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1 Top bo.om e# side TEST Right side

2 Atoms around Optical Nanofibers, modifications on the spontaneous emission Shanxi University July 2018 Luis A. Orozco

3 Graduate Students and Postdoctoral associates: J. E. Hoffman, J. A. Grover, J. Lee, S. Ravets (I. d Optique), P. Solano. Undergraduate Students: U. Chukwu, C. Ebongue, E. Fenton, B. Friedman, X. Gutierrez, D. Hemmer, A. Khan, P. Kordell, E. Magnan, D. Ornelas, A. Preciado, J. E. Uruñuela, J. D. Wong-Campos, A. Wood. Professors and Researchers: P. Barberis Blostein, G. Beadie, F. K. Fatemi, L. A. Orozco, S. L. Rolston. University of Maryland, Institute D Optique, National Institute of Standards and Technology, Naval Research Laboratory, Army Research Laboratory. Support from Atomtronics MURI from ARO, DARPA, the Fulbright Foundation, NSF through PFC@JQI, ONR.

4 THE TEAM Sylvain Jonathan Jeff Eliot Jeff Pablo

5 Optical Nanofibers

6 Optical Nanofibers (a) Taper lenght 28 mm Angle 2 mrad Core diameter 5 μm Cladding diameter 125 μm Unmodified fiber Waist 480 nm, 7 mm long (not to scale)

7 The scale

8 λ=780 nm Optical Nanofibers

9 Lowest order fiber modes Intensities HE 11 TM 01 TE 01 HE 21

10 Polarization of the lowest order modes

11 Very large radial gradients of E Div E=0 implies large longitudinal components. E r r + E z z = 0 The evanescent field can have a longitudinal component of the polarization!

12 Polarization at the fiber waist Rotates like a bicycle wheel

13 Atoms interacting with light (decay) near an ONF.

14 Rate of decay (Fermi s golden rule) rad Phase space density Interaction

15 Rate of decay free space (Fermi s golden rule) γ 0 = ω 0 3 d 2 πε 0!c 3

16 Evanescent Coupling γ Tot = γ rad +γ 1D γ rad γ 1D Not to scale γ 0 γ Tot γ 0

17 Decay into the nanofiber mode Density of modes in 1D

18 Decay into the nanofiber mode Density of modes roportional to the electric field of the guided mode.

19 Cooperativity γ rad γ 1D Not to scale C 1 = β (1 β) = γ 1D γ rad C 1 is the ratio of what goes into the selected mode to what goes into all the rest

20 ONF Optical Density OD 1 (! r) = σ 0 A(! r) Not to scale 50nm away from the surface 1 atom can block 10% of the light!!

21 ONF Optical Density OD 1 (! r) = σ 0 A(! r) 50nm away from the surface 1 atom can block 10% of the light!! σ 0 /A eff r (nm) Not to scale

22 Many atoms interacting with light (decay) near an ONF. Super- and sub-radiance.

23 Super- and Sub-radiance (a classical explanation) When two organ pipes of the same pitch stand side by side, complications ensue which not infrequently give trouble in practice. In extreme cases the pipes may almost reduce one another to silence. Even when the mutual influence is more moderate, it may still go so far as to cause the pipes to speak in absolute unison, in spite of inevitable small differences. Lord Rayleigh (1877) in "The Theory of Sound".

24 Super- and Sub-radiance (a classical explanation) We need the response of one oscillator due to a nearby oscillator:!!a 1 +γ 0!a 1 +ω 0 2 a 1 = 3 2 ω 0γ 0 ˆd1! E 2! r ( )a 1, γ = γ γ 0 Im ˆd! {! E ( r )}, with ˆd ω = ω γ 0 Re ˆd 1!! r ( ) { E } 2! E ( 0) = 2 2 3

25 Super- and Sub-radiance (a classical explanation) P = ε Δt = IA Δt = ε IA For N dipoles ε Nε

26 Super- and Sub-radiance (a classical explanation) Normal radiance Im{E} Re{E} I = E 0 2 = I 0 Δt = τ 0

27 Super- and Sub-radiance (a classical explanation) Normal radiance Super-radiance Im{E} Im{E} Re{E} Re{E} I = E 0 2 = I 0 I = 4I 0 Δt = τ 0 Δt = 1 2 τ 0

28 Super- and Sub-radiance (a classical explanation) Normal radiance Super-radiance Sub-radiance Im{E} Im{E} Im{E} Re{E} Re{E} Re{E} I = E 0 2 = I 0 I = 4I 0 I = 0 Δt = τ 0 Δt = 1 2 τ 0 Δt =

29 Super- and Sub-radiance (a classical explanation) Normal radiance Super-radiance Sub-radiance Im{E} Im{E} Im{E} Re{E} Re{E} Re{E} ge + eg ge eg Δt = τ 0 Δt = 1 2 τ 0 Δt =

30 Super- and Sub-radiance (a classical explanation) Super-radiance Sub-radiance Super- and subradiance are interference effects! Im{E} ge + eg Re{E} Im{E} ge eg Re{E} Δt = 1 2 τ 0 Δt =

31 Observation of infinite-range interactions

32 Infinite Range Interactions Not to scale

33 Infinite Range Interactions Not to scale

34 Infinite Range Interactions Not to scale

35 Infinite Range Interactions U 1D exp(ikr) Ω 12 sinkz γ 12 coskz The limit is now how many atoms can we put withing the coherence length associated with the spontaneous emission.

36 Long distance modification of the atomic radiation

37 Infinite Range Interactions V free exp(ikr) kr V 1D exp(ikr)

38 Experimental idea

39 The idea behind the experiment Probe Beam

40 The idea behind the experiment Probe Beam We look for modifications of the radiative lifetime of an ensemble of atoms around the ONF.

41 The idea behind the experiment Probe Beam The sub- and super-radiant behavior depend on the phase relation of the atomic dipoles along the common mode

42 Preparing the atoms 42

43 Coupling Enhancement α = γ 1D γ 0 JQI trap We use untrapped atoms!

44 Atomic density distribution around the ONF

45 Atomic distribution 1.0 Van der Walls shift ρ(r), p abs (r), α(r) (arb.units) Density of atoms ONF mode Distribution of atoms Atom-surface distance (nm)

46 Preparing the Atoms F =3 F =2 F =1 F =0 Re-pump De-pump F=2 F=1 Probe De-pump Re-pump Probe

47 Preparing the Atoms F =3 F =2 F =1 F =0 Δ Frecuency shift [MHz] Δ F=2 F= Atom-surface position [nm] De-pump Re-pump Probe

48 Atomic distribution Density distribution (arb. unit) with optical pumping Van der Walls shift Density of atoms ONF mode Distribution of atoms Atom-surface distance (nm)

49 Atomic distribution 1.0 with optical pumping Density distribution (arb. unit) Atom-surface distance (nm)

Measurment of N Probe 1.0 Transmission 0.9 0.8 0.

50 Measurment of N Probe 1.0 Transmission OD = N OD 1 (! r 0 ) frequency (MHz)

51 Measuring the Radiative Lifetime

52 Measuring the Radiative Lifetime 1 mm

53 Two distinct lifetimes 0-1 Log 10 count rate t/τ 0

54 Two distinct lifetimes 0 Log 10 count rate τ 0.9τ 0 τ 7.7τ t/τ 0

55 Two distinct lifetimes 0 Log 10 count rate τ 0.9τ 0 τ 7.7τ t/τ 0

56 Subradiance versus Radiation Trapping N

57 Subradiance versus Radiation Trapping τ OD 2 ( Δ) Radiation trapping depends on the OD, which depends on the excitation frequency

58 Decay time vs detunning It is not radiation trapping. It has to be subradiance!!

59 Understanding the Signal

60 Understanding the Signal

61 Fitting the Simulation (a) Log 10 normalized count rate Log 10 normalized count rate t/τ 0 (b) Normalized Residuals t/τ 0

62 Polarization dependent signal Vertically polarized probe Horizontally polarized probe

63 Polarization dependent signal Log 10 count rate Vertically polarized probe t/τ 0 Horizontally polarized probe

64 Fitting the Simulation (a) Log 10 count rate Log 10 count rate t/τ 0 (b) Normalized Residuals t/τ 0

65 Fitting the Simulation

66 Can we see a collective atomic effect of atoms around the nanofiber?

67 Long distance modification of the atomic radiation

68 Splitting the MOT in two 400λ nanofiber Left MOT Right MOT

69 Evidence of infinite-range interactions Right MOT Both MOTs Left MOT

70 Observations: The limit is less than the natural decay rate due to geometry (Purcell effect). About one in 100 of the decays is superadiant. Quantitative agreement with simulations.

71 Summary We have seen collective atomic effects (sub and superadiance) induced by the presence of the nanofiber. Superadiance shows long-range dipoledipole interactions (many times the wavelength) scaling with the optical density (number of atoms). Sub-radiance is more fragile but persists for long enough to observe it.

72 Thanks!

73 The slope (0.02) is smaller than γ 1D (0.10) because it is an average over different realizations, non all of them superradiant.

arxiv: v1 [physics.optics] 8 Aug 2013

arxiv: v1 [physics.optics] 8 Aug 2013 A low-loss photonic silica nanofiber for higher-order modes S. Ravets,,2 J. E. Hoffman, L. A. Orozco,, S. L. Rolston, G. Beadie, 3 and F. K. Fatemi 3 Joint Quantum Institute, Department of Physics, University