### Session Z1: Strong Interaction Effects in Small Conductors

 Friday, March 17, 2006 11:15AM - 11:51AM Z1.00001: Controlling a Singlet-Triplet Spin Qubit Invited Speaker: Jason Petta An attractive candidate for a solid-state quantum bit is based on semiconductor quantum dots, which allow controlled coupling of one or more electrons, using rapidly switchable voltages applied to electrostatic gates [1]. Due to tight confinement and the high degree of isolation from the environment, spin relaxation times in quantum dots can approach millisecond timescales [2]. In this talk I will describe how fast electrical control of the exchange interaction can be used to coherently manipulate two-electron spin states [3]. By separating a spin singlet state on-chip, we measure an ensemble averaged spin dephasing time $T_2^*$ of 10 ns, limited by the contact hyperfine interaction with the GaAs host nuclei. We develop quantum control techniques based on the exchange interaction to correct for hyperfine dephasing. Coherent spin state rotations are achieved, including spin SWAP. By using a spin-echo pulse sequence based on the exchange interaction we extend the spin coherence time, $T_2$ beyond 1.2 microseconds. The quantum control techniques demonstrated here are general and may be used to manipulate singlet-triplet spin qubits in carbon nanotubes, electrons on helium, and semiconducting nanowires. \par In collaboration with A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard. \par [1] J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, A. C. Gossard, M. P. Hanson, Phys. Rev. B {\bf 72}, R161301 (2005). \par [2] A. C. Johnson, J. R. Petta, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard, Nature {\bf 435}, 925 (2005). \par [3] J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard, Science {\bf 309}, 2180 (2005). Friday, March 17, 2006 11:51AM - 12:27PM Z1.00002: Conductance of a quantum wire at low electron density Invited Speaker: Konstantin Matveev We study the transport of electrons through a long quantum wire connecting two bulk leads. As the electron density in the wire is lowered, the Coulomb interactions lead to short-range crystalline ordering of electrons. In this Wigner crystal state the spins of electrons form an antiferromagnetic Heisenberg spin chain with exponentially small exchange coupling $J$. Inhomogeneity of the electron density due to the coupling of the wire to the leads results in violation of spin-charge separation in the device. As a result the spins affect the conductance of the wire. At zero temperature the low-energy spin excitations propagate freely through the wire, and its conductance remains $2e^2/h$. At finite temperature some of the spin excitations are reflected by the wire and contribute to its resistance. Since the energy of the elementary excitations in the spin chain (spinons) cannot exceed $\pi J/2$, the conductance of the wire acquires an exponentially small negative correction $\delta G \propto - \exp(-\pi J/2T)$ at low temperatures $T \ll J$. At higher temperatures, $T \gg J$, most of the spin excitations in the leads are reflected by the wire, and the conductance levels off at a new universal value $e^2/h$. This result is consistent with experimental observations of a mini-plateau of conductance at $e^2/h$ in quantum wires in the absence of magnetic field. Friday, March 17, 2006 12:27PM - 1:03PM Z1.00003: Localization Transition in a Ballistic Quantum Wire. Invited Speaker: Hadar Steinberg We report measurements probing the many-body wave-function of localized states in one dimension. We utilize tunneling between two long, clean, parallel quantum wires in a GaAs/AlGaAs heterostructure, where one of the two wires is driven into the localized regime using a density tuning gate, and the other wire, still in the regime of extended electronic states, serves as a momentum spectrometer. Our measurements show that as the electron density is lowered to a critical value, the many-body state abruptly changes from an extended state with a well-defined momentum to a localized state with a wide range of momentum components. The signature of the localized states appears as discrete tunneling features at resonant gate-voltages, corresponding to the depletion of single electrons from the localized region and showing Coulomb-blockade behavior. Typically 5 - 10 such features appear, where the one-electron state has a single-lobed momentum distribution, and the few-electron states have double-lobed distributions with peaks at the Fermi momenta. Friday, March 17, 2006 1:03PM - 1:39PM Z1.00004: Spin incoherent effects in momentum resolved tunneling, transport, and Coulomb drag in Luttinger liquids Invited Speaker: Gregory Fiete In a one dimensional electron gas at low enough density the magnetic exchange energy $J$ between neighboring electrons is exponentially suppressed relative to the Fermi energy, $E_F$. At finite temperature $T$, the energy hierarchy $J << T << E_F$ can be reached, and we refer to this as the spin incoherent (SI) Luttinger liquid state. By using a model of a fluctuating Wigner solid, we theoretically explore the signatures of spin incoherence in the single particle Green’s function[1], momentum resolved tunneling[2], transport[3], and Coulomb drag[4]. In the SI Green’s function the spin modes of a Luttinger liquid (LL) are thermally washed out leaving only singular behavior from the charge modes. The charge modes are broadened in momentum space by an amount of order $k_F$ and the energy dependence of the tunneling density of states qualitatively changes from the low energy suppression of the LL regime to a possible low energy divergence in the SI regime. Such a state may be probed directly in momentum resolved tunneling between parallel quantum wires. Deep in the SI regime, the physics of transport and Coulomb drag can be mapped onto spinless electrons. Various crossovers in temperature and for finite systems connected to Fermi liquid leads are discussed. Both transport and Coulomb drag may exhibit interesting non-monotonic temperature dependence. [1] G. A. Fiete and L. Balents, Phys. Rev. Lett. 93, 226401 (2004). [2] G. A. Fiete, J. Qian, Y. Tserkovnyak, and B. I. Halperin, Phys. Rev. B 72, 045315 (2005). [3] G. A. Fiete, K. Le Hur, and L. Balents, Phys. Rev. B 72, 125416 (2005). [4] G. A. Fiete, K. Le Hur, and L. Balents, Submitted, cond-mat/0511715. Friday, March 17, 2006 1:39PM - 2:15PM Z1.00005: Dephasing of mesoscopic interferences from Electron Fractionalization Invited Speaker: Karyn LeHur The understanding of dephasing processes (the physical causes of supressed interference effects) constitutes a topics of perpetual interest in mesoscopic systems. Phase-breaking mechanisms in ballistic systems of dimensionality less than two are presently not completely understood and therefore deserve intensive theoretical and experimental endeavors. In this talk, we investigate the dephasing of mesoscopic interferences by electron-electron interactions in a well-defined geometry composed of two tunnel-coupled wires embodied by a Luttinger liquid. We thoroughly demonstrate that interactions can produce a visible attenuation of Aharonov-Bohm oscillations [1]. Moreover, in our geometry, we firmly emphasize that the emerging dephasing time results from the electron factionalization phenomenon that is known to produce an electron life-time in 1/T with T being the temperature [2]. A dephasing time in 1/T has been reported in one-dimensional GaAs rings. \newline \newline [1] Karyn Le Hur, Phys. Rev. Lett. 95, 076801 (2005). \newline [2] Karyn Le Hur, Phys. Rev. B 65, 233314 (2002).