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:1007.2568 · Physical Review A

Atomic-number fluctuations in a mixture of condensates

Jie Zhang, Zhi-Fang Xu, Li You, Yunbo Zhang

Published Jul 19, 2010• 11 citations
arXivHTMLPDF

Abstract

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction ${c}_{12}\ensuremath{\beta}$ is adjusted. The two spin-1 condensates forming the mixture are, respectively, ferromagnetic and polar in the absence of an external magnetic (B) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when ${c}_{12}\ensuremath{\beta}>0$), where the ground state becomes fragmented and atomic-number fluctuations exhibit drastically different features from a single standalone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.

DOI
10.1103/physreva.82.013625

Related papers

Interspecies singlet pairing in a mixture of two spin-1 Bose condensates

Jie Zhang, Tiantian Li, Yunbo Zhang

We study the ground-state properties of a mixture formed by two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction ($\ensuremath{\beta}$) and interspecies singlet-pairing interaction ($\ensuremath{\gamma}$) arise. The ground state can be calculated using the angular momentum theory analytically for $\ensuremath{\gamma}=0$. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case as $\ensuremath{\gamma}\ensuremath{\ne}0$. We illustrate the competition between the two interspecies interactions and find that as singlet-pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by $\ensuremath{\beta}$.

arXiv:1105.0271•Physical Review A•Feb 22, 2011•14 citations

Fragmentation of a spin-1 mixture in a magnetic field

Jie Zhang, Xue Hou, Bin Chen +1 more

We study ground-state quantum fragmentation in a mixture of a polar condensate and a ferromagnetic condensate when subjected to an external magnetic field. We pay more attention to the polar condensate, due to the fact that fragmentation of a polar condensate, which typically occurs only in a very weak magnetic field, can occur in a mixture at higher magnetic fields, where both atom numbers and number fluctuations will remain of a macroscopic magnitude, of the order of $N$. The role of the ferromagnetic condensate is to provide a uniform and stable background which can delay the rapid shrinkage of the zero-component population and make it possible to capture ``superfragmentation.'' Our method has potential applications in measurement of the interspecies spin-coupling interaction by adjusting the magnetic field.

arXiv:1411.7633•Physical Review A•Jan 28, 2015•3 citations

Binary mixture of spinor atomic Bose-Einstein condensates

Zhi-Fang Xu, Yunbo Zhang, Li You

We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic $(B)$ field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.

arXiv:0901.1505•Physical Review A•Feb 10, 2009•31 citations

Quantum entangled ground states of two spinor Bose-Einstein condensates

Zhi-Fang Xu, Rong Lü, Li You

We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The noncommuting terms in the spin-dependent Hamiltonian under the single-spatial-mode approximation make it difficult to obtain exact eigenstates. Utilizing spin-z-component conservation and total spin angular momentum conservation, we numerically derive information on the building blocks and evaluate the von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.

arXiv:1112.0837•Physical Review A•Dec 27, 2011•13 citations

Spontaneously axisymmetry-breaking phase in a binary mixture of spinor Bose-Einstein condensates

Zhi-Fang Xu, Jia‐Wei Mei, Rong Lü +1 more

We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic ($B$) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.

arXiv:1011.0505•Physical Review A•Nov 24, 2010•16 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
We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction c12\ensuremathβ{c}_{12}\ensuremath{\beta}c12​\ensuremathβ is adjusted. The two spin-1 condensates forming the mixture are, respectively, ferromagnetic and polar in the absence of an external magnetic (B) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when c12\ensuremathβ>0{c}_{12}\ensuremath{\beta}>0c12​\ensuremathβ>0), where the ground state becomes fragmented and atomic-number fluctuations exhibit drastically different features from a single standalone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.
We study the ground-state properties of a mixture formed by two spin-1 condensates in the absence of an external magnetic field. As the collisional symmetry between interspecies bosonic atoms is broken, the interspecies coupling interaction ($\ensuremath{\beta}$) and interspecies singlet-pairing interaction ($\ensuremath{\gamma}$) arise. The ground state can be calculated using the angular momentum theory analytically for $\ensuremath{\gamma}=0$. The full quantum approach of exact diagonalization is adopted numerically to consider the more general case as $\ensuremath{\gamma}\ensuremath{\ne}0$. We illustrate the competition between the two interspecies interactions and find that as singlet-pairing interaction dominates (or the total spin vanishes), there are still different types of singlet formations which are well determined by $\ensuremath{\beta}$.
We study ground-state quantum fragmentation in a mixture of a polar condensate and a ferromagnetic condensate when subjected to an external magnetic field. We pay more attention to the polar condensate, due to the fact that fragmentation of a polar condensate, which typically occurs only in a very weak magnetic field, can occur in a mixture at higher magnetic fields, where both atom numbers and number fluctuations will remain of a macroscopic magnitude, of the order of NNN. The role of the ferromagnetic condensate is to provide a uniform and stable background which can delay the rapid shrinkage of the zero-component population and make it possible to capture ``superfragmentation.'' Our method has potential applications in measurement of the interspecies spin-coupling interaction by adjusting the magnetic field.
We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic (B)(B)(B) field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.
We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The noncommuting terms in the spin-dependent Hamiltonian under the single-spatial-mode approximation make it difficult to obtain exact eigenstates. Utilizing spin-z-component conservation and total spin angular momentum conservation, we numerically derive information on the building blocks and evaluate the von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.
We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic (BBB) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.
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.