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Interaction of two Rydberg atoms in the vicinity of an optical nanofibre

Erwan Stourm, Maxence Lepers, Jacques Robert, Síle Nic Chormaic, Klaus Mølmer, E. Brion

Published Feb 16, 2023• 0 citations
OpenAlex

Abstract

We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.

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Interaction of two Rydberg atoms in the vicinity of an optical nanofibre

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Abstract We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.

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Resonance dispersion interaction of alkali metal atoms in Rydberg states

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With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ ( R < R F ) this dependence transforms to the formula for electric dipole interaction energy Δ E d − d = C 3 / R 3 and for R > R F it transforms to the formula for the van der Waals interaction energy Δ E VdW = − C 6 / R 6 . The van der Waals constant C 6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J . The numerical values of the irreducible components of tensor C 6 were calculated for rubidium atoms in the same Rydberg states | nlJM 〉 with large quantum numbers n . We present the calculated resonance interaction energy of two rubidium atoms in the states |43D 5/2 M 〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P 3/2 M 〉 and of the other in the state |41F 7/2 M 〉.

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Rydberg Atoms In the Vicinity of an Optical Nanofiber

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We investigate how van der Waals interaction between Rydberg atoms is modified in the vicinity of an optical nanofiber with respect to free-space. This work paves the way to promising light-matter interfaces for quantum technologies.

Quantum 2.0 Conference and Exhibition•Jan 1, 2023•0 citations
We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.
Abstract We consider two rubidium atoms, prepared in the same S or P Rydberg states, near an optical nanofibre, and we determine their van der Waals interaction potential as a function of their separation along the nanofibre axis, their distance to the nanofibre axis, and their relative azimuthal angle. We compare results obtained through direct diagonalisation of the Hamiltonian (including quadrupolar interaction terms) with second-order perturbation calculations, and we identify which couplings mainly contribute to the potential in the presence of the nanofibre and in free-space. We relate the appearance of new allowed couplings to the broken rotation symmetry around the interatomic axis due to the presence of the fibre. These couplings induce novel features and cause a reshaping of the interaction anisotropy and formation of an interaction potential well for P states near the nanofibre. Our work constitutes an important step in the assessment of Rydberg atom-nanofibre quantum interfaces and devices.
With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ ( R < R F ) this dependence transforms to the formula for electric dipole interaction energy Δ E d − d = C 3 / R 3 and for R > R F it transforms to the formula for the van der Waals interaction energy Δ E VdW = − C 6 / R 6 . The van der Waals constant C 6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J . The numerical values of the irreducible components of tensor C 6 were calculated for rubidium atoms in the same Rydberg states | nlJM 〉 with large quantum numbers n . We present the calculated resonance interaction energy of two rubidium atoms in the states |43D 5/2 M 〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P 3/2 M 〉 and of the other in the state |41F 7/2 M 〉.
We report on numerical calculations of the spontaneous emission rate of a Rydberg-excited sodium atom in the vicinity of an optical nanofibre. In particular, we study how this rate varies with the distance of the atom to the fibre, the fibre's radius, the symmetry s or p of the Rydberg state as well as its principal quantum number. We find that a fraction of the spontaneously emitted light can be captured and guided along the fibre. This suggests that such a setup could be used for networking atomic ensembles, manipulated in a collective way due to the Rydberg blockade phenomenon.
We report on numerical calculations of the spontaneous emission rate of a Rydberg-excited sodium atom in the vicinity of an optical nanofibre. In particular, we study how this rate varies with the distance of the atom to the fibre, the fibre's radius, the symmetry s or p of the Rydberg state as well as its principal quantum number. We find that a fraction of the spontaneously emitted light can be captured and guided along the fibre. This suggests that such a setup could be used for networking atomic ensembles, manipulated in a collective way due to the Rydberg blockade phenomenon.