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Professorship Ultracold Quantum Gases
Department of Physics
Student sits at workstation and looks at laptop. © Aliona Kardash​/​TU Dortmund

A Phase Microscope for Quantum Systems

Pictures of the phase microscope for a bosonic superfluid of ultracold atoms in a triangular optical lattice. The upper row show the raw data, the lower row shows the phase profiles determined from it. With increasing temperature of the system, the phase fluctuations become stronger. © Justus Brüggenjürgen
Pictures of the phase microscope for a bosonic superfluid of ultracold atoms in a triangular optical lattice. The upper row show the raw data, the lower row shows the phase profiles determined from it. With increasing temperature of the system, the phase fluctuations become stronger.
In collaboration with the University of Hamburg, researchers of TU Dortmund have developped a new microscopy method, which allows for direct imaging of the phase profile of a coherent quantum system with high spatial resolution. They used the methods to study the characteristic properties of a two-dimensional bosonic superfluid. The results are published in the journal Science.

Microscopy is essential for understanding nature. In physics methods were developed to even resolve individual lattice sites in solid-state materials, although their distance is smaller than one billionth of meter. However, these methods do not allow to capture the fluctuations, which often carry crucial information of the states. An alternative approach is to create larger systems, which are easier to resolve. For example, one can emulate the complex behavior of electrons in a solid via an artificial quantum system composed of ultracold atoms in a standing wave of laser light, a so-called optical lattice. These systems have lattice distances of a millionth of a meter and can therefore be resolved with a very good optical microscope. Christof Weitenberg from TU Dortmund University and his team have now substantially increased these possibilities by not only measuring the density distribution, but also the phase profiles of such coherent quantum systems with full resolution of individual lattice sites.

In quantum systems, particles behave like waves and at very low temperatures different locations of a system have a fixed phase relation of these waves. With increasing temperature the phase fluctuations grow until phase coherence is completely lost at a phase transition, where the system switches from a superfluid to a thermal gas. In two-dimensional systems of bosons, i.e. particles with an integer spin, these phase fluctuations have a specific shape, which the researchers could investigate here. The phase correlations fall with distance via a power law and the corresponding exponent grows linear with temperature. 

The researchers manipulate the atoms such that the original phase fluctuations are converted to relative density fluctuations, which are then optically imaged. This works analoguous to phase contrast imaging in optical microscopy, but relies here on manipulation of the atomic matter wave. “The phase fluctuations interfere with the coherent part of the system and transform into density fluctuations, from which we can directly reconstruct the phases,“ explains Justus Brüggenjürgen, the first author of the study. Christof Weitenberg remarks: “The method offers completely complementary microscopic insights into quantum systems. In the future, variants of the method could for example map out the coherence in strongly-correlated systems and enable the identification of d-wave superconductivity.“

The results are published in Science 393, 167 (2026).

Contact person for further information: Prof. Dr. Christof Weitenberg

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