DOI: 10.1126/science.1113719. Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field

Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field

10.1126/science.1113719

Crossref journal-article

American Association for the Advancement of Science (AAAS)

Science (221)

Abstract

We observed mixing between two-electron singlet and triplet states in a double quantum dot, caused by interactions with nuclear spins in the host semiconductor. This mixing was suppressed when we applied a small magnetic field or increased the interdot tunnel coupling and thereby the singlet-triplet splitting. Electron transport involving transitions between triplets and singlets in turn polarized the nuclei, resulting in marked bistabilities. We extract from the fluctuating nuclear field a limitation on the time-averaged spin coherence time T \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\begin{array}{l}{\ast}\\2\end{array}\) \end{document} of 25 nanoseconds. Control of the electron-nuclear interaction will therefore be crucial for the coherent manipulation of individual electron spins.

Bibliography

Koppens, F. H. L., Folk, J. A., Elzerman, J. M., Hanson, R., van Beveren, L. H. W., Vink, I. T., Tranitz, H. P., Wegscheider, W., Kouwenhoven, L. P., & Vandersypen, L. M. K. (2005). Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field. Science, 309(5739), 1346â1350.

Authors 10

F. H. L. Koppens (first)
J. A. Folk (additional)
J. M. Elzerman (additional)
R. Hanson (additional)
L. H. Willems van Beveren (additional)
I. T. Vink (additional)
H. P. Tranitz (additional)
W. Wegscheider (additional)
L. P. Kouwenhoven (additional)
L. M. K. Vandersypen (additional)

References 32 Referenced 497

F. Meier B. P. Zakharchenya Eds. Optical Orientation (North-Holland New York 1984).
10.1126/science.277.5322.85
10.1103/PhysRevA.57.120
10.1103/PhysRevB.65.205309
10.1103/PhysRevLett.94.116601
10.1103/PhysRevLett.94.047402
10.1143/JPSJ.73.307
10.1038/30156
10.1103/PhysRevLett.91.246802
J. Schliemann, A. Khaetskii, D. Loss, J. Phys. Condens. Matter15, R1809 (2003). (10.1088/0953-8984/15/50/R01) / J. Phys. Condens. Matter (2003)
10.1103/PhysRevLett.88.186802
10.1103/PhysRevB.70.195340
W. G. van der Wielet al., Rev. Mod. Phys.75, 1 (2003). / Rev. Mod. Phys. (2003)
10.1126/science.1070958
A. C. Johnson J. R. Petta C. M. Marcus M. P. Hanson A. C. Gossard cond-mat /0410679 (2004).
The electrostatic gates are on the surface of a GaAs/AlGaAs heterostructure. The two-dimensional electron gas is 90 nm below the surface with density 1.33 × 10 11 cm –2 and mobility 9.71 × 10 5 cm 2 /Vs. Measurements were performed in a dilution refrigerator at 150 mK with a magnetic field in the plane of the heterostructure.
10.1103/PhysRevB.15.5780
10.1103/PhysRevLett.86.5176
10.1126/science.282.5390.932
O. N. Jouravlev Y. Nazarov personal communication.
The difference between the field dependence of the resonant and inelastic currents can be explained by the coupling with the leads. The S(0 2) state is lifetime-broadened because of coupling with the right lead (∼0.3 μeV) giving a weaker field dependence for the resonant current. The field dependence of the inelastic leakage is not affected by the lead coupling because under the high-bias conditions of this experiment there were no available states in the left lead that could broaden S(1 1).
10.1038/nature03815
10.1103/PhysRevLett.61.1650
10.1103/PhysRevB.69.073302
The leakage current is sensitive to magnetic fields of only a few mT corresponding to 0.1% nuclear polarization. Given that the dot has ∼10 6 nuclei changes in the nuclear polarization of 0.1% can be caused by 1000 electron-nuclear flip-flop processes. For typical currents (∼100 fA) 1000 electrons move through the dot in 1 ms so in principle current fluctuations as fast as 1 kHz are possible.
10.1103/PhysRevLett.92.256803
10.1103/PhysRevB.67.033301
Bracker et al. ( 6 ) found a \batchmode \documentclass[fleqn 10pt legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(T_{2}^{{\ast}}\) \end{document} of 16 ns in a GaAs quantum dot slightly shorter than in our experiment presumably because of a smaller dot size. Braun et al. ( 5 ) measured a considerably shorter time scale 500 ps in InAs dots because of a notable difference in dot size nuclear spin I and the stronger hyperfine coupling constant in InAs.
10.1103/PhysRevLett.93.016601
10.1038/nature02693
10.1038/nature03008
We thank O. N. Jouravlev and Y. Nazarov for developing a model that helped greatly with the physical interpretation of the data; G. Burkard W. A. Coish V. N. Golovach A. C. Johnson D. Loss and C. M. Marcus for fruitful discussions; R. Schouten B. van den Enden and M. van Oossanen for technical assistance; and J. Caro for supporting infrastructure. Supported by the Defense Advanced Research Projects Agency Quantum Information Science and Technology program the Dutch Organization for Fundamental Research on Matter (FOM) the Netherlands Organization for Scientific Research (NWO) the Office of Naval Research Exploratory Research for Advanced Technology and the EU Research Training Network on spintronics.

Dates

Type	When
Created	20 years, 1 month ago (July 21, 2005, 8:33 p.m.)
Deposited	1 year, 7 months ago (Jan. 9, 2024, 10:28 p.m.)
Indexed	4 weeks, 1 day ago (Aug. 7, 2025, 4:50 p.m.)
Issued	20 years ago (Aug. 26, 2005)
Published	20 years ago (Aug. 26, 2005)
Published Print	20 years ago (Aug. 26, 2005)

Funders 0

None

BibTeX

@article{Koppens_2005, title={Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field}, volume={309}, ISSN={1095-9203}, url={http://dx.doi.org/10.1126/science.1113719}, DOI={10.1126/science.1113719}, number={5739}, journal={Science}, publisher={American Association for the Advancement of Science (AAAS)}, author={Koppens, F. H. L. and Folk, J. A. and Elzerman, J. M. and Hanson, R. and van Beveren, L. H. Willems and Vink, I. T. and Tranitz, H. P. and Wegscheider, W. and Kouwenhoven, L. P. and Vandersypen, L. M. K.}, year={2005}, month=aug, pages={1346–1350} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        7
      ]
    ],
    "date-time": "2025-08-07T20:50:33Z",
    "timestamp": 1754599833339
  },
  "reference-count": 32,
  "publisher": "American Association for the Advancement of Science (AAAS)",
  "issue": "5739",
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2005,
        8,
        26
      ]
    ]
  },
  "abstract": "<jats:p>\n            We observed mixing between two-electron singlet and triplet states in a double quantum dot, caused by interactions with nuclear spins in the host semiconductor. This mixing was suppressed when we applied a small magnetic field or increased the interdot tunnel coupling and thereby the singlet-triplet splitting. Electron transport involving transitions between triplets and singlets in turn polarized the nuclei, resulting in marked bistabilities. We extract from the fluctuating nuclear field a limitation on the time-averaged spin coherence time\n            <jats:italic>T</jats:italic>\n            <jats:sub>\n              <jats:inline-formula>\n                <jats:tex-math notation=\"LaTeX\">\\batchmode \\documentclass[fleqn,10pt,legalpaper]{article} \\usepackage{amssymb} \\usepackage{amsfonts} \\usepackage{amsmath} \\pagestyle{empty} \\begin{document} \\(\\begin{array}{l}{\\ast}\\\\2\\end{array}\\) \\end{document}</jats:tex-math>\n              </jats:inline-formula>\n            </jats:sub>\n            of 25 nanoseconds. Control of the electron-nuclear interaction will therefore be crucial for the coherent manipulation of individual electron spins.\n          </jats:p>",
  "DOI": "10.1126/science.1113719",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        7,
        22
      ]
    ],
    "date-time": "2005-07-22T00:33:45Z",
    "timestamp": 1121992425000
  },
  "page": "1346-1350",
  "source": "Crossref",
  "is-referenced-by-count": 497,
  "title": "Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field",
  "prefix": "10.1126",
  "volume": "309",
  "author": [
    {
      "given": "F. H. L.",
      "family": "Koppens",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "J. A.",
      "family": "Folk",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "J. M.",
      "family": "Elzerman",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "R.",
      "family": "Hanson",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "L. H. Willems",
      "family": "van Beveren",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "I. T.",
      "family": "Vink",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "H. P.",
      "family": "Tranitz",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "W.",
      "family": "Wegscheider",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "L. P.",
      "family": "Kouwenhoven",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    },
    {
      "given": "L. M. K.",
      "family": "Vandersypen",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Kavli Institute of Nanoscience, Delft University of Technology, Post Office Box 5046, 2600 GA Delft, Netherlands."
        },
        {
          "name": "Institut fu\u0308r Angewandte und Experimentelle Physik, Universita\u0308t Regensburg, Regensburg, Germany."
        }
      ]
    }
  ],
  "member": "221",
  "reference": [
    {
      "key": "e_1_3_2_2_2",
      "unstructured": "F. Meier B. P. Zakharchenya Eds. Optical Orientation (North-Holland New York 1984)."
    },
    {
      "key": "e_1_3_2_3_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.277.5322.85"
    },
    {
      "key": "e_1_3_2_4_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevA.57.120"
    },
    {
      "key": "e_1_3_2_5_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.65.205309"
    },
    {
      "key": "e_1_3_2_6_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.94.116601"
    },
    {
      "key": "e_1_3_2_7_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.94.047402"
    },
    {
      "key": "e_1_3_2_8_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1143/JPSJ.73.307"
    },
    {
      "key": "e_1_3_2_9_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/30156"
    },
    {
      "key": "e_1_3_2_10_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.91.246802"
    },
    {
      "key": "e_1_3_2_11_2",
      "doi-asserted-by": "crossref",
      "first-page": "R1809",
      "DOI": "10.1088/0953-8984/15/50/R01",
      "volume": "15",
      "year": "2003",
      "unstructured": "J. Schliemann, A. Khaetskii, D. Loss, J. Phys. Condens. Matter15, R1809 (2003).",
      "journal-title": "J. Phys. Condens. Matter"
    },
    {
      "key": "e_1_3_2_12_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.88.186802"
    },
    {
      "key": "e_1_3_2_13_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.70.195340"
    },
    {
      "key": "e_1_3_2_14_2",
      "first-page": "1",
      "volume": "75",
      "year": "2003",
      "unstructured": "W. G. van der Wielet al., Rev. Mod. Phys.75, 1 (2003).",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "e_1_3_2_15_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.1070958"
    },
    {
      "key": "e_1_3_2_16_2",
      "unstructured": "A. C. Johnson J. R. Petta C. M. Marcus M. P. Hanson A. C. Gossard cond-mat /0410679 (2004)."
    },
    {
      "key": "e_1_3_2_17_2",
      "unstructured": "The electrostatic gates are on the surface of a GaAs/AlGaAs heterostructure. The two-dimensional electron gas is 90 nm below the surface with density 1.33 \u00d7 10 11 cm \u20132 and mobility 9.71 \u00d7 10 5 cm 2 /Vs. Measurements were performed in a dilution refrigerator at 150 mK with a magnetic field in the plane of the heterostructure."
    },
    {
      "key": "e_1_3_2_18_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.15.5780"
    },
    {
      "key": "e_1_3_2_19_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.86.5176"
    },
    {
      "key": "e_1_3_2_20_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1126/science.282.5390.932"
    },
    {
      "key": "e_1_3_2_21_2",
      "unstructured": "O. N. Jouravlev Y. Nazarov personal communication."
    },
    {
      "key": "e_1_3_2_22_2",
      "unstructured": "The difference between the field dependence of the resonant and inelastic currents can be explained by the coupling with the leads. The S(0 2) state is lifetime-broadened because of coupling with the right lead (\u223c0.3 \u03bceV) giving a weaker field dependence for the resonant current. The field dependence of the inelastic leakage is not affected by the lead coupling because under the high-bias conditions of this experiment there were no available states in the left lead that could broaden S(1 1)."
    },
    {
      "key": "e_1_3_2_23_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nature03815"
    },
    {
      "key": "e_1_3_2_24_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.61.1650"
    },
    {
      "key": "e_1_3_2_25_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.69.073302"
    },
    {
      "key": "e_1_3_2_26_2",
      "unstructured": "The leakage current is sensitive to magnetic fields of only a few mT corresponding to 0.1% nuclear polarization. Given that the dot has \u223c10 6 nuclei changes in the nuclear polarization of 0.1% can be caused by 1000 electron-nuclear flip-flop processes. For typical currents (\u223c100 fA) 1000 electrons move through the dot in 1 ms so in principle current fluctuations as fast as 1 kHz are possible."
    },
    {
      "key": "e_1_3_2_27_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.92.256803"
    },
    {
      "key": "e_1_3_2_28_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevB.67.033301"
    },
    {
      "key": "e_1_3_2_29_2",
      "unstructured": "Bracker et al. ( 6 ) found a \\batchmode \\documentclass[fleqn 10pt legalpaper]{article} \\usepackage{amssymb} \\usepackage{amsfonts} \\usepackage{amsmath} \\pagestyle{empty} \\begin{document} \\(T_{2}^{{\\ast}}\\) \\end{document} of 16 ns in a GaAs quantum dot slightly shorter than in our experiment presumably because of a smaller dot size. Braun et al. ( 5 ) measured a considerably shorter time scale 500 ps in InAs dots because of a notable difference in dot size nuclear spin I and the stronger hyperfine coupling constant in InAs."
    },
    {
      "key": "e_1_3_2_30_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1103/PhysRevLett.93.016601"
    },
    {
      "key": "e_1_3_2_31_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nature02693"
    },
    {
      "key": "e_1_3_2_32_2",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/nature03008"
    },
    {
      "key": "e_1_3_2_33_2",
      "unstructured": "We thank O. N. Jouravlev and Y. Nazarov for developing a model that helped greatly with the physical interpretation of the data; G. Burkard W. A. Coish V. N. Golovach A. C. Johnson D. Loss and C. M. Marcus for fruitful discussions; R. Schouten B. van den Enden and M. van Oossanen for technical assistance; and J. Caro for supporting infrastructure. Supported by the Defense Advanced Research Projects Agency Quantum Information Science and Technology program the Dutch Organization for Fundamental Research on Matter (FOM) the Netherlands Organization for Scientific Research (NWO) the Office of Naval Research Exploratory Research for Advanced Technology and the EU Research Training Network on spintronics."
    }
  ],
  "container-title": "Science",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.science.org/doi/pdf/10.1126/science.1113719",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        1,
        10
      ]
    ],
    "date-time": "2024-01-10T03:28:00Z",
    "timestamp": 1704857280000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.science.org/doi/10.1126/science.1113719"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2005,
        8,
        26
      ]
    ]
  },
  "references-count": 32,
  "journal-issue": {
    "issue": "5739",
    "published-print": {
      "date-parts": [
        [
          2005,
          8,
          26
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1126/science.1113719"
  ],
  "URL": "http://dx.doi.org/10.1126/science.1113719",
  "relation": {},
  "ISSN": [
    "0036-8075",
    "1095-9203"
  ],
  "subject": [],
  "container-title-short": "Science",
  "published": {
    "date-parts": [
      [
        2005,
        8,
        26
      ]
    ]
  }
}