arXiv subjects

N. E. Bonesteel

Publications and source records attributed to N. E. Bonesteel.

35 records · Page 2Linked to original sources

arXiv2004

Universal Quantum Computation through Control of Spin-Orbit Coupling

We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.

quant-ph↗

arXiv2003

Spin-Orbit Coupling and Time-Reversal Symmetry in Quantum Gates

We study the effect of spin-orbit coupling on quantum gates produced by pulsing the exchange interaction between two single electron quantum dots. Spin-orbit coupling enters as a small spin precession when electrons tunnel between dots. For adiabatic pulses the resulting gate is described by a unitary operator acting on the four-dimensional Hilbert space of two qubits. If the precession axis is fixed, time-symmetric pulsing constrains the set of possible gates to those which, when combined with single qubit rotations, can be used in a simple CNOT construction. Deviations from time-symmetric pulsing spoil this construction. The effect of time asymmetry is studied by numerically integrating the Schrödinger equation using parameters appropriate for GaAs quantum dots. Deviations of the implemented gate from the desired form are shown to be proportional to dimensionless measures of both spin-orbit coupling and time asymmetry of the pulse.

cond-mat.mes-hall↗

arXiv2003

Conductivity of Paired Composite Fermions

We develop a phenomenological description of the nu=5/2 quantum Hall state in which the Halperin-Lee-Read theory of the half-filled Landau level is combined with a p-wave pairing interaction between composite fermions (CFs). The electromagnetic response functions for the resulting mean-field superconducting state of the CFs are calculated and used in an RPA calculation of the q and omega dependent longitudinal conductivity of the physical electrons, a quantity which can be measured experimentally.

cond-mat.mes-hall↗

arXiv2001

Anisotropic Spin Exchange in Pulsed Quantum Gates

We show how to eliminate the first-order effects of the spin-orbit interaction in the performance of a two-qubit quantum gate. Our procedure involves tailoring the time dependence of the coupling between neighboring spins. We derive an effective Hamiltonian which permits a systematic analysis of this tailoring. Time-symmetric pulsing of the coupling automatically eliminates several undesirable terms in this Hamiltonian. Well chosen pulse shapes can produce an effectively isotropic exchange gate, which can be used in universal quantum computation with appropriate coding.

quant-ph↗

arXiv2000

Chiral Spin Liquids and Quantum Error Correcting Codes

The possibility of using the two-fold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error correcting codes is investigated. It is shown that codes constructed using these states on finite periodic lattices do not meet the necessary and sufficient conditions for correcting even a single qubit error with perfect fidelity. However, for large enough lattice sizes these conditions are approximately satisfied, and the resulting codes may therefore be viewed as approximate quantum error correcting codes.

quant-ph↗

arXiv2000

Quantum Projector Method on Curved Manifolds

A generalized stochastic method for projecting out the ground state of the quantum many-body Schrödinger equation on curved manifolds is introduced. This random-walk method is of wide applicability to any second order differential equation (first order in time), in any spatial dimension. The technique reduces to determining the proper ``quantum corrections'' for the Euclidean short-time propagator that is used to build up their path-integral Monte Carlo solutions. For particles with Fermi statistics the ``Fixed-Phase'' constraint (which amounts to fixing the phase of the many-body state) allows one to obtain stable, albeit approximate, solutions with a variational property. We illustrate the method by applying it to the problem of an electron moving on the surface of a sphere in the presence of a Dirac magnetic monopole.

cond-mat.stat-mech↗

arXiv1999

Skyrmion Physics Beyond the Lowest Landau Level Approximation

The effects of Landau level mixing and finite thickness of the two-dimensional electron gas on the relative stability of skyrmion and single spin-flip excitations at Landau level filling factor $ν=1$ have been investigated. Landau level mixing is studied by fixed-phase diffusion Monte Carlo and finite thickness is included by modifying the effective Coulomb interaction. Both Landau level mixing and finite thickness lower skyrmion excitation energies and favor skyrmions with fewer spin flips. However, the two effects do not work `coherently'. When finite thickness is included the effect of Landau level mixing is strongly suppressed.

cond-mat.mes-hall↗

arXiv1998

Monte Carlo Comparison of Quasielectron Wave Functions

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions $ν=1/3$, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interactions the results obtained using these two wave functions are essentially the same, though the energy gap obtained using the composite fermion quasielectron is slightly smaller, and closer to extrapolated exact-diagonalization results.

cond-mat.mes-hall↗

arXiv1998

Singular Pair Breaking in the Composite Fermi Liquid Description of the Half-Filled Landau Level

Fluctuations of the Chern-Simons gauge field in the composite Fermi liquid description of the half-filled Landau level are pair breaking in all angular momentum channels. For short-range electron-electron interactions these fluctuations are sufficiently strong to drive any T=0 pairing transition first order. For Coulomb interactions these fluctuations are weaker and a continuous transition is possible.

cond-mat.mes-hall↗

arXiv1998

Possibility of p-wave pairing of composite fermions at $ν=1/2$

We find that for the pure Coulomb repulsion the composite Fermi sea at $ν=1/2$ is on the verge of an instability to triplet pairing of composite fermions. It is argued that a transition into the paired state, described by a Pfaffian wave function, may be induced if the short-range part of the interaction is softened by increasing the thickness of the two-dimensional electron system.

cond-mat.mes-hall↗

arXiv1997

Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study

A generalized diffusion Monte Carlo method for solving the many-body Schrödinger equation on curved manifolds is introduced and used to perform a `fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the $ν=1/3$ energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations.

cond-mat.mes-hall↗

arXiv1996

Gauge Fields and Pairing in Double-Layer Composite Fermion Metals

A symmetrically doped double layer electron system with total filling fraction $ν=1/m$ decouples into two even denominator ($ν=1/2 m$) composite fermion `metals' when the layer spacing is large. Out-of-phase fluctuations of the statistical gauge fields in this system mediate a singular attractive pairing interaction between composite fermions in different layers. A strong-coupling analysis shows that for any layer spacing $d$ this pairing interaction leads to the formation of a paired quantum Hall state with a zero-temperature gap $Δ(0) \propto 1/d^2$. The less singular in-phase gauge fluctuations suppress the size of the zero-temperature gap, $Δ(0) \propto 1/\left({d^2}{(\ln d)^6}\right)$, but do not eliminate the instability.

cond-mat↗

arXiv1995

Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $λ= (e^2/εl_0)/\hbarω_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $ν=1/3$ and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in $n$-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in $p$-type systems.

cond-mat↗

arXiv1994

Composite Fermions and the Energy Gap in the Fractional Quantum Hall Effect

The energy gaps for the fractional quantum Hall effect at filling fractions 1/3, 1/5, and 1/7 have been calculated by variational Monte Carlo using Jain's composite fermion wave functions before and after projection onto the lowest Landau level. Before projection there is a contribution to the energy gaps from the first excited Landau level. After projection this contribution vanishes, the quasielectron charge becomes more localized, and the Coulomb energy contribution increases. The projected gaps agree well with previous calculations, lending support to the composite fermion theory.

cond-mat↗

arXiv1993

Compressible Phase of a Double-Layer Electron System with Total Landau-Level Filling Factor One-Half

Following recent work of Halperin, Lee, and Read, and Kalmeyer and Zhang, a double-layer electron system with total Landau-level filling factor $ν=1/2$ is mapped onto an equivalent system of fermions in zero average magnetic field interacting via a Chern-Simons gauge field. Within the random-phase approximation a new, low-lying, diffusive mode, not present in the $ν=1/2$ single-layer system, is found. This mode leads to more singular low-energy scattering than appears in the single layer system, and to an attractive pairing interaction between fermions in different layers which grows stronger as the layer spacing is decreased. The possible connection between this pairing interaction and the experimentally observed fractional quantum Hall effect in double-layer systems is discussed.

cond-mat↗

arXiv1993

Spin-Orbit Scattering and Pair Breaking in a Structurally Disordered Copper-Oxide Layer

To leading order in displacement size, the scattering of electrons in a Cu-O plane from O displacements perpendicular to that plane is due to spin-orbit coupling. This scattering is investigated with the following results: (1) As a consequence of time-reversal symmetry, spin fluctuations, which can strongly enhance scattering from a spin impurity, do not enhance spin-orbit scattering; and (2) for a superconductor with a $d_{x^2-y^2}$ gap function, pair-breaking from spin-orbit scattering can be strong, particularly in a structurally disordered phase in which locally CuO$_6$ octahedra tilt as in the orthorhombic phase of La$_2$CuO$_4$, but globally the average structure is tetragonal. These results are discussed in the context of the (La,Nd)-(Sr,Ba)-Cu-O system where certain structural transitions are observed to suppress superconductivity.

cond-mat↗

arXiv1992

Theory of Anisotropic Superexchange in Insulating Cuprates

Spin-orbit corrections to superexchange are calculated using the method of Moriya [T.\ Moriya, {\it Phys.\ Rev.}~{\bf 120} 91, (1960)] for two of the insulating parent compounds of the cuprate superconductors: (1) La$_{2-x}$Nd$_x$CuO$_4$ where the CuO$_6$ octahedra forming each Cu-O layer are tilted in staggered fashion about an axis which depends on $x$ and temperature; and (2) YBa$_2$Cu$_3$O$_{6+x}$ ($x \alt 0.4$) where the Cu-O layers form CuO$_2$-Y-CuO$_2$ bilayers in which the in-plane O$^{2-}$ ions are displaced uniformly towards the Y$^{3+}$ layer. For (1) a simple formula is derived for the weak ferromagnetic moment in each Cu-O layer as a function of the tilting axis and magnitude. For (2) it is shown that the anisotropic corrections to superexchange are different from what has previously been assumed. For the correct spin Hamiltonian a classical Néel state in which the Cu spins are lying in the plane is unstable in a single Cu-O layer, but when a bilayer is considered there is a critical value of the interlayer exchange coupling which stabilizes this state. For both cases (1) and (2) spin-wave spectra are calculated and shown to compare favorably with experiment.

cond-mat↗