arXiv subjects

G. S. Uhrig

Publications and source records attributed to G. S. Uhrig.

At least 37 records · Page 2Linked to original sources

arXiv2015

Coupling of Higgs and Leggett modes in nonequilibrium superconductors

Collective excitation modes are a characteristic feature of symmetry-broken phases of matter. For example, superconductors exhibit an amplitude Higgs mode and a phase mode, which are the radial and angular excitations in the Mexican-hat potential of the free energy. In two-band superconductors there exists in addition a Leggett phase mode, which corresponds to collective fluctuations of the interband phase difference. In equilibrium systems amplitude and phase modes are decoupled, since they are mutually orthogonal excitations. The direct detection of Higgs and Leggett modes by linear-response measurements is challenging, because they are often overdamped and do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump-probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes. Moreover, we predict that the coupled Higgs and Leggett modes are clearly visible in the pump-probe absorption spectra as oscillations at their respective frequencies.

cond-mat.supr-con↗

arXiv2015

Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets

A quantitative description of magnons in long-range ordered quantum antiferromagnets is presented which is consistent from low to high energies. It is illustrated for the generic $S=1/2$ Heisenberg model on the square lattice. The approach is based on a continuous similarity transformation in momentum space using the scaling dimension as truncation criterion. Evidence is found for significant magnon-magnon attraction inducing a Higgs resonance. The high-energy roton minimum in the magnon dispersion appears to be induced by strong magnon-Higgs scattering.

cond-mat.str-el↗

arXiv2014

Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity

We theoretically study the pump-probe response of nonequilibrium BCS superconductors coupled to optical phonons. For ultrashort pump pulses a nonadiabatic regime emerges, which is characterized by oscillations of the superconducting order parameter as well as by the generation of coherent phonons. Using the density-matrix formalism, we compute the pump-probe response in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon system and determine the signatures of the order parameter and of the phonon oscillations in the pump-probe conductivity. We find that the nonadiabatic dynamics of the BCS superconductor reflects itself in oscillations of the pump-probe response as functions of delay time between pump and probe pulses. We argue that from the analysis of this oscillatory behavior both frequency and decay time of the algebraically decaying order-parameter oscillations can be inferred. Similarly, the coherent phonons are evidenced in the pump-probe conductivity by oscillations with the frequency of the phonons. Remarkably, we find that the oscillatory response in the pump-probe conductivity is resonantly enhanced when the frequency of the order-parameter oscillations is tuned to the phonon energy.

cond-mat.supr-con↗

arXiv2012

Enhanced Perturbative Continuous Unitary Transformations

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.

cond-mat.str-el↗

arXiv2011

Symmetry-Enhanced Performance of Dynamical Decoupling

We consider a system with general decoherence and a quadratic dynamical decoupling sequence (QDD) for the coherence control of a qubit coupled to a bath of spins. We investigate the influence of the geometry and of the initial conditions of the bath on the performance of the sequence. The overall performance is quantified by a distance norm $d$. It is expected that $d$ scales with $T$, the total duration of the sequence, as $T^{\min \{N_x,N_z\}+1}$, where $N_x$ and $N_z$ are the number of pulses of the outer and of the inner sequence, respectively. We show both numerically and analytically that the state of the bath can boost the performance of QDD under certain conditions: The scaling of QDD for a given number of pulses can be enhanced by a factor of 2 if the bath is prepared in a highly symmetric state and if the system Hamiltonian is SU(2) invariant.

quant-ph↗

arXiv2011

High Order Coherent Control Sequences of Finite-Width Pulses

The performance of sequences of designed pulses of finite length $τ$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(τ^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.

quant-ph↗

arXiv2011

Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations

The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-$T_c$ superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.

cond-mat.str-el↗

arXiv2010

Vertex corrections in the dynamic structure factor in spin ladders

We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg $S=1/2$ ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present; (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La$_{4}$Sr$_{10}$Cu$_{24}$O$_{41}$ showing convincing agreement for established values of the exchange constants.

cond-mat.str-el↗

arXiv2010

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.

cond-mat.str-el↗

arXiv2009

Neutron scattering evidence for isolated spin-1/2 ladders in (C$_5$D$_{12}$N)$_2$CuBr$_4$

Inelastic neutron scattering was used to determine the spin Hamiltonian for the singlet ground state system of fully deuterated BPCB, (C$_{5}$D$_{12}$N)$_{2}$CuBr$_{4}$. A 2-leg spin-1/2 ladder model, with $J_\bot = (1.09 \pm 0.01)$ meV and $J_\| = (0.296 \pm 0.005)$ meV, accurately describes the data. The experimental limit on the effective inter-ladder exchange constant is $|J_{\rm int}^{\rm eff}|\lesssim 0.006$ meV, and the limit on total diagonal, intra-ladder exchange is $|J_F+J_{F'}|\leq 0.1$ meV. Including the effects of copper to bromide covalent spin transfer on the magnetic form-factor, the experimental ratios of intra-ladder bond energies are consistent with the predictions of continuous unitary transformation.

cond-mat.str-el↗

arXiv2009

Optimized Dynamical Decoupling for Power Law Noise Spectra

We analyze the suppression of decoherence by means of dynamical decoupling in the pure-dephasing spin-boson model for baths with power law spectra. The sequence of ideal $π$ pulses is optimized according to the power of the bath. We expand the decoherence function and separate the cancelling divergences from the relevant terms. The proposed sequence is chosen to be the one minimizing the decoherence function. By construction, it provides the best performance. We analytically derive the conditions that must be satisfied. The resulting equations are solved numerically. The solutions are very close to the Carr-Purcell-Meiboom-Gill (CPMG) sequence for a soft cutoff of the bath while they approach the Uhrig dynamical-decoupling (UDD) sequence as the cutoff becomes harder.

quant-ph↗

arXiv2009

Optimized pulses for the perturbative decoupling of spin and decoherence bath

In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $τ_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $τ_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coupling between the spin and the environment. The resulting corrections can be made vanish by an appropriate design of the pulse. For $π$ and $π/2$ pulses, we demonstrate explicitly that pulses exist which annihilate the first and the second order corrections even if the bath is fully quantum mechanical, i.e., it displays internal dynamics. Such pulses will also be useful for quantum information processing.

quant-ph↗

arXiv2008

Numerical Analysis of Optimized Coherent Control Pulses

Numerically we simulate the effect of optimized coherent control pulses with a finite duration on a qubit in a bath of spins. The pulses of finite duration are compared with ideal instantaneous pulses. In particular, we show that properly designed short pulses can approximate ideal instantaneous pulses up to a certain order in the shortness of the pulse. We provide examples of such pulses, quantify the discrepancy from the ideal case and compare their effect for various ranges of the coupling constants.

quant-ph↗

arXiv2008

Generalization of short coherent control pulses: extension to arbitrary rotations

We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.

quant-ph↗

arXiv2008

Collective orbital excitations in orbitally ordered YVO3 and HoVO3

We study orbital excitations in the optical absorption spectra of YVO3 and HoVO3. We focus on an orbital absorption band observed at 0.4 eV for polarization E parallel c. This feature is only observed in the intermediate, monoclinic phase. By comparison with the local crystal-field excitations in VOCl and with recent theoretical predictions for the crystal-field levels we show that this absorption band cannot be interpreted in terms of a local crystal-field excitation. We discuss a microscopic model which attributes this absorption band to the exchange of two orbitals on adjacent sites, i.e., to the direct excitation of two orbitons. This model is strongly supported by the observed dependence on polarization and temperature. Moreover, the calculated spectral weight is in good agreement with the experimental result.

cond-mat.str-el↗

arXiv2008

Optimization of Short Coherent Control Pulses

The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $π$ and $\fracπ{2}$ pulses.

quant-ph↗

arXiv2007

Two-Dimensionality of Magnetic Excitations on the Trellis Lattice: (La,Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$ and SrCu$_2$O$_3$

We explore the properties of magnetic excitations on the trellis lattice which is relevant for the so-called telephone-number compounds A$_{14}$Cu$_{24}$O$_{41}$ and the system SrCu$_2$O$_3$. The trellis lattice consists of two-leg ladders which are coupled in a strongly frustrated fashion. We use the effective model obtained for a single two-leg spin ladder to calculate the two-dimensional one-triplon dispersion and the corresponding one-triplon contribution to the dynamical structure factor. Special attention is laid on signatures of the frustrating inter-ladder magnetic exchange. A detailed suggestion is made for an experimental detection of this exchange in inelastic neutron scattering experiments.

cond-mat.str-el↗

arXiv2007

The fate of orbitons coupled to phonons

The key feature of an orbital wave or orbiton is a significant dispersion, which arises from exchange interactions between orbitals on distinct sites. We study the effect of a coupling between orbitons and phonons in one dimension using continuous unitary transformations (CUTs). Already for intermediate values of the coupling, the orbiton band width is strongly reduced and the spectral density is dominated by an orbiton-phonon continuum. However, we find sharp features within the continuum and an orbiton-phonon anti-bound state above. Both show a significant dispersion and should be observable experimentally.

cond-mat.str-el↗