Effect of phonons on the optical properties of color ...200.145.112.249/webcast/files/Ariel Talk ICTP 2017.pdf · Aharonovich, I. et.al. Optics Letters 38, 4170 -4173 (2013) Symmetry
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Institute of Physics Pontificia Universidad Católica, Santiago, Chile Effect of phonons on the optical properties of color centers in diamond Ariel Norambuena [email protected]School on Interaction of Light with Cold Atoms January 30 – February 10, 2017 São Paulo, Brazil ICTP-SAIFR/IFT-UNESP
Electronic distribution Spin degree of freedom Local vibrational modes (3N-6 = 15) Symmetry of the defect
Local properties
𝑁𝑁 atoms in a 3D lattice 3N-6 Vibrational modes Random nuclear spins (~1%)
(phonons) (electrons)
Hamiltonian of the whole system (spin-boson model)
(absorption and emission of one phonon)
Apresentador
Notas de apresentação
Color centers in diamond can be considered as trapped molecules in the diamond lattice. Here, you can observe the silicon-vacancy center inside of a diamond lattice. Now, I will introduce a quantum open system description of the role of phonons on the optical properties trapped molecules in solids. First, we considered this defect in diamond as a small quantum system. The Hamiltonian of this system it will be described by the localized electronic distribution of the defect atoms. Also, only for simplicity, we can consider this system as a two-level system in contact with the environment. Here, we do not include the effect of the spin-orbit interaction because it is not relevant for determining the main properties of the optical emission spectrum. On the other side, the environment is given by the diamond lattice. Here, we model a finite lattice composed by N carbon atoms in a 3D diamond structure with a single defect at the center. The Hamiltonian of the environment it will be described by many harmonic oscillators. Each harmonic oscillator describe the Vibrational modes of the whole system, the defect and the diamond lattice. The defect-environment interaction is described by the electron-phonon coupling between every Vibrational mode and the localized electronic degrees of freedom of the defect. However, at this level, we do not include the effect of electronic transitions induced by phonons. This Hamiltonian will be considered by means of the dynamical symmetry breaking.
Phonons and emission spectrum
ZPL = zero-phonon line transition
vibrational energy levels
Electrons contribute to the equilibrium potential of ions
Emission spectrum
phonon sideband
ZPL transition inte
nsity
frequency
Apresentador
Notas de apresentação
The emission spectrum of a solid-state system is very different from a simple two-level system. In the case of color centers in diamond phonons plays a fundamental role in the emission spectrum and the relaxation dynamics induced by vibrations. In this diagram, we have a two-level system dessed by the quantized molecular vibrations of the environment. Each parabola represents the potential energy of a nuclear configuration in a many-body state and the horizontal lines inside each parabola represents the vibrational energies of the system. Initially, we have the system in the ground vibronic state (vibronic means electronic and vibrational states), so if we apply some external laser we can induce an optical excitation from the ground to some excited vibronic state.��In this excited vibronic state phonons decay very quickly by inducing vibrations on the lattice. Therefore, this processes is a non radiative transition. Then, the system decay from this excited vibronic state to some dressed ground vibronic state. In this radiative transition we can observe and measure a real photon with a well defined energy.
• If (very small phonon contribution to the emission spectrum)
Emission spectrum (Kubo formula from linear response theory)
Spectral density function
Model for the emission spectrum
density of states
• depend crucially on the symmetry of the color center
electron-phonon coupling SiV-center
excited state ground state
Apresentador
Notas de apresentação
The mathematical description of the emission spectrum is based on the linear response theory of this system when is excited by a pumping laser. The model takes into account the quantum probabilities of every radiative transition, the average effect of phonons in thermal equilibrium and the electron-phonon coupling between the lattice and the color center in diamond. The shape of the emission spectrum and the effect of temperature is determined by the function Phi(t). In particular, this function can be obtained if you know the spectral density function J(w). In general , the spectral density function depends on the difference between the electron-phonon coupling constants of the excited and the ground state and the density of phonons. Therefore, if you can estimate the vibrational dynamics of the system and the electron-phonon coupling constants of the systems, so yo can microscopically model the emission spectrum of your system. It is interesting to note the following: if the electronic states interacts in the same way with the lattice phonons, both coupling constants for the ground and excited states are very similar and the spectral density function is small leading to a transition that has the form of a very narrow peak around the zero-phonon line transition. Also, the electron-phonon coupling constants depends on the symmetry of the molecular structure. In some way, the electronic distribution in a molecular system can be determined by using the symmetry group of the molecule (group theory). For example, a molecule with inversion symmetry has symmetric and antisymmetric electronic distributions around the center of inversion (in this case the silicon atom). In the case of the silicon-vacancy center the electronic distribution of the excited and ground states are very similar, as a consequence, during the emission processes the change in the trapping potential seen by the ions is very small leading to a very small phonon contribution to the spectral density function, and therefore a very small contribution to the emission spectrum.
Experimental emission spectra of color centers in diamond
NV-center SiV-center
Aharonovich, I. et.al. Optics Letters 38, 4170-4173 (2013)
Here we can observe the experimental emission spectra of two color centers in diamond: the nitrogen-vacancy center and the silicon-vacancy center in diamond. At the same room temperature, both emission spectra are very different between them. For example, the nitrogen vacancy center has a very broad emission spectrum (about 100 nm), meanwhile the silicon-vacancy center in diamond has a very narrow emission spectrum (around 5 nm). In the language of group theory, the only difference between these two color centers is the additional inversion symmetry of the silicon-vacancy center. As a result of this particular symmetry, this color center has a Weak electron-phonon coupling with the environment and a very narrow emission spectrum. Now I will show you some particular experimental result of the phonon sideband associated to the silicon-vacancy center in diamond.
Andreas Dietrich et.al. New J. Phys. (2014)
Localized phonon mode
Isotopic shift of the phonon sideband
Physical interpretation from experiments
Apresentador
Notas de apresentação
Here, we can observe the isotopic shift of the phonon sideband associated to the silicon-vacancy center in diamond. In particular, the experimental data shows that the sharp peak of the phonon sideband moves to the left if the mass of the silicon atom increases. This isotopic shift effect only can be possible if the phonon responsible of this peak induce a large oscillation of the silicon atom in some direction. ��One interpretation is the effect of some localized phonon mode in which the silicon atom oscillates along the symmetry axis.
Local mode
Dynamical symmetry breaking
Antisymmetric (ungerade) vibrational mode
Dynamical symmetry reduction
symmetric
antysymmetric
For each antisymmetric mode
Therefore, antisymmetrical phonon modes are not observed!
Isotopic shift?
Apresentador
Notas de apresentação
However, a local mode with an oscillation of the silicon atom along the symmetry axis has an antisymmetric character. Using symmetry arguments we can deduce that antisymmetric vibrational modes leads to zero electron-phonon coupling constants, and therefore, they not contribute to the emission spectrum. Obviously, this is a contradiction with experiments.��This indicates that inversion symmetry is broken by some external perturbation that mixes both ground and excited states. With this in mind, we can introduce the following dynamical symmetry breaking mechanisism. Here, we observe the new mixed electronic wavefunction for the ground and the excited states, where épsilon is a mixing parameter and theta is an arbitrary phase. Using these new electronic wavefunctions the new spectral density function incorporates the effect of all type of phonons: symmetric and antysimmetric. The new spectral density fucntion Jeg(w) depends on the expectation value between different electronic states.
Numerical spectral density functions
𝜔𝜔1 [meV] Si28 Si29 Si30
Our model 63.19 62.66 62.16
Exp. Data1 63.76 62.74 61.55
If , is the largest contribution to the emission spectrum
Ariel Norambuena et.al. Phys. Rev. B 94 134305, (2016) 1. Andreas Dietrich et.al. New J. Phys. (2014)
Andreas Dietrich et.al. New. J. Phys. 16, (2014)
Experimental emission spectra
Numerical and experimental emission spectra
Ariel Norambuena et.al. Phys. Rev. B 94 134305, (2016)
294 K
Numerical
Conclusions
• We have presented a microscopic model for estimating the emission spectrum of a color center in diamond.
• This approach allows us to gain a detailed insight of the microscopic origin and the role of symmetries on the emission spectrum.
• The spectral density function can be useful to understand and model the optical properties of trapped molecules in solids.
Thanks
Silicon-vacancy center in diamond carbon
silicon
vacancies
Igor I. Vlasov and et.al. Nature Nanotechnology 9, 54–58 (2014)
Quantum applications Single photon sources Quantum information Quantum communications Flourescent marker for biology Optomechanical cooling
Si28 Si29 Si30
Apresentador
Notas de apresentação
Color centers in diamond can be considered as trapped molecules in the diamond lattice. Here, you can observe the silicon-vacancy center inside of a diamond lattice. This molecular system is composed by seven atoms: six carbon atoms, two vacancy sites and one silicon atom at the center of this small molecule. The silicon has three possible isotopes and the only magnetic isotope is the silicon twenty nine. This molecule is very stable at temperatures (from one kelvin to three hundred kelvins) and can be optically manipulated in to order to perform very interesting applications such as single photon sources, quantum information, quantum information and even optomechanical cooling in nano-devices.
Strong electron-phonon coupling with a localized phonon mode
I. Wilson-Rae and A. Imamoglu, Phys. Rev. B. 65, 235311 (2002).
Spectral density function and absorption spectra Spectral density function Absorption spectra at different temperatures
