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:cond-mat/0505539 · Physical Review B

Bose-Einstein condensation in tight-binding bands

R. Ramakumar, A. N. Das

Published Sep 2, 2005• 9 citations
arXivHTMLPDF

Abstract

We present a theoretical study of the condensation of bosons in tight-binding bands corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. We have analyzed noninteracting bosons, weakly interacting bosons using the Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for the number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body-centered cubic lattice have the highest Bose condensation temperature. The growth of the condensate fraction of noninteracting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes the bosons to form a Bose-Mott-Hubbard insulator for integer filling.

DOI
10.1103/physrevb.72.094301

Related papers

Bose-Einstein Condensation of Spin-1 Atoms in Tight-binding Bands

Guo Wang

We present a theoretical study of Bose-Einstein condensation(BEC) of trapped ideal gas of spin-1 ultracold atoms in tight-binding bands corresponding to simple cubic(SC) optical lattices.Under the constraints that both the total number of atoms (N) and the total magnetization (M) are conserved,we first investigate the phase transitions process of noninteracting spin-1 atomic system,by investigating the critical condensation temperature and condensate fraction,we find BEC with spin degrees of freedom shows richer phase transitions than BEC of scalar atoms.We then extend our studies to the case with a uniform external magnetic field included,the phase transitions for this case make interesting changes again.

Shinjang dashösi ilmiy jurnili•Jan 1, 2010•0 citations

Interaction-driven crossover from Mott insulator–superfluid criticality to Bose-Einstein condensation in a simple cubic lattice

T. K. Kopeć

We investigate how strongly interacting bosons, described by the Bose-Hubbard Hamiltonian, transition from the Mott insulator to the superfluid phase and, ultimately, to a regime of vanishing interaction where the system smoothly transitions to an ensemble of free bosons undergoing Bose-Einstein condensation. Our study focuses on bosons residing on a three-dimensional simple cubic lattice, with tight-binding interactions characterized by the kinetic energy $t$ between neighboring lattice sites and on-site repulsion $U$. To achieve this, we develop a formalism based on mapping the original quantum mechanical Hamiltonian onto an effective quantum spherical model. This approach is nonperturbative in interaction energy and spans the entire range of the interaction parameter $U$. Our findings are presented through a series of multiparameter phase diagrams that include temperature, interaction energy, chemical potential, and particle density, highlighting the corresponding critical surfaces and lines. In this context, we address the issue of quantum critical points at fixed densities, which appear as endpoints in the temperature-interaction phase diagram. We also compare our theoretical results, where applicable, with other approaches, including quantum Monte Carlo simulations.

Physical review. B./Physical review. B•Oct 17, 2024•4 citations

Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Ali A. Shams, H. R. Glyde

We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.

Physical Review B•Jun 8, 2009•9 citations

Fermion pair formation and condensation in extended Hubbard models in body-centered-cubic optical lattices

Ganiyu D. Adebanjo, P. E. Kornilovitch, J. P. Hague

We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite $U$ and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.

•Feb 15, 2021•0 citations

Bose–Einstein condensation in one-dimensional optical lattices: Bogoliubov’s approximation and beyond

Mohamed K. Al-Sugheir, Mufeed A. Awawdeh, H. B. Ghassib +1 more

Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.

Canadian Journal of Physics•Apr 27, 2016•2 citations

Functional renormalization for Bose-Einstein condensation

Stefan Floerchinger, CHRISTOF WETTERICH

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three-dimensional dilute gases, we find an upper bound on the scattering length $a$ which is of the order of the microphysical scale---typically the range of the van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density $n$, and find for the critical temperature ${T}_{c}$ a deviation from the free theory, $\ensuremath{\Delta}{T}_{c}/{T}_{c}=2.1a{n}^{1/3}$. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.

arXiv:0801.2910•Physical Review A•May 8, 2008•53 citations
We present a theoretical study of the condensation of bosons in tight-binding bands corresponding to simple cubic, body-centered cubic, and face-centered cubic lattices. We have analyzed noninteracting bosons, weakly interacting bosons using the Bogoliubov method, and strongly interacting bosons through a renormalized Hamiltonian approach valid for the number of bosons per site less than or equal to unity. In all the cases studied, we find that bosons in a body-centered cubic lattice have the highest Bose condensation temperature. The growth of the condensate fraction of noninteracting bosons is found to be very close to that of free bosons. The interaction partially depletes the condensate at zero temperature and close to it, while enhancing it beyond this range below the Bose-Einstein condensation temperature. Strong interaction enhances the boson effective mass as the band-filling is increased and eventually localizes the bosons to form a Bose-Mott-Hubbard insulator for integer filling.
We present a theoretical study of Bose-Einstein condensation(BEC) of trapped ideal gas of spin-1 ultracold atoms in tight-binding bands corresponding to simple cubic(SC) optical lattices.Under the constraints that both the total number of atoms (N) and the total magnetization (M) are conserved,we first investigate the phase transitions process of noninteracting spin-1 atomic system,by investigating the critical condensation temperature and condensate fraction,we find BEC with spin degrees of freedom shows richer phase transitions than BEC of scalar atoms.We then extend our studies to the case with a uniform external magnetic field included,the phase transitions for this case make interesting changes again.
We investigate how strongly interacting bosons, described by the Bose-Hubbard Hamiltonian, transition from the Mott insulator to the superfluid phase and, ultimately, to a regime of vanishing interaction where the system smoothly transitions to an ensemble of free bosons undergoing Bose-Einstein condensation. Our study focuses on bosons residing on a three-dimensional simple cubic lattice, with tight-binding interactions characterized by the kinetic energy ttt between neighboring lattice sites and on-site repulsion UUU. To achieve this, we develop a formalism based on mapping the original quantum mechanical Hamiltonian onto an effective quantum spherical model. This approach is nonperturbative in interaction energy and spans the entire range of the interaction parameter UUU. Our findings are presented through a series of multiparameter phase diagrams that include temperature, interaction energy, chemical potential, and particle density, highlighting the corresponding critical surfaces and lines. In this context, we address the issue of quantum critical points at fixed densities, which appear as endpoints in the temperature-interaction phase diagram. We also compare our theoretical results, where applicable, with other approaches, including quantum Monte Carlo simulations.
We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.
We investigate the formation and condensation of fermion pairs in cold atom quantum simulators for extended Hubbard models (UV models) with body center cubic (BCC) optical lattices, predicting small and light pairs with Bose--Einstein condensation (BEC) temperatures up to the order of 100 nK. Pair mass, radius, and binding conditions are calculated, and then used to compute transition temperatures. We predict that: (a) local pairs can form in BCC optical lattices; (b) for particular cases where the onsite UUU and intersite V are attractive with similar size, the pairs are both small and light; and (c) that transition temperatures could be as high as 100 nK (50 nK) for 6Li atoms in blue (red) BCC optical lattices. Beyond the application to pairs on BCC optical lattices, we expect our results to be relevant to strong-coupling BCC superconductors.
Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.
We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three-dimensional dilute gases, we find an upper bound on the scattering length aaa which is of the order of the microphysical scale---typically the range of the van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density nnn, and find for the critical temperature Tc{T}_{c}Tc​ a deviation from the free theory, $\ensuremath{\Delta}{T}_{c}/{T}_{c}=2.1a{n}^{1/3}$. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.