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:1205.3178 · Physical Review B

Superfluid-insulator transition of two-species bosons with spin-orbit coupling

Saptarshi Mandal, Kush Saha, K. Sengupta

Published Oct 1, 2012• 33 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude $t$ and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero $t$. We propose experiments to test our theory.

DOI
10.1103/physrevb.86.155101

Related papers

Optical lattice modulation spectroscopy for spin-orbit coupled bosons

S. Sarkar, Rajdeep Sensarma, K. Sengupta

Interacting bosons with two ``spin'' states in a lattice show superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero-momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum-resolved optical modulation spectroscopy can identify both the gapless (Goldstone) and gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero-momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.

arXiv:1505.06372•Physical Review B•Nov 30, 2015•3 citations

QUANTUM PHASE TRANSITION IN SPIN-ORBIT COUPLED BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES OF DIFFERENT GEOMETRIES

Oladunjoye A. Awoga

Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.

131•Jan 1, 2014•0 citations

Ultracold bosons in a synthetic periodic magnetic field: Mott phases and reentrant superfluid-insulator transitions

Kush Saha, K. Sengupta, Koushik Ray

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ $(q/2)$ in real space for odd (even) $q$ and suggest experiments to test our theory.

arXiv:1005.4476•Physical Review B•Nov 29, 2010•8 citations

Thermal transitions of the modulated superfluid for spin-orbit coupled correlated bosons in an optical lattice

Arijit Dutta, Abhishek Joshi, K. Sengupta +1 more

We investigate the thermal physics of a Bose-Hubbard model with Rashba spin-orbit coupling starting from a strong coupling mean-field ground state. The essential role of the spin-orbit coupling $\left(\ensuremath{\gamma}\right)$ is to promote condensation of the bosons at a finite wave vector ${\mathbit{k}}_{0}$. We find that the bosons display either homogeneous or phase-twisted or orbital ordered superfluid phases, depending on $\ensuremath{\gamma}$ and the interspecies interaction strength $\left(\ensuremath{\lambda}\right)$. We show that an increase of $\ensuremath{\gamma}$ leads to suppression of the critical interaction ${U}_{c}$ for the superfluid to Mott insulator transition in the ground state and a reduction of the ${T}_{c}$ for superfluid to Bose-liquid transition at a fixed interaction strength. We capture the thermal broadening in the momentum distribution function, and the real space profiles of the thermally disordered magnetic textures, including their homogenization for $T\ensuremath{\gtrsim}{T}_{c}$. We provide a Landau theory based description of the ground state phase boundaries and thermal transition scales and discuss experiments which can test our theory.

arXiv:1901.10672•Physical review. B./Physical review. B•May 14, 2019•3 citations

Interaction-driven exotic quantum phases in spin-orbit-coupled spin-1 bosons

J. H. Pixley, Stefan S. Natu, Ian B. Spielman +1 more

We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two-dimensional optical lattice, focusing on the spin-1 spin-orbit-coupled system recently realized at the Joint Quantum Institute [Campbell et al., arXiv:1501.05984]. We find a rich quantum phase diagram where, in addition to the conventional phases---superfluid and insulator---contained in the spin-1 Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave vector, induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a nonzero spin-orbit strength. This state is characterized by spin-density-wave order, which arises from the spin-1 nature of the system. Interactions suppress spin-density-wave order, and favor a superfluid only at the Brillouin zone edge. This state has spatially oscillating mean-field order parameters, but a homogeneous density. We show that the spin-density-wave superfluid phase survives in a two-dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on $^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}$, and $^{41}\mathrm{K}$.

arXiv:1509.00005•Physical review. B./Physical review. B•Feb 1, 2016•14 citations

Superfluid–Mott-insulator transition in the spin-orbit-coupled Bose-Hubbard model

Ahmet Tuna Bolukbasi, M. Iskin

We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling and Zeeman field on the ground-state, i.e., Mott-insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase-transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit-coupled SF phase is a nonuniform (twisted) one, with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insights into the numerical results are also given.

arXiv:1401.0527•Physical Review A•Apr 4, 2014•15 citations
Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude ttt and in the presence of a spin-orbit coupling characterized by a tunable strength \ensuremathγ\ensuremath{\gamma}\ensuremathγ. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning \ensuremathγ\ensuremath{\gamma}\ensuremathγ. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at t/\ensuremathγ=0t/\ensuremath{\gamma}=0t/\ensuremathγ=0, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on \ensuremathγ\ensuremath{\gamma}\ensuremathγ. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of \ensuremathγ\ensuremath{\gamma}\ensuremathγ for nonzero ttt. We propose experiments to test our theory.
Interacting bosons with two ``spin'' states in a lattice show superfluid-insulator phase transitions in the presence of spin-orbit coupling. Depending on the parameter regime, bosons in the superfluid phase can condense to either a zero-momentum state or to one or multiple states with finite momentum, leading to an unconventional superfluid phase. We study the response of such a system to modulation of the optical lattice potential. We show that the change in momentum distribution after lattice modulation shows distinct patterns in the Mott and the superfluid phase and these patterns can be used to detect these phases and the quantum phase transition between them. Further, the momentum-resolved optical modulation spectroscopy can identify both the gapless (Goldstone) and gapped amplitude (Higgs) mode of the superfluid phase and clearly distinguish between the superfluid phases with a zero-momentum condensate and a twisted superfluid phase by looking at the location of these modes in the Brillouin zone. We discuss experiments which can test our theory.
Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength ppp and a period l=qal=qal=qa, where qqq is an integer and aaa is the lattice spacing. We show that the Schr\"odinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields qqq energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying ppp for a given qqq. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the ppp and qqq dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period qqq. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity qqq (q/2)(q/2)(q/2) in real space for odd (even) qqq and suggest experiments to test our theory.
We investigate the thermal physics of a Bose-Hubbard model with Rashba spin-orbit coupling starting from a strong coupling mean-field ground state. The essential role of the spin-orbit coupling $\left(\ensuremath{\gamma}\right)$ is to promote condensation of the bosons at a finite wave vector ${\mathbit{k}}_{0}$. We find that the bosons display either homogeneous or phase-twisted or orbital ordered superfluid phases, depending on $\ensuremath{\gamma}$ and the interspecies interaction strength $\left(\ensuremath{\lambda}\right)$. We show that an increase of $\ensuremath{\gamma}$ leads to suppression of the critical interaction Uc{U}_{c}Uc​ for the superfluid to Mott insulator transition in the ground state and a reduction of the Tc{T}_{c}Tc​ for superfluid to Bose-liquid transition at a fixed interaction strength. We capture the thermal broadening in the momentum distribution function, and the real space profiles of the thermally disordered magnetic textures, including their homogenization for $T\ensuremath{\gtrsim}{T}_{c}$. We provide a Landau theory based description of the ground state phase boundaries and thermal transition scales and discuss experiments which can test our theory.
We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two-dimensional optical lattice, focusing on the spin-1 spin-orbit-coupled system recently realized at the Joint Quantum Institute [Campbell et al., arXiv:1501.05984]. We find a rich quantum phase diagram where, in addition to the conventional phases---superfluid and insulator---contained in the spin-1 Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave vector, induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a nonzero spin-orbit strength. This state is characterized by spin-density-wave order, which arises from the spin-1 nature of the system. Interactions suppress spin-density-wave order, and favor a superfluid only at the Brillouin zone edge. This state has spatially oscillating mean-field order parameters, but a homogeneous density. We show that the spin-density-wave superfluid phase survives in a two-dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on 87Rb,7Li^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}87Rb,7Li, and 41K^{41}\mathrm{K}41K.
We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling and Zeeman field on the ground-state, i.e., Mott-insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase-transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit-coupled SF phase is a nonuniform (twisted) one, with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insights into the numerical results are also given.