1. Propagation of polariton fluids and its control Tomas Ostatnický, Alexey V. Kavokin

2. Motivation Spintronics – information stored in spin Need of spin transport and processing Microcavity polaritons: half-photon, half-exciton combination of both, may carry spin and interact promising for spin-optronic circuits ElectronicsPhotonics DiffusiveBallisticPropagation ResistivityLosses ~ 0Interactions ~ 10  m Spin transport

3. Theoretical approach: fluids Assume local thermal equilibrium Thermodynamical description Parameters: density, current, entropy Propagation controlled by static potential and chemical potential

4. Towards superfluidity: multiple fluids Superfluidity in He II explained by L. Landau in terms of two-fluid model Coexistence of two interacting fluids: a normal fraction and a superfluid fraction Mutual interactions much weaker than interactions within fluid fractions

5. Multiple fluids & polaritons (1) Helium atoms Infinite lifetime Constant density One normal fraction Polaritons Finite lifetime Variable density Multiple normal fractions LA-phonon assisted transition rate (depending on QW width)

6. Multiple fluids & polaritons (2) Concept of Landau adapted for polaritons Conservation laws + Navier-Stokes equation + friction + lifetime 4 equations for and S: the last equation is the equation of state Determines potential, pressure and temperature Both superfluid (coherent) and normal fractions present in model

7. Superfluidity of polaritons Expansion of normal componentShock waves in superfluid

8. Polariton circuits (1) 1D quantum wire with single parabolic band One or Two “sources” on sides Variable potential barrier by electric field

9. Polariton circuits (2) Steady-state chemical potential – comparison with electrons Lifetime taken to be infinite Source on the left,  0 on the right

10. Polariton circuits (3) Equilibrium established after t = lifetime Here  = 1 ns

11. Polariton circuits (4) Variable friction Variable lifetime

12. Polariton circuits (5) Two normal fluids from two sources with and without mutual friction

13. Polariton circuits (6) Control by locally applied electric field in normal direction

14. Conclusions Modelling of polariton fluid propagation Superfluidity and coexistence of both fractions included Results of simulations reveal behaviour of polaritons similar to electronics but with some peculiarities Possibility of construction of circuits with propagating polaritons Possibility of dynamical control by external electric field ElectronicsPhotonicsPolaritons DiffusiveBallistic Propagation ResistivityLifetimeLosses ~ 0Interactions ~ 10  m Spin transport