial theoretical exploration of this problem approaches it from a few-body perspective using the adiabatic hyperspherical representation\footnote{J. Macek, J. Phys. B: At. Mol. Phys., \textbf{1} 831 (1968).} developed originally for atomic systems. Such a 2D system with interacting charged particles that move in an external magnetic field can be simulated for cold atoms using artificial vector gauge potentials. [Preview Abstract] |
Tuesday, March 3, 2015 1:03PM - 1:15PM |
G36.00010: Majorana modes in single channel cold atomic gases with short-ranged attractive interactions Jay Sau, Xiaopeng Li Majorana modes have been predicted to exist in topological superfluids that generated by a combination of spin-orbit coupling and short-ranged attractive interactions. One dimensional superfluids with intrinsic interactions, however, present a precarious competition between phase fluctuations and topological superfluidity. Previously, it has been argued that the Majorana nature survives with some modification in multi-channel and proximity-induced superfluidity in systems of ultra-cold atoms. This discussion is more subtle in the single channel case because the universal properties of one dimensional fermions with attractive interactions are known to be described by a simple Luttinger liquid in the low-energy limit. In this talk, we will discuss the properties of Galilean invariant one dimensional fermi gases with attractive interactions and show how they display properties consistent with both being a topological (or non-topological) superfluid and a Luttinger liquid. [Preview Abstract] |
Tuesday, March 3, 2015 1:15PM - 1:27PM |
G36.00011: Floquet FFLO superfluids and Majorana fermions in a shaken fermionic optical lattice Zhen Zheng, Chunlei Qu, Xubo Zou, Chuanwei Zhang Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids, Cooper pairings with finite momentum, and Majorana fermions (MFs), quasiparticles with non-Abelian exchange statistics, are two topics under intensive investigation in the past several decades, but unambiguous experimental evidences for them have not been found yet in any physical system. Here we show that the recent experimentally realized shaken optical lattice provides a new pathway to realize FFLO superfluids and MFs. By tuning the shaking frequency and amplitude, various coupling between the $s$- and $p$-orbitals of the lattice (denoted as the pseudo-spins) can be generated. We show that the combination of the inverted $s$- and $p$-band dispersions, the engineered pseudo-spin coupling, and the on-site attractive interaction, naturally allows the observation of FFLO superfluids as well as MFs in different parameter regions. [Preview Abstract] |
Tuesday, March 3, 2015 1:27PM - 1:39PM |
G36.00012: Majorana edge modes in Kitaev model on honeycomb lattice Manisha Thakurathi, Krishnendu Sengupta, Diptiman Sen We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes of the model in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic $\delta$-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic $d$-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice. [Preview Abstract] |
Tuesday, March 3, 2015 1:39PM - 1:51PM |
G36.00013: Fractionalized Majorana modes in ultracold bosonic systems Mohammad F. Maghrebi, Sriram Ganeshan, David Clarke, Alexey Gorshkov, Jay Deep Sau Fractionalized Majorana fermions, also known as parafermions, are exotic topologically protected modes that go beyond the simplest non-Abelian anyons, Majorana fermions. They commute up to a nontrivial phase factor in contrast to the minus sign for fermions. These modes are proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. With recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of two Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trench and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. [Preview Abstract] |
Tuesday, March 3, 2015 1:51PM - 2:03PM |
G36.00014: Extracting Entanglement Entropy Via Non-Destructive Imaging of an Ultracold Atomic Gas Craig Price, Qi Liu, Nathan Gemelke Entanglement plays an important role in determining the thermodynamic ground state of many many-body quantum systems, and recent theoretical studies have provided evidence that broad classes of quantum critical and topologically ordered states may be characterized by the scaling properties of their entanglement entropy (EE)[1,2]. We describe how EE can be extracted in a QND imaging process, in which information is transferred from one quantum gas to another using pairwise entangling schemes, and how the subsequent non-local thermal back-action of detection may be used to probe pre-existing entanglement in the sample. We discuss related applications of quantum collisional microscopy, including minimally destructive imaging of non-equilibrium quantum gases, and the algorithmic cooling of a Mott-insulator by non-destructive detection and removal of thermal defects. [1] V. Vedral, M.B. Plenio, M.A. Rippin, P. L. Knight. Quantifying Entanglement. Phys. Rev. Lett 78, 2275 (1997) [2] G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev. Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003) [Preview Abstract] |
Tuesday, March 3, 2015 2:03PM - 2:15PM |
G36.00015: Two-dimensional topological order of kinetically constrained quantum particles Stefanos Kourtis Motivated by recent experimental and theoretical work on driven optical lattices, we investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as an approximate generalization of strongly interacting particles hopping on Haldane and equivalent lattices and are pertinent to systems irradiated by circularly polarized light. After introducing a broad class of models, we focus on particular realizations and show numerically that they exhibit topological order, by observing topological ground-state degeneracies and the quantization of corresponding invariants. Apart from potentially being crucial for the interpretation of forthcoming cold-atom experiments, our results also hint at unexplored possibilities for the realization of topologically ordered matter. A further implication, relevant to fractional quantum Hall (FQH) physics, is that the correlations responsible for FQH-like states can arise from processes other than density-density interactions. [Preview Abstract] |
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