A superconductor is a homogeneous quantum condensate of Cooper pairs, each formed by binding two electrons into a zero-spin, zero-momentum eigenstate. In 1964 Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) [1,2] proposed an alternative ground state wavefunction of Cooper pairs thus arriving at a new super state of electronic matter. The resulting pairs carry momentum Q requiring the superfluid density to modulate with wavevector Q. Remarkably, the same phenomenology appears in the theory of strong interactions described by quantum chromodynamics. At high baryonic densities, the quark-quark condensate, which forms the superfluid, is predicted to also develop spatial variations and the idea has found applicability in the physics of compact stars.
The last 40 years has seen a proliferation of novel and exotic superconductors (organics, iron-based, ruthenates, heavy fermions, and cuprates) but, despite decades of effort, FFLO-like states have not been observed in any material. The challenge to detect modulated superfluids has become particularly urgent because of implications for the modern theory of high temperature superconductivity, and in particular for the class of materials with the highest of superconducting transition temperatures. The presence of a modulated super state in the cuprate compounds, referred to as a Pair Density Wave, provides a possible missing link to unify our understanding of the cuprate phase diagram and ultimately the mechanism for high temperature superconductivity.
To search for a pair density wave state in the cuprates we developed a nanometer resolution, scanned Josephson (Cooper-pair) tunneling microscope (SJTM) . We imaged Cooper-pair tunneling from a d-wave superconducting STM tip at millikelvin temperatures to the electronic superfluid state in the cuprate compound Bi2Sr2CaCu2O8. By visualizing the condensate with nanometer resolution we observed clear Cooper-pair density modulations.
Our new technique for imaging Cooper-pair condensates, furthermore, opens the prospect of condensate visualizations in other cuprates, iron-based and unconventional superconductors, and will be especially advantageous in the study of topological superconductors.
 Fulde, P. & Ferrell, R. A. Phys. Rev. 135, A550 (1964).
 Larkin, A. I. & Ovchinnikov, Yu. N. Zh. Eksp. Teor. Fis. 37, 1146 (1964).
 M. H. Hamidian et al. Nature, 532, 343-347 (2016).