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:1411.7633 · Physical Review A

Fragmentation of a spin-1 mixture in a magnetic field

Jie Zhang, Xue Hou, Bin Chen, Yunbo Zhang

Published Jan 28, 2015• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.91.013628

Related papers

Atomic-number fluctuations in a mixture of condensates

Jie Zhang, Zhi-Fang Xu, Li You +1 more

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.

arXiv:1007.2568•Physical Review A•Jul 19, 2010•11 citations

Fragmented and Single Condensate Ground States of Spin-1 Bose Gas

Tin-Lun Ho, Sungkit Yip

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order N) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.

arXiv:cond-mat/9905339•Physical Review Letters•May 1, 2000•271 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

Spin fragmentation of Bose–Einstein condensates with antiferromagnetic interactions

L. De Sarlo, Lingxuan Shao, Vincent Le Corre +4 more

We study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeeman populations, into a regular polar condensate, where the atoms all condense in the m = 0 state along the field direction. We calculate the average value and variance of the population of the Zeeman state m = 0 to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is q ∼ k B T / N , where q is the QZ energy, T the spin temperature and N the atom number. This shows that the spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit N → ∞ , but are observable for a sufficiently small atom number.

arXiv:1307.0744•New Journal of Physics•Nov 19, 2013•23 citations

GROUND STATES OF A MIXTURE OF TWO SPECIES OF SPIN-1 BOSE GASES WITH INTERSPECIES SPIN EXCHANGE IN A MAGNETIC FIELD

Yu Shi, Li Ge

We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground states. This is a complicated problem of energy minimization, with three quantum variables under constraints, i.e., the total spin of each species and the total spin of the whole mixture, as well as four parameters, including intraspecies and interspecies spin coupling strengths and the magnetic field. The quantum phase diagram is very rich. Compared with the case without a magnetic field, the ground states are modified by a magnetic field, which also modifies the ground state boundaries or introduces new crossover regimes on the phase diagram. Without interspecies spin coupling, the quantum phase transitions existing in absence of a magnetic field disappear when a magnetic field is applied, which leads to crossover regimes in the phase diagram. Under ferromagnetic interspecies spin coupling, the ground states remain disentangled no matter whether there is a magnetic field. For antiferromagnetic interspecies spin coupling, a magnetic field entangles the ground states in some parameter regimes. When the intraspecies spin couplings are both ferromagnetic, the quantum phase transition between antiferromagnetic and zero interspecies spin couplings survives the magnetic field. When the intraspecies spin couplings are both antiferromagnetic, a magnetic field induces new quantum phase transitions between antiferromagnetic and zero interspecies spin couplings.

arXiv:1111.2644•International Journal of Modern Physics B•Jan 10, 2012•9 citations

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
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 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.
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 study spin fragmentation of an antiferromagnetic spin 1 condensate in the presence of a quadratic Zeeman (QZ) effect breaking spin rotational symmetry. We describe how the QZ effect turns a fragmented spin state, with large fluctuations of the Zeeman populations, into a regular polar condensate, where the atoms all condense in the m = 0 state along the field direction. We calculate the average value and variance of the population of the Zeeman state m = 0 to illustrate clearly the crossover from a fragmented to an unfragmented state. The typical width of this crossover is q ∼ k B T / N , where q is the QZ energy, T the spin temperature and N the atom number. This shows that the spin fluctuations are a mesoscopic effect that will not survive in the thermodynamic limit N → ∞ , but are observable for a sufficiently small atom number.
We consider a mixture of two species of spin-1 atoms with both interspecies and intraspecies spin exchanges in a weak magnetic field. Under the usual single mode approximation, it can be reduced to a model of coupled giant spins. We find most of its ground states. This is a complicated problem of energy minimization, with three quantum variables under constraints, i.e., the total spin of each species and the total spin of the whole mixture, as well as four parameters, including intraspecies and interspecies spin coupling strengths and the magnetic field. The quantum phase diagram is very rich. Compared with the case without a magnetic field, the ground states are modified by a magnetic field, which also modifies the ground state boundaries or introduces new crossover regimes on the phase diagram. Without interspecies spin coupling, the quantum phase transitions existing in absence of a magnetic field disappear when a magnetic field is applied, which leads to crossover regimes in the phase diagram. Under ferromagnetic interspecies spin coupling, the ground states remain disentangled no matter whether there is a magnetic field. For antiferromagnetic interspecies spin coupling, a magnetic field entangles the ground states in some parameter regimes. When the intraspecies spin couplings are both ferromagnetic, the quantum phase transition between antiferromagnetic and zero interspecies spin couplings survives the magnetic field. When the intraspecies spin couplings are both antiferromagnetic, a magnetic field induces new quantum phase transitions between antiferromagnetic and zero interspecies spin couplings.
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 $\ensuremath{\beta}$.