Quantum Physics of LightMatter Interactions So Se 20
- Slides: 48
Quantum Physics of Light-Matter Interactions So. Se 20 --- April 24 th to July 24 th 2020 -- Lecturer: Claudiu Genes Max Planck Institute for the Science of Light (Erlangen, Germany) -- Lecture 9 --- 26. 06. 2020 -- Genes Research Group Cooperative Quantum Phenomena
From atoms to molecules – increasing complexity q Up to here we have mostly considered simple TLS models (and took the Hydrogen atom as an example as it is analytically solvable) +
From atoms to molecules – increasing complexity q Up to here we have mostly considered simple TLS models (and took the Hydrogen atom as an example as it is analytically solvable) + q Let us now focus on more complicated arrangements of charges (molecules where electronic orbitals define the inter-nuclear distance in equilibrium)
From atoms to molecules – increasing complexity q Up to here we have mostly considered simple TLS models (and took the Hydrogen atom as an example as it is analytically solvable) + q Let us now focus on more complicated arrangements of charges (molecules where electronic orbitals define the inter-nuclear distance in equilibrium) q The TLS usually not a good approximation for the dynamics of electrons in molecules
From atoms to molecules – increasing complexity q Let’s see some simple example - diatomic homonuclear molecules
From atoms to molecules – increasing complexity q Let’s see some simple example - diatomic homonuclear molecules o One assumes that the center-of-mass of the nuclei is fixed while the electronic orbitals define the equilibrium relative distance (internuclear coordinate) o Ground and excited potential surfaces are typically not positioned at the same coordinate (and form is given approximately by a Morse-Lange function)
Deriving the Holstein Hamiltonian o We will expand the potential curve around the equilibria where it is approximately parabolic
Deriving the Holstein Hamiltonian o We will expand the potential curve around the equilibria where it is approximately parabolic o First around the excited state equilibrium position (with the proper projector)
Deriving the Holstein Hamiltonian o We will expand the potential curve around the equilibria where it is approximately parabolic o First around the excited state equilibrium position (with the proper projector) o Then around the ground state equilibrium position (with the complementary projector)
Deriving the Holstein Hamiltonian o Now we define the variations around the ground state equilibrium and assume that the two minima are not so far so we are still in the harmonic approximation
Deriving the Holstein Hamiltonian o Now we define the variations around the ground state equilibrium and assume that the two minima are not so far so we are still in the harmonic approximation
Deriving the Holstein Hamiltonian Harmonic oscillator (for vibrations)
Deriving the Holstein Hamiltonian Bare two level system Hamiltonian
Deriving the Holstein Hamiltonian Constant energy shift
Deriving the Holstein Hamiltonian Vibronic coupling
Deriving the Holstein Hamiltonian Introducing the Huang-Rhys factor and bosonic operators for the harmonic motion Ø Remember the definition of the zero point motion displacement and momentum
Deriving the Holstein Hamiltonian Introducing the Huang-Rhys factor and bosonic operators for the harmonic motion Ø Remember the definition of the zero point motion displacement and momentum
Deriving the Holstein Hamiltonian Introducing the Huang-Rhys factor and bosonic operators for the harmonic motion Holstein Hamiltonian Ø Remember the definition of the zero point motion displacement and momentum
Deriving the Holstein Hamiltonian Introducing the Huang-Rhys factor and bosonic operators for the harmonic motion Holstein Hamiltonian Ø Remember the definition of the zero point motion displacement and momentum Ø Notice that when the potential landscapes are perfectly aligned there is no vibronic coupling !!
Diagonalizing the Holstein Hamiltonian
Diagonalizing the Holstein Hamiltonian The polaron transformation We used the usual displacement operator
Diagonalizing the Holstein Hamiltonian The polaron transformation Let‘s rewrite and notice that Now we can work out all the transformed terms We used the usual displacement operator
Diagonalizing the Holstein Hamiltonian The polaron transformation Let‘s rewrite and notice that Now we can work out all the transformed terms We used the usual displacement operator
Diagonalizing the Holstein Hamiltonian The polaron transformation Let‘s rewrite and notice that Now we can work out all the transformed terms We used the usual displacement operator
Diagonalizing the Holstein Hamiltonian The polaron transformation Eigenstates (solve this as Exercise 10 for both displaced and bare basis) We used the usual displacement operator
The Franck-Condon principle Holstein Hamiltonian + Laser drive
The Franck-Condon principle Holstein Hamiltonian + Laser drive We have used (solve this as Exercise 10)
The Franck-Condon principle Holstein Hamiltonian + Laser drive We have used (solve this as Exercise 10) Transition rates Absorption Ø The probabilities of the transitions are distributed according to a Poissonian
The Franck-Condon principle Holstein Hamiltonian + Laser drive We have used (solve this as Exercise 10) Transition rates Absorption Emission Ø The probabilities of the transitions are distributed according to a Poissonian
The Franck-Condon principle (illustrated) Franck-Condon principle illustrated
The Franck-Condon principle (illustrated) Franck-Condon principle illustrated Zero phonon line – reduction by
The Franck-Condon principle (illustrated) Franck-Condon principle illustrated Zero phonon line – reduction by Not a good quantum emitter !! – quantum efficiency far from 100%
The Franck-Condon principle (illustrated) Franck-Condon principle illustrated Zero phonon line – reduction by Not a good quantum emitter !! – quantum efficiency far from 100% Enhancing decay into the zero phonon line via the cavity Purcell effect (experimental work in the Sandoghdar division at MPL)
The Franck-Condon principle (illustrated) Franck-Condon principle illustrated Non-overlapping absorption and emission spectra Vibrational lines visible
Adding vibrational relaxation Introducing vibrational relaxation - Molecular vibrations can be damped either because of coupling to other intramolecular vibrational modes or because of coupling to the surrounding crystal vibrations - Two loss rates: radiative (emitting photons) and non-radiative (because of mechanisms above)
Adding vibrational relaxation Stimulated absorption
Adding vibrational relaxation Quick vibrational relaxation
Adding vibrational relaxation Spontaneously emitted photon
Adding vibrational relaxation Quick vibrational relaxation
Adding vibrational relaxation Branching ratio Dominant emission line Branching ratio = emission in 00 line / total emission
Extra material – cavity QED with molecules
Quantum Langevin equations M. Reitz, C. Sommer and C. Genes, Phys. Rev. Lett. 122, 203602 (2019) Langevin approach to quantum optics with molecules
Quantum Langevin equations Thermal reservoir Polaron operator Input non-zero noise
Quantum Langevin equations Thermal reservoir Polaron operator Input non-zero noise Solution transient steady state
Quantum Langevin equations Absorption profile Emission profile
Quantum Langevin equations for cavity molecule spectroscopy
Quantum Langevin equations Absorption profile Emission profile
Polaritons (cross-talk)
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