1Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
2School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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Abstract
When an emitter ensemble interacts with the electromagnetic field, dipole-dipole interactions are induced between the emitters. The magnitude and shape of these interactions are fully determined by the specific form of the electromagnetic field modes. If the emitters are placed in the vicinity of a nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional form of these modes makes the analytical evaluation of the dipole-dipole interaction cumbersome and numerically costly. In this work, we provide a full detailed description of how to successfully calculate these interactions, outlining a method that can be easily extended to other environments and boundary conditions. Such exact evaluation is of importance as, due to the collective character of the interactions and dissipation in this kind of systems, any small modification of the interactions may lead to dramatic changes in experimental observables, particularly as the number of emitters increases. We illustrate this by calculating the transmission signal of the light guided by a cylindrical nanofiber in the presence of a nearby chain of emitters.
Featured image: A chain of emitters coupled to a waveguide driven with fiber-guided light with Rabi frequency $Omega$ and detuning $Delta$. The emitters interact collectively through radiation modes with strength $V^{rd}$ and guided modes with strength $V^{gd}$. Our calculated transmission signal $T$ is compared with the solution using vacuum modes $T^0$ for $N=20$ emitters.
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[1] R. H. Dicke. “Coherence in spontaneous radiation processes”. Phys. Rev. 93, 99–110 (1954).
https://doi.org/10.1103/PhysRev.93.99
[2] R. H. Lehmberg. “Radiation from an ${N}$-Atom System. I. General Formalism”. Phys. Rev. A 2, 883–888 (1970).
https://doi.org/10.1103/physreva.2.883
[3] D. F. V. James. “Frequency shifts in spontaneous emission from two interacting atoms”. Phys. Rev. A 47, 1336–1346 (1993).
https://doi.org/10.1103/PhysRevA.47.1336
[4] R. T. Sutherland and F. Robicheaux. “Collective dipole-dipole interactions in an atomic array”. Phys. Rev. A 94, 013847 (2016).
https://doi.org/10.1103/PhysRevA.94.013847
[5] J. A. Needham, I. Lesanovsky, and B. Olmos. “Subradiance-protected excitation transport”. New J. Phys. 21, 073061 (2019).
https://doi.org/10.1088/1367-2630/ab31e8
[6] F. Damanet, D. Braun, and J. Martin. “Master equation for collective spontaneous emission with quantized atomic motion”. Phys. Rev. A 93, 022124 (2016).
https://doi.org/10.1103/PhysRevA.93.022124
[7] R. Jones, J. A. Needham, I. Lesanovsky, F. Intravaia, and B. Olmos. “Modified dipole-dipole interaction and dissipation in an atomic ensemble near surfaces”. Phys. Rev. A 97, 053841 (2018).
https://doi.org/10.1103/PhysRevA.97.053841
[8] K. Sinha, B. P. Venkatesh, and P. Meystre. “Collective effects in casimir-polder forces”. Phys. Rev. Lett. 121, 183605 (2018).
https://doi.org/10.1103/PhysRevLett.121.183605
[9] S. Fuchs and S. Y. Buhmann. “Purcell-dicke enhancement of the casimir-polder potential”. EPL (Europhysics Letters) 124, 34003 (2018).
https://doi.org/10.1209/0295-5075/124/34003
[10] A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble. “Atom-light interactions in quasi-one-dimensional nanostructures: A green’s-function perspective”. Phys. Rev. A 95, 033818 (2017).
https://doi.org/10.1103/PhysRevA.95.033818
[11] D. Dzsotjan, A. S. Sørensen, and M. Fleischhauer. “Quantum emitters coupled to surface plasmons of a nanowire: A green’s function approach”. Phys. Rev. B 82, 075427 (2010).
https://doi.org/10.1103/PhysRevB.82.075427
[12] E. M. Purcell, H. C. Torrey, and R. V. Pound. “Resonance absorption by nuclear magnetic moments in a solid”. Phys. Rev. 69, 37–38 (1946).
https://doi.org/10.1103/PhysRev.69.37
[13] P. Goy, J. M. Raimond, M. Gross, and S. Haroche. “Observation of cavity-enhanced single-atom spontaneous emission”. Phys. Rev. Lett. 50, 1903–1906 (1983).
https://doi.org/10.1103/PhysRevLett.50.1903
[14] G. Gabrielse and H. Dehmelt. “Observation of inhibited spontaneous emission”. Phys. Rev. Lett. 55, 67–70 (1985).
https://doi.org/10.1103/PhysRevLett.55.67
[15] R. G. Hulet, E. S. Hilfer, and D. Kleppner. “Inhibited spontaneous emission by a rydberg atom”. Phys. Rev. Lett. 55, 2137–2140 (1985).
https://doi.org/10.1103/PhysRevLett.55.2137
[16] J. Martorell and N. M. Lawandy. “Observation of inhibited spontaneous emission in a periodic dielectric structure”. Phys. Rev. Lett. 65, 1877–1880 (1990).
https://doi.org/10.1103/PhysRevLett.65.1877
[17] E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel. “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber”. Phys. Rev. Lett. 104, 203603 (2010).
https://doi.org/10.1103/PhysRevLett.104.203603
[18] L. Ding, C. Belacel, S. Ducci, G. Leo, and I. Favero. “Ultralow loss single-mode silica tapers manufactured by a microheater”. Appl. Opt. 49, 2441–2445 (2010).
https://doi.org/10.1364/AO.49.002441
[19] P. Lodahl, S. Mahmoodian, and S. Stobbe. “Interfacing single photons and single quantum dots with photonic nanostructures”. Rev. Mod. Phys. 87, 347–400 (2015).
https://doi.org/10.1103/RevModPhys.87.347
[20] R. Ritter, N. Gruhler, H. Dobbertin, H. Kübler, S. Scheel, W. Pernice, T. Pfau, and R. Löw. “Coupling thermal atomic vapor to slot waveguides”. Phys. Rev. X 8, 021032 (2018).
https://doi.org/10.1103/PhysRevX.8.021032
[21] A. Skljarow, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, R. Löw, and H. Alaeian. “Integrating two-photon nonlinear spectroscopy of rubidium atoms with silicon photonics”. Opt. Express 28, 19593–19607 (2020).
https://doi.org/10.1364/OE.389644
[22] A. Skljarow, H. Kübler, C. S. Adams, T. Pfau, R. Löw, and H. Alaeian. “Purcell-enhanced dipolar interactions in nanostructures”. Phys. Rev. Research 4, 023073 (2022).
https://doi.org/10.1103/PhysRevResearch.4.023073
[23] D. Reitz, C. Sayrin, R. Mitsch, P. Schneeweiss, and A. Rauschenbeutel. “Coherence properties of nanofiber-trapped cesium atoms”. Phys. Rev. Lett. 110, 243603 (2013).
https://doi.org/10.1103/PhysRevLett.110.243603
[24] P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller. “Chiral quantum optics”. Nature 541, 473 (2017).
https://doi.org/10.1038/nature21037
[25] V. A. Pivovarov, L. V. Gerasimov, J. Berroir, T. Ray, J. Laurat, A. Urvoy, and D. V. Kupriyanov. “Single collective excitation of an atomic array trapped along a waveguide: A study of cooperative emission for different atomic chain configurations”. Phys. Rev. A 103, 043716 (2021).
https://doi.org/10.1103/PhysRevA.103.043716
[26] P. Solano, P. Barberis-Blostein, F. K Fatemi, and et al. “Super-radiance reveals infinite-range dipole interactions through a nanofiber”. Nat. Commun. 8, 1857 (2017).
https://doi.org/10.1038/s41467-017-01994-3
[27] R. Pennetta, D. Lechner, M. Blaha, A. Rauschenbeutel, P. Schneeweiss, and J. Volz. “Observation of coherent coupling between super- and subradiant states of an ensemble of cold atoms collectively coupled to a single propagating optical mode”. Phys. Rev. Lett. 128, 203601 (2022).
https://doi.org/10.1103/PhysRevLett.128.203601
[28] C. Vega, M. Bello, D. Porras, and A. González-Tudela. “Qubit-photon bound states in topological waveguides with long-range hoppings”. Phys. Rev. A 104, 053522 (2021).
https://doi.org/10.1103/PhysRevA.104.053522
[29] M. Bello, G. Platero, and A. González-Tudela. “Spin many-body phases in standard- and topological-waveguide qed simulators”. PRX Quantum 3, 010336 (2022).
https://doi.org/10.1103/PRXQuantum.3.010336
[30] C. McDonnell and B. Olmos. “Subradiant edge states in an atom chain with waveguide-mediated hopping”. Quantum 6, 805 (2022).
https://doi.org/10.22331/q-2022-09-15-805
[31] A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang. “Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays”. Phys. Rev. X 7, 031024 (2017).
https://doi.org/10.1103/PhysRevX.7.031024
[32] A. Albrecht, L. Henriet, A. Asenjo-Garcia, P. B. Dieterle, O. Painter, and D. E. Chang. “Subradiant states of quantum bits coupled to a one-dimensional waveguide”. New J. Phys. 21, 025003 (2019).
https://doi.org/10.1088/1367-2630/ab0134
[33] G. Buonaiuto, R. Jones, B. Olmos, and I. Lesanovsky. “Dynamical creation and detection of entangled many-body states in a chiral atom chain”. New J. Phys. 21, 113021 (2019).
https://doi.org/10.1088/1367-2630/ab4f50
[34] S. Mahmoodian, G. Calajó, D. E. Chang, K. Hammerer, and A. S. Sørensen. “Dynamics of many-body photon bound states in chiral waveguide qed”. Phys. Rev. X 10, 031011 (2020).
https://doi.org/10.1103/PhysRevX.10.031011
[35] Y. L. Wang, Y. Yang, J. Lu, and L. Zhou. “Photon transport and interference of bound states in a one-dimensional waveguide”. Opt. Express 30, 14048–14060 (2022).
https://doi.org/10.1364/OE.455294
[36] D. D. Sedov, V. K. Kozin, and I. V. Iorsh. “Chiral waveguide optomechanics: First order quantum phase transitions with ${mathbb{z}}_{3}$ symmetry breaking”. Phys. Rev. Lett. 125, 263606 (2020).
https://doi.org/10.1103/PhysRevLett.125.263606
[37] G. Buonaiuto, F. Carollo, B. Olmos, and I. Lesanovsky. “Dynamical phases and quantum correlations in an emitter-waveguide system with feedback”. Phys. Rev. Lett. 127, 133601 (2021).
https://doi.org/10.1103/PhysRevLett.127.133601
[38] Fam Le Kien and A. Rauschenbeutel. “Nanofiber-mediated chiral radiative coupling between two atoms”. Phys. Rev. A 95, 023838 (2017).
https://doi.org/10.1103/PhysRevA.95.023838
[39] D. F. Kornovan, A. S. Sheremet, and M. I. Petrov. “Collective polaritonic modes in an array of two-level quantum emitters coupled to an optical nanofiber”. Phys. Rev. B 94, 245416 (2016).
https://doi.org/10.1103/PhysRevB.94.245416
[40] E. Stourm, M. Lepers, J. Robert, S. Nic Chormaic, K. Mølmer, and E. Brion. “Spontaneous emission and energy shifts of a rydberg rubidium atom close to an optical nanofiber”. Phys. Rev. A 101, 052508 (2020).
https://doi.org/10.1103/PhysRevA.101.052508
[41] A. S. Sheremet, M. I. Petrov, I. V. Iorsh, A. V. Poshakinskiy, and A. N. Poddubny. “Waveguide quantum electrodynamics: collective radiance and photon-photon correlations” . Rev. Mod. Phys. 95, 015002 (2023).
https://doi.org/10.1103/RevModPhys.95.015002
[42] A. Sipahigil, R. E. Evans, D. D. Sukachev, M. J. Burek, J. Borregaard, M. K. Bhaskar, C. T. Nguyen, J. L. Pacheco, H. A. Atikian, C. Meuwly, R. M. Camacho, F. Jelezko, E. Bielejec, H. Park, M. Lončar, and M. D. Lukin. “An integrated diamond nanophotonics platform for quantum-optical networks”. Science 354, 847–850 (2016).
https://doi.org/10.1126/science.aah6875
[43] Y. V. Vladimorova and V. N. Zadkov. “Quantum optics in nanostructures”. Nanomaterials (Basel) 11, 1919 (2021).
https://doi.org/10.3390/nano11081919
[44] M. Gross and S. Haroche. “Superradiance: An essay on the theory of collective spontaneous emission”. Phys. Rep. 93, 301–396 (1982).
https://doi.org/10.1016/0370-1573(82)90102-8
[45] A. Crubellier, S. Liberman, D. Pavolini, and P. Pillet. “Superradiance and subradiance. i. interatomic interference and symmetry properties in three-level systems”. J. Phys. B: At. Mol. Phys. 18, 3811–3833 (1985).
https://doi.org/10.1088/0022-3700/18/18/022
[46] H. T. Dung, L. Knöll, and D.-G. Welsch. “Resonant dipole-dipole interaction in the presence of dispersing and absorbing surroundings”. Phys. Rev. A 66, 063810 (2002).
https://doi.org/10.1103/PhysRevA.66.063810
[47] Fam Le Kien. “Force of light on a two-level atom near an ultrathin optical fiber”. New J. Phys. 20, 093031 (2018).
https://doi.org/10.1088/1367-2630/aadf6d
[48] L. Knöll, S. Scheel, and Welsch D.-G. “Qed in dispersing and absorbing media”. In J. Peri$breve{text{n}}$a, editor, Coherence and Statistics of Photons and Atoms. Wiley, New York (2001).
[49] S. Y. Buhmann. “Dipsersion forces ii: Many-body effects, excited atoms, finite temperature and quantum friction”. Springer, Berlin. (2012).
[50] B. A. van Tiggelen and S. E. Skipetrov. “Longitudinal modes in diffusion and localization of light”. Phys. Rev. B 103, 174204 (2021).
https://doi.org/10.1103/PhysRevB.103.174204
[51] R. Balian and C. Bloch. “Distribution of eigenfrequencies for the wave equation in a finite domain: I. three-dimensional problem with smooth boundary surface”. Ann. Phys. 60, 401–447 (1970).
https://doi.org/10.1016/0003-4916(70)90497-5
[52] R. J. Glauber and M. Lewenstein. “Quantum optics of dielectric media”. Phys. Rev. A 43, 467–491 (1991).
https://doi.org/10.1103/PhysRevA.43.467
[53] T. Søndergaard and B. Tromborg. “General theory for spontaneous emission in active dielectric microstructures: Example of a fiber amplifier”. Phys. Rev. A 64, 033812 (2001).
https://doi.org/10.1103/PhysRevA.64.033812
[54] I. H. Malitson. “Interspecimen comparison of the refractive index of fused silica$ast$,†”. J. Opt. Soc. Am. 55, 1205–1209 (1965).
https://doi.org/10.1364/JOSA.55.001205
[55] C. W. Peterson and B. W. Knight. “Causality calculations in the time domain: An efficient alternative to the kramers–kronig method$ast$”. J. Opt. Soc. Am. 63, 1238–1242 (1973).
https://doi.org/10.1364/JOSA.63.001238
[56] W. O. Saxton. “Phase determination in bright-field electron microscopy using complementary half-plane apertures”. J. Phys. D: App. Phys. 7, L63–L64 (1974).
https://doi.org/10.1088/0022-3727/7/4/102
[57] https://github.com/MathiasBMS/Collective-Coefficients-atom-nanofiber-system.
https://github.com/MathiasBMS/Collective-Coefficients-atom-nanofiber-system
[58] C. Liedl, F. Tebbenjohanns, C. Bach, S. Pucher, A. Rauschenbeutel, and P. Schneeweiss. “Observation of superradiant bursts in waveguide qed” (2022).
[59] S. J. Masson and A. Asenjo-Garcia. “Universality of dicke superradiance in arrays of quantum emitters”. Nat. Commun. 13, 2285 (2022).
https://doi.org/10.1038/s41467-022-29805-4
[60] C. Sayrin, C. Clausen, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel. “Storage of fiber-guided light in a nanofiber-trapped ensemble of cold atoms”. Optica 2, 353–356 (2015).
https://doi.org/10.1364/OPTICA.2.000353
[61] B. Gouraud, D. Maxein, A. Nicolas, O. Morin, and J. Laurat. “Demonstration of a memory for tightly guided light in an optical nanofiber”. Phys. Rev. Lett. 114, 180503 (2015).
https://doi.org/10.1103/PhysRevLett.114.180503
[62] H. T. Dung, S. Y. Buhmann, L. Knöll, D.-G. Welsch, S. Scheel, and J. Kästel. “Electromagnetic-field quantization and spontaneous decay in left-handed media”. Phys. Rev. A 68, 043816 (2003).
https://doi.org/10.1103/PhysRevA.68.043816
[63] N.-A. P. Nicorovici, R. C. McPhedran, and L. C. Botten. “Relative local density of states for homogeneous lossy materials”. Physica B Condens. 405, 2915–2919 (2010).
https://doi.org/10.1016/j.physb.2010.01.003
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