Derivation of Markovian master equations for spatially correlated decoherence

Jeske, Jan; Cole, Jared H.

doi:10.1103/physreva.87.052138

Cited by 47 publications

(68 citation statements)

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“…These results are applicable to any spin network or qubit array and give an intuition for the analysis of any particular system. We model decoherence with Bloch-Redfield equations which derive directly from the interaction between system and environment [37][38][39][40][41]. This interaction consists of longitudinal coupling terms (leading to dephasing) and transversal coupling terms (leading to relaxation),…”

Section: Spatially Correlated Effects In a System Of Several Spinsmentioning

confidence: 99%

“…For details see Ref. [37]. Since there is generally no experimental control of the environment the spatial correlations are difficult to obtain and often are simply neglected.…”

Section: Spatially Correlated Effects In a System Of Several Spinsmentioning

confidence: 99%

“…In a perfectly correlated environment, however, the dephasing rate between two states with a difference of n e excitations is proportional to n 2 e and n f is irrelevant [37,43]. Therefore the dephasing rate between states with equal excitation number is reduced to zero when the noise correlation length increases well beyond the qubits' separation.…”

Section: A Spatially Correlated Dephasingmentioning

confidence: 99%

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Excitation and state transfer through spin chains in the presence of spatially correlated noise

2013

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We investigate the influence of environmental noise on spin networks and spin chains. In addition to the common model of an independent bath for each spin in the system we also consider noise with a finite spatial correlation length. We present the emergence of decoherence-free subspaces and different dynamics with increasing correlation length for both dephasing and dissipating environments. This leads to relaxation blocking of one spin by uncoupled surrounding spins. We then consider perfect state transfer through a spin chain in the presence of decoherence and discuss the dependence of the transfer quality on spatial noise correlation length. We identify qualitatively different features for dephasing and dissipative environments in spin-transfer problems.

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Section: Spatially Correlated Effects In a System Of Several Spinsmentioning

confidence: 99%

“…For details see Ref. [37]. Since there is generally no experimental control of the environment the spatial correlations are difficult to obtain and often are simply neglected.…”

Section: Spatially Correlated Effects In a System Of Several Spinsmentioning

confidence: 99%

Section: A Spatially Correlated Dephasingmentioning

confidence: 99%

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Excitation and state transfer through spin chains in the presence of spatially correlated noise

2013

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“…However, much less attention has been paid to develop quantifiers of spatial correlations in the dynamics, although some works e.g. [44,45] have addressed this issue for some specific models. This may be partially due to the well-known fact that under many, though not all practical circumstances, dynamical correlations can be detected by studying the time evolution of correlation functions of properly chosen observables A  and B  , acting respectively on the two parties A and B of interest.…”

Section: Introductionmentioning

confidence: 99%

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

Rivas

Müller

2015

New J. Phys.

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“…, , respectively, from which the master equation can be directly derived via Bloch-Redfield approach [13,30,31]. This is a convenient version of the equivalent master equation techniques [29,34,40,41].…”

Section: Master Equation and Thermalisation Of Magnonsmentioning

confidence: 99%

The effects of thermal and correlated noise on magnons in a quantum ferromagnet

et al. 2018

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The dynamics and thermal equilibrium of spin waves (magnons) in a quantum ferromagnet as well as the macroscopic magnetisation are investigated. Thermal noise due to an interaction with lattice phonons and the effects of spatial correlations in the noise are considered. We first present a Markovian master equation approach with analytical solutions for any homogeneous spatial correlation function of the noise. We find that spatially correlated noise increases the decay rate of magnons with low wave vectors to their thermal equilibrium, which also leads to a faster decay of the ferromagnet's magnetisation to its steady-state value. For long correlation lengths and higher temperature we find that additionally there is a component of the magnetisation which decays very slowly, due to a reduced decay rate of fast magnons. This effect could be useful for fast and noise-protected quantum or classical information transfer and magnonics. We further compare ferromagnetic and antiferromagnetic behaviour in noisy environments and find qualitatively similar behaviour in Ohmic but fundamentally different behaviour in super-Ohmic environments. different dynamics to uncorrelated noise, even in the Markovian regime. In ion traps for example the occurrence of decoherene-free subspaces has inspired quantum computation solutions [18,19]. In the field of quantum metrology a re-instatement of the superior Heisenberg precision scaling has been proven possible in the presence of spatial noise correlations [20]. In spin chains and light-harvesting complexes spatial noise correlations have shown to enable robust transport through protected states [21][22][23]. These results pose the question how correlated noise affects the dynamics of magnons and macroscopic quantities in a quantum ferromagnet This paper is structured as follows: in section 2 we introduce the spin-wave Hamiltonian, in section 3 we discuss its interaction with a thermal environment, in section 4 we derive and solve a master equation for magnons, in section 5 we discuss the macroscopic magnetisation, in section 6 we point out relevant differences between ferro-and antiferromagnetic behaviour and reach our conclusions in section 7. Spin-wave HamiltonianWe begin by introducing the key concepts and the Heisenberg model Hamiltonian for spins in real space with nearest-neighbour interaction. We then show how this Hamiltonian maps via the Holstein-Primakoff transform with a spin-wave approximation to a bosonic system. Subsequent transformation into k-space via Fourier lattice transform of the operators diagonalises the Hamiltonian and yields the dispersion relation of the system. This is the Hamiltonian describing 'magnons', the elementary collective magnetic excitations.We start with a Heisenberg model for the spins in the quantum ferromagnet with only nearest-neighbour interaction and a uniform magnetic field B in the negative z-direction: Figure 1. Ferromagnetic spins (symbolised by arrows) interact with a noise environment of lattice phonons (symbolised by dots). Close spin...

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Derivation of Markovian master equations for spatially correlated decoherence

Cited by 47 publications

References 48 publications

Excitation and state transfer through spin chains in the presence of spatially correlated noise

Excitation and state transfer through spin chains in the presence of spatially correlated noise

Erratum: Quantifying spatial correlations of general quantum dynamics (2015 New J. Phys. 17 062001)

The effects of thermal and correlated noise on magnons in a quantum ferromagnet

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