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Spin-Tensor-Momentum Coupling Effects on Bright Solitons Dynamics

In a pre-proof study from the journal Optik, researchers have explored the bright solitons' motion in one-dimensional spin-1 Bose-Einstein condensates (BEC) subjected to a spin-tensor momentum coupling (STMC).

Study: Motions of bright soliton in spin-tensor-momentum coupled spin-1 Bose–Einstein condensates. Image Credit: Anusorn Nakdee/

What is a Soliton?

The word "soliton" is derived from solitary since it is a solitary wave that acts as a particle and satisfies several specific conditions. These conditions include maintaining shape while moving at a constant velocity and remaining unchanged (except for possible phase shift) when colliding with another soliton.

Due to its physical properties, unique potential applications make soliton an interesting topic in several science fields, including Bose-Einstein condensation (BEC), bions, atomic nuclei, magnets, and, most notably, nonlinear systems.

How is Bose-Einstein Condensate (BEC) Established?

Electrons spin around an axis and have orbital and angular momentum due to spin, defined in terms of spin quantum number.

Angular momentum is a vector quantity with a direction that can be positive or negative and a magnitude (1/2).

Subatomic particles have two primary classes, bosons and fermions. Bosons are subatomic particles with an integer value of spin quantum numbers as 0,1,2,3 and so on, whereas fermions have odd half-integer spin.

When a low-density gas of bosons cools to near absolute zero temperatures, many bosons get the lowest quantum state, and microscopic quantum mechanical phenomena are visible macroscopically; this state of matter is known as Bose-Einstein condensate.

Exploring Wave Solitons

Exploring wave solitons such as cortex soliton, soliton train, and vector soliton has become more accessible due to a versatile platform provided by ultracold atomic gases.

Its application in atom transport, atom interferometry, and coherent atom optics has drawn vast research interest, particularly half-vortex gap soliton, 2D composite soliton and the stripe soliton have been found in Bose-Einstein condensation due to the realization of synthetic spin-orbit coupling (SOC) in ultracold atoms leading to unique dynamics of soliton.

Synthetic spin-orbit coupling induces Majorana fermions inside a soliton in superfluid Fermi gases revealing that it plays a crucial role in novel solitons' dynamics and formation.

Dynamics of Matter-Wave Solitons in Multicomponent Spinor Bose-Einstein Condensation (BEC)

The artificial spin-tensor-momentum coupling in Fermi gases has been recently realized using atom-light coupling. Moreover, the theoretical procedure for realizing spin-tensor-momentum coupling STMC in ultracold spin-1 Bose atoms is also proposed.

In contrast to synthetic spin-orbit coupling, in the spin-tensor-momentum coupling, rank-2 spin-quadrupole tensor and linear momentum are coupled, making atoms condense on a finite momentum, producing novel stripe superfluid phase and various profiles of soliton in Bose-Einstein condensation. This will pave the way for new dynamics of matter-wave solitons in multicomponent spinor Bose-Einstein condensation.

What Did the Researchers Do?

This pre-proof studies bright soliton's motion in spin-1 Bose-Einstein condensation with spin-tensor-momentum coupling.

The researchers derived the equations of motion of soliton's parameters by utilizing a variational approach and hyperbolic secant function as the trial function for bright soliton.

This showed that the center of mass of soliton and its amplitude are coupled by spin-tensor-momentum coupling, and spin-tensor-momentum coupling and Raman coupling also pair the amplitudes of three components.

For this purpose, the researchers considered 1D spin-1 Bose-Einstein condensation having three hyperfine states of RB atoms. Spin-tensor-momentum coupling is produced via dressing the atoms with Raman beams. One of the Raman beams is propagated in the opposite direction, while the other two are propagated with the same linear polarization. 

The resulting equation showed the conservation of momentum of soliton, indicating that it will propagate with a non-zero velocity. If the total spin of the system is conserved, the soliton's width is described by atomic interactions; else, it changes with the total spin of the system.

Important Findings of the Study

In conclusion, the study has explored how spin-tensor-momentum coupling affects the dynamics of bright solitons in spin-1 Bose-Einstein condensation. Employing the variational technique, the researchers developed the motion equations for the parameters of solitons. They found the precise variational solutions using the hyperbolic sine function as the trial characterized the bright soliton.

The results of the numerical simulations of the Gross-Pitaevskii (GP) equation demonstrate that spin-tensor-momentum coupling will cause soliton's motion which can be superpositioned between periodic oscillation and linear motion in some situations.

This can be demonstrated by motion equations' solution of soliton parameters, and linear velocity and oscillation frequency depend on the strengths of STMC and Raman coupling.

This study is a significant step in quantum physics since it reveals the unique properties of solitons that are affected by spin-tensor-momentum coupling.


Xiao-Li Peng, Xu Qiu, Yi Liang. Ai-Yuan Hu, Lin Wen (2022) Motions of bright soliton in spin-tensor-momentum coupled spin-1 Bose–Einstein condensates. Optik.

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Taha Khan

Written by

Taha Khan

Taha graduated from HITEC University Taxila with a Bachelors in Mechanical Engineering. During his studies, he worked on several research projects related to Mechanics of Materials, Machine Design, Heat and Mass Transfer, and Robotics. After graduating, Taha worked as a Research Executive for 2 years at an IT company (Immentia). He has also worked as a freelance content creator at Lancerhop. In the meantime, Taha did his NEBOSH IGC certification and expanded his career opportunities.  


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