In a recent study in Nature, an international team of researchers demonstrates theoretically and experimentally the capabilities that solid-state simulators could have in reproducing peculiar states of matter by mimicking electronic behaviour and observing their outcomes. Quantum simulation with excitons

Simple Quantum-Mechanical Models

To describe matter on a microscopic level, physicists rely on very simple quantum-mechanical models. Amongst the most famous of these is the Hubbard model in which quantum particles hop between neighbouring lattice sites, and repel each other when they are at the same site.

Emergence of Macroscopic Behavior

Intriguing macroscopic behaviour can emerge even from this very simple model: if the interaction is dominant, particles tend to isolate on individual sites, and if the number of particles equals the number of sites (or a multiple thereof), the interactions turn the system into an insulating phase known as the Mott state. On the other hand, if the hopping is dominant, particles tend to spread over many sites, giving rise to metallic or even superfluid behaviour (where all atoms form a coherent wavepacket spread over the lattice and forms a non-viscous state of matter).

Extended Interactions and Checkerboard Configuration

More scenarios become possible if interactions act over extended ranges, i. e. particles to repel each other at longer distances. A striking effect of these longer-range interactions is the possibility of stabilization of an insulating phase distinct from the Mott phase, when only half of the sites are occupied. The particles then seek a so-called “checkerboard” configuration in which every second site remains empty on a bipartite periodic structure like a square lattice.

Experimental Observation of Excitonic Phases

For the first time, experimental observations of such a phase of quasi-particles, known as excitons (a bound state of an electron and a hole), have now been witnessed by experimentalists Camille Lagoin and ICFO alumnus François Dubin, from CNRS and Sorbonne Université, in collaboration with theoretical researchers and OPTOlogic partners Utso Bhattacharya, Tobias Grass, Tymoteusz Salamon and ICREA Professor Maciej Lewenstein, from ICFO, Ravindra Chhajlany from Institute of Spintronics and Quantum Information of the Adam Mickiewicz University, and Markus Holzmann from CNRS and Université Grenoble. In their study, the team of researchers have been able to observe this phenomenon by optically exciting a semiconductor sample fabricated in PRISM by Kirk Baldwin and Loren Pfeiffer, from Princeton University. The results have been published in Nature.

Experimental Setup

In this study, a laser pulse injects electrons and holes in two coupled GaAs quantum wells. The spatially-separated and oppositely charged particles then attractively bind together to form a composite particle called an exciton, with an electric dipole moment pointing from the hole to the electron. This dipole moment, through the dipolar forces, makes individual excitons feel each other, even if they are far apart. Additionally, gate electrodes at the surface imprint a square lattice potential for these excitons. These ingredients make the system well represented by a generalized Hubbard model with an extended range of interactions.

Experimental Findings

Cooling down to a temperature of 300 milli-Kelvin (mK) reveals suppressed compressibility of the system, providing evidence of the sought-after insulating phase in the half-filled lattice. Advanced multi-orbital theoretical modeling reveals the presence of the checkerboard pattern. Entering this regime constitutes a well-identified research advancement, where quantum particles spontaneously break the lattice symmetry and arrange themselves into a crystalline structure distinct from the underlying lattice. By tuning the exciton density per site, the experiment also reveals the existence of the incompressible Mott phase at unitary filling. Thus, varying the filling, which serves as a tuning parameter, allows tracing the competition between various insulating phases at finite temperatures.

Potential for Exotic Phases

An important difference between electrons and excitons could allow in the future to reach even more exotic phases: while electrons are so-called fermions (particles that cannot simultaneously occupy the same quantum state according to the Paul exclusion principle) excitons are bosons, and hence can form a condensate, like Cooper pairs of electrons in superconductivity, Helium-4 atoms forming superfluids, or some atomic gases forming Bose Einstein condensates. At very low temperatures, still not attained so far, the three key ingredients: 1) excitons’ ability to condense, 2) the surrounding lattice potential, and 3) the long-range interactions between excitons, may conspire to give rise to a striking “supersolid” phase, in which the constituents would simultaneously show crystalline order (like in a solid) and flow without viscosity (like in a superfluid).

Future Directions and Impact

Thus, the observations achieved by this study highlight the ability of dipolar excitons to enable a controlled environment for the quantum simulation of the “Extended Bose-Hubbard model” at 300 mK.  Lowering this temperature to around 10 mK is within experimental reach and an objective for the near future, and will allow the long-coveted lattice supersolids to be expected as a stable phase of matter. By further exploiting the excitons’ orbital and spin degrees of freedom in the lattice, more exotic phases like multi-component supersolids may also be feasible. The experimental achievement attained in this study sets a major step forward and establishes a milestone in research in atomic to condensed matter physics, opening the door to staggering possibilities for the future.

The European OPTOlogic project held its first in-person CGA meeting in Benasque, Huesca, at the “Pedro Pascual” Science Center on March 9th and 10th, 2023. Notably, ICREA Professor of ICFO Dr. Jens Biegert and project manager Judith Salvador from ICFO organized the successful meeting to unite the entire project consortium. The primary objectives of the meeting were threefold: first, to share updates on each work unit’s current status and progress; second, to present and learn about the diverse results and latest advancements; and finally, to foster discussions to exchange ideas and find solutions to complex challenges in the project’s final stages.

Furthermore, this CGA meeting marked a significant milestone as the consortium’s first in-person gathering since the project began in September 2020. The productive two-day event provided a valuable platform for consortium members to engage in discussions and collaboratively address potential theoretical and experimental changes. Consequently, these in-depth conversations and collaborative efforts were crucial for ensuring the project’s continued success and advancement towards its ultimate goals. Moreover, the meeting fostered a sense of community and renewed motivation among the participants, who departed with a clearer vision for the project’s remaining tasks. In addition, the picturesque setting of Benasque further enhanced the collaborative atmosphere, providing a serene environment for focused discussions and the exchange of innovative ideas.