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Introduction to the NV center: Electronic structure and optical transitions

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Introduction to the NV center: Electronic structure and optical transitions Lily Childress Bates College Sonderborg, Denmark, August 27 2010 * The research going on ... – PowerPoint PPT presentation

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Title: Introduction to the NV center: Electronic structure and optical transitions


1
Introduction to the NV center Electronic
structure and optical transitions
Lily Childress Bates College
Sonderborg, Denmark, August 27 2010
2
The nitrogen-vacancy defect
Why the NV- defect in diamond?
NV0 5 electrons NV- 6 electrons
  • Diamond is a good host
  • Wide bandgap
  • 0 nuclear spin isotope
  • Stiff lattice
  • Ground state spin triplet
  • Optical transitions
  • Spin-dependent fluorescence
  • Optical pumping possible
  • gt Very atom-like
  • Formation natural or
  • N implantation
  • irradiation creates vacancies
  • annealing removes barrier to vacancy diffusion

Charging state depends on local Fermi energy
From Weber et al. 2010 PNAS
What is the electronic structure of the NV-
center?
3
Electronic structure new symmetries
Atomic physics approach NV an atom embedded in
a crystal
N
V
Spherical symmetry
C3v symmetry
s,p,d,f irreducible representations of the
group of rotations
A1, A2, E irreducible representations of the
group of trigonal symmetries
4
Electronic structure new symmetries
N
Excited state
Strain
E
3E
V
637 nm
637 nm
Inhomogeneous broadening
C3v symmetry
Ground state
ms 1
A1, A2, E irreducible representations of the
group of trigonal symmetries
ms 0
A2
3A2
fine structure
5
Electronic structure
Singlet state(s)?
Triplet states
N
Excited state
ISC
metastable
3E
1A1
V
637 nm
Ground state
Explains observed optical pumping into ms 0
ms 1
ms 0
3A2
Explains observed higher fluorescence intensity
for ms 0
Spin-conserving optical transitions
Drabenstedt PRB 1999
6
Electronic structure
Singlet state(s)?
Triplet states
N
Excited state
3E
1E
V
1046 nm
1A1
637 nm
1E
Ground state
ms 1
ms 0
3A2
Ma PRB 2010
Rogers NJP 2008
7
Electronic structure
Singlets
Triplet states
N
Excited state
300K
3E
V
?
637 nm
Phonon sidebands
Ground state
ms 1
ZPL
ms 0
3A2
Questions?
Rogers NJP 2009
8
Symmetry and quantum mechanics
The set of transformations associated with that
symmetry leave the Hamiltonian invariant
A system exhibits a symmetry
?
Operators SR commute with the Hamiltonian
e.g. for atoms, the group of rotations
For the NV center
C3v symmetry group elements E identity 2C3
rotations by 2pn/3 3?v reflections
1
3
2
9
Symmetry and quantum mechanics
The set of transformations associated with that
symmetry leave the Hamiltonian invariant
A system exhibits a symmetry
?
Operations SR form a group group of the
Schrodinger equation
Operators SR commute with the Hamiltonian
How do eigenstates of H transform under these
symmetry operations?
gt
Symmetry operations yield degenerate eigenstates
Applying the set SR yields all
(non-accidentally) degenerate states
10
Symmetry and quantum mechanics
Suppose that energy level En has ln distinct
degenerate states .
Applying any symmetry operators to one state must
yield some linear combination of the degenerate
states
The set of ?R (for all symmetry group elements R)
forms an ln dimensional representation of the
symmetry group
preserves the group multiplication rules
It is also an irreducible representation
because every state is connected to every other
state by a symmetry operator, regardless of the
basis chosen to describe the degenerate
eigenstates.
11
Classifying energy levels
An energy level can be classified according to
the irreducible representation that describes the
action of the symmetry group on its eigenstates
Example 3d states of hydrogen form a 5-fold
degenerate level with states that transform under
rotations according to a 5-dimensional matrix
representation of the group SO3.
  • Knowing the IRs for the group of symmetries of a
    system yields
  • degeneracy of the levels
  • transformation properties of the basis
    functions (states)
  • selection rules for e.g. dipole transitions

12
Irreducible representations of C3v
A1
A2
E
Dimensionality degeneracy
2
1
1
Basis functions transform into each other the way
that the vectors x and y transform into each
other under the C3v symmetry operations
The identity representation the basis function
transforms into itself under all symmetry
operations.
The 1, -1 representation the basis function
picks up a minus sign under reflections.
like s or pz
like triplet ms 0
like px and py
Two a1 orbitals
Symmetrized orbitals
N
Two e orbitals
V
N
C
C
C
V
C
C
C
13
Orbital electronic configurations of the NV center
First orbital excited state a1(1)2a1(2)e3
one hole in a1(2) and one hole in e
E
Now add in spin triplet or singlet
Symmetrized orbitals
Ground state a1(1)2a1(2)2e2
a1, a1, ex, ey
two holes in the e orbitals
A2
S 1 transforms as A2 (Sz) and E (Sx, Sy)
14
Electronic states of the NV center
from Jeronimo Maze, thesis 2010
Strain breaks symmetry, shifts energies, and
mixes levels
Optical transitions to excited state spin triplet
Spin-orbit mediated crossing to spin singlet
levels
States with ms0
Selection rules also from group theory
Ground state spin triplet
Optically induced spin polarization into ms 0
spin projection
15
Optical transitions at low temperature
Optical spectroscopy typically uses ZPL
excitation and sideband detection
(only few into ZPL)
Confocal geometry to isolate single
defects Required to resolve excited state
structure!
Detect
Excite
Batalov et al. 2009
Early ensemble work Davies, Collins, Manson, Rand
16
Optical transitions at low temperature
Optical spectroscopy typically uses ZPL
excitation and sideband detection
(only few into ZPL)
high strain configuration (typical)
In the absence of microwaves, only this
transition would be visible
And even then, it could disappear from a (1
probability) spin-flip
  • Important questions
  • Stability
  • Coherence
  • Tunability
  • Selection rules

Optical spin polarization gt mix spin states with
MW to see all lines
Batalov et al. 2009
17
Stability
Photoionization
In a few, select samples, stable
lifetime-broadened lines possible
Even when spin-flips arent a problem, continuous
resonant illumination leads to photoionization
Robledo et al. 2010, arXiv
532nm repump reverses ionization but causes
spectral diffusion
Spectral diffusion may be caused by ionization of
nearby nitrogen impurities
Tamarat et al. 2006 PRL
Very sample dependent
Fu et al. 2009, PRL
18
Coherence
Batalov et al. 2008 PRL
Optical Rabi oscillations
Typical decay of oscillations yields a pure
dephasing time similar to or longer than the
lifetime 12 ns
Consistent with observed linewidths
Promising for two-photon interference experiments
lifetime radiative lifetime?
Robledo et al. 2010 arXiv
19
Optical properties depend strongly on strain
Batalov et al. 2009 PRL
High transverse strain (typical)
Low strain C3v symmetry
Linearly polarized emission, spin conserving in
the limit of high strain
A2
A1
Selection rules determined by C3v symmetry
Ex,y
E1,2
Togan et al. 2010 Nature
Significant mixing between spin states in lower
branch creates lambda transitions at moderate
strain
Electric fields have the same effect as strain
Tamarat et al. 2008 NJP
20
Stark shift control
Ey transitions for several NV centers can be
tuned several GHz with electric fields. Offset
depends on local strain.
Possible to bring different NV centers into
resonance
Or control selection rules, degree of mixing
Tamarat et al. 2006 PRL
21
Selection rules low strain
Can be roughly understood from angular momentum
conservation
Difficult to realize for most NVs
22
Moderate strain Lambda transitions
Santori et al. PRL 2006
Coherent population trapping signatures (same
mechanism as EIT)
Mechanism for all-optical spin manipulation
23
Selection rules high strain
Resonant excitation
Sideband detection
Good linear selection rules in high strain NVs
Phonon averaging between branches (worse at high
temperatures)
Kaiser et al. 2009, arXiv
Degrades with temperature, indications of
phonon-induced averaging between orbital states
24
The transition from low to high temperature
Linewidths broaden, selection rules disappear
Electron spin resonance signal emerges in the
excited state at 100K
Batalov et al. 2009 PRL
Interpretation Phonon processes average over the
orbital degrees of freedom, leaving only the
spin-spin interaction
Strain independent
Strain dependent
Fu et al. 2009 PRL
Rogers et al. 2009 NJP
Degrades with temperature, indications of
phonon-induced averaging between orbital states
25
Room temperature optical transitions
Optical spin polarization and detection
Room temperature
Excited state
Initial differential fluorescence gt readout
mechanism
?
Fluorescence
Few ?s gt polarization
Ground state
ms 1
Time
ms 0
Green on
This method isnt single shot typical
experiments get 1/100 of a photon per shot
Preparation and detection mechanism for spin
resonance experiments
26
Room temperature optical transitions
Single defect imaging
Confocal imaging of single defects
Wrachtrup, Weinfurter, Grangier
Photon anti-bunching
  • Applications
  • single photon sources
  • fluorescent bio-markers

Subwavelength imaging Stimulated emission
depletion (STED)
Overlap beams only see fluorescence at central
point (size depends on depletion beam intensity)
Rittweger et al. 2009 Nature Photonics
Other methods for selective depletion using spin
manipulation or shelving
27
Summary Electronic structure and optical
transitions
Electronic structure and selection rules governed
by C3v symmetry but highly affected by strain,
which is almost always present
Triplet-singlet intersystem crossings lead to
spin polarization and spin-dependent
fluorescence even at room temperature
Lifetime broadened optical transitions at low
temperature (ZPL) promising for interference
experiments
Strong coupling to phonons Significant phonon
sidebands Orbital averaging at room temperature
  • Collection efficiency
  • typically 0.1 of expected counts
  • ZPL only a few of that!

Stability questions remain Spectral diffusion
Photoionization Sample dependent properties
28
Increasing collection efficiency
Coupling to cavities
Directed emission
Plasmon enhanced emission
Degrades with temperature, indications of
phonon-induced averaging between orbital states
29
Increasing collection efficiency
Plasmon enhanced emission
Directed emission
Degrades with temperature, indications of
phonon-induced averaging between orbital states
30
Increasing collection efficiency
Coupling to cavities
Coupling nanocrystals to non-diamond optical
resonators
Q1000
Typical results NV up to 10 times brighter at
cavity resonance
Diamond fabrication
Challenge couple to stable (likely bulk) NVs
Also polycrystalline Awschalom group
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