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:1512.07317 · Europhysics Letters (EPL)

Quantum phase diagram and time-of-flight absorption pictures of an ultracold Bose system in a square optical superlattice

Fan Wei, Jun Zhang, Ying Jiang

Published Jan 1, 2016• 4 citations
arXivHTMLPDF

Abstract

In this letter, by the use of the generalized effective potential theory, with the help of the process chain approach under the framework of the Kato formulation of the perturbation expansion, we calculate out the quantum phase diagram up to the 8th order for an ultracold Bose system in a square optical superlattice. Based on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are obtained, which are in excellent agreement with recent Monte Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.

DOI
10.1209/0295-5075/113/16004

Related papers

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

Zhi Lin, Jun Zhang, Ying Yan Jiang

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at $$\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)$$ in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.

Frontiers of Physics•Mar 22, 2018•2 citations

Visibility of ultracold Bose system in triangular optical lattices

Zhi Lin, Jun Zhang, Ying Yan Jiang

In this paper, by treating the hopping parameter in the Bose-Hubbard model as a perturbation, with the help of the resummed Green's function method and cumulant expansion, the momentum distribution function of an ultracold Bose system in a triangular optical lattice is calculated analytically. By its use, the time-of-flight absorption picture is plotted and the corresponding visibility is determined. A comparison between our analytical results and the experimental data of Becker et al. [New J. Phys. 12, 065025 (2010)] exhibits a qualitative agreement.

arXiv:1205.6949•Physical Review A•Sep 24, 2012•6 citations

Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices

Jun Zhang, Ying Yan Jiang

By treating the hopping parameter as a perturbation, with the help of cumulant expansion and the re-summing technique, the one-particle Green's function of a spin-1 Bose system in a honeycomb optical lattice is calculated analytically. By the use of the re-summed Green's function, the quantum phase diagrams of the system in ferromagnetic cases as well as in antiferromagnetic cases are determined. It is found that in antiferromagnetic cases the Mott insulating states with even filling factor are more robust against the hopping parameter than that with odd filling factor, in agreement with results via other different approaches. Moreover, in order to illustrate the effectiveness of the re-summed Green's function method in calculating time-of-flight pictures, the momentum distribution function of a honeycomb lattice spin-1 Bose system in the antiferromagnetic case is also calculated analytically and the corresponding time-of-flight absorption pictures are plotted.

Laser Physics•Jun 29, 2016•2 citations

Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

Zhi Lin, Wanli Liu

We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) to make the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero temperature. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.

arXiv:1804.08465•Frontiers of Physics•Jul 11, 2018•3 citations

An analytical approach to quantum phase transitions of ultracold Bose systems in bipartite optical lattices: Along the avenue of Green's function

Zhi Lin, Jun Zhang, Chen, Yan +1 more

In this paper, we present a generalized Green's function method which can be used to investigate the quantum phase transitions analytically in a systematic way for ultracold Bose systems in bipartite optical lattices. As an example, to the lowest order, we calculate the quantum phase boundaries of the localized states (Mott insulator or charge density wave) of an ultracold Bose system in a $d$-dimensional hypercubic optical lattice with nearest-neighbor repulsive interactions. Due to the inhomogeneity of the system, in the generalized Green's function method, cumuants on different sublattices are calculated separately, together with re-summed Green's function technique, the analytical expression of the phase boundaries of the localized phases in the system is presented.

arXiv:1402.3925•Feb 17, 2014•0 citations

Cell strong-coupling perturbative approach to the phase diagram of ultracold bosons in optical superlattices

Pierfrancesco Buonsante, A. Vezzani

The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order cell strong coupling perturbative expansions for the Bose-Hubbard model describing the system. Taking advantage of the cell partition inherent in the complex periodic modulation of a superlattice, this technique allows for the description of the unusual loophole-shaped insulator domains that may occur in the phase diagram of the system, unlike the standard perturbative approach. Furthermore, comparisons with quantum Monte Carlo simulations show that our approach provides quantitatively satisfactory results at a significantly lower computational cost than brute force numerical methods. We explicitly consider the phase diagrams for two realistic 3-periodic optical superlattices. These show that many insulator domains exhibit an unusual reentrant character, which we discuss, and suggest that the quantum phase transition relevant to the loophole-shaped insulating domains does not require extreme experimental condition in order to be observed.

arXiv:cond-mat/0503232•Physical Review A•Jul 25, 2005•31 citations
In this letter, by the use of the generalized effective potential theory, with the help of the process chain approach under the framework of the Kato formulation of the perturbation expansion, we calculate out the quantum phase diagram up to the 8th order for an ultracold Bose system in a square optical superlattice. Based on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are obtained, which are in excellent agreement with recent Monte Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.
In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at (±πa,±πa)\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)(±aπ​,±aπ​) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.
In this paper, by treating the hopping parameter in the Bose-Hubbard model as a perturbation, with the help of the resummed Green's function method and cumulant expansion, the momentum distribution function of an ultracold Bose system in a triangular optical lattice is calculated analytically. By its use, the time-of-flight absorption picture is plotted and the corresponding visibility is determined. A comparison between our analytical results and the experimental data of Becker et al. [New J. Phys. 12, 065025 (2010)] exhibits a qualitative agreement.
By treating the hopping parameter as a perturbation, with the help of cumulant expansion and the re-summing technique, the one-particle Green's function of a spin-1 Bose system in a honeycomb optical lattice is calculated analytically. By the use of the re-summed Green's function, the quantum phase diagrams of the system in ferromagnetic cases as well as in antiferromagnetic cases are determined. It is found that in antiferromagnetic cases the Mott insulating states with even filling factor are more robust against the hopping parameter than that with odd filling factor, in agreement with results via other different approaches. Moreover, in order to illustrate the effectiveness of the re-summed Green's function method in calculating time-of-flight pictures, the momentum distribution function of a honeycomb lattice spin-1 Bose system in the antiferromagnetic case is also calculated analytically and the corresponding time-of-flight absorption pictures are plotted.
In this paper, we present a generalized Green's function method which can be used to investigate the quantum phase transitions analytically in a systematic way for ultracold Bose systems in bipartite optical lattices. As an example, to the lowest order, we calculate the quantum phase boundaries of the localized states (Mott insulator or charge density wave) of an ultracold Bose system in a ddd-dimensional hypercubic optical lattice with nearest-neighbor repulsive interactions. Due to the inhomogeneity of the system, in the generalized Green's function method, cumuants on different sublattices are calculated separately, together with re-summed Green's function technique, the analytical expression of the phase boundaries of the localized phases in the system is presented.
The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order cell strong coupling perturbative expansions for the Bose-Hubbard model describing the system. Taking advantage of the cell partition inherent in the complex periodic modulation of a superlattice, this technique allows for the description of the unusual loophole-shaped insulator domains that may occur in the phase diagram of the system, unlike the standard perturbative approach. Furthermore, comparisons with quantum Monte Carlo simulations show that our approach provides quantitatively satisfactory results at a significantly lower computational cost than brute force numerical methods. We explicitly consider the phase diagrams for two realistic 3-periodic optical superlattices. These show that many insulator domains exhibit an unusual reentrant character, which we discuss, and suggest that the quantum phase transition relevant to the loophole-shaped insulating domains does not require extreme experimental condition in order to be observed.