David W. Snoke

Bose-Einstein Condensation of Microcavity Polaritons in a Trap

We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.

Long-range transport in excitonic dark states in coupled quantum wells

During the past ten years, coupled quantum wells have emerged as a promising system for experiments on Bose condensation of excitons, with numerous theoretical and experimental studies aimed at the demonstration of this effect. One of the issues driving these studies is the possibility of long-range coherent transport of excitons. Excitons in quantum wells typically diffuse only a few micrometres from the spot where they are generated by a laser pulse; their diffusion is limited by their lifetime (typically a few nanoseconds) and by scattering due to disorder in the well structure. Here we report photoluminescence measurements of InGaAs quantum wells and the observation of an effect by which luminescence from excitons appears hundreds of micrometres away from the laser excitation spot. This luminescence appears as a ring around the laser spot; almost none appears in the region between the laser spot and the ring. This implies that the excitons must travel in a dark state until they reach some critical distance, at which they collectively revert to luminescing states. It is unclear whether this effect is related to macroscopic coherence caused by Bose condensation of excitons.

Polariton lasing vs. photon lasing in a semiconductor microcavity

Nearly one decade after the first observation of Bose–Einstein condensation in atom vapors and realization of matter-wave (atom) lasers, similar concepts have been demonstrated recently for polaritons: half-matter, half-light quasiparticles in semiconductor microcavities. The half-light nature of polaritons makes polariton lasers promising as a new source of coherent and nonclassical light with extremely low threshold energy. The half-matter nature makes polariton lasers a unique test bed for many-body theories and cavity quantum electrodynamics. In this article, we present a series of experimental studies of a polariton laser, exploring its properties as a relatively dense degenerate Bose gas and comparing it to a photon laser achieved in the same structure. The polaritons have an effective mass that is twice the cavity photon effective mass, yet seven orders of magnitude less than the hydrogen atom mass; hence, they can potentially condense at temperatures seven orders of magnitude higher than those required for atom Bose–Einstein condensations. Accompanying the phase transition, a polariton laser emits coherent light but at a threshold carrier density two orders of magnitude lower than that needed for a normal photon laser in a same structure. It also is shown that, beyond threshold, the polariton population splits to a thermal equilibrium Bose–Einstein distribution at in-plane wave number k∥ > 0 and a nonequilibrium condensate at k∥ > 0, with a chemical potential approaching to zero. The spatial distributions and polarization characteristics of polaritons also are discussed as unique signatures of a polariton laser.

Coherent Exciton Waves

Excitons are electrically neutral energetic pairs of electrons and holes, created by the absorption of photons in a solid. These energy-carrying pairs can be used to produce light for microscopes and are used by plants to collect sunlight for photosynthesis. In his Perspective, Snoke describes work carried out at Ecolé Polytechnique in Palaiseau, France, and the University of Ottawa, Canada, in which excitons were produced by stimulated emission. Such processes may someday be used to create a laserlike source of excitons.

Bose–Einstein condensation of excitons in Cu2O: progress over 30 years

Experiments on Bose-Einstein condensation (BEC) of excitons in the semiconductor Cu2O started over 30 years ago, as one of the first serious attempts at exciton BEC. Early claims were based on spectroscopic signatures and transport data which have since been reinterpreted, in large part because the Auger recombination process for excitons was not well understood. Understanding of the Auger process has advanced, and recent experiments have made significant progress toward exciton BEC. We review the history of experiments on exciton BEC in Cu2O, the Auger recombination process, and the prospects for observing exciton BEC in this system in the near future.

Long-distance diffusion of excitons in double quantum well structures.

In this Letter we report on lateral diffusion measurements of excitons at low temperature in double quantum wells of various widths. The structure is designed so that excitons live up to 30 micros and diffuse up to 500 microm. Particular attention is given to establishing that the transport occurs by exciton motion. The deduced exciton diffusion coefficients have a very strong well width dependence, and obey the same power law as the diffusion coefficient for electrons.

Simulating evolution by gene duplication of protein features that require multiple amino acid residues.

Gene duplication is thought to be a major source of evolutionary innovation because it allows one copy of a gene to mutate and explore genetic space while the other copy continues to fulfill the original function. Models of the process often implicitly assume that a single mutation to the duplicated gene can confer a new selectable property. Yet some protein features, such as disulfide bonds or ligand binding sites, require the participation of two or more amino acid residues, which could require several mutations. Here we model the evolution of such protein features by what we consider to be the conceptually simplest route—point mutation in duplicated genes. We show that for very large population sizes N, where at steady state in the absence of selection the population would be expected to contain one or more duplicated alleles coding for the feature, the time to fixation in the population hovers near the inverse of the point mutation rate, and varies sluggishly with the λth root of 1/N, where λ is the number of nucleotide positions that must be mutated to produce the feature. At smaller population sizes, the time to fixation varies linearly with 1/N and exceeds the inverse of the point mutation rate. We conclude that, in general, to be fixed in 108 generations, the production of novel protein features that require the participation of two or more amino acid residues simply by multiple point mutations in duplicated genes would entail population sizes of no less than 109.

Stretching quantum wells: A method for trapping free carriers in GaAs heterostructures

We have demonstrated a method of using inhomogeneous stress to create an in-plane harmonic potential in GaAs quantum wells which works equally well for excitons and for free conduction electrons. The depth of the well can be continuously varied via an external control. This essentially provides a type of gate for controlling the motion of carriers, e.g., a two-dimensional electron gas, without using electric field.

Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory.

Actively tuned and spatially trapped polaritons

We report active tuning of the polariton resonance of quantum well excitons in a semiconductor microcavity using applied stress. Starting with the quantum well exciton energy higher than the cavity photon mode, we use stress to reduce the exciton energy and bring it into resonance with the photon mode. At the point of zero detuning, line narrowing and strong increase of the photoluminescence are seen. By the same means, we create an in-plane harmonic potential for the polaritons, which allows trapping, potentially making possible Bose-Einstein condensation of polaritons analogous to trapped atoms. We demonstrate drift of the polaritons into this trap.