Nuclear Magnetic Resonance Quantum Computing Using Liquid Crystal Solvents

Liquid crystals offer several advantages as solvents for molecules used for nuclear magnetic resonance quantum computing (NMRQC). The dipolar coupling between nuclear spins manifest in the NMR spectra of molecules oriented by a liquid crystal permits a significant increase in clock frequency, while short spin-lattice relaxation times permit fast recycling of algorithms, and save time in calibration and signal-enhancement experiments. Furthermore, the use of liquid crystal solvents offers scalability in the form of an expanded library of spin-bearing molecules suitable for NMRQC. These ideas are demonstrated with the successful execution of a 2-qubit Grover search using a molecule ($^{13}$C$^{1}$HCl$_3$) oriented in a liquid crystal and a clock speed eight times greater than in an isotropic solvent. Perhaps more importantly, five times as many logic operations can be executed within the coherence time using the liquid crystal solvent.Comment: Minor changes. Published in Appl. Phys. Lett. v.75, no.22, 29 Nov 1999, p.3563-356

Magnetic Properties of Undoped C60C_{60}

The Heisenberg antiferromagnet, which arises from the large $U$ Hubbard model, is investigated on the $C_{60}$ molecule and other fullerenes. The connectivity of $C_{60}$ leads to an exotic classical ground state with nontrivial topology. We argue that there is no phase transition in the Hubbard model as a function of $U/t$, and thus the large $U$ solution is relevant for the physical case of intermediate coupling. The system undergoes a first order metamagnetic phase transition. We also consider the S=1/2 case using perturbation theory. Experimental tests are suggested.Comment: 12 pages, 3 figures (included

Polaron Excitations in Doped C60: Effects of Disorders

Effects on C$_{60}$ by thermal fluctuations of phonons, misalignment of C$_{60}$ molecules in a crystal, and other intercalated impurities (remaining C$_{70}$, oxygens, and so on) are simulated by disorder potentials. The Su-Schrieffer-Heeger--type electron-phonon model for doped C$_{60}$ is solved with gaussian bond disorders and also with site disorders. Sample average is performed over sufficient number of disorder configurations. The distributions of bond lengths and electron densities are shown as functions of the disorder strength and the additional electron number. Stability of polaron excitations as well as dimerization patterns is studied. Polarons and dimerizations in lightly doped cases (C$_{60}^{-1,-2}$) are relatively stable against disorders, indicated by peak structures in distribution functions. In more heavily doped cases, the several peaks merge into a single peak, showing the breakdown of polaron structures as well as the decrease of the dimerization strength. Possibility of the observation of polaronic lattice distortions and electron structures in doped C$_{60}$ is discussed.Comment: Note: This manusript was accepted for publication in Physical Review B. Figures will be sent to you via snail (conventional) mai

Lattice distortion and energy level structures in doped C_{60} and C_{70} studied with the extended Su-Schrieffer-Heeger model: Polaron excitations and optical absorption

We extend the Su-Schrieffer-Heeger model of polyacetylene to C_{60} and C_{70} molecules, and solve numerically. The calculations of the undoped systems agree well with the known results. When the system (C_{60} or C_{70}) is doped with one or two electrons (or holes), the additional charges accumulate almost along an equatorial line of the molecule. The dimerization becomes weaker almost along the same line. Two energy levels intrude largely in the gap. The intrusion is larger in C_{70} than in C_{60}. Therefore, ``polarons'' are predicted in doped buckminster- fullerenes. We calculate optical absorption coefficient for C_{60} in order to look at how ``polarons'' will be observed. It is predicted that there appears a new peak at the lower energy than the intergap transition peaks. It is also found that C_{60} and C_{70} are related mutually with respect to electronical structures as well as lattice geometries. (to be published in Phys. Rev. B 45, June 15 issue)Comment: 21 page

Orientational Melting in Carbon Nanotube Ropes

Using Monte Carlo simulations, we investigate the possibility of an orientational melting transition within a "rope" of (10,10) carbon nanotubes. When twisting nanotubes bundle up during the synthesis, orientational dislocations or twistons arise from the competition between the anisotropic inter-tube interactions, which tend to align neighboring tubes, and the torsion rigidity that tends to keep individual tubes straight. We map the energetics of a rope containing twistons onto a lattice gas model and find that the onset of a free "diffusion" of twistons, corresponding to orientational melting, occurs at T_OM > 160 K.Comment: 4 page LaTeX file with 3 figures (10 PostScript files

Non-Ergodic Nuclear Depolarization in Nano-Cavities

Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of a gas in a closed nano-cavities are independent of the spacing between all spins. We derive exact time-dependent polarization for all spins in spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin,$P_1(0)= 1$ then the exact spin dynamics of the model is shown to exhibit a periodical short pulses of the polarization of the first spin, the effect being typical of the systems having a large number, $N$, of spins. If $N \gg 1$, then within the period $4\pi/g$ ($2\pi/g$) for odd (even) $N$-spin clusters, with $g$ standing for spin coupling, the polarization of spin 1 switches quickly from unity to the time independent value, 1/3, over the time interval about $(g\sqrt{N})^{-1}$, thus, almost all the time, the spin 1 spends in the time independent condition $P_1(t)= 1/3$. The period and the width of the pulses determine the volume and the form-factor of the ellipsoidal cavity. The formalism is adopted to the case of time varying nano-fluctuations of the volume of the cavitation nano-bubbles. If the volume $V(t)$ is varied by the Gaussian-in-time random noise then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of the single spin exhibits the Gaussian (or exponential) time dependence when the correlation time of the fluctuations of the nano-volume is larger (or smaller) than the $<(\delta g)^2 >^{-1/2}$, where the $$ is the variance of the $g(V(t))$ coupling. Finally, we report the exact calculations of the NMR line shape for the $N$-spin gaseous aggregate.Comment: 26 pages, 3 figure

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr