Long-range Interactions in One-Dimensional Gases Achieve Crossover to Clustering with Cavity Fields

Understanding the behaviour of quantum systems with long-range interactions represents a significant challenge in modern physics, with implications for diverse areas such as many-body physics and quantum simulation. Marta Domínguez-Navarro, Abel Rojo-Francàs, Bruno Juliá-Díaz, and Grigori E. Astrakharchik, from the Universitat de Barcelona and the Universitat Politècnica de Catalunya, have investigated one-dimensional gases subject to infinite-range interactions mediated by a cavity using advanced Quantum Monte Carlo techniques. Their research constructs a highly accurate Jastrow wavefunction to model these systems, allowing for detailed analysis of both bosonic and fermionic gases. This work reveals a crossover from stable modulated phases to delocalized states as interactions change, and proposes a phase diagram illustrating how short-range interactions further refine the system’s behaviour, offering new insights into the complex interplay of quantum forces.

This work unveils a crossover from stable, modulated phases for repulsive interactions to delocalized bound states for attractive interactions, characterised by clustering and a loss of superfluidity, ultimately revealing the absence of a thermodynamic limit in certain conditions. The study rigorously examines three fundamental quantum systems, an ideal Bose gas, an interacting Bose gas, and an ideal Fermi gas, all subject to these long-range interactions.

Researchers identified that, without short-range interactions, the system transitions from a stable, weakly modulated phase with repulsive forces to a delocalized bound state when attractive forces dominate, exhibiting clustering behaviour and a complete loss of superfluidity. Introducing short-range repulsion, through contact interactions or fermionic statistics, leads to the formation of a mesoscopic gas-like regime that diminishes as the system size increases. This research establishes a new understanding of how long-range interactions influence quantum gases, providing insights into the emergence of distinct structural regimes. Experiments show that the interplay between short- and long-range interactions dramatically alters the system’s behaviour, leading to unique structural properties and phases.

The team’s development of a non-translationally invariant Jastrow wavefunction is a key innovation, accurately capturing the spatial structure induced by the cavity field and serving as an efficient starting point for many-body calculations. The work opens avenues for exploring complex quantum phenomena in systems with tailored long-range interactions, mirroring the capabilities of modern quantum simulators. This detailed analysis of bosonic and fermionic systems provides a foundation for understanding self-organization, collective friction, and symmetry-breaking phase transitions in these novel quantum systems. A qualitative phase diagram is proposed, illustrating the combined effects of both short- and long-range interactions and highlighting the emergence of distinct regimes with characteristic structural properties. Researchers began with an exact two-body solution, constructing a non-translationally invariant Jastrow wavefunction to effectively capture the spatial structure induced by the cavity field. This wavefunction serves as an efficient many-body ansatz applicable to both bosonic and fermionic systems, enabling precise calculations of ground-state properties. The team analysed three distinct systems: an ideal Bose gas, an interacting Bose gas, and an ideal Fermi gas, all subject to these long-range interactions.

Scientists pioneered a methodology to explore the crossover between a stable, weakly modulated phase, observed for repulsive interactions, and a delocalized bound state arising from attractive interactions. This transition is characterised by clustering, a loss of superfluidity, and the absence of a thermodynamic limit, revealing fundamental changes in the system’s behaviour. Introducing short-range repulsion, through contact interactions or inherent fermionic statistics, led to the formation of a mesoscopic gas-like regime which diminishes as the system size increases. This approach achieves a non-perturbative framework, crucial for strongly interacting regimes where mean-field and perturbative methods fail. The research team constructed a Jastrow wavefunction, accurately capturing spatial structure induced by the cavity field, and applied it to analyze three distinct systems: an ideal Bose gas, an interacting Bose gas, and an ideal Fermi gas. Experiments revealed a crossover from a stable, weakly modulated phase for repulsive interactions to a delocalized bound state for attractive interactions, evidenced by clustering and a loss of superfluidity. Measurements confirm the absence of a stable limit for strongly attractive systems, demonstrating a fundamental shift in the gas’s behaviour.

The study meticulously analyzed the ground-state properties of these quantum gases, obtaining accurate estimates of experimentally relevant observables including ground-state energy, density profiles, and the static structure factor. Data shows that in the absence of short-range interactions, the system transitions from a stable phase with weak modulation to a delocalized bound state as interactions become more attractive. Researchers recorded a qualitative phase diagram illustrating the combined effects of both short- and long-range interactions, highlighting the emergence of distinct regimes with characteristic structural properties. The team successfully implemented these methods, making the full implementation publicly available via a GitHub repository. Analysis of the ideal Bose gas revealed detailed ground-state energy and density profiles for varying particle numbers, establishing a baseline for understanding the impact of long-range correlations. Introducing short-range repulsion, through contact interactions for bosons and Pauli exclusion for fermions, led to the formation of a mesoscopic gas-like regime that disappears as interactions intensify.

The breakthrough delivers a comprehensive framework for investigating ground-state properties and correlation functions in correlated quantum gases, particularly those subject to long-range forces. Measurements confirm that the interaction strength, V0, is approximately proportional to ħη(∆c−U₀B₀), where η represents the two-photon Rabi frequency, ∆c is the cavity detuning, U₀ is the on-site interaction strength, and B₀ is the magnetic field. The work demonstrates how the system’s behaviour is strongly influenced by the sign of the interaction strength, revealing a transition from a stable, weakly modulated phase for repulsive interactions to a delocalized bound state characterised by clustering and a loss of superfluidity when interactions become attractive. A novel Jastrow wavefunction, constructed from the exact two-body solution, proved effective in capturing the spatial structure induced by the cavity field and facilitating accurate many-body calculations for both bosonic and fermionic systems. The introduction of short-range repulsion, through contact interactions or fermionic statistics, further complicates the system’s behaviour, leading to the emergence of a mesoscopic phase exhibiting intricate spatial correlations and a finite superfluid fraction.

Researchers observed that increasing attraction eventually drives the system back into the delocalized bound state, highlighting a competition between repulsive and attractive forces. The authors acknowledge limitations related to the continuous space considered and the focus on ground-state properties, noting that future work could extend these methods to higher dimensions or incorporate more realistic models, such as those with a deep transverse lattice. The methodological advancements, including the development and validation of the many-body trial wavefunction and the numerical techniques employed, ensure the reliability of quantitative predictions for ground-state energies and correlation functions in cavity-mediated many-body systems. These validated methods offer a robust framework for exploring the complex interplay of long- and short-range interactions in quantum gases.