## Final Report Summary - NANOFIBER OPTICS (Nanofiber-Based Optical Drag Force and Cavity Quantum Electrodynamics)

The aim of the Nanofiber Optics project was to theoretically investigate new approaches to fundamental and applied problems of classical and quantum electrodynamics offered by light–matter interfaces based on tapered optical fibers with a subwavelength-diameter waist, termed nanofiber in the following. The project focussed on two specific topics:

(1) The mechanical effects of the evanescent field of a nanofiber on dielectric nanoparticles which are placed in regions where the poynting vector in negative.

(2) Cavity quantum electrodynamical (CQED) effects for an ensemble of optically trapped atoms coupled to a nanofiber-based Fabry-Pérot-type resonator.

The project began one year after its acceptance. During the time gap, the first topic was actively studied by another group in the field [1]. Therefore, Dr. Pham Le Kien and his host scientist, Prof. A. Rauschenbeutel, started and accomplished the research on the first topic before the official project start date. The results of the research on the first topic have been reported in [2].

Meanwhile, after the project was started, Dr. Pham Le Kien and Prof. A. Rauschenbeutel realized that the scope of the research on the second topic was much broader and more complex and difficult than initially expected. In particular, it required heavy numerical calculations and a broad spectrum of theoretical approaches. Therefore, Dr. Pham Le Kien and Prof. A. Rauschenbeutel decided to spend the whole term of the project on the second topic.

For the first topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have calculated the force of a field on a dielectric spherical particle outside a nanofiber [2]. They found that, when the size and the refractive index of the particle are chosen appropriately, the azimuthal component of the force is directed oppositely to the circulation direction of the energy flow around the nanofiber. The occurrence of such a negative azimuthal force indicates the occurrence of a negative torque upon the particle.

For the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the propagation of guided light in an array of multilevel cesium atoms outside a nanofiber [3]. They found that, in the neighborhood of the Bragg resonance, most of the guided light can be reflected back in a broad region of field detunings even though there is an irreversible decay channel into radiation modes. When the atom number is large enough, two different band gaps may be formed. This work has already received considerable attention and the considered situation was experimentally studied on two recent experimental studies [4, 5].

Furthermore, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the propagation of guided light along an array of three-level atoms trapped in the vicinity of an optical nanofiber under the electromagnetically induced transparency conditions [6]. They have numerically demonstrated that, under experimentally realistic conditions, 200 cesium atoms in a linear array with a length of 100 µm along a nanofiber can slow down the speed of guided probe light by a factor of about 3.5x106 (the group delay is about 1.17 µs). Under the Bragg resonance condition, the array of atoms can transmit guided light that is suitably polarized and that propagates in one specific direction even in the limit of infinitely large atom numbers.

For a work that is closely related to the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the scattering of nanofiber-guided light from a multilevel cesium atom [7]. They have shown that the rate of scattering of guided light from the atom in the steady-state regime into the guided modes is in general asymmetric with respect to the forward and backward directions and depends on the polarization of the probe field.

For the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied all-optical switches operating on a single four-level atom with the N-type transition configuration in a two-mode nanofiber-based Fabry-Pérot-type cavity with a significant length and a moderate finesse [8]. They have investigated the dependencies of the switching contrast on various parameters, such as the cavity length, the mirror reflectivity, and the detunings and powers of the cavity driving field pulses. For experimentally realistic parameters, they have numerically obtained a switching contrast on the order of about 95%.

For a work that is closely related to the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have investigated spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface [9]. They have shown that an asymmetry of the angular distribution of spontaneous emission occurs when the ellipticity vector of the atomic dipole polarization overlaps with the ellipticity vector of the field mode polarization.

References:

1. Left-handed optical radiation torque. D. Hakobyan and E. Brasselet, Nat. Photonics 8, 610 (2014).

2. Negative azimuthal force of a nanofiber-guided light on a particle. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 88, 063845 (2013).

3. Propagation of nanofiber-guided light through an array of atoms. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 063816 (2014).

4. Coherent backscattering of light off one-dimensional atomic strings. H. L. Sørensen, J.-B. Béguin, K. W. Kluge, I. Iakoupov, A. S. Sørensen, J. H. Müller, E. S. Polzik, and J. Appel, arXiv:1601.04869 (2016).

5. Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide. N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, arXiv:1604.03129 (2016).

6. Electromagnetically induced transparency for guided light in an atomic array outside an optical nanofiber. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 91, 053847 (2015).

7. Anisotropy in scattering of light from an atom into the guided modes of a nanofiber. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).

8. Nanofiber-based all-optical switches. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 93, 013849 (2016).

9. Spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 93, 043828 (2016).

(1) The mechanical effects of the evanescent field of a nanofiber on dielectric nanoparticles which are placed in regions where the poynting vector in negative.

(2) Cavity quantum electrodynamical (CQED) effects for an ensemble of optically trapped atoms coupled to a nanofiber-based Fabry-Pérot-type resonator.

The project began one year after its acceptance. During the time gap, the first topic was actively studied by another group in the field [1]. Therefore, Dr. Pham Le Kien and his host scientist, Prof. A. Rauschenbeutel, started and accomplished the research on the first topic before the official project start date. The results of the research on the first topic have been reported in [2].

Meanwhile, after the project was started, Dr. Pham Le Kien and Prof. A. Rauschenbeutel realized that the scope of the research on the second topic was much broader and more complex and difficult than initially expected. In particular, it required heavy numerical calculations and a broad spectrum of theoretical approaches. Therefore, Dr. Pham Le Kien and Prof. A. Rauschenbeutel decided to spend the whole term of the project on the second topic.

For the first topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have calculated the force of a field on a dielectric spherical particle outside a nanofiber [2]. They found that, when the size and the refractive index of the particle are chosen appropriately, the azimuthal component of the force is directed oppositely to the circulation direction of the energy flow around the nanofiber. The occurrence of such a negative azimuthal force indicates the occurrence of a negative torque upon the particle.

For the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the propagation of guided light in an array of multilevel cesium atoms outside a nanofiber [3]. They found that, in the neighborhood of the Bragg resonance, most of the guided light can be reflected back in a broad region of field detunings even though there is an irreversible decay channel into radiation modes. When the atom number is large enough, two different band gaps may be formed. This work has already received considerable attention and the considered situation was experimentally studied on two recent experimental studies [4, 5].

Furthermore, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the propagation of guided light along an array of three-level atoms trapped in the vicinity of an optical nanofiber under the electromagnetically induced transparency conditions [6]. They have numerically demonstrated that, under experimentally realistic conditions, 200 cesium atoms in a linear array with a length of 100 µm along a nanofiber can slow down the speed of guided probe light by a factor of about 3.5x106 (the group delay is about 1.17 µs). Under the Bragg resonance condition, the array of atoms can transmit guided light that is suitably polarized and that propagates in one specific direction even in the limit of infinitely large atom numbers.

For a work that is closely related to the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied the scattering of nanofiber-guided light from a multilevel cesium atom [7]. They have shown that the rate of scattering of guided light from the atom in the steady-state regime into the guided modes is in general asymmetric with respect to the forward and backward directions and depends on the polarization of the probe field.

For the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have studied all-optical switches operating on a single four-level atom with the N-type transition configuration in a two-mode nanofiber-based Fabry-Pérot-type cavity with a significant length and a moderate finesse [8]. They have investigated the dependencies of the switching contrast on various parameters, such as the cavity length, the mirror reflectivity, and the detunings and powers of the cavity driving field pulses. For experimentally realistic parameters, they have numerically obtained a switching contrast on the order of about 95%.

For a work that is closely related to the second topic, Dr. Pham Le Kien and Prof. A. Rauschenbeutel have investigated spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface [9]. They have shown that an asymmetry of the angular distribution of spontaneous emission occurs when the ellipticity vector of the atomic dipole polarization overlaps with the ellipticity vector of the field mode polarization.

References:

1. Left-handed optical radiation torque. D. Hakobyan and E. Brasselet, Nat. Photonics 8, 610 (2014).

2. Negative azimuthal force of a nanofiber-guided light on a particle. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 88, 063845 (2013).

3. Propagation of nanofiber-guided light through an array of atoms. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 063816 (2014).

4. Coherent backscattering of light off one-dimensional atomic strings. H. L. Sørensen, J.-B. Béguin, K. W. Kluge, I. Iakoupov, A. S. Sørensen, J. H. Müller, E. S. Polzik, and J. Appel, arXiv:1601.04869 (2016).

5. Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide. N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, arXiv:1604.03129 (2016).

6. Electromagnetically induced transparency for guided light in an atomic array outside an optical nanofiber. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 91, 053847 (2015).

7. Anisotropy in scattering of light from an atom into the guided modes of a nanofiber. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 90, 023805 (2014).

8. Nanofiber-based all-optical switches. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 93, 013849 (2016).

9. Spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. Fam Le Kien and A. Rauschenbeutel, Phys. Rev. A 93, 043828 (2016).