Exotic States of Matter Finally Realised in Lab

Scientists have, for the first time, experimentally realised fractional Fermi seas, exotic states of matter predicted by extensions to the Pauli exclusion principle. Yi Zeng, from CEREMADE, CNRS, Universit e Paris-Dauphine, Universit e PSL, and Alvise Bastianello, working with colleagues including Sudipta Dhar and Milena Horvath from the Institut f ur Experimentalphysik und Zentrum f ur Quantenphysik, Universit at Innsbruck, Zekui Wang from the State Key Laboratory of Quantum Optics Technologies and Devices, Institute of Opto-Electronics, Shanxi University, Xudong Yu, Grigori E. Astrakharchik from the Departament de F ısica, Universitat Politècnica de Catalunya, Yanliang Guo from the Key Laboratory of Quantum State Construction and Manipulation, Renmin University of China, and Hanns-Christoph Nägerl and Manuele Landini, achieved this breakthrough by creating excited one-dimensional Bose gases with carefully controlled interactions. The observation of Friedel oscillations within these stable, yet unusual, states provides compelling evidence for the existence of these fractional Fermi seas, opening new avenues for exploring physics beyond standard fermionic behaviour and potentially enabling advancements in quantum information and sensing technologies.

For decades, physicists have theorised about states of matter beyond our everyday experience. Now, experiments with a specially prepared gas confirm the existence of ‘fractional Fermi seas’. A bizarre quantum state where particles occupy energy levels in a fundamentally different way. This realisation opens a new window onto the behaviour of matter governed by unusual rules.

Scientists have long understood that matter’s behaviour is governed by fundamental quantum statistics, most in particular the Pauli exclusion principle. Recent theoretical work suggests these principles can be extended, predicting the existence of exotic states of matter exhibiting fractional Fermi seas. These states, characterised by unusual momentum distributions, represent a departure from conventional understanding of how particles occupy energy levels within a system.

Scientists have achieved the experimental realisation of these fractional Fermi seas within a specially prepared one-dimensional Bose gas. This breakthrough involved carefully manipulating the interactions between atoms in an ultracold gas of cesium. By employing precisely controlled ramping cycles of interaction strength, the team created excited, yet stable, Bose-gas states.

Crucially, these states display Friedel oscillations, distinct patterns in momentum space — this serve as definitive evidence of the underlying fractional Fermi sea. The ability to create and observe these states opens new avenues for exploring quantum thermodynamics under unusual conditions and has potential implications for quantum technologies, and at the heart of this effort lies the concept of quantum statistics. Here, this dictates how particles behave at low temperatures.

Bosons condense into a single quantum state. Meanwhile, fermions fill available energy levels up to a certain limit, forming a Fermi sea. However, in one-dimensional systems, interactions between particles can blur the lines between bosonic and fermionic behaviour. In turn, this interaction between statistics and interactions is central to the emergence of fractional Fermi seas, where particles effectively occupy a fractional number of states.

Realising these states required a delicate balance of control and measurement — the trial utilised a unique setup involving an array of one-dimensional tubes created by a 2D optical lattice, confining the cesium atoms. By dynamically tuning the interactions between atoms using Feshbach resonances and confinement-induced resonances, and the team induced the formation of fractional Fermi seas with specific fractional occupancies. The team employed a hydrodynamic approach, based on the Lieb-Liniger model, to model The trial and gain deeper insights into their properties.

Momentum distribution broadening and Friedel oscillation emergence signal fractional Fermi seas

Through following ramp cycles in interaction strength, researchers observed broadening and flattening of momentum distributions for l=2 and l=4 states, with full width at half maximum (FWHM) widths of 5.19μm−1 and 6.69μm−1 respectively. These values represent a clear departure from the comparatively narrow distribution of the initial l=0 state, which exhibited a FWHM of 1.72μm−1, consistent with low-energy bosons in a finite-temperature environment.

Once the system reached the l=2 and l=4 points, the first-order correlation functions, G(x) — deviated from the smooth decay expected for a standard bosonic gas. At the same time, the most striking result was the development of oscillatory behaviour in G(x) for the excited states, and with minima at approximately 1.6μm for l=2 and 1.2μm for l=4. Here, this behaviour directly reflects the onset of Friedel oscillations, providing strong evidence for the formation of fractional Fermi seas.

At l=0, G(x) remained positive and decayed smoothly, as expected. Researchers derived a momentum occupancy of n(k) ≃ 2a∥ 3πl2N 2max [2lNmax −a2 ∥k2]3/2. Meanwhile, this accurately captured the observed Friedel oscillation data. A trialal data aligned well with GHD simulations, which incorporated trapping potential, time-dependent interactions, and finite-temperature effects.

These simulations required calibration of two parameters: a 1D temperature of T1D ≃5nK and a dimensional cross-over temperature of Tco ≃2nK — beyond the first two nodes, further oscillations predicted by both numerical and analytical models were masked by noise. For any cycle, atom losses during the forward ramp were limited to about 20%, and meanwhile, the reverse cycle resulted in losses of up to 45%, indicating a strong asymmetry in the process. This irreversibility correlated with the formation of bound states, or Bethe strings, during the reverse ramp, particularly around the transition to attractive interaction.

Realisation of fractional Fermi seas in excited one-dimensional Bose gases using a superconducting processor

A 72-qubit superconducting processor forms the foundation of the methodology for realising fractional Fermi seas (FFS) within an excited one-dimensional Bose gas. These states were prepared by employing ramping cycles that precisely control the interaction strength between atoms, allowing access to exotic quantum phases. The resulting excited Bose-gas states were carefully examined for signatures of the underlying FFS, specifically Friedel oscillations.

Initially, atom number distributions across the one-dimensional tubes were calculated using a continuum approximation — modelling tubes arranged on a square grid with a spacing of 0.532μm. This approach simplifies the complex geometry, allowing for efficient computation of the number of tubes, P(N), containing N atoms, and once the number of tubes with a given number of atoms was determined, the total number of atoms, Natm, was obtained through integration. Leading to the result: P(N) = 2Natm N 2max.

To account for these effects, the thermodynamics of the 1D interacting Bose gases were solved using the Thermodynamic Bethe Ansatz method, allowing determination of a local chemical potential within each tube, renormalised by the shallow three-dimensional trap. At the start of the lattice loading, initial trap frequencies were set to {ωx, ωy, ωz}/2π= {4, 9, 7}Hz, with ωx also serving as the longitudinal trap frequency at the dimensional crossover0.0.5 × 104 atoms with a 3D scattering length of 500a0 were loaded, approximating the 1D scattering length to be −2/a1D = 17.88μm−1 at the end of the state preparation.

By comparing the resulting momentum distribution with experimental data, an optimal coherence temperature, Tco, of 1.5 nK0.6 was determined. For refined theoretical modelling, the atom population across the tubes and thermal fluctuations within the initial state were considered, utilising the framework of Generalised Hydrodynamics.

Engineering a fractional Fermi sea challenges the Pauli exclusion principle

Scientists have long sought to control matter at its most fundamental level. Recent work from the Nagerl group in Heidelberg represents a step forward in that pursuit. For decades, the Pauli exclusion principle, the rule dictating how electrons fill energy levels, has been considered absolute. Theoretical extensions predicted the possibility of circumventing this principle, leading to exotic states of matter with unusual properties.

This team has now created and observed one such state, a “fractional Fermi sea”, within a carefully manipulated Bose gas. The ability to engineer systems that deviate from standard quantum behaviour opens doors to technologies reliant on precise control of matter’s building blocks. Once a theoretical curiosity, fractional Fermi seas are now experimentally accessible.

Scientists employed a ramping cycle, creating a stable excited state exhibiting clear “Friedel oscillations”. These oscillations serve as definitive proof of the underlying fractional Fermi sea, validating decades of theoretical work. By creating these states demands precise control over the Bose gas, and maintaining their stability remains a challenge.

The current demonstration is limited to a one-dimensional system, raising questions about how these principles might translate to more complex, real-world materials. The implications extend beyond fundamental physics. Unlike conventional materials where electrons behave as individual entities, these fractional Fermi seas exhibit collective behaviour. By manipulating these collective properties, it may be possible to design new types of sensors or information storage devices.

By scaling up this technology presents a considerable hurdle, as the system is highly sensitive to external disturbances and maintaining coherence in larger, more complex systems will require significant advances in control and isolation techniques. Rather than immediate applications, this effort establishes a platform for exploring exotic quantum phenomena and testing the limits of our understanding of matter.

A compelling direction lies in exploring similar states in different physical systems — since the current experiment relies on ultracold atoms, future work could investigate whether analogous fractional Fermi seas can be realised in solid-state materials. For instance, could carefully engineered quantum dots or nanowires exhibit similar behaviour, and also, understanding how these exotic states interact with light or other forms of energy could unlock entirely new functionalities. In the end, this project is not just about creating a specific state of matter, while but about expanding the set of tools for controlling and manipulating the quantum world.