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Cited by 247Quantum optics and atomic interactionsCold Atom Physics and Bose-Einstein CondensatesStrong Light-Matter Interactions

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Super-radiance reveals infinite-range dipole interactions through a nanofiber

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Solano, P., Barberis-Blostein, P., Fatemi, F. K., Orozco, L. A., Rolston, S. L.·2017·Nature Communications
DOI 10.1038/s41467-017-01994-3PMC PMC5707363
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Abstract

Abstract Atoms interact with each other through the electromagnetic field, creating collective states that can radiate faster or slower than a single atom, i.e., super- and sub-radiance. When the field is confined to one dimension it enables infinite-range atom–atom interactions. Here we present the first report of infinite-range interactions between macroscopically separated atomic dipoles mediated by an optical waveguide. We use cold 87 Rb atoms in the vicinity of a single-mode optical nanofiber (ONF) that coherently exchange evanescently coupled photons through the ONF mode. In particular, we observe super-radiance of a few atoms separated by hundreds of resonant wavelengths. The same platform allows us to measure sub-radiance, a rarely observed effect, presenting a unique tool for quantum optics. This result constitutes a proof of principle for collective behavior of macroscopically delocalized atomic states, a crucial element for new proposals in quantum information and many-body physics.

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Figures

Fig. 1 Position-dependent atom–atom coupling along the optical nanofiber. a Schematic of an ONF as a platform for generating single photon collective atomic states, excited from the side by a weak probe of polarization V or H. When two atoms are close together, the dipolar interaction is mostly mediated by the modes of the electromagnetic field radiating outside the nanofiber. This is a limited-range interaction that decays inversely with distance. When the atoms are widely separated, the guided mode of an ideal ONF mediates the interaction for arbitrary distances. b, c Show the atom–atom interaction rate γ 12 (see Eq. (4)) experienced by an atom around the fiber given another atom at the position denoted by the white cross (see “Methods” section for the details of the calculation). Its amplitude is shown for a longitudinal and a transversal cut (specified by dashed black lines). Both plots share the color scale, but in b the interaction rate is normalized by the single atom total decay rate γ 0 and in c by the decay rate into the guided mode γ 1D. Along the z-axis, the interaction among atoms through free space radiation modes decreases as γ12^(rad)∝sin(k∣Δz∣)∕kΔz (with k being the wavenumber and Δz the separation between two atoms). The infinite interaction through the ONF-guided mode changes as γ12^(1D)∝cos(β0Δz)cos(Δϕ) (with β 0 being the propagation constant of the resonant-guided mode and Δϕ the angle difference in cylindrical coordinates). The wavelength λ sets the scale in b, c
Fig. 1 Position-dependent atom–atom coupling along the optical nanofiber. a Schematic of an ONF as a platform for generating single photon collective atomic states, excited from the side by a weak probe of polarization V or H. When two atoms are close together, the dipolar interaction is mostly mediated by the modes of the electromagnetic field radiating outside the nanofiber. This is a limited-range interaction that decays inversely with distance. When the atoms are widely separated, the guided mode of an ideal ONF mediates the interaction for arbitrary distances. b, c Show the atom–atom interaction rate γ 12 (see Eq. (4)) experienced by an atom around the fiber given another atom at the position denoted by the white cross (see “Methods” section for the details of the calculation). Its amplitude is shown for a longitudinal and a transversal cut (specified by dashed black lines). Both plots share the color scale, but in b the interaction rate is normalized by the single atom total decay rate γ 0 and in c by the decay rate into the guided mode γ 1D. Along the z-axis, the interaction among atoms through free space radiation modes decreases as γ12^(rad)∝sin(k∣Δz∣)∕kΔz (with k being the wavenumber and Δz the separation between two atoms). The infinite interaction through the ONF-guided mode changes as γ12^(1D)∝cos(β0Δz)cos(Δϕ) (with β 0 being the propagation constant of the resonant-guided mode and Δϕ the angle difference in cylindrical coordinates). The wavelength λ sets the scale in b, cCC BY · PubMed Central
Fig. 2 Measured super- and sub-radiant decay of excited atoms near the optical nanofiber. a Normalized rate of photons detected through the ONF mode (blue circles in a logarithmic scale) as a function of time in units of natural lifetime (τ 0 = 1/γ 0 = 26.24 ns) with 5 ns bins. The signal is taken after a probe beam polarized along the nanofiber turns off. In this realization OD = 0.66 ± 0.05. The individual statistical error bars are not plotted but they are taken into account for the normalized residuals in b. The number of counts at t = 0 exceeds 106. We see two distinct slopes (red and green), at short and long times. The initial slope (red) deviates toward decay rates faster than γ 0, a signature of super-radiance. The second slope (green) comes from the natural post-selection of purely sub-radiant states. The red dashed (green dashed) line is the best fit to a pure exponential decay of the initial (final) decay. The decay rate of the fit at short times is 1.10 ± 0.02 γ 0, and 0.13 ± 0.01 γ 0 for the fit at longer times, with one-sigma error. The one-sigma fractional systematic errors are ±0.01. The full description of the measured temporal evolution of the system involves averaging over many different decay rates through Monte Carlo methods (explained in “Methods” section). The solid black line is a simulation of 7 atoms along the ONF, with reduced χ 2 of 1.60. b The red circles, green circles, and black diamonds are the normalized residuals of the exponential fits to the initial decay, final decay, and the theoretical model. c Shows two different decay signals from an excitation driving the atoms with light polarized along (cyan rectangles) and perpendicular (blue triangles) to the ONF for 25 ns bins. When the driving field is polarized along the ONF, we observe super- and sub-radiance, and when it is polarized perpendicular to the ONF the super-radiance increases and the sub-radiance decreases. This feature is qualitatively captured by the theoretical model
Fig. 2 Measured super- and sub-radiant decay of excited atoms near the optical nanofiber. a Normalized rate of photons detected through the ONF mode (blue circles in a logarithmic scale) as a function of time in units of natural lifetime (τ 0 = 1/γ 0 = 26.24 ns) with 5 ns bins. The signal is taken after a probe beam polarized along the nanofiber turns off. In this realization OD = 0.66 ± 0.05. The individual statistical error bars are not plotted but they are taken into account for the normalized residuals in b. The number of counts at t = 0 exceeds 106. We see two distinct slopes (red and green), at short and long times. The initial slope (red) deviates toward decay rates faster than γ 0, a signature of super-radiance. The second slope (green) comes from the natural post-selection of purely sub-radiant states. The red dashed (green dashed) line is the best fit to a pure exponential decay of the initial (final) decay. The decay rate of the fit at short times is 1.10 ± 0.02 γ 0, and 0.13 ± 0.01 γ 0 for the fit at longer times, with one-sigma error. The one-sigma fractional systematic errors are ±0.01. The full description of the measured temporal evolution of the system involves averaging over many different decay rates through Monte Carlo methods (explained in “Methods” section). The solid black line is a simulation of 7 atoms along the ONF, with reduced χ 2 of 1.60. b The red circles, green circles, and black diamonds are the normalized residuals of the exponential fits to the initial decay, final decay, and the theoretical model. c Shows two different decay signals from an excitation driving the atoms with light polarized along (cyan rectangles) and perpendicular (blue triangles) to the ONF for 25 ns bins. When the driving field is polarized along the ONF, we observe super- and sub-radiance, and when it is polarized perpendicular to the ONF the super-radiance increases and the sub-radiance decreases. This feature is qualitatively captured by the theoretical modelCC BY · PubMed Central
Fig. 3 Super-radiant decay as a function of atom number including separated clouds. a Relationship of the decays as a function of average number of atoms (OD) along the optical nanofiber. The normalized fast decay rates are plotted as a function of the OD (lower abscissa) and N (upper abscissa) measured through the ONF-guided mode. The blue circles correspond to the signals from a single cloud of atoms. We split the atomic cloud in two (as shown in b). The dashed light and dotted dark green diamonds, and the solid red square correspond to the right, left, and the combination of both atomic clouds, respectively. The systematic errors (not shown) are estimated to be 1% for the decay rates and smaller than 20% for the atom number. The plotted error bars represent the statistical uncertainty of the fitting to an exponential decay. The gray region represents the one-sigma confidence band of a linear fit to the data. The red dashed line is the theoretical prediction, and the red shaded region represents a confidence interval set by a fractional error of 1%. The curve goes below γ/γ 0 = 1 because the natural decay rate is modified given the geometry of the ONF and the alignment of the atomic dipoles (Purcell effect)36. b Separated atom clouds show long-range interactions. The top of the figure shows in black and white a fluorescence image of a split MOT. The white dotted line represents the ONF location. The fluorescence signal of the split MOT along the nanofiber is plotted as a function of position. The dashed light (dotted dark) green dashed lines is the intensity distribution of the right (left) atomic cloud when the other one is blocked. The solid red line is the intensity distribution when both clouds are present. The separation between the center of both clouds is 318 ± 1 μm, given by standard error of the mean of a Gaussian fit. This distance is equivalent to 408 wavelengths
Fig. 3 Super-radiant decay as a function of atom number including separated clouds. a Relationship of the decays as a function of average number of atoms (OD) along the optical nanofiber. The normalized fast decay rates are plotted as a function of the OD (lower abscissa) and N (upper abscissa) measured through the ONF-guided mode. The blue circles correspond to the signals from a single cloud of atoms. We split the atomic cloud in two (as shown in b). The dashed light and dotted dark green diamonds, and the solid red square correspond to the right, left, and the combination of both atomic clouds, respectively. The systematic errors (not shown) are estimated to be 1% for the decay rates and smaller than 20% for the atom number. The plotted error bars represent the statistical uncertainty of the fitting to an exponential decay. The gray region represents the one-sigma confidence band of a linear fit to the data. The red dashed line is the theoretical prediction, and the red shaded region represents a confidence interval set by a fractional error of 1%. The curve goes below γ/γ 0 = 1 because the natural decay rate is modified given the geometry of the ONF and the alignment of the atomic dipoles (Purcell effect)36. b Separated atom clouds show long-range interactions. The top of the figure shows in black and white a fluorescence image of a split MOT. The white dotted line represents the ONF location. The fluorescence signal of the split MOT along the nanofiber is plotted as a function of position. The dashed light (dotted dark) green dashed lines is the intensity distribution of the right (left) atomic cloud when the other one is blocked. The solid red line is the intensity distribution when both clouds are present. The separation between the center of both clouds is 318 ± 1 μm, given by standard error of the mean of a Gaussian fit. This distance is equivalent to 408 wavelengthsCC BY · PubMed Central

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Cites

Research works printed but not linked: 3

  1. Solano, P. et al. in Advances In Atomic, Molecular, and Optical Physics Vol. 66 (eds Arimondo, E., Lin, C. C. & Yelin, S. F.) 439–505 (Academic Press, New York, 2017).
  2. Asenjo-Garcia, A., Moreno-Cardoner, M., Albrecht, A., Kimble, H. J. & Chang, D. E. Exponential improvement in photon storage fidelities using subradiance and selective radiance in atomic arrays. Phys. Rev. X 7, 031024 (2017).
  3. O’Connor, D. & Phillips, D. Time-Correlated Single Photon Counting (Academic Press, London, 1984).

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Metadata

Authors
Solano, P., Barberis-Blostein, P., Fatemi, F. K., Orozco, L. A., & Rolston, S. L.
Affiliations
  • National Institute of Standards and Technology (US)
  • Joint Quantum Institute (US)
  • DEVCOM Army Research Laboratory (US)
Corresponding author
Solano, P.
ORCID
Solano, P.
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2017-11-30
Volume
8
Issue
1
Pages
1857-1857
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-017-01994-3
PMC
PMC5707363
OpenAlex
W2729354929
Cited by
247
References
37
Citations by year
2026: 17 · 2025: 36 · 2024: 32 · 2023: 27 · 2022: 30 · 2021: 26 · 2020: 33 · 2019: 26 · 2018: 19 · 2017: 1
FWCI
10.60
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1430094, 1307416)
  • U.S. Department of Commerce
  • Joint Quantum Institute (PHY-1430094, 70NANB16H168)
  • National Institute of Standards and Technology (PHY-1430094, 70NANB16H168)
  • Office of the Secretary of Defense
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
Keywords
superradiance, optical nanofibers, optical waveguides, cold rubidium atoms, evanescent coupling, collective atomic states, quantum information

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