Spin, pseudo-spin or whatelse? (cavity)Polariton polarimetry question

[dchafatinos]

Hi, this is my first thread :)

I am doing my PhD about polariton in microcavities. I was just reading about the polarization of polaritons (a cuasi-particle mixing photons with semiconductors excitons) in GaAlAs microcavities. So a lot of concepts appear: pseudo-spin, chiriality, TE-TM splitting, etc...

I understand the Stoke vector summarize all of them (pseudo-spin in plane, and spin or chiriality out of plane). But I don't understand the conection between Stoke vector and the spin of exciton (or the hole-electrons). Is it correct think in this conection?

 

[Cthugha]

I assume that you are talking about quantum well microcavity polaritons. In that case, the QW excitons consist of holes (spin 3/2) and electrons (spin 1/2), which may team up to form optically dark excitons (spin +2 or -2) and bright excitons (spin +1 and -1). Of course you need to choose a quantization axis, but in quantum wells, this is simple. QWs are effective 2D systems, so you consider the projection on the structure axis.

The bright excitons may then couple to circularly polarized photons in the microcavity and form polaritons. This is one component of the Stokes vector. However, you could shoot linearly polarized light into the cavity. Linearly polarized light is a superposition of the two circularly polarized modes. Depending on the relative phase, you may get horizontally or vertically polarized light. Accordingly, you will be able to create polaritons which contain a superposition of spins with +1 and -1. This is another component of the Stokes vector. Finally, you may also use diagonally polarized light. This may, e.g., be realized as a superposition of horizontal and vertical light. This will also result in superpositions of spins +1 and -1. However, the relative phase will be different. This is another component of the stokes vector.

Taken together, the Stokes vector tells you about the full pseudospin of your polaritons. For example, if you put a circular polarization filter in the path of the light leaking out of your cavity and you find that the transmission for left-circularly and right-circularly polarized light is the same, you might have a 50%/50% incoherent mixture of spin +1 and spin -1 polaritons in your cavity or you might have linearly polarized polaritons which are a coherent superposition of spin +1 and -1. Measuring the full Stokes vector (in the circular, linear and diagonal basis) tells you the difference.

This is for example important when TE-TM splitting comes into play. This splits the energies of the +1/- polaritons at finite wavevector and thus rotates the pseudospin of movinf polaritons depending on their propagation direction and velocity. This may give rise to fancy effects, such as the optical spin Hall effect for polaritons.

 

[dchafatinos]

Thanks a lot! Very nice explication.

I don't understand the last part:

This is for example important when TE-TM splitting comes into play. This splits the energies of the +1/- polaritons at finite wavevector and thus rotates the pseudospin of movinf polaritons depending on their propagation direction and velocity. This may give rise to fancy effects, such as the optical spin Hall effect for polaritons.

If the TE TM splitting just occurs by the spin of polariton (+-1), and the chiriality of photons also can induce an optical Zeeman splitting energy in the polariton level. How can I understand each effect? What is the principal difference?

 

[Cthugha]

It is not exactly clear to me what you mean by "the chirality of photons also can induce an optical zeeman splitting energy". Usually, it is the other way round. You introduce some effect that acts as an effective Zeeman splitting and the polaritons will acquire some kind of circular polarization. However, there are a lot of ways to achieve that. The basic fundament for most of them is that the polariton-polariton interaction is spin-anisotropic: polaritons with the same pseudospin repel each other, while polaritons of opposite spin attract each other very weakly (about 1/10 of the repulsive interaction). Accordingly, any population imbalance in the spin species results in an effective energy shift of the polariton levels, which resembles a Zeeman splitting. This can be achieved in many ways. For example, spin-polarized non-resonant excitation will also result in a spin-dependent level shift as the polariton-exciton interaction is also spin-anisotropic. There was a recent paper by the Amo group showing that.

Now what is the difference to the TE-TM splitting? The TE-TM splitting also gives rise to an energy splitting. However, this is a splitting between the linear polarization modes of the cavity and it depends on the wavevector: the splitting gets larger for larger k. . If you do the math, you will find that while the energy splitting in the circularly polarized modes discussed above can be mapped to an effective magnetic field pointing along the growth axis of the sample (that would give rise to a Zeeman splitting, I will call this direction the z-axis), a splitting in the linearly polarized modes can be mapped to an effective magnetic field that is oriented inside the sample plane (the x-y plane) and it depends strongly on the wavevector of the polaritons. This means that polaritons propagating along different directions will see a different effective magnetic field. The latter insight was one of Alexey Kavokin's early insights on polaritons. Alexey published it in Phys. Rev. Lett. 95, 136601 (2005).

 

[dchafatinos]

Cthugha lot of thanks! Your explanation clarified several concepts and thinkings-way for me.