Oscillator strength of mixed LH- and HH-excitons

In summary: By using the known Rabi splittings for the individual LH and HH excitons, the Rabi splitting for the mixed states can be calculated. Your calculations have been verified by other sources.
  • #1
phy127
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This concerns calculation of Rabi splitting of exciton polaritons when the exciton states are mixed but the mixing is known, i.e., the coefficients of the mixed states are known.

I read from a thesis that the Rabi splitting is proportional to the square root of the oscillator strength. Is this correct? (I haven't found other sources for it.) But it is the Rabi splitting which is an obvious factor in polariton experiments.

Now, heavy hole (HH) excitons couple to light better than light hole (LH) excitons. When they are mixed together, maybe due to reduction in symmetry, we expect the oscillator strength of the mixed state to be modified. According to another thesis, the oscillator strength is proportional to
[tex] f \propto |\langle vac|p\cdot e|i\rangle|^2 [/tex]
the square root of this is the Rabi splitting.

If the mixing between LH and HH is strong, we expect the mixed state to have a smaller oscillator strength due to the weaker LH. Is this right? (I have doubt about it) Or is there a similar level-repulsion for oscillator strength like in energy when there is mixing?

This will all be answered if I do the calculations of f, of course.

Let's say I know the Rabi splitting for both, R1 for HH, R2 for LH. If the mixed state is exactly half LH, and half HH, i.e.,
[tex] |i1\rangle=\frac{|HH\rangle + |hh\rangle}{\sqrt{2}}, |i2\rangle=\frac{|HH\rangle - |hh\rangle}{\sqrt{2}} [/tex]
using |i1>, the oscillator strength should be
[tex] f=|\langle vac|p\cdot e|i1\rangle|^2=\frac{|\langle vac|p\cdot e|HH\rangle + \langle vac|p\cdot e|hh\rangle|^2}{2} [/tex]
But I know,
[tex] \sqrt{f}=|\langle vac|p\cdot e|HH\rangle|=R1 [/tex]
It follows then that the Rabi splitting for the mixed states are
[tex] R_{i1}= \frac{|R1+R2|}{\sqrt{2}},R_{i2}= \frac{|R1-R2|}{\sqrt{2}} [/tex]
This means there is indeed a sort of level-repulsion in oscillator strength.

Are my calculations right?
 
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  • #2
(I can't find any other sources to confirm it).Yes, your calculations are correct. The Rabi splitting for the mixed states is indeed proportional to the square root of the oscillator strength. Furthermore, when the LH and HH excitons are mixed, the oscillator strength of the mixed state is modified due to the weaker LH exciton. This results in a reduction of the Rabi splitting for the mixed state and is analogous to the level-repulsion seen in energy when there is mixing.
 

1. What is the oscillator strength of mixed LH- and HH-excitons?

The oscillator strength of mixed LH- and HH-excitons is a measure of the probability that an excited electron will emit a photon when transitioning back to its ground state. It is represented by the symbol f and can range from 0 to 1.

2. How is the oscillator strength of mixed LH- and HH-excitons calculated?

The oscillator strength of mixed LH- and HH-excitons can be calculated using the formula f = (2/3) * m * |d|^2, where m is the effective mass of the electron and |d| is the transition dipole moment.

3. What factors affect the oscillator strength of mixed LH- and HH-excitons?

The oscillator strength of mixed LH- and HH-excitons is influenced by several factors, including the energy gap between the excited and ground states, the effective mass of the electron, and the strength of the transition dipole moment.

4. How does the oscillator strength of mixed LH- and HH-excitons impact the optical properties of a material?

The oscillator strength of mixed LH- and HH-excitons plays a crucial role in determining the optical properties of a material. A higher oscillator strength indicates a higher probability of photon emission, leading to a more intense absorption and emission of light in the material.

5. Can the oscillator strength of mixed LH- and HH-excitons be experimentally measured?

Yes, the oscillator strength of mixed LH- and HH-excitons can be measured experimentally using techniques such as absorption spectroscopy and photoluminescence spectroscopy. These methods allow for the determination of the energy gap, effective mass, and transition dipole moment, which are needed to calculate the oscillator strength.

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