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:1406.6833 · Physical Review E

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

Armando Relaño, J. Dukelsky, P. Pérez-Fernández, J. M. Arias

Published Oct 27, 2014• 22 citations
arXivHTMLPDF

Abstract

The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

DOI
10.1103/physreve.90.042139

Related papers

Quantum particle-number fluctuations in a two-component Bose gas in a double-well potential

Paweł Zin, Bartłomiej Oleś, Krzysztof Sacha

A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.

arXiv:1004.1541•Physical Review A•Sep 14, 2011•8 citations

Quantum Phase Transitions in the Bose Hubbard Model and in a Bose-Fermi Mixture

Eric Duchon

Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .

•Jan 1, 2013•0 citations

Particle-localized ground state of atom-molecule Bose-Einstein condensates in a double-well potential

篤 本橋, Tetsuro Nikuni

We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.

arXiv:1006.2954•Physical Review A•Sep 30, 2010•5 citations

Quantum phase transition in a three-level atom-molecule system

Sheng-Chang Li, Libin Fu, Fuli Li

We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy-level structure, fidelity, and adiabatic geometric phase, we confirm that the system exhibits a second-order phase transition from an atom-molecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular, we find that both the critical exponents and the behavior of the ground-state geometric phase have obviously changed in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to $\ensuremath{\pi}/3$ at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.

arXiv:1212.4933•Physical Review A•Jul 1, 2013•7 citations

Critical fluctuations of an attractive Bose gas in a double-well potential

Jan Chwedeńczuk, Barbara Oleś, Krzysztof Sacha +1 more

We consider a Bose gas with an attractive interaction in a symmetric double-well potential. In the mean-field approximation, the ground-state solution spontaneously breaks the symmetry of the trapping potential above a certain value of the interaction strength. We demonstrate how the Landau-Ginzburg scheme of the second-order phase transition emerges from the quantum model and show the link to the spontaneous symmetry breaking mentioned above. We identify the order parameter, the critical point and analyze quantum fluctuations around it.

arXiv:0804.3705•Europhysics Letters (EPL)•Sep 1, 2008•36 citations

Shift of the Bose-Einstein condensation transition in the presence of a second atomic species

P. M. Gaspar, Vanderlei Salvador Bagnato, P. C. M. Castilho

Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na 23 − K 39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.

arXiv:2602.12880•APS Open Science•Jun 24, 2026•0 citations
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.
A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.
Ultracold atomic gases may be the ultimate quantum simulator.These isolated systems have the lowest temperatures in the observable universe, and their properties and interactions can be precisely and accurately tuned across a full spectrum of behaviors, from few-body physics to highly-correlated many-body effects.The ability to impose potentials on and tune interactions within ultracold gases to mimic complex systems mean they could become a theorist's playground.One of their great strengths, however, is also one of the largest obstacles to this dream: isolation.This thesis touches on both of these themes.First, methods to characterize phases and quantum critical points, and to construct finite temperature phase diagrams using experimentally accessible observables in the Bose Hubbard model are discussed.Then, the transition from a weakly to a strongly interacting Bose-Fermi mixture in the continuum is analyzed using zero temperature numerical techniques.Real materials can be emulated by ultracold atomic gases loaded into optical lattice potentials.We discuss the characteristics of a single boson species trapped in an optical lattice (described by the Bose Hubbard model) and the hallmarks of the quantum critical region that separates the superfluid and the Mott insulator ground states.We propose a method to map the quantum critical region using the single, experimentally accessible, local quantity R, the ratio of compressibility to local number fluctuations.The procedure to map a phase diagram with R is easily generalized to inhomogeneous systems and generic many-body Hamiltonians.We illustrate it here using quantum Monte Carlo simulations of the 2D Bose Hubbard model.Secondly, we investigate the transition from a degenerate Fermi gas weakly coupled List of Tables Table Page 2.1 Techniques to Probe Atoms in Optical Lattices . . . . . .
We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.
We adopt a three-level bosonic model to investigate the quantum phase transition in an ultracold atom-molecule conversion system which includes one atomic mode and two molecular modes. Through thoroughly exploring the properties of energy-level structure, fidelity, and adiabatic geometric phase, we confirm that the system exhibits a second-order phase transition from an atom-molecule mixture phase to a pure molecule phase. We give the explicit expression of the critical point and obtain two scaling laws to characterize this transition. In particular, we find that both the critical exponents and the behavior of the ground-state geometric phase have obviously changed in contrast to a similar two-level model. Our analytical calculations show that the ground-state geometric phase jumps from zero to $\ensuremath{\pi}/3$ at the critical point. This discontinuous behavior has been checked by numerical simulations and it can be used to identify the phase transition in the system.
We consider a Bose gas with an attractive interaction in a symmetric double-well potential. In the mean-field approximation, the ground-state solution spontaneously breaks the symmetry of the trapping potential above a certain value of the interaction strength. We demonstrate how the Landau-Ginzburg scheme of the second-order phase transition emerges from the quantum model and show the link to the spontaneous symmetry breaking mentioned above. We identify the order parameter, the critical point and analyze quantum fluctuations around it.
Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na 23 − K 39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.