Erdoped endohedral metallofullerenes for quantum computing

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Er-doped endohedral metallofullerenes for
quantum computing
Géraldine Dantelle
QIP IRC Department of Materials - University of
Oxford, UK
Workshop on QI in rare-earth doped solids
Paris, April 2007
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Endohedral metallofullerenes
R_at_C82
R2_at_C82
R3N_at_C80
N_at_C60

• The endohedral metallofullerenes produced are
  centred on group II and III metallofullerenes
  such as Sc, Y, La, Ca, Sr and Ba as well as
  lanthanide metallofullerenes (CeLu).
• These metal atoms have been encapsulated in high
  fullerenes, especially in C82 or C80.

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Endohedral metallofullerenes

• Macroscopic quantities of endohedral
  metallofullerenes were also produced by the Rice
  group (US) in 1991. The major fullerene, stable
  in air, is La_at_C82. The work has been extended to
  endohedral yttrium compounds in 1992 (Y_at_C82,
  Y2_at_C82).
• Scandium metallofullerenes were also produced in
  macroscopic quantity by Shinohara (1992, Japan).
  The Sc fullerenes exist in a variety of species
  (mono-, di-, tri- and tetra-scandium fullerenes),
  typically Sc_at_C82, Sc2_at_C74, Sc2_at_C82, Sc2_at_C84,
  Sc3_at_C82 and Sc4_at_C82.
• The formation of lanthanide metallofullerenes
  R_at_C82 (R Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho,
  Er, Yb and Lu) was also reported in 1992.
• More recently (1996), group 2 metal atoms (Ca,
  Sr, Ba) were also found to form endohedral
  metallofullerenes, and have been produced and
  isolated in mg quantity.

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Endohedral metallofullerenes

• Many studies have been performed to determine
  the electronic structure of metallofullerenes.
• Exohedral / endohedral?
• Electron transfer from the metal to the cage?
• Number of isomers? Stability of them?

• Different techniques have been used Mass
  spectrum analysis, HRTEM, EXAFS, NMR, EPR,
  UV-Vis-NIR absorption, DFT calculations. But,
  because of the small quantity of materials
  available, these measurements are difficult.

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Endohedral metallofullerenes
La_at_C82, a mono-metallofullerene

• The calculations show that La is located at the
  off-centre position.
• The La atom is in the 3 oxidation state.
• The electronic structure can be written La3
  C823-
• Typically, the EPR signal shows eight hyperfine
  lines, resulting from the coupling of one
  unpaired electron residing in the LUMO of the
  cage with 139La (I7/2)

La2_at_C82, a di-metallofullerene

• The two La atoms are equivalently encapsulated
  inside a C82 cage and can circulate inside the
  cage.
• The La atoms are in the 3 oxidation state.
• The electronic structure can be written (La3)2
  C826-.

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Endohedral metallofullerenes
Sc2_at_C84

• The Sc atoms are in the 2 oxidation state.
• The electronic structure can be written (Sc2)2
  C844-

Er3N_at_C80, a TNT fullerene

• The Er3N entity is planar.
• The Er3 atoms are in the 3 oxidation state and
  N is in the 3- oxidation state.
• The electronic structure can be written (Er3N)6
  C806-

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Metallofullerenes for QIP
1_ A scalable physical system with well
characterized qubits 2_ The ability to initialize
the state of the qubits to a simple state 3_ Long
relevant coherence times, much longer than the
gate operation time 4_ A universal set of
quantum gates 5_ A qubit-specific measurement
capability
D. DiVincenzo, Fortschr. Phys. 48 (9-11) (2000)
771
The optical detection of a single spin might be a
good tool to achieve the qubit readout. The
experiment, consisting of detecting the
luminescence or absorption of a sample under a
magnetic field, requires molecules which are
optically and spin active.
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Metallofullerenes for QIP
Er3 is a Kramers ion which present an optical
absorption / emission around 1.5 µm,
corresponding to the transition 4I15/2 ? 4I13/2.
4I11/2
4I13/2
4I13/2
B0, Zeeman effect
CF
103-104 cm-1
1.5 µm
4I15/2
101-102 cm-1
1gt
1 cm-1
0gt
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Metallofullerenes for QIP
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Synthesis
Endohedral metallofullerenes are synthesized by a
DC arc discharge method, as shown below.
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Synthesis
1. Main arc chamber 2. Collection chamber 3.
Solvent reservoir 4. He-pressure gauge
(a) Arc-discharge apparatus (b) Image of the arc
in operation through the viewport. The two
graphite rods are glowing as they are baked,
moments before the arc is formed between them.
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Extraction from the primary soot

• The soot is composed of metallofullerenes and
  the hollow cages, but also amorphous carbon and
  broken cages.
• The yield of the production of endohedral
  metallofullerenes is generally relatively weak.
  In the soot, 10-15 are fullerenes. 1 of these
  10-15 is metallofullerenes.
• By increasing the doping concentration of the
  rods, it is possible to control the number of
  doping ions encapsulated inside the cage.
• With rods doped with 0.8 Er2O3, we produce
  mainly Er_at_C82.
• With rods doped with 1.6 Er2O3, we produce
  mainly Er2_at_C80.
• The extraction of metallofullerenes and hollow
  fullerenes is performed using boiled solvents
  (toluene, DMF, oxylene). The soluble fullerenes
  are easily separated from the insoluble
  components by filtration.

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and purification by HPLC

• The solution containing empty fullerenes and
  metallofullerenes is then dried. The obtained
  powder is dissolved in toluene and the molecules
  are separated by HPLC.
• High Performance LC (HPLC) allows separation of
  fullerenes according to their molecular weight,
  size, shape or other parameters.

• It took almost two years for metallofullerenes
  to be completely isolated by the HPLC method
  after the first extraction of La_at_C82 by the Rice
  group

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Solubility of metallofullerenes

• The solubility of fullerenes is high in toluene,
  CS2 or decalin.
• Because CS2 does not absorb around 1.5 µm, we
  are using this solvent to dissolve fullerenes and
  metallofullerenes.

• The maximum concentration of Er3N_at_C80 is around
  2.10-4 mol/L.

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Optical properties
The absorption of the metallofullerenes has been
recorded at room temperature.
Er3 4I15/2 ? 4I13/2
Er3N_at_C80

• The closed-shell electronic structure of C806-
  accounts for an absence of absorption in the NIR
  region.
• The incorporation of a single trivalent ion in
  C82 induces a broad absorption peaking at 1400 nm
  and extending down to 2300 nm.

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Optical properties
We have done some photoluminescence measurements
at liquid helium temperature to detect the Er3
emission around 1.5 µm.
Cage States
4I13/2
Fluorescence (1.5 µm)
InGaAs detector
532 nm
1.5 µm
4I15/2
Cage States
Er3
Laser excitation (532 nm)
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Optical properties
Er2_at_C84

• In these four samples, Er3 emits around 1.5 µm,
  corresponding to the transition 4I13/2 ? 4I15/2.
• A spectral fine-structure can be observed,
  evidencing the presence of different sites for
  Er3.

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Optical properties

• The inhomogeneous line width is narrow (lt 5
  cm-1). It evidences that the Er3 ions are
  shielded from the environment. Er3 ions are in a
  homogeneous environment provided by the cage.

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Optical properties
We have recorded the photoluminescence excitation
spectra at liquid helium temperature to identify
the different sublevels of the first excited
state 4I13/2.
PLE intensity (a. u)
Excitation wavelength
Emission wavelength (nm)
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Optical properties
We have monitored the two more intense
transitions ( 1520 and 1544 nm) to scan all the
4I13/2 level.
Er2ScN_at_C80
ErSc2N_at_C80
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Optical properties
We have selectively looked at the PLE of one site
or the other into a sample by monitoring the
right wavelength.
ErSc2N_at_C80
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Magnetic properties
We could not observe any EPR signal from
Er3N_at_C80, even at very low temperature. We
characterized this molecule by SQUID to
understand better the behaviour of Er3N_at_C80.
The curves evidence a paramagnetic behaviour.
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Magnetic properties
The magnetization curves do not perfectly with
the classical Langevin or Brillouin simulations.
We have improved these models by taking into
account the anisotropy of the material.
Bo
z
?
H g µB Sz.Bo D S?2
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Magnetic properties
We did see the EPR signature of ErSc2N_at_C80,
operating with an X-band spectrometer at low
temperature.

• ErSc2N_at_C80 is both optically and spin active.

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Optically detected magnetic resonance
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Optically detected magnetic resonance
ODMR via Magnetic Circular Dichroism
4I13/2
ms1/2
ms-1/2
s
s-
4I15/2
ms1/2
ms-1/2
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Conclusions and outlook

• Er-doped metallofullerenes (Er3N_at_C80,
  ErSc2N_at_C80, Er2ScN_at_C80, Er2_at_C84) give a
  detectable luminescence around 1.5 µm.
• Er3N_at_C80 appears to be spin-silent.
• but ErSc2N_at_C80 is both spin- and optically
  active.

• The electronic properties of ErSc2N_at_C80 will be
  investigated further, in particular by combining
  both optical and magnetic measurements.
• The coherence time of Er3 in ErSc2N_at_C80 will be
  determined by pulsed EPR.
• Er_at_C82 will be purified and studied as it could
  be a good candidate.

• An ODMR experiment will be set up to detect the
  magnetic resonance via the optical transitions.

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Acknowledgments
Andrew A.R. Watt John J.L. Morton Kyriakos
Porfyrakis
Archana Tiwari Simon Plant Mark Jones
G. Andrew D. Briggs Arzhang Ardavan Robert
Taylor
Has submitted his thesis in October 2006
Clarendon Laboratory Department of Physics -
University of Oxford, UK