Theory of p-orbital bosons

A generalized one-dimensional $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ spin-orbital model is studied by means of Schwinger boson mean-field theory (SBMFT). We focus on exploring the dimer phases and clarify how to capture properly the low-temperature properties of the system. The phase diagrams for the cases of $S=T=1∕2$ and of $S=1$ and $T=1∕2$ are presented. Three dimer phases, the orbital valence bond state, spin valence bond state and spin-orbital valence bond state, are found to arise in proper parameter regions. The results indicate that the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ type of spin-orbit coupling can serve as both the spin-Peierls and orbital-Peierls mechanisms which are responsible for the formations of spin singlet and orbital singlet, respectively. We have also calculated the static spin and pseudospin susceptibilities in the SBMFT scheme to characterize and distinguish the three types of dimer phases.A generalized one-dimensional $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ spin-orbital model is studied by means of Schwinger boson mean-field theory (SBMFT). We focus on exploring the dimer phases and clarify how to capture properly the low-temperature properties of the system. The phase diagrams for the cases of $S=T=1∕2$ and of $S=1$ and $T=1∕2$ are presented. Three dimer phases, the orbital valence bond state, spin valence bond state and spin-orbital valence bond state, are found to arise in proper parameter regions. The results indicate that the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ type of spin-orbit coupling can serve as both the spin-Peierls and orbital-Peierls mechanisms which are responsible for the formations of spin singlet and orbital singlet, respectively. We have also calculated the static spin and pseudospin susceptibilities in the SBMFT scheme to characterize and distinguish the three types of dimer phases.

arXiv:cond-mat/0508086Physical Review BDec 30, 20056 citations

Confined p-Orbital Bosons

Fernanda Pinheiro

Springer thesesJan 1, 20161 citation

Properties of fragmented repulsive condensates

Alexej I. Streltsov, L. S. Cederbaum

Repulsive Bose-Einstein condensates immersed into a double-well trap potential are studied within the framework of the recently introduced mean-field approach which allows for bosons to reside in several different orthonormal orbitals. In the case of a one-orbital mean-field theory (Gross-Pitaevskii) the ground state of the system reveals a bifurcation scenario at some critical values of the interparticle interaction and/or the number of particles. At about the same values of the parameters the two-orbital mean field predicts that the system becomes twofold fragmented. By applying the three-orbital mean field we verify numerically that for the double-well external potential studied here the overall best mean field is achieved with two orbitals. The variational principle minimizes the energy at a vanishing population of the third orbital. To discuss the energies needed to remove a boson from and the energies gained by adding a boson to the condensate, we introduce boson ionization potentials and boson affinities and relate them to the chemical potentials. The impact of the finite number of bosons in the condensate on these quantities is analyzed. We recall that within the framework of the multiorbital mean-field theory each fragment is characterized by its own chemical potential. Finally, the stability of fragmented states is discussed in terms of the boson transfer energy which is the energy needed to transfer a boson from one fragment to another.Repulsive Bose-Einstein condensates immersed into a double-well trap potential are studied within the framework of the recently introduced mean-field approach which allows for bosons to reside in several different orthonormal orbitals. In the case of a one-orbital mean-field theory (Gross-Pitaevskii) the ground state of the system reveals a bifurcation scenario at some critical values of the interparticle interaction and/or the number of particles. At about the same values of the parameters the two-orbital mean field predicts that the system becomes twofold fragmented. By applying the three-orbital mean field we verify numerically that for the double-well external potential studied here the overall best mean field is achieved with two orbitals. The variational principle minimizes the energy at a vanishing population of the third orbital. To discuss the energies needed to remove a boson from and the energies gained by adding a boson to the condensate, we introduce boson ionization potentials and boson affinities and relate them to the chemical potentials. The impact of the finite number of bosons in the condensate on these quantities is analyzed. We recall that within the framework of the multiorbital mean-field theory each fragment is characterized by its own chemical potential. Finally, the stability of fragmented states is discussed in terms of the boson transfer energy which is the energy needed to transfer a boson from one fragment to another.

arXiv:cond-mat/0412222Physical Review AJun 22, 200518 citations

Unified Theory of Interacting Bosons

Eugene P. Gross

Physical ReviewApr 1, 1957190 citations

Multiconfigurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems

Ofir E. Alon, Alexej I. Streltsov, L. S. Cederbaum

The evolution of Bose-Einstein condensates is amply described by the time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent one-particle state throughout the propagation process. In this work, we go beyond mean field and develop an essentially exact many-body theory for the propagation of the time-dependent Schr\"odinger equation of $N$ interacting identical bosons. In our theory, the time-dependent many-boson wave function is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are time-dependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations of motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and nonlinear integrodifferential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multiconfigurational time-dependent Hartree for bosons, or $\text{MCTDHB}(M)$ , where $M$ specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed. The convergence of the method with a growing number $M$ of orbitals is demonstrated in a specific example of four interacting bosons in a double well.The evolution of Bose-Einstein condensates is amply described by the time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent one-particle state throughout the propagation process. In this work, we go beyond mean field and develop an essentially exact many-body theory for the propagation of the time-dependent Schr\"odinger equation of $N$ interacting identical bosons. In our theory, the time-dependent many-boson wave function is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are time-dependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations of motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and nonlinear integrodifferential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multiconfigurational time-dependent Hartree for bosons, or $\text{MCTDHB}(M)$, where $M$ specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed. The convergence of the method with a growing number $M$ of orbitals is demonstrated in a specific example of four interacting bosons in a double well.

arXiv:cond-mat/0703237Physical Review AMar 14, 2008355 citations

S=T=1∕2

and of

S=1

and

T=1∕2

are presented. Three dimer phases, the orbital valence bond state, spin valence bond state and spin-orbital valence bond state, are found to arise in proper parameter regions. The results indicate that the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ type of spin-orbit coupling can serve as both the spin-Peierls and orbital-Peierls mechanisms which are responsible for the formations of spin singlet and orbital singlet, respectively. We have also calculated the static spin and pseudospin susceptibilities in the SBMFT scheme to characterize and distinguish the three types of dimer phases.

N

interacting identical bosons. In our theory, the time-dependent many-boson wave function is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are time-dependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations of motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and nonlinear integrodifferential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multiconfigurational time-dependent Hartree for bosons, or

\text{MCTDHB}(M)

, where

M

specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed. The convergence of the method with a growing number

M

of orbitals is demonstrated in a specific example of four interacting bosons in a double well.