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Transport spectroscopy of non-equilibrium many-particle spin states in self-assembled quantum dots.

Marquardt B, Geller M, Baxevanis B, Pfannkuche D, Wieck AD, Reuter D, Lorke A - Nat Commun (2011)

Bottom Line: For these systems, great progress has been made in addressing spin states by optical means.The excitation spectra of the one- (QD hydrogen), two- (QD helium) and three- (QD lithium) electron configuration are shown and compared with calculations using the exact diagonalization method.An exchange splitting of 10 meV between the excited triplet and singlet spin states is observed in the QD helium spectrum.

View Article: PubMed Central - PubMed

Affiliation: Fakultät für Physik and CeNIDE, Universität Duisburg-Essen, Lotharstraße 1, Duisburg 47048, Germany.

ABSTRACT
Self-assembled quantum dots (QDs) are prominent candidates for solid-state quantum information processing. For these systems, great progress has been made in addressing spin states by optical means. In this study, we introduce an all-electrical measurement technique to prepare and detect non-equilibrium many-particle spin states in an ensemble of self-assembled QDs at liquid helium temperature. The excitation spectra of the one- (QD hydrogen), two- (QD helium) and three- (QD lithium) electron configuration are shown and compared with calculations using the exact diagonalization method. An exchange splitting of 10 meV between the excited triplet and singlet spin states is observed in the QD helium spectrum. These experiments are a starting point for an all-electrical control of electron spin states in self-assembled QDs above liquid helium temperature.

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Calculated excitation spectra and comparison with the experimental data.The table lists the energies of the ground state (GS) and nth excited states for QD helium and lithium, calculated using an exact diagonalization method (Etheo). Also shown are the leading configurations in the Slater determinant expansion with their relative contributions given in percent. Each level diagram represents an eigenstate to total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. For QD helium, the good agreement between Etheo and the experimental values Eexp makes it possible to identify the GS and the first two excited states (triplet and singlet, respectively). The higher-lying resonances, seen in the fine structure of the QD helium spectrum, are also listed for comparison with the theoretically obtained values. Similarly, the theoretical and experimental values are listed for QD lithium. The experimentally determined values have an error of about 5% for QD helium and QD lithium.
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f4: Calculated excitation spectra and comparison with the experimental data.The table lists the energies of the ground state (GS) and nth excited states for QD helium and lithium, calculated using an exact diagonalization method (Etheo). Also shown are the leading configurations in the Slater determinant expansion with their relative contributions given in percent. Each level diagram represents an eigenstate to total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. For QD helium, the good agreement between Etheo and the experimental values Eexp makes it possible to identify the GS and the first two excited states (triplet and singlet, respectively). The higher-lying resonances, seen in the fine structure of the QD helium spectrum, are also listed for comparison with the theoretically obtained values. Similarly, the theoretical and experimental values are listed for QD lithium. The experimentally determined values have an error of about 5% for QD helium and QD lithium.

Mentions: For a thorough identification of the different resonances, we have calculated the many-particle energy states in a 2D harmonic oscillator for n=1, 2 and 3 electrons using the exact diagonalization method, which provides numerically exact solutions2425. This yields the many-particle states of the interacting electrons in terms of superpositions of single-particle Slater determinants. Their coefficients give the probability of single-particle configuration to be found. The level spacing ħω=52 meV was taken from the single-particle spectrum in Figure 2b. The effective mass and the dielectric constant were chosen to be m*=0.067m0 and ɛr=16, respectively, which go into the calculations by the single adjustable parameter16. In Figure 4, the calculated energies for the GS and the first few excited states are listed, together with the leading terms in the Slater determinant expansion (relative contributions given in %). Each level diagram represents an eigenstate to a total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. Also shown are the experimental energies determined using the resonance condition for tunnelling En−En−1=eΔVp/λ and choosing the zero point of the energy scale such that the single-electron GS corresponds to E1GS=E(s1)=52 meV.


Transport spectroscopy of non-equilibrium many-particle spin states in self-assembled quantum dots.

Marquardt B, Geller M, Baxevanis B, Pfannkuche D, Wieck AD, Reuter D, Lorke A - Nat Commun (2011)

Calculated excitation spectra and comparison with the experimental data.The table lists the energies of the ground state (GS) and nth excited states for QD helium and lithium, calculated using an exact diagonalization method (Etheo). Also shown are the leading configurations in the Slater determinant expansion with their relative contributions given in percent. Each level diagram represents an eigenstate to total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. For QD helium, the good agreement between Etheo and the experimental values Eexp makes it possible to identify the GS and the first two excited states (triplet and singlet, respectively). The higher-lying resonances, seen in the fine structure of the QD helium spectrum, are also listed for comparison with the theoretically obtained values. Similarly, the theoretical and experimental values are listed for QD lithium. The experimentally determined values have an error of about 5% for QD helium and QD lithium.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3105341&req=5

f4: Calculated excitation spectra and comparison with the experimental data.The table lists the energies of the ground state (GS) and nth excited states for QD helium and lithium, calculated using an exact diagonalization method (Etheo). Also shown are the leading configurations in the Slater determinant expansion with their relative contributions given in percent. Each level diagram represents an eigenstate to total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. For QD helium, the good agreement between Etheo and the experimental values Eexp makes it possible to identify the GS and the first two excited states (triplet and singlet, respectively). The higher-lying resonances, seen in the fine structure of the QD helium spectrum, are also listed for comparison with the theoretically obtained values. Similarly, the theoretical and experimental values are listed for QD lithium. The experimentally determined values have an error of about 5% for QD helium and QD lithium.
Mentions: For a thorough identification of the different resonances, we have calculated the many-particle energy states in a 2D harmonic oscillator for n=1, 2 and 3 electrons using the exact diagonalization method, which provides numerically exact solutions2425. This yields the many-particle states of the interacting electrons in terms of superpositions of single-particle Slater determinants. Their coefficients give the probability of single-particle configuration to be found. The level spacing ħω=52 meV was taken from the single-particle spectrum in Figure 2b. The effective mass and the dielectric constant were chosen to be m*=0.067m0 and ɛr=16, respectively, which go into the calculations by the single adjustable parameter16. In Figure 4, the calculated energies for the GS and the first few excited states are listed, together with the leading terms in the Slater determinant expansion (relative contributions given in %). Each level diagram represents an eigenstate to a total spin and total angular momentum including the corresponding Slater determinants with permuted orbital configuration. For each degenerate spin and angular momentum multiplet, only one representative is shown. Also shown are the experimental energies determined using the resonance condition for tunnelling En−En−1=eΔVp/λ and choosing the zero point of the energy scale such that the single-electron GS corresponds to E1GS=E(s1)=52 meV.

Bottom Line: For these systems, great progress has been made in addressing spin states by optical means.The excitation spectra of the one- (QD hydrogen), two- (QD helium) and three- (QD lithium) electron configuration are shown and compared with calculations using the exact diagonalization method.An exchange splitting of 10 meV between the excited triplet and singlet spin states is observed in the QD helium spectrum.

View Article: PubMed Central - PubMed

Affiliation: Fakultät für Physik and CeNIDE, Universität Duisburg-Essen, Lotharstraße 1, Duisburg 47048, Germany.

ABSTRACT
Self-assembled quantum dots (QDs) are prominent candidates for solid-state quantum information processing. For these systems, great progress has been made in addressing spin states by optical means. In this study, we introduce an all-electrical measurement technique to prepare and detect non-equilibrium many-particle spin states in an ensemble of self-assembled QDs at liquid helium temperature. The excitation spectra of the one- (QD hydrogen), two- (QD helium) and three- (QD lithium) electron configuration are shown and compared with calculations using the exact diagonalization method. An exchange splitting of 10 meV between the excited triplet and singlet spin states is observed in the QD helium spectrum. These experiments are a starting point for an all-electrical control of electron spin states in self-assembled QDs above liquid helium temperature.

Show MeSH
Related in: MedlinePlus