Superconductors, lasers, and Bose-Einstein condensates combined into a common macro quantum effect

Superconductors are one of the most remarkable phenomena in physics, with amazing technological implications. Some of the technologies that would not be possible without superconductivity are extremely powerful magnets that levitate trains and MRI machines used to image the human body. The reason that superconductivity arises is now understood as a fundamentally quantum mechanical effect.

The basic idea of quantum mechanics is that at the microscopic scale everything, including matter and light, has a wave property to it. Normally the wave nature is not noticeable as the waves are very small, and all the waves are out of synchronization with each other, so that their effects are not important. For this reason, to observe quantum mechanical behavior experiments generally have to be performed at a very low temperature, and at microscopic length scales.

Superconductors, on the other hand, have a dramatic effect in the disappearance of resistance, changing the entire property of the material. The key quantum effect that occurs is that the quantum waves become highly synchronized and occur at a macroscopic level. This is now understood to be the same basic effect as that seen in lasers. The similarity is that in a laser, all the photons making up the light are synchronized, and appear as one single coherent wave. In a superconductor the macroscopic wave is for the quantum waves of the electrons, instead of the photons, but the basic quantum feature is the same. Such macroscopic quantum waves have also been observed in Bose-Einstein condensates, where atoms cooled to nanokelvin temperatures all collapse into a single state.

Up until now, these related but distinct phenomena have only been observed separately. However, as superconductors, lasers, and Bose-Einstein condensates all share a common feature, it has been expected that it should be able to see these features at the same time. A recent experiment in a global collaborative effort with teams from Japan, the United States, and Germany have observed for the first time experimental indication that this expectation is true.

Energy diagrams of the dressed states in the two level emitter (A) and the e–h–p dispersion (B). In the left panel of (B), the dipole coupling to the cavity photons and the e–h attractive Coulomb interactions are neglected, while it is include in the right panel. In this case, the electron band (the solid blue curve) is mixed with the +ω0-shifted hole band (the dashed red curve). In the same manner, the hole band (the solid red curve) is mixed with the −ω0-shifted electron band (the dashed blue curve). The triplet spectrum is formed in a certain wavenumber regime, where the valence band of the n + 1 total excitation numbers and the conduction band of the n coincide.

Nature Scientific Reports – High-energy side-peak emission of exciton-polariton condensates in high density regime

They tackled this problem by highly exciting exciton-polaritons, which are particle-like excitations in a semiconductor systems and formed by strong coupling between electron-hole pairs and photons. They observed high-energy side-peak emission that cannot be explained by two mechanisms known to date: Bose-Einstein condensation of exciton-polaritons, nor conventional semiconductor lasing driven by the optical gain from unbound electron hole plasma.

By combining the experimental data with their latest theory, they found a possibility that the peak originates from a strongly bound e-h pairs, which can persist in the presence of the high-quality optical cavity even for the lasing state. This scenario has been thought to be impossible since an e-h pair experiencing weakened binding force due to other electrons and/or holes breaks up in high-density. The proposed scenario is closely related to the BCS physics, which was originally introduced by John Bardeen, Leon Cooper, and John Robert Schrieffer to explain the origin of superconductivity. In the BCS theory, the superconductivity is an effect caused by a condensation of weakly bound electron pairs (Cooper pairs). In the latest theory of e-h pairs plus photons (e-h-p), bound e-h pairs’ survival can be described in BCS theory of e-h-p system as an analogy of Cooper pairs in superconductivity.

“Although a full understanding of this observation has not yet been reached,” said Dr. Tomoyuki Horikiri at Yokohama National University, and one of the authors on the study. “The discovery provides an important step toward the clarification of the relationship between the BCS physics and the semiconductor lasers. The observation not only deepens the understanding of the highly-excited exciton-polariton systems, but also opens up a new avenue for exploring the non-equilibrium and dissipative many-body physics. In such practical application studies, there are still many quantum foundational questions.”


In a standard semiconductor laser, electrons and holes recombine via stimulated emission to emit coherent light, in a process that is far from thermal equilibrium. Exciton-polariton condensates–sharing the same basic device structure as a semiconductor laser, consisting of quantum wells coupled to a microcavity–have been investigated primarily at densities far below the Mott density for signatures of Bose-Einstein condensation. At high densities approaching the Mott density, exciton-polariton condensates are generally thought to revert to a standard semiconductor laser, with the loss of strong coupling. Here, we report the observation of a photoluminescence sideband at high densities that cannot be accounted for by conventional semiconductor lasing. This also differs from an upper-polariton peak by the observation of the excitation power dependence in the peak-energy separation. Our interpretation as a persistent coherent electron-hole-photon coupling captures several features of this sideband, although a complete understanding of the experimental data is lacking. A full understanding of the observations should lead to a development in non-equilibrium many-body physics.


They have performed a study of high density exciton-polariton condensates towards the Mott density and observed a high-energy sideband PL. We have compared this to a theory of non-equilibrium e-h-p system, generalizing polariton BCS theory to the non-equilibrium regime. After the comparison, several disagreements between our experiment and theory still exist. We point out that this theory is only one possible explanation of the physics observed in our experiment. Further work would be required to show that the observations are consistent with other possible explanations, some of which are discussed below.

Here, they add some discussions on the discrepancy between the theory and experiments, and mention some important factors and the effects which are neglected in our model. One is the observed relaxation dynamics after a pulse excitation, while the theory is dealing with the stationary state. Therefore, whether the stationary condition is fulfilled remains questionable. If the relaxation time to the (transient) stationary state (corresponding to Time ~100 ps) is taken into account, the high-energy peak emission could be enhanced, since the carriers initially supplied from the high-energy region. Dephasing omitted in our mean-field theory is known to enhance the emission from off-resonant modes (the side-peak emission in our case) in cavity-QED research. It is also well-known to destroy coherence and reduce the gap (the peak separation in our case) in the condensed matter research. Besides, the spontaneous emission from the quantum wells directly into free space was also neglected in our theory. Taking all these effects into account in the theory might reduce the large quantitative discrepancy from the experimental results, which is far beyond the scope of this paper.

One may seek for the origin of the high-energy side peak by other explanations different from our coherent e-h-p coupling scenario. In particular, the single-emitter Mollow triplet in the presence of detuning and dephasing has been shown to give an asymmetric Mollow spectrum. However, our experiments were performed at high densities towards the Mott density. Therefore, it is essential to take into account of the underlying Fermionic nature of the electrons and holes together with their Coulomb interaction. While a single-emitter Mollow triplet under suitable conditions may have superficial similarities, we believe that it is less plausible than the theoretical analysis we have presented in this work.

Another scenario would be for instance that the upper energy peak could be the band to band transition, with the lower energy peak being the bare cavity mode. We believe that it is unlikely that the band-edge emission account for the upper energy peak as the renormalized band edge is lower in energy than the cavity resonance (=QW exciton resonance) in this high density regime. In contrast, the Fermi-edge emission, which was actually observed in Kim et al. in highly-excited semiconductor QWs without coupling to a cavity by using a streak camera, can be a possible candidate for our upper energy peak. For this scenario, the Fermi-edge should lower as time proceeds due to the radiation decay, hence, the emission energy should show a red shift, e.g., from 1.622 eV to 1.612 eV. In this case, there are two possibilities: (i) the red shift of the Fermi-edge emission energy is very fast and occurs within the time resolution of our streak camera. This could be possible because the radiative decay rate should be higher than Kim et al. in our system with the microcavity and higher excitation density. (ii) the red shift of the emission energy occurs in a time scale longer than the time-resolution. In the former case (i), the observed PL spectra at the emission time should consist of a strong emission at cavity energy 1.612 eV plus a broad tail spread between 1.622 eV and 1.612 eV, which is quite different from the observed PL spectra with clear two peaks. Thus, this possibility can be safely excluded. In the latter case (ii), the red shift should have been observed by our streak camera. However, our experimental data does not exhibit such red shift, at any pump power with a well-defined side peak. Therefore, the latter possibility is also excluded. In either case, the Fermi-edge emission does not account for the observed high-energy side peak.

On the other hand, this absence of the red shift of the high-energy peak does not contradict with our coherent e-h-p coupling scenario. In our theory, the high-energy peak emission occurs only if the Fermi-edge (=μB − μ, measured from the main emission) is close to the gap energy, whereas the gap energy robustly stays at the same energy position as long as the strong main peak emission exists (the intensity ~κ |a0|2). As time proceeds, the Fermi-edge is quickly lowered and detuned from the gap energy. This violates the requirement for the emission to occur, resulting in a sudden quench of the upper energy emission.

SOURCES – Nature Scientific Reports, Chapman’s Insititute for Quantum Studies