Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session D7: Signatures of Non-Abelian Quantum Hall States |
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Sponsoring Units: DCMP Chair: Steven Simon, Lucent Technologies Room: Colorado Convention Center Korbel 4A-4B |
Monday, March 5, 2007 2:30PM - 3:06PM |
D7.00001: Non-Abelian quantum Hall states of fermions and bosons Invited Speaker: In a non-Abelian quantum Hall state, there are types of elementary excitations or quasiparticles that obey non-Abelian statistics. This is an extension of the idea of fractional statistics that means that when several of these quasiparticles are present in the system and are well-separated at well-defined positions, there is a degenerate space of lowest-energy states. When the quasiparticles are then exchanged adiabatically, the result is a matrix operation on this space of states. Greg Moore and the author$^1$ introduced this idea to condensed matter physics in 1991. They proposed a basic example called the Moore-Read Pfaffian state. The physics of the existence of the degenerate states for the quasiparticles in this system can be understood by viewing it as a $p_x-ip_y$ paired state of composite fermions, in which quasiparticles are $hc/2e$ vortices that carry Majorana fermion zero modes. This state is expected to be realized in the filling factor $\nu=5/2$ fractional quantum Hall (FQH) state. In later work, a series (labeled by an integer $k$) of ``parafermion'' states was proposed$^2$. This talk will review these ideas, and describe recent numerical work that strongly supports the idea that the $k=3$ member of the sequence occurs in the filling factor $12/5$ FQH state for electrons$^3$, and also$^4$ in a system of bosons, such as rotating cold atoms, at filling factor $3/2$. It will also describe recent analytical results$^5$ on the explicit quasihole trial wavefunctions of the parafermion states. \newline 1. G. Moore and N. Read, Nucl. Phys. {\bf B 360}, 362 (1991). \newline 2. N. Read and E. Rezayi, Phys. Rev. B {\bf 59}, 8084 (1999). \newline 3. E.H. Rezayi and N. Read, cond-mat/0608346. \newline 4. E.H. Rezayi, N. Read, and N.R. Cooper, Phys. Rev. Lett.{\bf 95}, 160404 (2005). \newline 5. N. Read, Phys. Rev. B {\bf 73}, 245334 (2006). [Preview Abstract] |
Monday, March 5, 2007 3:06PM - 3:42PM |
D7.00002: Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors Invited Speaker: |
Monday, March 5, 2007 3:42PM - 4:18PM |
D7.00003: Current noise and AC conductivity as probes of non-abelian quasi-particles Invited Speaker: We consider two scenarios for probing signatures of non-abelian quasi-particles through transport and noise measurements in the $\nu=5/2$ fractional quantum Hall effect. In the first scenario we study bulk transport in the presence of a Wigner crystal of quasi-particles, which would form at filling factors close to $\nu=5/2$. For immobile quasi-particles, we find a mechanism for dissipative transport at frequencies below the gap, which is manifested in a nonzero conductivity in response to an electric field with finite wave vector ${\bf q}$ and frequency $\omega$, and reflects the exponential degeneracy of the ground state. The second scenario deals with noise measurements in a Hall bar geometry where two quantum point contacts (QPCs) introduce two interfering amplitudes for back-scattering. Thermal fluctuations of the number of quasi-particles enclosed between the two point contacts induce current noise of the telegraph type. The non-abelian $\nu=5/2$ state is characterized by a unique switching pattern of current, originating from the suppression and revival of the interference term as the parity of the number of quasi-particles between the two QPCs fluctuates. This work was done in collaboration with Ady Stern and Steve Simon. [Preview Abstract] |
Monday, March 5, 2007 4:18PM - 4:54PM |
D7.00004: Toplogical Quantum Compiling Invited Speaker: A quantum computer must be capable of manipulating quantum information while simultaneously protecting it from error and loss of quantum coherence due to coupling to the environment. Topological quantum computation (TQC) offers a particularly elegant way to achieve this. In TQC quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum computation is carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three-dimensional space-time, and the corresponding computation depends only on the topology of the braids formed by these world-lines. A variety of proposed fractional quantum Hall states are believed to possess quasiparticles that can be used for TQC -- among them the so-called ``Fibonacci anyons". These quasiparticles are conjectured to exist in the experimentally observed $\nu = 12/5$ fractional quantum Hall state. In this talk, I will review the basic ideas behind TQC, and describe our recent work showing explicitly how to translate (compile) arbitrary quantum algorithms into specific braiding patterns for Fibonacci anyons. (Work done in collaboration with N.E. Bonesteel, S.H. Simon, and G. Zikos.) [Preview Abstract] |
Monday, March 5, 2007 4:54PM - 5:30PM |
D7.00005: Detecting fractional statistics with anyonic Mach-Zehnder interferometer Invited Speaker: Fractionally charged quasiparticles in the quantum Hall state with filling factor $\nu=5/2$ are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in a recently fabricated device, an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a non-analytic dependence on the tunneling amplitudes which can be controlled by gate voltages. In contrast to the case of Abelian statistics, the I-V curve is asymmetric. \vskip 3mm [1] K. T. Law, D. E. Feldman, and Y. Gefen, Phys. Rev. B 74, 045319 (2006). \vskip 1mm [2] D. E. Feldman and A. Kitaev, cond-mat/0607541. [Preview Abstract] |
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