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arXiv:cond-mat/9912495 · Physical Review Letters

Spin Correlations in Nonlinear Optical Response: Light-Induced Kondo Effect

Tigran V. Shahbazyan, I. E. Perakis, M. É. Raǐkh

Published Jun 19, 2000• 31 citations
arXivHTMLPDF

Abstract

We study the role of spin correlations in nonlinear absorption due to transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons at the impurity leads to a logarithmic divergence in chi(3) at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump.

DOI
10.1103/physrevlett.84.5896

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arXiv:cond-mat/0007379•Physical review. B, Condensed matter•Dec 14, 2000•12 citations
We study the role of spin correlations in nonlinear absorption due to transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons at the impurity leads to a logarithmic divergence in chi(3) at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump.
We discuss the role of many-body spin correlations in nonlinear optical response of a Fermi sea system with a deep impurity level. Due to the Hubbard repulsion between electrons at the impurity, the optical transitions between the impurity level and the Fermi sea states lead to an optically-induced Kondo effect. In particular, the third- order nonlinear optical susceptibility logarithmically diverges at the absorption threshold. The shape of the pump- probe spectrum is governed by the light-induced Kondo temperature, which can be tuned by varying the intensity and frequency of the pump optical field. In the Kondo limit, corresponding to off-resonant pump excitation, the nonlinear absorption spectrum exhibits a narrow peak below the linear absorption onset.
We address the fundamental question how the spatial Kondo correlations are building up in time assuming an initially decoupled impurity spin ${\stackrel{P\vec}{S}}_{\mathrm{imp}}$. We investigate the time-dependent spin-correlation function $\ensuremath{\chi}(\stackrel{P\vec}{r},t)=\ensuremath{\langle}{\stackrel{P\vec}{S}}_{\mathrm{imp}}\stackrel{P\vec}{s}(\stackrel{P\vec}{r})\ensuremath{\rangle}(t)$ in the Kondo model with antiferromagnetic and ferromagnetic couplings, where $\stackrel{P\vec}{s}(\stackrel{P\vec}{r})$ denotes the spin density of the conduction electrons after switching on the Kondo coupling at time t=0t=0t=0. We present data obtained from a time-dependent numerical renormalisation group (TD-NRG) calculation. We gauge the accuracy of our two-band NRG by the spatial sum rules of the equilibrium correlation functions and the reproduction of the analytically exactly known spin-correlation function of the decoupled Fermi sea. We find a remarkable building up of Kondo correlation outside of the light cone defined by the Fermi velocity of the host metal. By employing a perturbative approach exact in second-order of the Kondo coupling, we connect these surprising correlations to the intrinsic spin-density entanglement of the Fermi sea. The thermal wavelength supplies a cutoff scale at finite temperatures beyond which correlations are exponentially suppressed. We present data for the frequency dependent retarded spin-spin susceptibility and use the results to calculate the real-time response of a weak perturbation in linear response: within the spatial resolution no response outside of the light cone is found.
The Kondo effect in condensed-matter systems manifests itself most sharply in their transport measurements. Here we propose an analogous transport signature of the orbital Kondo effect realized with ultracold atoms. Our system consists of imbalanced Fermi seas of two components of fermions and an impurity atom of different species which is confined by an isotropic potential. We first apply a $\ensuremath{\pi}/2$ pulse to transform two components of fermions into two superposition states. Their interactions with the impurity atom then cause a ``transport'' of fermions from majority to minority superposition states, whose numbers can be measured after applying another $3\ensuremath{\pi}/2$ pulse. In particular, when the interaction of one component of fermions with the impurity atom is tuned close to a confinement-induced ppp-wave or higher partial-wave resonance, the resulting conductance is shown to exhibit the Kondo signature, i.e., universal logarithmic growth by lowering the temperature. The proposed transport measurement will thus provide a clear evidence of the orbital Kondo effect accessible in ultracold atom experiments and pave the way for developing new insights into Kondo physics.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e. the Hubbard model in the spatial dimension D=1,2,D=1,2,D=1,2, and 3. For the 1D system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, 1/T1T∼χ21/T_1T \sim \chi^21/T1​T∼χ2. In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T11/T_11/T1​.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension D=1,2,D=1,2,D=1,2, and 3.3.3. For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.$ In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of 1/T1.{1/T}_{1}.1/T1​.