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

Scientific Reports

Localization-delocalization transition in spin-orbit-coupled Bose-Einstein condensate

Chunyan Li, Fangwei Ye, Yaroslav V. Kartashov, V. V. Konotop, Xianfeng Chen

Published Aug 17, 2016• 16 citations
Publisher

Abstract

We address the impact of the spin-orbit (SO) coupling on the localization-delocalization-transition (LDT) in a spin-orbit coupled Bose-Einstein condensate in a bichromatic potential. We find that SO coupling significantly alters the threshold depth of the one of sublattices above which the lowest eigenstates transform from delocalizated into localized. For some moderate coupling strengths the threshold is strongly reduced, which is explained by the SO coupling-induced band flattening in one of the sub-lattices. We explain why simultaneous Rabi and SO coupling are necessary ingredients for LDT threshold cancellation and show that strong SO coupling drives the system into the state where its evolution becomes similar to the evolution of a one-component system. We also find that defocusing nonlinearity can lead to localization of the states which are delocalized in the linear limit.

DOI
10.1038/srep31700

Related papers

Signature of localization–delocalization in collisional inhomogeneous spin-orbit coupled condensates

Swarup K. Sarkar, Rajamanickam Ravisankar, Tapan Mishra +2 more

Abstract We study the localization transition in spin–orbit (SO) coupled binary Bose–Einstein condensates with collisional inhomogeneous interaction trapped in a one-dimensional quasiperiodic potential. Our numerical analysis shows that the competition between the quasiperiodic disorder and inhomogeneous interaction leads to a localization–delocalization transition as the interaction strength is tuned from attractive to repulsive in nature. Furthermore, we analyse the combined effect of the SO and Rabi coupling strengths on the localization transition for different interaction strengths and obtain signatures of similar localization–delocalization transition as a function of SO coupling in the regime of weak interactions. We complement our numerical observation with the analytical model using the Gaussian variational approach. In the end, we show how the localization–delocalization is manifested in the quench dynamics of the condensate. Our study provides an indirect approach to achieve localization transition without tuning the quasiperiodic potential strength, but rather by tuning the inhomogeneity in the interaction.

arXiv:2403.02027•Journal of Physics B Atomic Molecular and Optical Physics•Mar 3, 2025•4 citations

Spin-dependent localization of spin–orbit and Rabi-coupled Bose–Einstein condensates in a random potential

Swarup K. Sarkar, Sh. Mardonov, Eugene Ya. Sherman +2 more

Abstract We investigate the effect of the spin–orbit (SO) and Rabi couplings on the localization of the spin-1/2 condensate trapped in a one-dimensional random potential. Our studies reveal that the spin-dependent couplings create distinct localization regimes, resulting in various relations between localization and spin-related properties. First, we examine the localization in the linear condensate and find that the SO coupling can lead to a transition of the localized state from the ‘basin-like’ to the ‘void’ region of the potential. For a weak random potential upon an increase in the SO coupling, we find a re-entrant transition from a broad to narrow localized state and back at a higher SO coupling. Further, we analyze the competing role of inter-species and intra-species interactions on the localization of the condensate. We find the appearance of spin-dependent localization as the interactions increase beyond threshold values for a sufficiently strong disorder. Our findings on controlling spin-dependent localization may be useful for future ultracold atomic experiments and corresponding spin-related quantum technologies.

arXiv:2410.06005•New Journal of Physics•Jan 29, 2025•3 citations

Controlling Anderson localization of a Bose-Einstein condensate via spin-orbit coupling and Rabi fields in bichromatic lattices

Bar Alluf, C. A. R. Sá de Melo

We perform theoretical studies of the interplay between disorder, spin-orbit coupling (SOC), and Rabi fields, and show that both SOC and Rabi fields can be used to dramatically control the degree of Anderson localization of a Bose-Einstein condensate in bichromatic lattices. We obtain ground-state phase diagrams in the SOC and Rabi field plane for different values of disorder strength and use realistic experimental parameters compatible with $^{39}\mathrm{K}$. We find cases of fixed disorder and SOC (Rabi field), where the Rabi field (SOC) reduces the threshold for localization and controls the localization length. We also show regimes of fixed disorder and Rabi field, where the extent of the ground-state wave function is periodic in the SOC, leading to alternating regions of stronger and weaker localization as SOC changes. Lastly, we describe examples of fixed disorder and SOC, where tuning the Rabi field leads to a strong localization peak.

Physical Review A•Mar 15, 2023•5 citations

Localization of a spin-orbit-coupled Bose-Einstein condensate in a bichromatic optical lattice

Yongshan Cheng, Gaohui Tang, Sadhan K. Adhikari

We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.

arXiv:1404.4017•Physical Review A•Jun 3, 2014•67 citations

Bose-Einstein condensates with localized spin-orbit coupling: Soliton complexes and spinor dynamics

Yaroslav V. Kartashov, V. V. Konotop, Dmitry A. Zezyulin

Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO ``defect'' can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.

arXiv:1411.7322•Physical Review A•Dec 15, 2014•59 citations

Localization and spin dynamics of spin-orbit-coupled Bose-Einstein condensates in deep optical lattices

Ai-Xia Zhang, Xiao-Wen Hu, Yan-Fang Jiang +4 more

We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.

Physical review. E•Dec 28, 2021•1 citation
We address the impact of the spin-orbit (SO) coupling on the localization-delocalization-transition (LDT) in a spin-orbit coupled Bose-Einstein condensate in a bichromatic potential. We find that SO coupling significantly alters the threshold depth of the one of sublattices above which the lowest eigenstates transform from delocalizated into localized. For some moderate coupling strengths the threshold is strongly reduced, which is explained by the SO coupling-induced band flattening in one of the sub-lattices. We explain why simultaneous Rabi and SO coupling are necessary ingredients for LDT threshold cancellation and show that strong SO coupling drives the system into the state where its evolution becomes similar to the evolution of a one-component system. We also find that defocusing nonlinearity can lead to localization of the states which are delocalized in the linear limit.
Abstract We study the localization transition in spin–orbit (SO) coupled binary Bose–Einstein condensates with collisional inhomogeneous interaction trapped in a one-dimensional quasiperiodic potential. Our numerical analysis shows that the competition between the quasiperiodic disorder and inhomogeneous interaction leads to a localization–delocalization transition as the interaction strength is tuned from attractive to repulsive in nature. Furthermore, we analyse the combined effect of the SO and Rabi coupling strengths on the localization transition for different interaction strengths and obtain signatures of similar localization–delocalization transition as a function of SO coupling in the regime of weak interactions. We complement our numerical observation with the analytical model using the Gaussian variational approach. In the end, we show how the localization–delocalization is manifested in the quench dynamics of the condensate. Our study provides an indirect approach to achieve localization transition without tuning the quasiperiodic potential strength, but rather by tuning the inhomogeneity in the interaction.
Abstract We investigate the effect of the spin–orbit (SO) and Rabi couplings on the localization of the spin-1/2 condensate trapped in a one-dimensional random potential. Our studies reveal that the spin-dependent couplings create distinct localization regimes, resulting in various relations between localization and spin-related properties. First, we examine the localization in the linear condensate and find that the SO coupling can lead to a transition of the localized state from the ‘basin-like’ to the ‘void’ region of the potential. For a weak random potential upon an increase in the SO coupling, we find a re-entrant transition from a broad to narrow localized state and back at a higher SO coupling. Further, we analyze the competing role of inter-species and intra-species interactions on the localization of the condensate. We find the appearance of spin-dependent localization as the interactions increase beyond threshold values for a sufficiently strong disorder. Our findings on controlling spin-dependent localization may be useful for future ultracold atomic experiments and corresponding spin-related quantum technologies.
We perform theoretical studies of the interplay between disorder, spin-orbit coupling (SOC), and Rabi fields, and show that both SOC and Rabi fields can be used to dramatically control the degree of Anderson localization of a Bose-Einstein condensate in bichromatic lattices. We obtain ground-state phase diagrams in the SOC and Rabi field plane for different values of disorder strength and use realistic experimental parameters compatible with 39K^{39}\mathrm{K}39K. We find cases of fixed disorder and SOC (Rabi field), where the Rabi field (SOC) reduces the threshold for localization and controls the localization length. We also show regimes of fixed disorder and Rabi field, where the extent of the ground-state wave function is periodic in the SOC, leading to alternating regions of stronger and weaker localization as SOC changes. Lastly, we describe examples of fixed disorder and SOC, where tuning the Rabi field leads to a strong localization peak.
We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in a quasiperiodic bichromatic optical lattice potential using the numerical solution and variational approximation of a binary mean-field Gross-Pitaevskii equation with two pseudospin components. We confirm the existence of the stationary localized states in the presence of the spin-orbit and Rabi couplings for an equal distribution of atoms in the two components. We find that the interaction between the spin-orbit and Rabi couplings favors the localization or delocalization of the BEC depending on the phase difference between the components. We also studied the oscillation dynamics of the localized states for an initial population imbalance between the two components.
Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO ``defect'' can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.