arXiv subjects

Abel Rojo-Francàs

Publications and source records attributed to Abel Rojo-Francàs.

14 recordsLinked to original sources

arXiv2026

Quantum Monte Carlo study of systems interacting via long-range interactions mediated by a cavity

We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using the variational and the diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a non-translationally invariant Jastrow wave function that accurately captures the spatial structure induced by the cavity field and provides an efficient many-body ansatz for both bosonic and fermionic systems. We analyze properties of three characteristic quantum systems, subject to long-range interactions: (i) ideal Bose gas, (ii) interacting Bose gas, (iii) ideal Fermi gas. In the absence of short-range interactions, we identify a crossover from a stable, weakly modulated phase realized at finite particle number for repulsive interactions to a self-organized state for attractive interactions, marked by clustering, loss of superfluidity, and, at fixed interaction strength, the absence of a thermodynamic limit. Introducing short-range repulsion, either through contact interactions or fermionic statistics, leads to the formation of a mesoscopic gas-like regime that disappears in the thermodynamic limit. A qualitative phase diagram is proposed to illustrate the combined effects of short- and long-range interactions, highlighting the emergence of distinct regimes with characteristic structural properties. Applying the Kac prescription, we obtain a well-defined thermodynamic limit and show that the periodic modulation found for a finite number of particles in the repulsive regime is a finite-size artifact, while the self-organized state survives with its onset shifted to substantially stronger coupling.

cond-mat.quant-gas↗

arXiv2026

Mobile impurity interacting with a Hubbard chain and the role of Friedel oscillations

This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly-attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.

cond-mat.quant-gas↗

arXiv2026

Coordinate space representation of a one-dimensional odd-parity pseudopotential

We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and successfully recovering the exact energy spectrum and eigenfunctions. Furthermore, we use the square-well and modified Pöschl--Teller potentials as finite-range representations of the odd-parity interaction and study their convergence to the contact interaction when the range tends to zero. Finally, we perform natural orbital analysis and compute the eigenvalues of the one-body density matrix for different particle numbers, examining their dependence on the one-dimensional scattering length and identifying distinct physical regimes.

cond-mat.quant-gas↗

arXiv2026

Bose-Einstein condensation in exotic lattice geometries

Modern quantum engineering techniques allow for synthesizing quantum systems in exotic lattice geometries, from self-similar fractal networks to negatively curved hyperbolic graphs. We demonstrate that these structures profoundly reshape Bose-Einstein condensation. Fractal lattices dramatically lower the condensation temperature and enhance condensation fluctuations. In a Sierpiński carpet, quasi-degeneracies in the tight-binding spectrum fragment the condensate. Hyperbolic lattices, on the other hand, exhibit condensation features similar to regular three-dimensional lattices, despite their embedding in only two dimensions: The critical temperature increases as the system grows, and the temperature-dependence of the condensate fraction follows the same power-law as for cubic lattices. We explain these similarities through the similarity of the densities of state at low energies. When strong repulsive interactions are included, the gas enters a Mott insulating state. Using a multi-site Gutzwiller approach as well as a simple strong-coupling expansion, for the Sierpiński triangle we find a smooth interpolation between the characteristic insulating lobes of one-dimensional and two-dimensional systems. Our findings establish lattice geometry as a powerful tuning knob for quantum phase phenomena and pave the way for experimental exploration in photonic waveguide arrays and Rydberg-atom tweezer arrays.

cond-mat.quant-gas↗

arXiv2025

Counterflow of lattice polarons in harmonically confined optical lattices

We study a mobile impurity in a one-dimensional harmonically confined optical lattice interacting repulsively with a bosonic bath. The behavior of the impurity across baths with superfluid and Mott-insulator domains is examined, including its full back-action effect on the bath. We characterize the bath-impurity phase diagram and reveal the appearance of a correlated counterflow phase, which we support with an analytical model for a mobile impurity-hole pair. This phase shows an extended combined insulator domain of unity filling but no independent domain of constant density. The transition to this phase features a sudden orthogonality and the change of the shape of the impurity's profile to that of a free particle in an infinite square well. The findings of this work suggest the appearance of unconventional counterflow in trapped imbalanced atomic mixtures.

cond-mat.quant-gas↗

arXiv2025

Bardeen-Cooper-Schrieffer State Representation and Pairing in the Fermionic Tonks-Girardeau Gas

We introduce an alternative expression for the ground state wave function of the fermionic Tonks-Girardeau gas. Our wave function is constructed based on the occupation numbers and natural orbitals of the one-body density matrix. We demonstrate that the newly found wave function describes the ground state of the fermionic Tonks-Girardeau gas under any external potential. By expressing the proposed wave function in the framework of second quantization, we show that the ground state of the fermionic Tonks-Girardeau gas is a number-conserving Bardeen-Cooper-Schrieffer (BCS) state. We provide explicit expressions for the corresponding coefficients that describe the fermionic Tonks-Girardeau gas as a number-conserving BCS state. Additionally, the suitable form of the proposed wave function in second quantization allows us to derive the necessary expectation values to experimentally detect pairing in the fermionic Tonks-Girardeau gas. With this, we prove and show how to detect that the fermionic Tonks-Girardeau gas not only exhibits non-trivial quantum correlations but is also a paired state.

cond-mat.quant-gas↗

arXiv2025

Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential

We provide a detailed study of the properties of a few interacting spin $1/2$ fermions trapped in a one-dimensional harmonic oscillator potential. The interaction is assumed to be well represented by a contact delta potential. Numerical results obtained by means of direct diagonalization techniques are combined with analytical expressions for both the non-interacting and strongly interacting regime. The $N=2$ case is used to benchmark our numerical techniques with the known exact solution of the problem. After a detailed description of the numerical methods, in a tutorial-like manner, we present the static properties of the system for $N=2, 3, 4$ and 5 particles, e.g. low-energy spectrum, one-body density matrix, ground-state densities. Then, we consider dynamical properties of the system exploring first the excitation of the breathing mode, using the dynamical structure function and corresponding sum-rules, and then a sudden quench of the interaction strength.

cond-mat.quant-gas↗

arXiv2025

Enhanced strong interaction effect in synthetic spin-orbit coupling with mixed spin symmetry

Synthetic spin-orbit coupling in cold atoms couples the pseudo-spin and spatial degrees of freedom, and therefore the inherent spin symmetry of the system plays an important role. In systems of two pseudo-spin degrees, two particles contain symmetric states and anti-symmetric states, but the spin symmetry can be mixed for more particles. This mixed spin symmetry has been overlooked and has not been investigated thoroughly. We study the role of mixed spin symmetry in the presence of spin-orbit coupling and consider the system of three bosons with two hyper-fine states trapped in a harmonic potential. We investigate the ground state and the energy spectrum by implementing exact diagonalization. Similarly to two-particle systems, the interplay between spin-orbit coupling and repulsive interactions between anti-aligned pseudo-spins increases the population of the unaligned spin components in the ground state. Also, the emergence of the mixed spin symmetric states compensates for the rise of the interaction energy. In contrast to two-particle systems, the pair correlation of the ground state is analogous to the Tonks-Girardeau gas even for relatively small contact interactions, and this feature is enhanced by the spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2024

Stable collective charging of ultracold atoms quantum batteries

We propose a novel quantum battery realized with a few interacting particles in a three-well system with different on-site energies, which could be realized with ultracold atom platforms. We prepare the initial state in the lowest energy well and charge the battery using a Spatial Adiabatic Passage (SAP)-based protocol, enabling the population of a higher energy well. We examine the charging under varying interaction strengths and reveal that the consideration of collective charging results in an intriguing oscillatory behavior of the final charge for finite interactions, through diabatic evolution. Our findings open a new avenue for building stable and controllable quantum batteries.

quant-ph↗

arXiv2024

Bound impurities in a one-dimensional Bose lattice gas: low-energy properties and quench-induced dynamics

We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.

cond-mat.quant-gas↗

arXiv2024

Few particles with an impurity in a one-dimensional harmonic trap

We present a comprehensive study of the static properties of a mobile impurity interacting with a bath with a few particles trapped in a one-dimensional harmonic trap. We consider baths with either identical bosons or distinguishable particles and we focus on the limiting case where the bath is non-interacting. We provide numerical results for the energy spectra and density profiles by means of the exact diagonalization of the Hamiltonian, and find that these systems show non-trivial solutions, even in the limit of infinite repulsion. A detailed physical interpretation is provided for the lowest energy states. In particular, we find a seemingly universal transition from the impurity being localized in the center of the trap to being expelled outside the majority cloud. We also develop an analytical ansatz and a mean-field solution to compare them with our numerical results in limiting configurations.

cond-mat.quant-gas↗

arXiv2024

Anomalous quantum transport in fractal lattices

Fractal lattices are self-similar structures with repeated patterns on different scales. As in other aperiodic lattices, the absence of translational symmetry can give rise to quantum localization effects. In contrast to low-dimensional disordered systems, co-existence of localized and extended states is possible in fractal structures, and can lead to subtle transport behavior. Here, we study the dynamical properties of two fractal lattices, the Sierpiński gasket and the Sierpiński carpet. Despite their geometric similarity, the transport turns out to behave very differently: In the Sierpiński gasket, we find a sub-diffusive behavior, whereas the Sierpiński carpet exhibits sub-ballistic transport properties. We show that the different dynamical behavior is in line with qualitative differences of the systems' spectral properties. Specifically, in contrast to the Sierpiński carpet, the Sierpiński gasket exhibits an inverse power-law behavior of the level spacing distribution. From the point of view of technological applications, we demonstrate that the sub-diffusive behavior in the Sierpiński gasket can be used as a quantum memory. By interpolating between fractal and regular lattices, a flexible tuning between different transport regimes becomes possible.

quant-ph↗

arXiv2024

Universal composite boson formation in strongly interacting one-dimensional fermionic systems

Attractive $p$-wave one-dimensional fermions are studied in the fermionic Tonks-Girardeau regime in which the diagonal properties are shared with those of an ideal Bose gas. We study the off-diagonal properties and present analytical expressions for the eigenvalues of the one-body density matrix. One striking aspect is the universality of the occupation numbers which are independent of the specific shape of the external potential. We show that the occupation of natural orbitals occurs in pairs, indicating the formation of composite bosons, each consisting of two attractive fermions. The formation of composite bosons sheds light on the pairing mechanism of the system orbitals, yielding a total density equal to that of a Bose-Einstein condensate.

cond-mat.quant-gas↗

arXiv2022

On the direct diagonalization method for a few particles trapped in harmonic potentials

We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a renormalization method for the interparticle interactions. The procedure is benchmarked with state-of-the-art numerical results for three and four symmetric fermions.

cond-mat.quant-gas↗