Two photon absorption or multi-photon absorption?

[fog37]

Hello Forum,

What does the process of two-photon absorption photon entail? That, in general, a molecule or atom (composed of many electrons) that is illuminated by an electromagnetic field can only absorb one photon at a time except in those special cases where two photons can be absorbed simultaneously?

thanks,

 

[Ygggdrasil]

Using a classical view of light: The intensity of the electromagnetic wave is so strong that the electric field from the light distorts the electronic structure of the atom/molecule, changing the spacing between the energy levels, so that it is capable of absorbing lower wavelengths of light.

Using a quantum view of light: When a photon of the wrong energy interacts with an atom/molecule, it excites the atom/molecule to a short-lived virtual state (similar to the distorted state posited by the explanation above). This virtual state is not an eigenstate of the Hamiltonian, so it is not stable and quickly decays back to the ground state with re-emission of the photon. In two-photon excitation, the density of photons is high enough that, before the virtual state can decay, another photon can promote the virtual state into a real excited state.

 

[fog37]

Thanks Ygggdrasil.
Very clear explanation. If possible, let me know if my understanding of classical scattering is correct when a substance is illuminated with EM radiation.

Scattering and Absorption from a Classical View
Resonant Dissipative Nonelastic Absorption: In solids and liquids (substances with medium and high density), it is very likely that the absorbed excitation energy (photon) will not be returned as an emitted photon. The absorbed photon will instead be converted into thermal energy (due to random collisions): the photon vanishes and its energy is converted into thermal energy. This conversion of incident photons to thermal energy process is called resonant dissipative (nonelastic) absorption. Only in the case of low-density gases incident photons with resonant frequencies will be absorbed and reemitted as light (line spectra), correct? Resonance implies the largest absorption and disappearance on the incident photons. In the mechanical world, injecting energy at resonance also implies large energy absorption but a large output mechanical response (not just heat).
Non-resonant, Elastic, Non-dissipative Scattering (which quantum mechanically involves virtual states): for solids and liquids (which are denser than gases) there is ground state,non-resonant elastic scatteringwhich occurs when the incoming light has frequencies which are not resonant. For example, if the incident photon energy is too small to cause an electron excitation to any higher state, the incident photon can still drive the electron cloud into oscillation (without atomic transitions). The atom will remain in its ground state while the cloud vibrates at the frequency of the incident light. The electron, being accelerated, reemits light of the same frequency as the incident light (hence elastic scattering). Each atom becomes an omnidirectional scattering center. Non-resonant elastic scattering accounts for the transmission of light through all transparent materials and reflection of light from surfaces.

Some follow-up questions:
Classically, the two-photon absorption process is a nonlinear process since the EM field intensity must be very strong for it to happen. The strong EM field causes an electronic structure distortion which consequently allows for the absorption of higher frequency (more energetic) photons which would not be absorbed otherwise. Two photons with frequency f can have the same energy as a single photon with frequency 2*f. Is this nonlinear process simply called "two-photon" because single photons of twice the energy (equivalent to two photons) can now be absorbed? Quantum-mechanically, as you explain, the virtual state is converted into a real excited state.

"...This virtual state is not an eigenstate of the Hamiltonian, so it is not stable and quickly decays back to the ground state with re-emission of the photon..."
What happens if a state is indeed an eigenstate of the Hamiltonian? Would the electron/atom remain in that stable state? For how long?

 

[ZapperZ]

Some follow-up questions:
Classically, the two-photon absorption process is a nonlinear process since the EM field intensity must be very strong for it to happen. The strong EM field causes an electronic structure distortion which consequently allows for the absorption of higher frequency (more energetic) photons which would not be absorbed otherwise. Two photons with frequency f can have the same energy as a single photon with frequency 2*f. Is this nonlinear process simply called "two-photon" because single photons of twice the energy (equivalent to two photons) can now be absorbed? Quantum-mechanically, as you explain, the virtual state is converted into a real excited state.

"...This virtual state is not an eigenstate of the Hamiltonian, so it is not stable and quickly decays back to the ground state with re-emission of the photon..."
What happens if a state is indeed an eigenstate of the Hamiltonian? Would the electron/atom remain in that stable state? For how long?

I'm not exactly sure I understand the arguments here.

As someone who has done multiphoton photoemission before, there are two things to consider here:

1. You get such effects only when you are using highly intense light source. And when I say "intense", I mean high photon density per unit area per unit time impinging on the surface of the material.

2. The scattering cross section between, say, single-photon photoemission and 2-photon photoemission, can be different by 3 orders of magnitude, with the 2-photon process being significantly lower in probability (see G. Petite et al., Phys. Rev. B 45, 12210 (1992)).

The mechanism here involves time scales. In a 2-photon process, you have the first photon exciting the electron to some higher, meta-stable state with a very short lifetime. In most cases, this will decay back to a lower state on the order of nanoseconds or shorter. It is only when you have a sufficiently-high photon density source that you will start seeing a significant probability that a second photon will get to this excited electron before it decays.

So no, I don't see how "... strong EM field causes an electronic structure distortion..." is the predominant description of such a process.

Zz.

 

[Ygggdrasil]

Scattering and Absorption from a Classical View
Resonant Dissipative Nonelastic Absorption: In solids and liquids (substances with medium and high density), it is very likely that the absorbed excitation energy (photon) will not be returned as an emitted photon. The absorbed photon will instead be converted into thermal energy (due to random collisions): the photon vanishes and its energy is converted into thermal energy. This conversion of incident photons to thermal energy process is called resonant dissipative (nonelastic) absorption. Only in the case of low-density gases incident photons with resonant frequencies will be absorbed and reemitted as light (line spectra), correct? Resonance implies the largest absorption and disappearance on the incident photons. In the mechanical world, injecting energy at resonance also implies large energy absorption but a large output mechanical response (not just heat).
Non-resonant, Elastic, Non-dissipative Scattering (which quantum mechanically involves virtual states): for solids and liquids (which are denser than gases) there is ground state,non-resonant elastic scatteringwhich occurs when the incoming light has frequencies which are not resonant. For example, if the incident photon energy is too small to cause an electron excitation to any higher state, the incident photon can still drive the electron cloud into oscillation (without atomic transitions). The atom will remain in its ground state while the cloud vibrates at the frequency of the incident light. The electron, being accelerated, reemits light of the same frequency as the incident light (hence elastic scattering). Each atom becomes an omnidirectional scattering center. Non-resonant elastic scattering accounts for the transmission of light through all transparent materials and reflection of light from surfaces.

That explanation seems good to me.

Some follow-up questions:
Classically, the two-photon absorption process is a nonlinear process since the EM field intensity must be very strong for it to happen. The strong EM field causes an electronic structure distortion which consequently allows for the absorption of higher frequency (more energetic) photons which would not be absorbed otherwise. Two photons with frequency f can have the same energy as a single photon with frequency 2*f. Is this nonlinear process simply called "two-photon" because single photons of twice the energy (equivalent to two photons) can now be absorbed? Quantum-mechanically, as you explain, the virtual state is converted into a real excited state

In two-photon absorption, photons of lower frequency (less energetic) are able to cause electronic excitation. Two photons of half the energy required for the electoronic transition are able to drive the transition.

"...This virtual state is not an eigenstate of the Hamiltonian, so it is not stable and quickly decays back to the ground state with re-emission of the photon..."
What happens if a state is indeed an eigenstate of the Hamiltonian? Would the electron/atom remain in that stable state? For how long?

If the state is an eigenstate of the Hamiltonian, you get a real state instead of a virtual state. This real state is much more stable, and its lifetime is defined by the rate of stimulated or spontaneous emission (for fluorescent molecules in aqueous solution, lifetimes for stiumulated emission tend to be on the ns scale).

 

[fog37]

Thank you Ygggdrasil and ZZ.

Sorry to go back to basics but I would to gain the correct understanding of certain important concepts.

Molecules and atoms are quantum mechanical multi-electron system and there is a single and total wavefunction that describes the entire system. This wavefuntion must satisfy the time independent Schroedinger equation. The Hamiltonian operator in SE is the energy operator which contains all the interaction terms (electron-electron, nuclei-electron, nuclei-nuclei, etc.). For mathematical convenience we can apply several simplifications and decompose the complicated total wavefunction so we can focus only on the electrons and introduce the concept of atomic and electronic orbitals. A series of important approximations and simplifications and steps (Born-Oppenheimer, Hartree-Fock, Boys expansions, etc.) lead to the concept of atomic orbitals. Orbitals are presented as different wavefunctions with each orbital hosting two paired electrons as if the system was comprised of several wavefunctions.

1) What does an electron represent in the context of this total wavefunction? Is an electron just a feature of the total system wavefunction? I know an electron is a particle.

2) We learn that when a molecule absorb external incident energy its valence electron jump from one orbital to the next while the other electrons remain undisturbed. In reality, when the molecule absorbs energy the entire wavefunction must be modified, correct?

3) The Stark-Einstein law states that a molecule, regardless of how many electrons it comprises, can only absorb one photon at a time and excite a electron at a time. Is that really what happens? Why? What limits the absorption to one photon at a time?

Thanks!

 

[ZapperZ]

I have a feeling that you might be barking up the wrong tree. Maybe you might want to read this, and possibly references therein:

http://qmlab.ubc.ca/ARPES/PUBLICATIONS/Articles/multiphoton.pdf

Zz.