Götz S. Uhrig

Keeping a Quantum Bit Alive by Optimized π -Pulse Sequences

A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized pi-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.

Exact results on dynamical decoupling by π pulses in quantum information processes

The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of ? pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of ? pulses. The effect of various cut-offs of the spectral density of the environment is investigated. As a result we show that the harder the cut-off is, the better an optimized pulse sequence can deal with it. For cut-offs which are neither completely hard nor very soft we advocate iterated optimized sequences.

Effective spin models for spin-phonon chains by flow equations

Abstract:We investigate the anti-adiabatic limit of an anti-ferromagnetic S = 1/2 Heisenberg chain coupled to Einstein phonons. The flow equation method is used to decouple the spin and the phonon part of the Hamiltonian. In the effective spin model long range spin-spin interactions are generated. We determine the phase transition from a gapless state to a gapped (dimerized) phase, which occurs at a non-zero value of the spin-phonon coupling. In the effective phonon sector a phonon hardening is observed.

Dispersion and symmetry of bound states in the shastry-sutherland model

Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)(14)] permit one to fix the parameters of SrCu2(BO3)(2) precisely: J1 = 6.16(10) meV, x J2/J1 = 0.603(3), J( perpendicular) = 1.3(2) meV. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x = 0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.

Concatenated control sequences based on optimized dynamic decoupling.

Two recent developments in quantum control, concatenation and optimization of pulse intervals, are combined to yield a strategy to suppress unwanted couplings in quantum systems to high order. Longitudinal relaxation and transverse dephasing can be suppressed so that systems with a small splitting between their energy levels can be kept isolated from their environment. The required number of pulses grows exponentially with the desired order but is only the square root of the number needed if only concatenation is used. An approximate scheme even brings the number down to polynomial growth. The approach is expected to be useful for quantum information and for high-precision nuclear magnetic resonance.

Exact demonstration of magnetization plateaus and first-order dimer-Neel phase transitions in a modified shastry-sutherland model for SrCu2(BO3)(2)

We study a generalized Shastry-Sutherland model for the material SrCu2(BO3)(2). Along a line in the parameter space, we show rigorously that the model has a first-order phase transition between dimerized and Neel-ordered ground states. Furthermore, when a magnetic field is applied in the dimerized phase, magnetization plateaus develop at commensurate values of the magnetization. We also discuss various aspects of the phase diagram and properties of this model away from this exactly soluble line, which include gap-closing continuous transitions between dimerized and magnetically ordered phases.

Raman response in antiferromagnetic two-leg S = 1/2 Heisenberg ladders

The Raman response in the antiferromagnetic 2-leg S = 1/2 Heisenberg ladder is calculated for various couplings by continuous unitary transformations. For leg couplings above 80% of the rung coupling a characteristic 2-peak structure occurs with a point of zero intensity within the continuum. Experimental data for CaV2O5 and La y Ca 14 − y Cu24O41 are analyzed and the coupling constants are determined. Evidence is found that the Heisenberg model is not sufficient to describe cuprate ladders. We argue that a cyclic exchange term is the appropriate extension.

Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime.

Unifying magnons and triplons in stripe-ordered cuprate superconductors.

Based on a two-dimensional model of coupled two-leg spin ladders, we derive a unified picture of recent neutron scattering data of stripe-ordered La15/8Ba1/8CuO4, namely, of the low-energy magnons around the superstructure satellites and of the triplon excitations at higher energies. The resonance peak at the antiferromagnetic wave vector Q(AF) in the stripe-ordered phase corresponds to a saddle point in the dispersion of the magnetic excitations. Quantitative agreement with the neutron data is obtained for J=130-160 meV and Jcyc/J=0.2-0.25.

Excitations in one-dimensional S = 1/2 quantum antiferromagnets.

The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations. The spectral weights in the S=1 channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped, or doped quantum antiferromagnets.