Shapiro steps – a series of abrupt jumps in the voltage–current characteristic of a Josephson junction that is exposed to microwave radiation – have been observed for the first time in ultracold gases by groups in Germany and Italy. Their work on atomic Josephson junctions provides new insights into the phenomenon, and could lead to a standard for chemical potential.
In 1962 Brian Josephson of the University of Cambridge calculated that, if two superconductors were separated by a thin insulating barrier, the phase difference between the wavefunctions on either side should induce quantum tunneling, leading to a current at zero potential difference.
A year later, Sidney Shapiro and colleagues at the consultants Arthur D. Little showed that inducing an alternating electric current using a microwave field causes the phase of the wavefunction on either side of a Josephson junction to evolve at different rates, leading to quantized increases in potential difference across the junction. The height of these “Shapiro steps” depends only on the applied frequency of the field and the electrical charge. This is now used as a reference standard for the volt.
Researchers have subsequently developed analogues of Josephson junctions in other systems such as liquid helium and ultracold atomic gases. In the new work, two groups have independently observed Shapiro steps in ultracold quantum gases. Instead of placing a fixed insulator in the centre and driving the system with a field, the researchers used focused laser beams to create potential barriers that divided the traps into two. Then they moved the positions of the barriers to alter the potentials of the atoms on either side.
Current emulation
“If we move the atoms with a constant velocity, that means there’s a constant velocity of atoms through the barrier,” says Herwig Ott of RPTU University Kaiserslautern-Landau in Germany, who led one of the groups. “This is how we emulate a DC current. Now for the Shapiro protocol you have to apply an AC current, and the AC current you simply get by modulating your barrier in time.”
Ott and colleagues in Kaiserslautern, in collaboration with researchers in Hamburg and the United Arab Emirates (UAE), used a Bose–Einstein condensate (BEC) of rubidium-87 atoms. Meanwhile in Italy, Giulia Del Pace of the European Laboratory for Nonlinear Spectroscopy at the University of Florence and colleagues (including the same UAE collaborators) studied ultracold lithium-6 atoms, which are fermions.
Both groups observed the theoretically-predicted Shapiro steps, but Ott and Del Pace explain that these observations do not simply confirm predictions. “The message is that no matter what your microscopic mechanism is, the phenomenon of Shapiro steps is universal,” says Ott. In superconductors, the Shapiro steps are caused by the breaking of Cooper pairs; in ultracold atomic gases, vortex rings are created. Nevertheless, the same mathematics applies. “This is really quite remarkable,” says Ott.
Del Pace says it was unclear whether Shapiro steps would be seen in strongly-interacting fermions, which are “way more interacting than the electrons in superconductors”. She asks, “Is it a limitation to have strong interactions or is it something that actually helps the dynamics to happen? It turns out it’s the latter.”
Magnetic tuning
Del Pace’s group applied a variable magnetic field to tune their system between a BEC of molecules, a system dominated by Cooper pairs and a unitary Fermi gas in which the particles were as strongly interacting as permitted by quantum mechanics. The size of the Shapiro steps was dependent on the strength of the interparticle interaction.
Ott and Del Pace both suggest that this effect could be used to create a reference standard for chemical potential – a measure of the strength of the atomic interaction (or equation of state) in a system.
“This equation of state is very well known for a BEC or for a strongly interacting Fermi gas…but there is a range of interaction strengths where the equation of state is completely unknown, so one can imagine taking inspiration from the way Josephson junctions are used in superconductors and using atomic Josephson junctions to study the equation of state in systems where the equation of state is not known,” explains Del Pace.
The two papers are published side by side in Science: Del Pace and Ott.
Rocío Jáuregui Renaud of the Autonomous University of Mexico is impressed, especially by the demonstration in both bosons and fermions. “The two papers are important, and they are congruent in their results, but the platform is different,” she says. “At this point, the idea is not to give more information directly about superconductivity, but to learn more about phenomena that sometimes you are not able to see in electronic systems but you would probably see in neutral atoms.”
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