Quantum gas microscopes have revolutionized quantum simulation by providing snapshots of many-body systems with single-atom resolution. However, they only see the diagonal of the density matrix—site occupancies. Off-diagonal elements, which encode phase relationships between sites, remained inaccessible locally. Related works on the arXiv are moving in the same direction: some propose a phase microscope for quantum gases, others use Talbot interferometry to measure finite phase coherence, and still others extract off-diagonal order from diagonal measurements. Our work belongs to this line but, for the first time, pushes spatial resolution down to a single site in the Hubbard regime.
In the experiment with erbium atoms in a two-dimensional layer of a three-dimensional optical lattice, the lattice is suddenly switched off, the wave function is allowed to evolve freely for fractions of the Talbot time (29 microseconds for half a period), and then a phase-adjustable lattice is switched on to recapture the atoms. By varying the phase of the recapture lattice, a modulation of the filling is observed, whose amplitude is proportional to the coherence between sites at a given distance. Numerical simulations were performed using DMRG and TEBD.
In a harmonic trap, the central region with near-unity filling showed a sharp drop in coherence as the interaction-to-tunneling ratio U/t increased from 10 to 30, corresponding to the superfluid–Mott insulator transition. The edge region with filling around one-third maintained high coherence even at U/t≈40. In an engineered two-leg ladder, coherence between second neighbors was measured: at U/t≈3 it grew rapidly with the inter-leg tunneling, while at U/t≈12 it remained low. The experimental data quantitatively agree with simulations under a single global scaling factor η=0.47.
The difference from neighboring works lies in the method: instead of long time-of-flight or interferometry with many atoms per site, here a short Talbot evolution followed by recapture is used, providing nearly single-site resolution in the single-atom regime. This allows distinguishing coexisting phases within a single cloud, which is impossible when averaging over the whole sample. The work establishes a new measurement protocol for quantum gas microscopy.
The technique can be extended to fermionic systems, where programmable evolution before measurement promises to reveal momentum distributions, Fermi surface structure, and signatures of unconventional superconductivity. It can also measure coherence over longer distances to study power-law decay of correlations in quasi-long-range order.
The method will impact quantum simulation of strongly correlated systems, quantum metrology, and the development of quantum simulators with local control.
Apply the microscope to fermionic gases and to systems with nontrivial topology, and improve recapture efficiency to quantitatively determine η.
In ultracold atomic physics, open questions remain about local phase transitions in inhomogeneous systems and the nature of quasi-long-range order in low-dimensional quantum gases. This method provides a tool for direct measurement of off-diagonal correlations needed to test theories.
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What the work does
The study introduces a quantum coherence microscope that leverages the Talbot effect to map off-diagonal correlations onto the atomic density with nearly single-site resolution. The method was validated on the superfluid–Mott insulator transition and on an engineered ladder, where coherence beyond nearest neighbors was measured. Experimental data align with numerical simulations using a single scaling factor.
Where its strength is
The method enables local measurement of phase correlations in the single-atom regime, paving the way for studying spatially inhomogeneous quantum phases and coexisting phases within a single cloud.
Where it could go next
Worth trying
Nearby works in our archive
The closest work in the archive sits at 0.68 by meaning — the usual level for our corpus.
The Talbot effect used here was described by Henry Fox Talbot in 1836 for light passing through a grating. Now it helps to examine quantum gases with single-atom precision.