The possibilities offered by Bose–Einstein condensation for investigating the quantum world continue to stretch the ingenuity of physicists. Quasiparticles known as excitons have become promising subjects for research.
The first Bose–Einstein condensate using atomic gases was created in 1995. This achievement, initially with rubidium, was made possible by the design of appropriate magnetic traps to hold the atoms, and the development of sophisticated cooling techniques1. Work on producing a new kind of condensate — this time, using 'excitons' — has so far produced controversial results. But on page 47 of this issue, Butov et al.2 provide firm evidence that high-density 'lakes' of cold excitons can be created in a semiconductor — a crucial step on the way to making an exciton Bose–Einstein condensate.
Excitons are quasiparticles: in semiconductors, electrons can be excited from the valence band to the conduction band using optical fields; this conduction electron is attracted, through the Coulomb interaction, to the positively charged hole left behind in the valence band. As a result, the electron and hole form a bound state called an exciton. Like a rubidium atom, this neutral bound complex can behave as a boson — a particle with integer spin which obeys Bose–Einstein statistics. When the temperature of a boson gas drops below a certain value, a large number of bosons 'condense' into a single quantum state — this is a Bose–Einstein condensate (BEC). All of these bosons then behave in exactly the same way, and quantum-mechanical effects become visible at a macroscopic level. Such collective boson behaviour gives rise to phenomena such as frictionless flow, or superfluidity, and quantum interference.
Several semiconductor systems have been investigated3 for evidence of an exciton BEC, with mixed results. Excitons have much lower mass than the atoms typically used to make BECs. This means that an exciton BEC can form at higher temperatures (although still only around the 1 K mark). The problem is that excitons exist only for a short time, just a few nanoseconds, before the electron and hole recombine. So it is difficult to create a 'gas' — a Bose gas — of excitons that is cold and dense enough to condense within this short time.
Butov's group addressed this problem in earlier work4. They studied excitons confined in a quantum well, an artificially grown two-dimensional structure of the semiconductors GaAs and AlGaAs. Such excitons can move freely only parallel to the quantum-well plane, and cannot move up and down in the perpendicular direction (the z-axis in Fig. 1a). Butov and colleagues designed a coupled quantum-well system in which 'indirect' excitons form when an electric field is applied in this perpendicular direction (Fig. 1b). This field pulls the oppositely charged electron and hole apart, trapping them tightly in the corners of their quantum wells. This reduces the spatial overlap of the electron and hole wavefunctions, with the result that the recombination rate is suppressed and the exciton lifetime increased. So indirect excitons have more time to cool down.
There is another advantage to using indirect excitons. Usually excitons are cooled through scattering with acoustic phonons (the quantized lattice vibrations in the semiconductor system). For quantum-well excitons, the cooling effect can happen up to a thousand times faster than for unconfined excitons. Butov et al.4 showed that the combination of these two effects can produce a gas of excitons that displays Bose statistics — the first step on the way to making an exciton BEC.
The next step is to confine the excitons sufficiently to make them condense. As the thermal energy decreases, a Bose gas condenses when the characteristic length at which quantum phenomena occur (the de Broglie wavelength) becomes comparable to the distance between particles. Confining a Bose gas in all directions decreases the interparticle distance and thus raises the value of the critical temperature at which condensation happens1,5.
In their new work2, Butov et al. observed the trapping of excitons in all three directions, within a radius of several micrometres (Fig. 1c). To achieve this, they took advantage of the natural potential wells that form within the plane of a quantum-well system. These wells are caused by the disorder in the system, which leads to random fluctuations in the potential energy. The excitons seek the regions of minimum potential energy, and eventually accumulate inside the bottom of the deepest potential trap. This trapping creates dense 'lakes' of cold excitons and, in combination with the small exciton mass, increases the condensation temperature to around 1 K — much higher than the critical temperature in atomic systems. Although Butov et al. haven't yet made an exciton BEC, the development of this trapping technique paves the way to creating exciton condensates in semiconductors.
Such condensates would open up exciting possibilities for observing and manipulating quantum properties, including coherence. On the technical side, researchers are mastering the art of growing high-quality GaAs/AlGaAs nanostructures, and advances in nanotechnology mean that arrays of exciton traps with novel quantum mechanical properties could now be engineered.
Quantum-well excitons are renowned for their linear and nonlinear optical properties6, and the quantum coherence in an exciton condensate could reveal novel optical effects and nonlinear optical dynamics, as all condensed excitons emit light in tandem. Ultimately, there could be applications in ultrafast digital logical elements and quantum computing. But in the meantime, an exciton BEC is an ideal system for studies of non-equilibrium quantum mechanics at the frontier of condensed-matter physics.
Pethick, C. J. & Smith, H. Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002).
Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. & Chemla, D. S. Nature 417, 47–52 (2002).
Griffin, A., Snoke, D. W. & Stringari, S. Bose–Einstein Condensation of Excitons and Biexcitons (Cambridge Univ. Press, 1995).
Butov, L. V. et al. Phys. Rev. Lett. 86, 5608–5611 (2001).
Trauernicht, D. P., Wolfe, J. P. & Mysyrowicz, A. Phys. Rev. B 34, 2561–2575 (1986).
Chemla, D. S. & Shah, J. Nature 411, 549–557 (2001).
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Bose-Einstein Condensation of Excitons in Planar Systems and Superconductive Phase Transition Temperature
Journal of Superconductivity and Novel Magnetism (2015)