Since the first demonstration of strong exciton-photon coupling in semiconductor microcavities (SMCs), these structures have revealed many unusual properties. Thanks to the half-light/half-matter properties of the resulting quasiparticles or ‘cavity polaritons,’ nonlinear effects such as parametric amplification^{1} and Bose-Einstein condensation^{2} have been observed.

More recently, research on SMCs has moved from completely optical experiments to investigating electrical injection and control, and a room-temperature polariton LED has been realized.^{3} We present here the use of such LED structures for electrical control of polariton interactions and optical gain using electronic tunneling. Control of the polariton-amplification process on picosecond timescales is demonstrated.

For the first time, we introduce double quantum wells (DQWs) into microcavity devices for tunneling control. The sample employed—see Figure 1(a)—comprises a 5λ/2 cavity (where λ is the operational wavelength) containing four sets of 10nm indium gallium arsenide (In_{0.1}Ga_{0.9}As) DQWs separated by 20nm GaAs barriers. This active region is sandwiched between two GaAs/aluminum arsenide distributed-Bragg reflectors to form a Fabry-Perot interferometer that is a few micrometers thick. The top (bottom) mirror is p (n)-doped. The sample is further processed into 400μm mesas that have electrical contacts, thus forming a p-i-n-diode structure.

**Figure 1. **(a) Sample structure incorporating a double quantum well (DQW). (b) Dispersion curves including the uncoupled modes and the lower and upper polariton branches (LPB and UPB, respectively). (c) Close-up of the LPB in (b), revealing the mechanism for parametric scattering. (d) Surface plot of the gain spectra versus the time delay. DBR: Distributed-Bragg reflector. InGaAs: Indium gallium arsenide. GaAs: Gallium arsenide. n+: n-doped. V: Power.

The coupling of excitons and cavity photons gives rise to polariton branches in the dispersion curve: see Figure 1(b). From a close-up of the lower polariton branch (LPB), shown in Figure 1(c), the curve's unusual shape suggests that two pump polaritons sent at the so-called magic angle can scatter into a ‘signal’ polariton at normal incidence and an ‘idler’ polariton at a larger angle, while conserving both energy and wave vector: see Figure 1(c).^{1} This interaction is driven by the exciton's dipole-dipole interactions in the quantum well and is stronger than any other known optical gain. We studied this phenomenon using pump-probe ultrafast spectroscopy. We injected a picosecond pump in resonance with the LPB at the magic angle and measured the parametric scattering of the signal with a broadband 150fs probe pulse sent at normal incidence. All measurements were performed at a temperature of 8K to ensure stability of the excitons and, therefore, of the strong-coupling regime. Above a certain pump threshold, a massive probe gain of up to a factor of several hundred for around 3ps is observed at the lower polariton energy: see Figure 1(d).

By biasing our p-i-n diode structure we can apply an electric field to the central insulating cavity region. This allows control of the electronic levels in the quantum wells thanks to the quantum-confined Stark effect. In particular, the results of simulations—see Figure 2(a)—show that, for an applied electric field of 11.4kV/cm, the energy separation between the left- and right-quantum-well (LQW, RQW) first energy levels is exactly equal to the longitudinal-optical (LO) phonon energy. In this resonance condition, electrons in the LQW can tunnel to the RQW, thus leading to an increased electron population. Their tunneling rate is dependent on the ratio between the different time constants shown in Figure 2(a). Currently, we estimate that the percentage of electrons that tunnel from the LQW into the RQW is (1+τ_{t}τ_{c}) ^{−1}__~__20%. Here τ_{t} is the time constant for tunneling from the LQW to the RQW and τ_{c} is the photon cavity lifetime. This process is followed by extremely rapid LO-phonon emission, which has a time constant of τ_{LO}=100fs. The LO-phonon emission is considerably faster than the tunneling escape from the RQW (for which the time constant τ_{o}=230fs), which means that 70% of the electrons drop into the ground state of the RQW, where they remain for τ_{e}=180ns. The extra electrons in the LQW are very efficient polariton scatterers thanks to their lighter effective mass. Important consequences for the parametric amplification are therefore expected in this condition.

**Figure 2. **(a) Calculated band edges for the left and right quantum well (LQW, RQW) in an electric field, F=11.4kV/cm. The probability densities for the lowest energies are shown in red. Blue/brown arrows show carrier/polariton processes. τ_{t}, τ_{o}, τ_{e}, τ_{LO}, τ_{c}, τ_{Ω}: Time constants for tunneling from LQW to RQW, tunneling from the RQW, lifetime in the RQW's ground state, photon cavity lifetime, Rabi flopping. LP: Lower polariton. (b) Parametric-gain peak value as a function of bias.

Figure 2(b) displays the effect of this electrical control on parametric scattering, showing the peak parametric gain as a function of the applied bias. A sharp gain dip (a reduction by over 90% for a bias change of 100mV) is observed at a bias of 0.73V. This corresponds to an internal electric field of 9.9kV/cm, which is in reasonable agreement with simulations that give 11.4kV/cm for LO-phonon-assisted tunneling. Modification of the polariton-polariton interactions by the extra electron population therefore allows rapid control of the parametric gain.^{4}

In conclusion, we have demonstrated an original way to control parametric gain in semiconductor microcavities incorporating DQWs. Stark tuning and resonant tunneling between neighboring quantum wells allows dramatic changes in the strong-coupling-induced optical gain for minimal applied-bias changes. As the mechanism involves Stark tuning, ultrafast switching speeds are expected, with similar loss of control to that in intersubband modulators. In addition, we suggest that spatial control and quantum entanglement of polaritons in microcavities might be possible using spatially localized electron tunneling. Our next steps are to use asymmetric DQWs in which the ground states of the two quantum wells can be tuned into resonance, creating a new type of oriented polariton that has greatly enhanced nonlinear interactions.^{5}

*This work was supported by the UK's Engineering and Physical Sciences Research Council through grants EP/C511786/1 and EP/F011393 and by the European Union project ‘Exciton polaritons: physics and applications’ (CLERMONT4).*

Jeremy Baumberg, Gabriel Christmann

NanoPhotonics Centre Cavendish Laboratory

University of Cambridge

Cambridge, UK

References:

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G. Christmann, C. Coulson, J. J. Baumberg, N. T. Pelekanos, Z. Hatzopoulos, S. I. Tsintzos, P. G. Savvidis, Control of polariton scattering in resonant-tunneling double-quantum-well semiconductor microcavities, *Phys. Rev. Lett*. 84 (7), pp. 1547-1550, 2000.