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A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

Huo MX, Nie W, Hutchinson DA, Kwek LC - Sci Rep (2014)

Bottom Line: Correspondingly, interference effects will play a role in transport.As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells.The scheme requires only standard optical access, and is robust to weak particle interactions.

View Article: PubMed Central - PubMed

Affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.

ABSTRACT
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

No MeSH data available.


Related in: MedlinePlus

Numerically calculated net flux for each cell on a 2D square lattice.We have chosen l = 1 for the LG laser, and the laser centre is addressed in the lattice centre. The flux is π when atoms tunnel along a loop including the laser centre. Although small fluctuations appear around the centre cell, the positive and negative phases cancel each other and the total flux for a loop including the centre cell remains a value of π.
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f2: Numerically calculated net flux for each cell on a 2D square lattice.We have chosen l = 1 for the LG laser, and the laser centre is addressed in the lattice centre. The flux is π when atoms tunnel along a loop including the laser centre. Although small fluctuations appear around the centre cell, the positive and negative phases cancel each other and the total flux for a loop including the centre cell remains a value of π.

Mentions: Numerical simulation for the accumulated flux ϕij is shown in Fig. 2, where an l = 1 LG laser drives the tunnelling of atoms along a loop enclosing the lattice centre that coincides with the laser centre. The flux is defined as ϕi,j = arg(Ji,j) − arg(Ji,j+1) + arg(Ji+1,j+1) − arg(Ji+1,j), where the tunneling strength Ji,j is given in Eq. (4). As shown in Fig. 2, the gauge field is non-zero within only a few cells around the centre. We would like to remark that even if the centre of the laser is slightly shifted from that of the lattice, it will not affect the results significantly, although some small fluctuations may appear around the solenoid. In a similar way, an LG laser drives tunnelling of atoms which are trapped in a ring lattice. For an l = 1 laser, the accumulated phase along the ring is π. It is straightforward to extend to the SU(2) case, where ψs becomes a 2 × 1 column matrix to include the two sub-states g1 and g2 (e1 and e2) in g (e) level [see Fig. 1(e)]. Two laser beams with l = 0 and l = 1 are employed to drive g1-e2 and g2-e1 transitions, respectively. To give a unitary hopping matrix for two spins, we should choose l = 0 and l = 1 lasers with the same amplitude to drive the spin-flipping transitions. It is satisfied when we apply an LG mode with p = 0, l = 1, and a superposition of two LG modes with p = 0, l = 0 and p = 1, l = 0. The non-Abelian tunneling matrix is then given by where Jij is given in Eq. (4).


A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

Huo MX, Nie W, Hutchinson DA, Kwek LC - Sci Rep (2014)

Numerically calculated net flux for each cell on a 2D square lattice.We have chosen l = 1 for the LG laser, and the laser centre is addressed in the lattice centre. The flux is π when atoms tunnel along a loop including the laser centre. Although small fluctuations appear around the centre cell, the positive and negative phases cancel each other and the total flux for a loop including the centre cell remains a value of π.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126000&req=5

f2: Numerically calculated net flux for each cell on a 2D square lattice.We have chosen l = 1 for the LG laser, and the laser centre is addressed in the lattice centre. The flux is π when atoms tunnel along a loop including the laser centre. Although small fluctuations appear around the centre cell, the positive and negative phases cancel each other and the total flux for a loop including the centre cell remains a value of π.
Mentions: Numerical simulation for the accumulated flux ϕij is shown in Fig. 2, where an l = 1 LG laser drives the tunnelling of atoms along a loop enclosing the lattice centre that coincides with the laser centre. The flux is defined as ϕi,j = arg(Ji,j) − arg(Ji,j+1) + arg(Ji+1,j+1) − arg(Ji+1,j), where the tunneling strength Ji,j is given in Eq. (4). As shown in Fig. 2, the gauge field is non-zero within only a few cells around the centre. We would like to remark that even if the centre of the laser is slightly shifted from that of the lattice, it will not affect the results significantly, although some small fluctuations may appear around the solenoid. In a similar way, an LG laser drives tunnelling of atoms which are trapped in a ring lattice. For an l = 1 laser, the accumulated phase along the ring is π. It is straightforward to extend to the SU(2) case, where ψs becomes a 2 × 1 column matrix to include the two sub-states g1 and g2 (e1 and e2) in g (e) level [see Fig. 1(e)]. Two laser beams with l = 0 and l = 1 are employed to drive g1-e2 and g2-e1 transitions, respectively. To give a unitary hopping matrix for two spins, we should choose l = 0 and l = 1 lasers with the same amplitude to drive the spin-flipping transitions. It is satisfied when we apply an LG mode with p = 0, l = 1, and a superposition of two LG modes with p = 0, l = 0 and p = 1, l = 0. The non-Abelian tunneling matrix is then given by where Jij is given in Eq. (4).

Bottom Line: Correspondingly, interference effects will play a role in transport.As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells.The scheme requires only standard optical access, and is robust to weak particle interactions.

View Article: PubMed Central - PubMed

Affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.

ABSTRACT
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.

No MeSH data available.


Related in: MedlinePlus