Stepwise Quantum Tunneling Seen in Ultracold Atoms
Superconducting circuits, such as those used in magnetic sensors and in certain qubits, rely on Josephson junctions, which are thin barriers sandwiched between two superconductors. Electrons can go through the barriers—a process called quantum tunneling. When an oscillating current is applied to the circuit, the voltage drop across the junction exhibits distinct steps as the current is varied. The height of these so-called Shapiro steps provides a metrological standard for the volt, the unit of voltage. Now a similar step-like behavior has been observed for the first time in circuits where atoms do the barrier crossing rather than electrons [1, 2]. The experimental breakthrough—performed by two separate teams—provides new insights into the dynamics of the “stepping” particles.
Researchers can trap and cool atoms in optical setups that resemble electronic circuits. One of the advantages of using atoms instead of electrons is that their dynamics are slower and thus easier to probe. “Ultracold atoms provide us with a real-time, uniquely pristine view of the microscopic processes that underlie the rich transport properties of Josephson junctions—the very same centerpiece of this year’s Nobel Prize,” comments Francesco Scazza of the University of Trieste in Italy, who was not involved in the studies.
The ultracold-atom experiments that showed Shapiro steps follow from previous theoretical work [3]. The basic setup is two ultracold gases separated by an optical barrier made from laser light. Unlike the barrier in an electronic Josephson junction, this atom barrier can move. “The superconducting current can be achieved by moving the barrier through the atoms, while the difference of the chemical potential across the barrier takes the place of the voltage drop,” explains Luigi Amico from the University of Catania in Italy and the Technology Innovation Institute (TII) in the United Arab Emirates. Together with Vijay Singh from TII, Amico worked on the theoretical proposal and on both experiments.
To test the onset of Shapiro steps in this configuration, two independent experiments were set up: one at the University of Kaiserslautern-Landau in Germany and another at the European Laboratory for Non-Linear Spectroscopy in Italy.
The German experiment studied a gas of rubidium-87 atoms that were placed in an elongated, cylinder-shaped optical trap and cooled to about 35 nK [1]. “The rubidium-87 atoms are bosons and thus condense into a collective quantum state at these low temperatures,” says Erik Bernhart from the team in Germany. He and his colleagues applied a laser to a point near the middle of the optical trap, creating a barrier between the two sides of the condensate. They moved this barrier in one direction, creating a current of atoms across the barrier. In addition to this forward motion, they varied the barrier’s movement with back-and-forth oscillations, driving the gases on the two sides. “The two gases behave like coupled pendula with a weak link,” says team member Ludwig Mathey from the University of Hamburg in Germany. At the end of this process, the researchers measured the number of atoms on either side, and from the relative number count, they determined the chemical potential difference across the barrier. They found that this difference increased in discrete steps as the forward-motion speed (or current) was increased.
After identifying this Shapiro-step behavior, the researchers used their atom-imaging capabilities to probe the dynamics around the barriers. They found small excitations in the atom density that resembled acoustic waves, but they also detected larger excitations, which were similar to solitonic excitations known as vortex rings. These vortex rings propagated backward with respect to the barrier motion. The number of vortex rings was directly related to the Shapiro steps: In the first step, only one vortex ring was emitted per oscillation; in the second, there were two vortex rings; and so on.
The Italian experiment conducted a similar study, with a gas of lithium-6 atoms in a nearly two-dimensional trap [2]. “As fermions, lithium-6 atoms cannot condense directly,” explains team member Giulia Del Pace from the University of Florence and from the National Institute of Optics of the National Research Council of Italy. She and her colleagues could, however, control the atom–atom interactions by applying a magnetic field. They looked at two regimes, one with weak and repulsive interactions and the other with strong interactions. In the weak case, the lithium atoms paired up to form molecules that behaved as bosons, similar to the formation of Cooper pairs by electrons in superconductors. In the strong case, the atoms formed a unitary Fermi gas, which is a state that describes nuclear matter and neutron stars.
As in the German experiment, the Italian team introduced an oscillating barrier and looked for a response in the gas dynamics. Remarkably, the researchers detected Shapiro steps for both the molecular and the strongly interacting regimes. Moreover, the behavior of the lithium atoms mirrored that of rubidium atoms in the German experiment and electrons in superconductors. Specifically, the height of the Shapiro steps was found to be directly proportional to the frequency of the oscillations, while their width was proportional to the amplitude of the oscillations.
The Italian setup did, however, produce different microscopic dynamics: Rather than vortex rings, the Italian team observed the creation of backward-moving vortex–antivortex pairs, with the number of pairs corresponding to the number of steps. Similar types of vortex structures are observed in superconducting circuits, where they are known to play a role in energy loss through dissipation. And this dissipation is what gives rise to the step-like behavior in the circuits. “These experiments nicely reveal how the motion of vortex-like excitations governs quantum transport phenomena,” Scazza says. He adds that further exploration of these atomic systems might help in building an ultraclean electronic Josephson junction, which has been an enduring quest in the field of superconducting qubits.
Besides revealing the microscopic dynamics inside circuits, the two experiments bode well for applications in atomtronics. Atomtronics is a field dedicated to creating devices, similar to electronic ones, but using atoms instead of electrons, with potential applications in quantum computing and quantum sensors. “The presented results could lead to the accurate cyclic transfer of atoms across an atomtronic circuit, which is an important step in the development of this architecture,” says Rocío Jauregui-Renaud of the National Autonomous University of Mexico, who was not involved in the research.
–Andrea Parlangeli
Andrea Parlangeli is a science writer based in Milan, Italy. He is the author of A Pure Soul: Ennio De Giorgi, A Mathematical Genius (Springer, 2019).
References
- E. Bernhart et al., “Observation of Shapiro steps in an ultracold atomic Josephson junction,” Science 390, 1130 (2025).
- G. Del Pace et al., “Shapiro steps in strongly-interacting Fermi gases,” Science 390, 1125 (2025).
- V. P. Singh et al., “Shapiro steps in driven atomic Josephson junctions,” Phys. Rev. Lett. 133, 093401 (2024).