Physicists at Harvard University and the Massachusetts Institute of Technology have introduced a novel protocol aimed at investigating high-temperature superconductivity on a practical experimental platform. Their findings, published in the journal Physical Review Letters, focus on a model known as the Fermi-Hubbard model, which is thought to encapsulate the essential physics behind cuprate high-temperature superconductors, which are materials primarily composed of copper and oxygen.
The Fermi-Hubbard model illustrates how fermions, such as electrons, navigate through a lattice structure, facing two competing phenomena: tunneling and on-site interaction. To visualize this, one might consider students in a classroom who expend energy to change seats (tunneling), avoid a crowded desk (repulsive on-site interaction), or share desks with friends (attractive on-site interaction). Such dynamics echo the behavior of electrons transitioning between lattice positions.
According to Daniel Mark, the lead author of the study, “After nearly four decades of research, there are many detailed numerical studies and theoretical models on how superconductivity can emerge from the Fermi-Hubbard model, but there is no clear consensus on exactly how it emerges.” A crucial step in understanding this phenomenon involves verifying whether the Fermi-Hubbard model can produce a significant characteristic of cuprate high-temperature superconductivity: d-wave pairing.
D-wave pairing denotes a specific pairing of electrons where the strength and sign of the interaction vary with the direction of electron movement, contrasting with conventional low-temperature superconductors that exhibit s-wave pairing, characterized by a uniform pairing strength across all directions. Although physicists have crafted robust methods to simulate the Fermi-Hubbard model using ultracold atoms, measuring d-wave pairing has proven exceptionally challenging. The newly established protocol seeks to resolve this issue.
Innovative Measurement Techniques
A pivotal aspect of this protocol is the use of what the researchers call “repulsive-to-attractive mapping.” Typically, the physics of high-temperature superconductivity is represented by the repulsive Fermi-Hubbard model, which imposes an energetic cost for electrons occupying the same lattice site, resembling conflicting students sharing a desk. In this framework, detecting d-wave pairing requires fermions to uphold a delicate quantum state while traversing considerable distances, which demands precise experimental conditions.
To enhance measurement resilience against experimental imperfections, the team employs a clever mathematical transformation that switches from the repulsive model to the attractive model. In this alternative approach, electrons gain an energetic advantage by being in proximity to one another, similar to two friends sitting together in a classroom. This transformation is realized through a particle-hole transformation, where spin-down electrons are interpreted as holes, and vice versa. Post-mapping, the d-wave pairing signal becomes an observable that conserves local fermion number, thus bypassing the challenges posed by long-range motion.
Pulse Sequences for Enhanced Readout
To facilitate easier measurement, the researchers devised a sequence of carefully timed pulses, including microwave, hopping, and idling pulses, to alter the state of the system. The sequence initiates with a global microwave pulse aimed at manipulating the spin of the fermions, succeeded by a series of hopping and idling steps. The hopping step reduces the barrier between lattice sites, amplifying tunneling, while the idling step raises the barrier, allowing the system to evolve without tunneling. Each step is meticulously timed to extract the d-wave pairing information at the conclusion of the sequence.
The researchers assert that their protocol is efficient in terms of sample usage, experimentally feasible, and applicable to other observables that maintain local fermion number and operate on dimers. This advancement contributes to the expanding field that merges elements of analog quantum systems with digital gate techniques to explore intricate quantum phenomena. Mark adds, “All the experimental ingredients in our protocol have been demonstrated in existing experiments, and we are in discussion with several groups on possible use cases.”
