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:1103.1021 · Physical Review A

Polarized entangled Bose-Einstein condensation

Jinlong Wang, Yu Shi

Published Dec 30, 2010• 2 citations
arXivHTMLPDF

Abstract

We consider a mixture of two distinct species of atoms of pseudospin $\frac{1}{2}$ with both intraspecies and interspecies spin-exchange interactions and find all the ground states in a general case of the parameters in the effective Hamiltonian. In general, corresponding to the two-species and two-pseudospin states, there are four orbital wave functions into which the atoms condense. We find that in certain parameter regimes, the ground state is the so-called polarized entangled Bose-Einstein condensation; that is, in addition to condensation of interspecies singlet pairs, there are unpaired atoms with spins polarized in the same direction. The interspecies entanglement and polarization significantly affect the generalized Gross-Pitaevskii equations governing the four orbital wave functions into which the atoms condense, as an interesting interplay between spin and orbital degrees of freedom.

DOI
10.1103/physreva.82.063637

Related papers

Entangled superfluids: Condensate dynamics of the entangled Bose-Einstein condensation

Yu Shi

We study the condensate dynamics of the so-called entangled Bose-Einstein condensation (EBEC), which is the ground state of a mixture of two species of pseudospin-$\frac{1}{2}$ atoms with interspecies spin-exchange scattering in certain parameter regimes. EBEC leads to four interdependent superfluid components, each corresponding to the orbital wave function associated with a spin component of a species. The four superflows have various counter-relations, and altogether lead to a conserved total supercurrent and a conserved total spin supercurrent. In the homogeneous case, we also obtain the elementary excitations due to variations of the single-particle orbital wave functions, by exactly solving the generalized time-dependent Bogoliubov equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like gapped mode. The origin of these excitations are also discussed from the perspective of spontaneous breaking of the symmetries possessed by the system.

arXiv:0909.4990•Physical Review A•Jul 27, 2010•8 citations

Ground states of a mixture of two species of spinor Bose gases with interspecies spin exchange

Yu Shi

We consider a mixture of two species of spin-1 atoms with interspecies spin exchange, which may cooperate or compete with intraspecies spin exchanges and thus dramatically affect the ground state. It represents a new class of bosonic gases differing from single-species spinor gases. We determine the exact ground states in several parameter regimes and study the composite structures using the generating function method generalized here to be applicable to a mixture of two species of spinor gases. The most interesting phase is the so-called entangled Bose-Einstein condensation (BEC), which is fragmented BEC with quantum entanglement between the two species and with both interspecies and intraspecies singlet pairs. For comparison, we also apply the generating function method to a mixture of two species of pseudospin-$\frac{1}{2}$ atoms, for which the total spin quantum number of each species is fixed as half of the atom number, in contrast with the case of spin $1$, for which it is a variable determined by energetics. Consequently, singlet pairs in entangled BEC of a pseudospin-$\frac{1}{2}$ mixture are all interspecies. Interspecies spin exchange leads to novel features beyond those of spinor BEC of a single species of atoms as well as mixtures without interspecies spin exchange.

arXiv:0912.2209•Physical Review A•Aug 5, 2010•24 citations

Ground states of a mixture of pseudospin-1 2 Bose gases with interspecies spin exchange

Rukuan Wu, Yu Shi

In this paper, we analytically find the ground states of a mixture of two species of pseudospin-[Formula: see text] Bose gases with interspecies spin exchange in quite generic parameter regimes. In the most interesting phase, the ground state is strongly entangled between the two species in a very wide parameter regime, and is an entangled Bose-Einstein condensate. The phase diagram and elementary excitations are studied.

Modern Physics Letters B•Feb 1, 2016•0 citations

Orbital elementary excitations as probes of entanglement and quantum phase transitions of collective spins in an entangled Bose-Einstein condensate

Rukuan Wu, Yu Shi

A mixture of two species of pseudospin-$\frac{1}{2}$ Bose gases exhibits interesting interplay between spin and orbital degrees of freedom. Expectation values of various quantities of the collective spins of the two species play crucial roles in the Gross-Pitaevskii-like equations governing the four orbital wave functions in which Bose-Einstein condensation occurs. Consequently, the elementary excitations of these orbital wave functions reflect properties of the collective spins. When the coupling between the two collective spins is isotropic, the energy gap of the gapped orbital excitation peaks. There is a quantum phase transition in the ground state of the effective Hamiltonian of the two collective spins, which have previously been found to be maximally entangled.

arXiv:1103.1022•Physical Review A•Feb 28, 2011•4 citations

Number and spin densities in the ground state of a trapped mixture of two pseudospin-$\frac{1}{2}$ Bose gases with interspecies spin-exchange interaction

Jinlong Wang, Yu Shi

We consider the ground state of a mixture of two pseudospin- Bose gases with interspecies spin exchange in a trapping potential. In the mean field approach, the ground state can be described in terms of four wavefunctions governed by a set of coupled Gross–Pitaevskii-like (GP-like) equations, which differ from the usual GP equations in the existence of an interference term due to spin-exchange coupling between the two species. Using these GP-like equations, we calculate such ground state properties as chemical potentials, density profiles and spin density profiles, which are directly observable in experiments. We compare the cases with and without spin exchange. It is demonstrated that the spin exchange between the two species lowers the chemical potentials, tends to equalize the wavefunctions of the two pseudospin components of each species, and, thus, homogenizes the spin density. The novel features of the density and spin density profiles can serve as experimental probes of this novel Bose system.

arXiv:1302.7217•Journal of Statistical Mechanics Theory and Experiment•Apr 9, 2013•1 citation

Spin-textures of the Bose-Einstein condensates with three kinds of spin-1 atoms

Y. Z. He, Y. M. Liu, Bao Cheng-guang

We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins $S_A$, $S_B$ and $S_C$ of the three species, the spin-textures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each others, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of $S_A$, $S_B$ and $S_C$ the spin-textures can be further classified into four kinds, namely, $p$+$p$+$p$ (all atoms of each species are in singlet-pairs), one species in $f$ (fully polarized) and two species in $q$ (a mixture of polarized atoms and singlet-pairs), two in $f$ and one in $q$, and $f$+$f$+$f$. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-texture have been specified. A number of spin-texture-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predicted.

arXiv:1910.04381•Oct 10, 2019•0 citations
We consider a mixture of two distinct species of atoms of pseudospin 12\frac{1}{2}21​ with both intraspecies and interspecies spin-exchange interactions and find all the ground states in a general case of the parameters in the effective Hamiltonian. In general, corresponding to the two-species and two-pseudospin states, there are four orbital wave functions into which the atoms condense. We find that in certain parameter regimes, the ground state is the so-called polarized entangled Bose-Einstein condensation; that is, in addition to condensation of interspecies singlet pairs, there are unpaired atoms with spins polarized in the same direction. The interspecies entanglement and polarization significantly affect the generalized Gross-Pitaevskii equations governing the four orbital wave functions into which the atoms condense, as an interesting interplay between spin and orbital degrees of freedom.
We study the condensate dynamics of the so-called entangled Bose-Einstein condensation (EBEC), which is the ground state of a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms with interspecies spin-exchange scattering in certain parameter regimes. EBEC leads to four interdependent superfluid components, each corresponding to the orbital wave function associated with a spin component of a species. The four superflows have various counter-relations, and altogether lead to a conserved total supercurrent and a conserved total spin supercurrent. In the homogeneous case, we also obtain the elementary excitations due to variations of the single-particle orbital wave functions, by exactly solving the generalized time-dependent Bogoliubov equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like gapped mode. The origin of these excitations are also discussed from the perspective of spontaneous breaking of the symmetries possessed by the system.
We consider a mixture of two species of spin-1 atoms with interspecies spin exchange, which may cooperate or compete with intraspecies spin exchanges and thus dramatically affect the ground state. It represents a new class of bosonic gases differing from single-species spinor gases. We determine the exact ground states in several parameter regimes and study the composite structures using the generating function method generalized here to be applicable to a mixture of two species of spinor gases. The most interesting phase is the so-called entangled Bose-Einstein condensation (BEC), which is fragmented BEC with quantum entanglement between the two species and with both interspecies and intraspecies singlet pairs. For comparison, we also apply the generating function method to a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms, for which the total spin quantum number of each species is fixed as half of the atom number, in contrast with the case of spin 111, for which it is a variable determined by energetics. Consequently, singlet pairs in entangled BEC of a pseudospin-12\frac{1}{2}21​ mixture are all interspecies. Interspecies spin exchange leads to novel features beyond those of spinor BEC of a single species of atoms as well as mixtures without interspecies spin exchange.
A mixture of two species of pseudospin-12\frac{1}{2}21​ Bose gases exhibits interesting interplay between spin and orbital degrees of freedom. Expectation values of various quantities of the collective spins of the two species play crucial roles in the Gross-Pitaevskii-like equations governing the four orbital wave functions in which Bose-Einstein condensation occurs. Consequently, the elementary excitations of these orbital wave functions reflect properties of the collective spins. When the coupling between the two collective spins is isotropic, the energy gap of the gapped orbital excitation peaks. There is a quantum phase transition in the ground state of the effective Hamiltonian of the two collective spins, which have previously been found to be maximally entangled.
Number and spin densities in the ground state of a trapped mixture of two pseudospin-12\frac{1}{2}21​ Bose gases with interspecies spin-exchange interaction
We consider the ground state of a mixture of two pseudospin- Bose gases with interspecies spin exchange in a trapping potential. In the mean field approach, the ground state can be described in terms of four wavefunctions governed by a set of coupled Gross–Pitaevskii-like (GP-like) equations, which differ from the usual GP equations in the existence of an interference term due to spin-exchange coupling between the two species. Using these GP-like equations, we calculate such ground state properties as chemical potentials, density profiles and spin density profiles, which are directly observable in experiments. We compare the cases with and without spin exchange. It is demonstrated that the spin exchange between the two species lowers the chemical potentials, tends to equalize the wavefunctions of the two pseudospin components of each species, and, thus, homogenizes the spin density. The novel features of the density and spin density profiles can serve as experimental probes of this novel Bose system.
We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins SAS_ASA​, SBS_BSB​ and SCS_CSC​ of the three species, the spin-textures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each others, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SAS_ASA​, SBS_BSB​ and SCS_CSC​ the spin-textures can be further classified into four kinds, namely, ppp+ppp+ppp (all atoms of each species are in singlet-pairs), one species in fff (fully polarized) and two species in qqq (a mixture of polarized atoms and singlet-pairs), two in fff and one in qqq, and fff+fff+fff. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-texture have been specified. A number of spin-texture-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predicted.