From quantum-mechanical to classical dynamics in the central-spin model

Stanek, Daniel; Raas, Carsten; Uhrig, Götz S.

doi:10.1103/physrevb.90.064301

Cited by 39 publications

(70 citation statements)

References 47 publications

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“…In practice one must average over an appropriate large number of configurations of the random fields. About 10 6 simulations are enough to reduce the relative statistical error below 10 −3 as expected [23]. This, however, limits the number of bath spins that can be treated in the classical simulation to about 1000.…”

Section: ŝmentioning

confidence: 90%

“…Besides the already mentioned Bethe ansatz, exact diagonalization [6,17], Chebyshev expansion (CE) [18][19][20], or a direct evolution of the density matrices via the Liouvillean [21] can be used for small systems of about 20 spins, but up to long times. Density-matrix renormalization group (DMRG) can tackle much larger systems up to about 1000 spins, but is restricted to short times up to about 40 /J Q [22][23][24]. The strict limit of infinite times, i.e., of persisting correlations has been tackled by mathematically rigorous bounds [25,26].…”

Section: Introductionmentioning

confidence: 99%

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Efficient algorithms for the dynamics of large and infinite classical central spin models

et al. 2017

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We investigate the time dependence of correlation functions in the central spin model, which describes the electron or hole spin confined in a quantum dot, interacting with a bath of nuclear spins forming the Overhauser field. For large baths, a classical description of the model yields quantitatively correct results. We develop and apply various algorithms in order to capture the longtime limit of the central spin for bath sizes from 1000 to infinitely many bath spins. Representing the Overhauser field in terms of orthogonal polynomials, we show that a carefully reduced set of differential equations is sufficient to compute the spin correlations of the full problem up to very long times, for instance up to 10 5 /JQ where JQ is the natural energy unit of the system. This technical progress renders an analysis of the model with experimentally relevant parameters possible. We benchmark the results of the algorithms with exact data for a small number of bath spins and we predict how the long-time correlations behave for different effective numbers of bath spins.

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Section: ŝmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Efficient algorithms for the dynamics of large and infinite classical central spin models

et al. 2017

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“…Alternative promising approaches towards calculation of the central-spin-model dynamics have been proposed, such as diagrammatic perturbation theory [51], exact time evolution [66], density matrix renormalization group (DMRG) methods [49,52,67], Monte Carlo methods [34], and approaches employing conserved quantities [68,69]. Each of these methods should be scrutinized as to how well they are suited and capable of capturing the mode locking effect.…”

Section: Discussionmentioning

confidence: 99%

“…The results also show the uncertainty in each of the three components O 52]. But here, we cannot apply a semiclassical approach, because the uncertainty defines a coarser frequency scale than the peak structure we desire to resolve.…”

Section: Transverse Components Of the Overhauser Fieldmentioning

confidence: 94%

Erratum: Quantum model for mode locking in pulsed semiconductor quantum dots [Phys. Rev. B 94 , 245308 (2016)]

Beugeling¹,

Uhrig²,

Anders³

2017

Phys. Rev. B

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Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is dramatically increased if the system is subjected to a magnetic field and to repeated optical pulsing. This enhancement is due to mode locking: Oscillation frequencies resonant with the pulsing frequencies are enhanced, while off-resonant oscillations eventually die out. Because the resonant frequencies are determined by the pulsing frequency only, the system becomes immune to frequency shifts caused by the nuclear coupling and by slight variations between individual quantum dots. The effects remain even after the optical pulsing is terminated. In this work, we explore the phenomenon of mode locking from a quantum mechanical perspective. We treat the dynamics using the central spin model, which includes coupling to 10-20 nuclei and incoherent decay of the excited electronic state, in a perturbative framework. Using scaling arguments, we extrapolate our results to realistic system parameters. We estimate that the synchronization to the pulsing frequency needs time scales in the order of 1 s.

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“…The Overhauser field caused by the hyperfine interaction with the nuclear spins is normally distributed so that its probability distribution has the form [23][24][25]…”

Section: Modelmentioning

confidence: 99%

Spin inertia and polarization recovery in quantum dots: Role of pumping strength and resonant spin amplification

Schering¹,

Uhrig²,

Smirnov³

2019

Phys. Rev. Research

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Spin inertia measurements are a novel experimental tool to study long-time spin relaxation processes in semiconductor nanostructures. We develop a theory of the spin inertia effect for resident electrons and holes localized in quantum dots. We consider the spin orientation by short optical pulses with arbitrary pulse area and detuning from the trion resonance. The interaction with an external longitudinal magnetic field and the hyperfine interaction with the nuclear spin bath is considered both in the ground and excited (trion) states of the quantum dots. We analyze how the spin inertia signal depends on the magnetic field (polarization recovery), on the modulation frequency of the helicity of the pump pulses as well as on their power and detuning. In particular, we elaborate how approaching the saturation limit of the spin polarization influences the measurements. The quantitative description of spin inertia measurements will enable the determination of the parameters of spin dynamics such as the spin relaxation times in the ground and excited states and the parameters of the hyperfine interaction. Finally, we predict a novel longitudinal spin mode locking effect, which manifests itself as oscillations of the spin polarization as function of the longitudinal magnetic field.

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From quantum-mechanical to classical dynamics in the central-spin model

Cited by 39 publications

References 47 publications

Efficient algorithms for the dynamics of large and infinite classical central spin models

Efficient algorithms for the dynamics of large and infinite classical central spin models

Erratum: Quantum model for mode locking in pulsed semiconductor quantum dots [Phys. Rev. B 94 , 245308 (2016)]

Spin inertia and polarization recovery in quantum dots: Role of pumping strength and resonant spin amplification

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