Research ArticlePHYSICS

Probing quantum coherence in single-atom electron spin resonance

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Science Advances  16 Feb 2018:
Vol. 4, no. 2, eaaq1543
DOI: 10.1126/sciadv.aaq1543
  • Fig. 1 High-signal ESR in a scanning tunneling microscope.

    (A) Experimental setup showing a colorized STM topography of a single Fe atom on MgO/Ag(001). For ESR, the applied voltage consists of the conventional DC bias voltage VDC and an additional RF voltage VRF. The green tip atom indicates the presence of a magnetic tip apex. (B) Energy-level diagram of the lowest five energy levels of the Fe atom. The out-of-plane component Bz of the magnetic field splits the lowest two levels, |0〉 and |1〉, by f0 ≈ 21 GHz (87 μeV). (C) ESR spectrum (change in tunnel current ΔI as a function of frequency f) for the atom shown in (A). Solid line is a fit to an asymmetric Lorentzian [Embedded Image; see section S2.1 for peak asymmetry caused by the contribution of homodyne detection]. Resonance frequency f0, peak height Ipeak, and linewidth Γ are indicated (I = 20 pA, VDC = 60 mV, VRF = 30 mV zero to peak). (D) ESR peaks for different VRF (I = 11 pA, VDC = 60 mV). (E) Ipeak (VRF) for the data sets shown in (D). The peak height is saturating at Isat, because the on-resonance population of states |0〉 and |1〉 is driven into nearly equal occupation (illustrated by bar graphs). The scale for the Rabi flop rate Ω is additionally shown.

  • Fig. 2 Phase coherence time measurements.

    (A) ESR peaks for different tunnel currents (color-coded), normalized and shifted vertically for visibility. The RF voltage is kept at VRF = 30 mV. (B) ESR linewidth Γ as a function of the adjusted drive amplitude Embedded Image for different tunnel currents I = 1 to 30 pA (color-coded). The resulting slope equals (πT2)−1. (The proportionality relating Ω2T1T2 and VRF was first determined independently for each I by fitting the peak height as in Fig. 1E; see sections S2.2 and S4.1.) (C) Phase coherence times T2(I) deduced from (B). The sketches emphasize the gain in phase coherence for diminishing tunnel current. We here find T2I−1 (or Embedded Image). (D) Dephasing rate per tunneling electron Embedded Image derived from (C) [offset in 1/T2 at I = 0 has been subtracted]. The dark orange (0.64 e−1) is the slope of the linear fit to the data in (C). The black dashed line indicates the case where every tunneling electron dephases the Fe atom’s spin.

  • Fig. 3 Tip, temperature, and bias dependence of T2.

    (A) T2 measured for six different spin-polarized STM tips (I = 1 to 2 pA, VDC = 60 mV, T = 1.2 K). Colors indicate different Fe atoms on the surface. The sketch illustrates the switching of magnetic atoms on the tip, which causes a decrease in T2 for some tips. Inset shows the independence of T2 on VDC (I = 2 pA). (B) Decoherence rate Embedded Image measured as a function of temperature for two different tips [tips #3 and #4 in (A)] on the same Fe atom (I = 1 pA, VDC = 60 mV). Solid lines are fits using the model of eq. S17 (see section S3.3).

  • Fig. 4 High-current readout at elevated temperatures.

    (A) Saturation current Isat (see Fig. 1E) as a function of I. Dark orange line is a linear fit to the data points (VDC = 60 mV, T = 1.2 K). (B) ESR spectra given for different temperatures (I = 20 pA, VDC = 60 mV, VRF = 30 mV). Spectra are offset by 40 fA. Inset: Temperature evolution for Ipeak(T) normalized to Ipeak(1.2 K). Symbols indicate different data sets, each taken at different current and bias voltage set points, with different tips, and on different atoms (see section S6). Red line is used as a guide to the eye.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/2/eaaq1543/DC1

    section S1. Local environment of the Fe atom

    section S2. Additional peak shape analysis

    section S3. Supplementary analysis of phase coherence time T2

    section S4. Evaluation of the T1 time of the Fe spin

    section S5. Theoretical treatment of the linear relation between adatom spin decoherence rate and current

    section S6. Temperature dependence of the ESR peak height

    fig. S1. Large topography of the Fe atom.

    fig. S2. Fano factor q(VRF) for different I and VDC.

    fig. S3. Change in drive Φ with VRF and I.

    fig. S4. Obtaining large ESR signals.

    fig. S5. Spin-torque initialization.

    fig. S6. Bias voltage analysis.

    fig. S7. Broadening of the resonant peak induced by tip vibrations.

    fig. S8. Additional data for the phase coherence time T2.

    fig. S9. Bias voltage analysis of the T2 time.

    fig. S10. Pump-probe spectroscopy to determine T1.

    fig. S11. Evaluation of spin lifetime T1.

    fig. S12. Temperature dependence of the peak height.

    Reference (51)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Local environment of the Fe atom
    • section S2. Additional peak shape analysis
    • section S3. Supplementary analysis of phase coherence time T2
    • section S4. Evaluation of the T1 time of the Fe spin
    • section S5. Theoretical treatment of the linear relation between adatom spin decoherence rate and current
    • section S6. Temperature dependence of the ESR peak height
    • fig. S1. Large topography of the Fe atom.
    • fig. S2. Fano factor q(VRF) for different I and VDC.
    • fig. S3. Change in drive Φ with VRF and I.
    • fig. S4. Obtaining large ESR signals.
    • fig. S5. Spin-torque initialization.
    • fig. S6. Bias voltage analysis.
    • fig. S7. Broadening of the resonant peak induced by tip vibrations.
    • fig. S8. Additional data for the phase coherence time T2.
    • fig. S9. Bias voltage analysis of the T2 time.
    • fig. S10. Pump-probe spectroscopy to determine T1.
    • fig. S11. Evaluation of spin lifetime T1.
    • fig. S12. Temperature dependence of the peak height.
    • Reference (51)

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