Universal Scaling of Many-Body Quantum Tunneling
Quantum tunneling—a cornerstone phenomenon key to superconductivity technologies—was probed using a cold-atom quantum simulator with an adjustable hexagonal-triangular lattice. Here, barrier height, temperature, and atomic interactions could be independently dialed in. The study zeroed in on how many-body effects reshape tunneling. In the weak-interaction regime, the critical tunneling coefficient varied quadratically with temperature across different conditions, a stark contrast to the linear single-particle case. Beyond the mean-field level, the power exponent dropped, aligning with quantum field theory predictions. These findings uncover a universal many-body renormalization of tunneling, directly relevant for correlated quantum materials and devices.
Context
Quantum tunneling underlies many phenomena: from thermonuclear fusion in stars and Big Bang nucleosynthesis to the operation of scanning tunneling microscopes and flash memory. However, with the development of superconducting technologies and quantum computing, many-body tunneling processes have come to the fore, such as macroscopic tunneling of Cooper pairs in Josephson junctions. Until now, it remained unclear how the interaction between particles changes the fundamental scaling law for the critical tunneling barrier with temperature change — a question directly relevant to organic superconductors and high-temperature materials.
Methods
The experimentalists prepared a Bose-Einstein condensate of rubidium-87 atoms and loaded it into a three-dimensional optical lattice formed by laser beams (quantum optics). By changing the polarization of the beams, they switched between hexagonal and triangular geometries of the two-dimensional lattice, and by varying the intensity, they controlled the tunneling coupling. The temperature and number of atoms were adjusted independently. The critical lattice depth at which tunneling vanishes was determined through the fraction of zero momentum in quantum measurement of the momentum distribution after ballistic expansion. The system dynamics was described by Schrödinger's equation with the Lieb-Liniger Hamiltonian, and the macroscopic state of the condensate obeyed Bose–Einstein statistics.
Results
In the quantum regime, below the Bose condensation temperature, a universal power-law dependence of the critical tunneling matrix element Jc ~ T^α was discovered. For weak interactions, the exponent α ≈ 2, which matches predictions of mean-field theory for a Luttinger liquid. Verification at different particle numbers (1–3×10^5), longitudinal lattice depths (0 and 5 Er), and both geometries showed that all data fall onto a single line on a log-log scale after proper renormalization, confirming universality with α = 1.96(6). In the classical regime, the critical lattice depth Vc grew linearly with temperature, as expected from equipartition of energy. Using numerical simulations with the quantum Monte Carlo method, the applicability of the one-dimensional description was confirmed. With increasing longitudinal potential V1D, the effective interaction increased, and α gradually decreased, following the theoretical curve α = (4K−1)/(2K) (where K is the Luttinger parameter). In the limit V1D ≥ 60 Er, the exponent reached unity, meaning a transition to single-particle tunneling. Thus, a continuous crossover from collective to individual behavior was observed.
Implications
The results prove for the first time that many-body effects drastically renormalize quantum tunneling and that the scaling Jc ~ T^α with non-integer α is universal for a broad class of systems. This deepens the understanding of the role of interactions in low-dimensional quantum systems and lays the groundwork for engineering tunneling properties in superconducting devices and quantum information platforms.
Future development
In the future, the proposed approach could be extended to fermionic systems, which is particularly relevant for organic superconductors and high-temperature cuprates, where tunneling between one-dimensional chains plays a key role. Another direction is testing the universality of scaling in astrophysical and biological tunneling processes, where many-body effects may also be significant.
Impact
Condensed matter physics, quantum computing, superconducting electronics, astrophysics.
Next steps
Measuring scaling for stronger interactions up to the fermionic regime and studying the role of dimensionality at the 2D–1D transition.
Key open problems
Mechanism of high-temperature superconductivity, many-body problem in non-equilibrium conditions, fundamental limits of quantum tunneling in complex media.
🎯 The transition from collective to single-particle tunneling with increasing lattice depth resembles how a crowd of people going through a narrow door changes its behavior under a strong crush: interaction makes everyone 'feel' each other, but when the passage becomes too tight, each one squeezes through on their own.
Key numbers
- Typical condensate temperature: 20–150 nK
- Exponent α in the weakly interacting regime: ≈1.9–2.1
- Number of atoms in the condensate: 1×10^5 – 3×10^5
- Critical temperature of Bose condensation: ≈250 nK
- Lattice constant in the longitudinal direction: 532 nm