New Microscope Reveals Hidden Quantum Order in Complex Materials

Scientists are developing new techniques to directly observe the phase and coherence of quantum matter, addressing a significant limitation of current gas microscopes. Christof Weitenberg from TU Dortmund University, Luca Asteria from Kyoto University, and Ola Carlsson, Annabelle Bohrdt, and Fabian Grusdt working with colleagues at Ludwig-Maximilians-Universität München, detail protocols for a ‘many-body phase microscope’ that utilises Fourier-space manipulation to access long-range off-diagonal correlators. This research demonstrates how matter-wave microscopy can directly measure key quantities such as the superconducting order parameter, non-equal time Green’s functions revealing spectral properties, and hidden orders within complex quantum systems like fractional Chern insulators. By enabling the observation of previously inaccessible phases and coherences, this work highlights the potential of matter microscopy to characterise and understand a wider range of intriguing many-body states.

Scientists have developed a novel matter-wave microscope capable of imaging quantum systems with unprecedented resolution and accessing previously hidden information about their behaviour. This breakthrough allows researchers to directly measure exotic properties of materials, including the subtle phases and coherences that govern their quantum states. The core of this advancement lies in a new technique for manipulating matter waves, enabling the observation of long-range correlations within complex quantum systems. The research introduces a method for probing the intricate behaviour of quantum materials, such as those exhibiting superconductivity or fractional Chern insulator properties. Existing quantum gas microscopes excel at measuring density and spin correlations, but struggle to capture phase information, a limitation overcome by utilising a matter-wave microscope that leverages the principles of interferometry to reveal the phase of quantum states. The technique involves applying Raman pulses to atoms in an optical lattice, creating interference patterns that encode information about the system’s coherence. Central to this innovation is the ability to achieve a magnification of 93, pushing the boundaries of resolution in matter-wave imaging. This high magnification, combined with access to Fourier space between matter-wave lenses, unlocks a powerful toolbox for investigating many-body quantum systems. Researchers demonstrate the potential to directly measure the fermionic d-wave superconducting order parameter in Hubbard-type models, the non-equal time Green’s function which yields the spectral function, and the hidden order of composite bosons in a fractional Chern insulator. The matter-wave microscope operates by creating a many-body interferometer, where atoms are manipulated in both real and momentum space. A Raman π/2 pulse transfers momentum to an auxiliary spin state, and subsequent matter-wave lenses convert this momentum into a spatial displacement. By analysing the interference fringes resulting from this process, scientists can extract information about the coherence between different points in the system, allowing for the characterisation of intriguing many-body states and the exploration of exotic correlators. A matter-wave microscope, employing time-domain matter-wave lenses, forms the core of this work to investigate many-body quantum systems. These lenses are created by utilising quarter-period (T/4) evolutions within harmonic traps, a technique chosen to precisely manipulate the spatial distribution of atoms. The ratio of trap frequencies dictates the magnification achieved, enabling detailed examination of atomic behaviour. Following the initial lensing, a Raman π/2 pulse into an auxiliary spin state in Fourier space transfers a controlled momentum determined by the wave vectors of the Raman beams. This momentum transfer is then converted into a real-space displacement via a second T/4 pulse, effectively creating a many-body interferometer. Subsequently, a second Raman pulse, devoid of momentum transfer, closes the interferometer sequence, inducing interference between the shifted and unshifted atomic configurations. Spin-resolved measurements then reveal coherence within the system over distances defined by the applied shift. The quantities measured are understood through the evolution of operators in the Heisenberg picture, defining creation operators for fermions or bosons at specific positions and momenta. The research leverages the unique ability of this method to swap the roles of position and momentum, as demonstrated by the T/4 pulses, which is fundamental to the interferometer’s operation. By analysing interference fringes as a function of Raman phases, the study aims to extract information about long-range off-diagonal correlators, including phases and coherences, within the many-body system. The density measurement after closing the interferometer reads as 1/4[⟨nx,↑⟩ + ⟨nx+d,↑⟩ − (e−iφ⟨a† x+d,↑ax,↑⟩ + h. c. )], where d represents the distance between lattice sites. If the system exhibits time-reversal and translational invariance, the phase coherence function, or equal-time single-particle Green’s function, g(d) = ⟨a† x+d,↑ax,↑⟩, is real. Fringe contrast, obtained by comparing measurements at Raman phases of 0 and π, directly quantifies this coherence. Evaluating multiple lattice sites allows for the extraction of average values from a single snapshot. Scientists have long sought to directly observe the subtle quantum states of matter, but peering into the realm of many-body physics has proven remarkably difficult. Traditional methods offer only indirect glimpses, relying on inferences drawn from bulk properties rather than direct imaging of the underlying quantum behaviour. Now, a new advance in matter-wave microscopy promises to circumvent these limitations, achieving a level of magnification previously thought unattainable. The ability to visualise these correlations represents a significant leap forward, potentially reconciling theoretical predictions with experimental observations often hampered by the inability to probe the relevant quantum states with sufficient precision. The achieved magnification of 93, while impressive, is merely a marker of the potential to resolve the delicate interplay of particles within these materials. However, it’s crucial to acknowledge that this is still early work. Maintaining the necessary level of control and precision to interpret these images will be a considerable challenge. Furthermore, the technique is currently limited to relatively simple, model systems. Scaling up to tackle the complexity of real materials will require substantial further development. Nevertheless, the prospect of a ‘many-body phase microscope’ is genuinely exciting, hinting at a future where we can not only predict but directly visualise the quantum world, potentially accelerating the development of novel materials and quantum technologies. The next step will likely involve applying this technique to more complex systems and refining the image analysis tools to extract meaningful physical insights.