Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2310.10222 · New Journal of Physics

Off-diagonal long-range order in arrays of dipolar droplets

Raúl Bombín, Ferran Mazzanti, Jordi Boronat

Published Jan 1, 2024• 5 citations
arXivHTMLPDF

Abstract

Abstract We report quantum Monte Carlo results of harmonically confined quantum Bose dipoles within a range of interactions covering the evolution from a gas phase to the formation of an array of droplets. Scaling the experimental setup to a computationally accessible domain we characterize that evolution in qualitative agreement with experiments. Our microscopic approach generates ground-state results free from approximations, albeit with some controlled statistical noise. The simultaneous estimation of the static structure factor and the one-body density matrix allows for a better knowledge of the quantum coherence between droplets. Our results show a narrow window of interaction strengths where diagonal and off-diagonal long-range order can coexist. This domain, which is the key signal of a supersolid state, is reduced with respect to the one predicted by the extended Gross–Pitaevskii equation. Differences are probably due to an increase of attraction in our model, observed previously in the calculation of critical atom numbers for single dipolar drops.

DOI
10.1088/1367-2630/ad1e91

Related papers

Classical and quantum filaments in the ground state of trapped dipolar Bose gases

Fabio Cinti, Massimo Boninsegni

We study, by quantum Monte Carlo simulations, the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments and with the inclusion of a repulsive two-body potential of varying range. Two different limits can clearly be identified, namely, a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.

arXiv:1703.10291•Physical Review A•Jul 26, 2017•64 citations

Binary quantum droplets and dipolar supersolids

 Joseph Smith

We consider a binary magnetic gas and develop an extended Gross-Pitaevskii theory to study the system. We apply this theory to the regime where the two- body interactions are attractive for some arrangements of the atoms, and mean- field theory predicts mechanical collapse. In this regime quantum droplets of the binary magnetic gas can emerge, stabilised by quantum fluctuations. These quantum droplets can exist in miscible and immiscible regimes, and we characterise their properties over a broad parameter space. Simplified theories are developed to describe the droplets, and benchmarked against the full numerical calculations. The system dynamics are simulated for scenarios involving droplet formation and crossing the miscible-immiscible transition. Three-body loss is modelled in the dynamical simulations to account for the dominant loss process expected in experiments. We also study the supersolidity of a single-component dipolar gas in an infinite tube potential. An accurate computational algorithm is developed to calculate the ground state of the system in a unit cell. This algorithm is used to determine the phase diagram by characterising the crystalline order and superfluid fraction. Our results reveal that a system confined in a radially harmonic trap has a continuous transition for a range of density values, but is discontinuous for densities above and below this range. The theory is used to calculate the crystalline and supersolid states of a binary magnetic gas in a tube potential.

•Jan 1, 2023•0 citations

Off-diagonal correlations in a one-dimensional gas of dipolar bosons

Tommaso Roscilde, Massimo Boninsegni

We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional (1D) dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded in favor of quasi-solidity. For all strengths of the dipolar interaction we considered, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay, while the momentum distribution shows sharp kinks at the wavevectors of the oscillations, Q =±2π n (where n is the atom density), beyond which it is strongly suppressed. This momentum filtering effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that 1D dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.

arXiv:0910.4165•New Journal of Physics•Mar 16, 2010•12 citations

Formation and fragmentation of quantum droplets in a quasi-one-dimensional dipolar Bose gas

S. De Palo, E. Orignac, R. Citro

We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitoniclike density profile evolves into a liquidlike droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signaled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, the numerical solution of a time-dependent generalized Gross-Pitaevskii equation shows either an evaporation of the cloud, the formation of a single self-bound droplet, or a fragmentation in multiple droplets. These results can be probed with lanthanide atoms and help in characterizing the effect of the dipolar interaction in a quasi-one-dimensional geometry.

arXiv:2202.12071•Physical review. B./Physical review. B•Jul 5, 2022•14 citations

Strongly Correlated Quantum Droplets in Quasi-1D Dipolar Bose Gas

Rafał Ołdziejewski, Wojciech Górecki, Krzysztof Pawłowski +1 more

We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multiatom Schrödinger equation, we discover that such systems can exhibit not only the well-known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multiatom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case.

arXiv:1908.00108•Physical Review Letters•Mar 2, 2020•33 citations

Squeezing Bose-Bose liquid drops

Ares Sanuy, R. Barač, Petar Stipanović +2 more

We explore ultradilute Bose-Bose liquid droplets squeezed by an external harmonic potential in one spatial direction. Our theoretical study is based on a functional that is built using quantum Monte Carlo results of the bulk phase and incorporates finite-range effects. A characteristic feature of these drops is the existence of a critical atom number, which is the minimum number of particles to have a many-body bound state. We report results on the critical atom numbers for different magnetic fields and applying confinement strengths towards a quasi-two-dimensional setup. In the regime where the local-density approximation is expected to be valid, we find that the critical atom number decreases linearly with the harmonic oscillator length of the confining potential. With the largest squeezing explored in our work, we predict stable drops containing from approximately 1000 to 2000 atoms for magnetic fields from 56.230 to 56.574 G, respectively. Our functional reduces the critical numbers for any confinement and applied magnetic field with respect to the estimations based on the Lee-Huang-Yang model. We observe saturated drops when the number of atoms in the drop is much larger than the critical value, their central density being higher for the quantum Monte Carlo functional than for the Lee-Huang-Yang one.

arXiv:2311.05244•Physical Review A•Jan 16, 2024•4 citations
Abstract We report quantum Monte Carlo results of harmonically confined quantum Bose dipoles within a range of interactions covering the evolution from a gas phase to the formation of an array of droplets. Scaling the experimental setup to a computationally accessible domain we characterize that evolution in qualitative agreement with experiments. Our microscopic approach generates ground-state results free from approximations, albeit with some controlled statistical noise. The simultaneous estimation of the static structure factor and the one-body density matrix allows for a better knowledge of the quantum coherence between droplets. Our results show a narrow window of interaction strengths where diagonal and off-diagonal long-range order can coexist. This domain, which is the key signal of a supersolid state, is reduced with respect to the one predicted by the extended Gross–Pitaevskii equation. Differences are probably due to an increase of attraction in our model, observed previously in the calculation of critical atom numbers for single dipolar drops.
We study, by quantum Monte Carlo simulations, the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments and with the inclusion of a repulsive two-body potential of varying range. Two different limits can clearly be identified, namely, a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.
We consider a binary magnetic gas and develop an extended Gross-Pitaevskii theory to study the system. We apply this theory to the regime where the two- body interactions are attractive for some arrangements of the atoms, and mean- field theory predicts mechanical collapse. In this regime quantum droplets of the binary magnetic gas can emerge, stabilised by quantum fluctuations. These quantum droplets can exist in miscible and immiscible regimes, and we characterise their properties over a broad parameter space. Simplified theories are developed to describe the droplets, and benchmarked against the full numerical calculations. The system dynamics are simulated for scenarios involving droplet formation and crossing the miscible-immiscible transition. Three-body loss is modelled in the dynamical simulations to account for the dominant loss process expected in experiments. We also study the supersolidity of a single-component dipolar gas in an infinite tube potential. An accurate computational algorithm is developed to calculate the ground state of the system in a unit cell. This algorithm is used to determine the phase diagram by characterising the crystalline order and superfluid fraction. Our results reveal that a system confined in a radially harmonic trap has a continuous transition for a range of density values, but is discontinuous for densities above and below this range. The theory is used to calculate the crystalline and supersolid states of a binary magnetic gas in a tube potential.
We present a quantum Monte Carlo study of the one-body density matrix (OBDM) and the momentum distribution of one-dimensional (1D) dipolar bosons, with dipole moments polarized perpendicular to the direction of confinement. We observe that the long-range nature of the dipole interaction has dramatic effects on the off-diagonal correlations: although the dipoles never crystallize, the system goes from a quasi-condensate regime at low interactions to a regime in which quasi-condensation is discarded in favor of quasi-solidity. For all strengths of the dipolar interaction we considered, the OBDM shows an oscillatory behavior coexisting with an overall algebraic decay, while the momentum distribution shows sharp kinks at the wavevectors of the oscillations, Q =±2π n (where n is the atom density), beyond which it is strongly suppressed. This momentum filtering effect introduces a characteristic scale in the momentum distribution, which can be arbitrarily squeezed by lowering the atom density. This shows that 1D dipolar Bose gases, realized e.g. by trapped dipolar molecules, show strong signatures of the dipolar interaction in time-of-flight measurements.
We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitoniclike density profile evolves into a liquidlike droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signaled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, the numerical solution of a time-dependent generalized Gross-Pitaevskii equation shows either an evaporation of the cloud, the formation of a single self-bound droplet, or a fragmentation in multiple droplets. These results can be probed with lanthanide atoms and help in characterizing the effect of the dipolar interaction in a quasi-one-dimensional geometry.
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multiatom Schrödinger equation, we discover that such systems can exhibit not only the well-known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multiatom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case.
We explore ultradilute Bose-Bose liquid droplets squeezed by an external harmonic potential in one spatial direction. Our theoretical study is based on a functional that is built using quantum Monte Carlo results of the bulk phase and incorporates finite-range effects. A characteristic feature of these drops is the existence of a critical atom number, which is the minimum number of particles to have a many-body bound state. We report results on the critical atom numbers for different magnetic fields and applying confinement strengths towards a quasi-two-dimensional setup. In the regime where the local-density approximation is expected to be valid, we find that the critical atom number decreases linearly with the harmonic oscillator length of the confining potential. With the largest squeezing explored in our work, we predict stable drops containing from approximately 1000 to 2000 atoms for magnetic fields from 56.230 to 56.574 G, respectively. Our functional reduces the critical numbers for any confinement and applied magnetic field with respect to the estimations based on the Lee-Huang-Yang model. We observe saturated drops when the number of atoms in the drop is much larger than the critical value, their central density being higher for the quantum Monte Carlo functional than for the Lee-Huang-Yang one.