Manipulation of quantum states in cold gases through statistical transmutation

5 January 2026

Photo: AG Schmelcher

Changing the statistical phase 𝜃 alters the zero-energy states (𝐸 = 0) without changing the energy itself (protection by chiral symmetry). (right) Checkered pattern in the density correlations shows the successful preparation and manipulation of the states.

A team from the University of Hamburg and American University in Washington has demonstrated that specific zero-energy states in cold atoms can be manipulated through statistical transmutation [1]. To achieve this, bosonic atoms are initially transformed into fermions and then back into bosons. The zero-energy states arise from chiral symmetry and are protected by it. The scheme, the fundamentals of which were first realized at Harvard shortly before [2], enriches our understanding of particles that are neither bosons nor fermions and potentially opens up a new path to holonomic quantum computing.

The statistical phase of particles typically determines the particle type and indicates what happens when two particles are exchanged. If the statistical phase is 0, or generally a multiple of 2π, the particles are bosons; if it is an odd multiple of π, they are fermions. Under exceptional circumstances, the statistical phase takes on values between 0 and 2π, characteristic of anyons. Normal interactions of bosons or fermions break the chiral symmetry in cold gases. Interestingly, this does not apply to statistical interactions of anyons. The authors of [1] exploit this circumstance to continuously change the statistical phase of bosonic zero-energy states from 0 to 2π in order to manipulate the states in a targeted manner. Due to chiral symmetry, the states remain protected for all statistical phases. Mathematically, these are non-Abelian holonomies that emerge from the geometry of the state space during adiabatic manipulation. The researchers consider, as an example, a system of atoms moving in a one-dimensional optical lattice and combine results with numerical simulations. Until now, adiabatic holonomies have been studied primarily in two-dimensional models. The study now shows that they are unexpectedly important in one dimension as well. A special feature of the zero-energy states are regular checkerboard patterns in the two- and many-particle density correlations, which are experimentally accessible. Furthermore, it is shown that the required bosonic zero-energy states can be reliably prepared by controlled modification of the statistical phase or other system properties. In the next step, these 1D anyonic zero states could be used in quantum computers or other quantum information systems as quantum gates.

References:
[1] F. Theel, M. Bonkhoff, P. Schmelcher, T. Posske, N. L. Harshman, PRL 135, 063401 (2025)
[2] J. Kwan, P. Segura, Y. Li, S. Kim, A. V. Gorshkov, A. Eckardt, B. Bakkali-Hassani, and M. Greiner, Science 386, 1055 (2024)