Darrick Chang ICFO The Institute of Photonic Sciences Barcelona, Spain. April 2, 2014

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1 Darrick Chang ICFO The Institute of Photonic Sciences Barcelona, Spain April 2, 2014

2 ICFO The Institute of Photonic Sciences 10 minute walk 11 years old 22 Research Groups 300 people Research themes: Quantum optics Nanophotonics Nonlinear optics Bio-photonics

3 My group Theoretical Quantum Nanophotonics Group Also thanks to: Oskar Painter, Jeff Kimble (Caltech), Kanu Sinha, Jake Taylor (JQI)

4 Rauschenbeutel (Vienna) Toward an atom-nanophotonics interface Goal: building blocks for complex quantum systems/devices HJ Kimble, The quantum internet, Nature (2008) Atoms provide quantum functionality, photonics provide control and scalability Vahala, Kimble (Caltech) Lukin (Harvard), Vuletic (MIT) Kimble (Caltech)

5 Example: nanofiber interface Tapered optical nanofibers MOT Rauschenbeutel (Vienna), PRL 104, (2010), also Hakuta (Tokyo) and Kimble (Caltech) Counter-propagating beams create lattice of atoms Evanescent field profile Lacroute et al., NJP 14, (2012) Current parameters: d 200 nm from surface OD~0.1 for single atom N atom ~1000

6 The limit of optical trapping Well-known tradeoff between trap depth and scattering U trap (r) = 1 2 Re α ω laser R sc Im α(ω laser )E 2 (r) E 2 (r) α Re Im Log Intensity Fixed scattering rate (I Δ 2 ) ω atom ω laser Max intensity Fixed trap depth (I Δ) Log Detuning Δ = (ω laser ω atom )

7 The limit of optical trapping Realistic functional traps U Optical trapping: U < 100 μk Δx > 50 nm ω m < 2π 100 khz Δx 1 nk BEC energy scales

8 The limit of optical trapping Well-known tradeoff between trap depth and scattering U trap (r) = 1 2 Re α ω laser R sc Im α(ω laser )E 2 (r) E 2 (r) α Re Im Log Intensity Fixed scattering rate (I Δ 2 ) ω atom ω laser Max intensity U vac (d) 1 d 3 Fixed trap depth (I Δ) d > 200 nm d Log Detuning Δ = (ω laser ω atom )

9 Motivation Quantum vacuum forces are dominant at nanoscale Loss of stability in atom traps Nanomechanical stiction in NEMS Can we flip the sign and create a super-trap? U vac x New regimes for cold atom physics! Illustration: vacuum potential + repulsive hard wall

10 A QED description An atom interacting with an optical mode (a) ω k e g H = ħg(σ eg a + h. c. ) Jaynes-Cummings Actually H = d E = ħg k σ eg + σ ge a k + a k k Perturbative shift in ground-state energy + broken symmetry near surface δω g (r) = k g k 2 (r) ω eg + ω k Casimir-Polder potential Green s functions, Buhmann et al., PRA 70, (2004) Is it possible to engineer a trap?

11 No-go theorem Vacuum force trapping not possible* (*) Assuming: no magnetic materials, surrounded by vacuum, thermal equilibrium Can t trap an atom in electronic ground state (ω eg K) Excited-state repulsion: H. Failache et al., PRL 83, 5467 (1999) Our result: can trap dressed state ψ g + δ e δ 0 for arbitrarily good nanophotonic system

12 Excited-state shifts Excited state has unique contribution: real photon emission Interaction energy between atom and its own photon e k ω k ω eg δω e r = δω g r + ω res (r) g Well-known: engineering spontaneous emission via dielectric structures Purcell factor in cavity QED, plasmonics,

13 Simple trapping model Simple 1D system: trap an atom normal to an infinite dielectric half-space laser ε(ω) p image = p 0 ε ω L 1 ε ω L +1 e iω L t x p 0 e iω Lt Example: simple Drude model (contains plasmon resonance) Useful parameterization: quality factor, detuning Q = ω pl γ, Δ d = ω L ω pl γ

14 Near-field results ω e x ω g x + Γ 0 k 0 x 3 Q Δ d ε(ω) Γ x Γ 0 k 0 x 3 Q Δ d 2 + Γ 0 e g ω 0 ω g x 3Γ k 0 x 3 k 0 = 2π/λ atom Casimir forces changing atomic resonance frequency Large excited state shifts and negligible emission: Q Δ d 1

15 Forming a trap Uniform laser intensity ε(ω) ω L e F g ω 0

16 Forming a trap Uniform laser intensity ε(ω) ω L e F g ω 0

17 Forming a trap Uniform laser intensity ε(ω) ω L e F g ω 0

18 Forming a trap ε(ω) ω L e g ω 0 Trapping of adiabatic dressed state Can create a repulsive hard wall for high material Q Barrier position is set by laser frequency (but decreased trap lifetime at small distances)

19 Comparison with optical dipole trapping What if we tried to counteract vacuum forces with an optical dipole force? U opt (r) = 1 2 Re α ω L E 2 (r) E min 1 k 0 x 3 x U vac x ħγ 0 k 0 x 3 Using our technique: E min 1 Q k 0 x 3 Key differences: Exploit strong position dependence of the polarizability α(ω L ω eg x ) Back-action: F ω e x σ ee (x) ω e x 2

20 Photon scattering rate Photon scattering rate at trap minimum x = x t R sc x t = Γ total x t σ ee x t Scattering contributes to trap heating Minimize (with respect to Δ d ): R sc Γ 0 Q k 0 x t 3/2 Infinitesimal violation of assumptions of no-go theorem Given arbitrarily high Q, ground state can be trapped!

21 Trap lifetime Four major heating mechanisms for atomic motion Recoil heating p photon = ħk Non-adiabatic motion (anti-damping) dp dt = βp

22 Trap lifetime Four major heating mechanisms for atomic motion Recoil heating p photon = ħk Non-adiabatic motion (anti-damping) Vacuum force fluctuations dp dt = βp emission Quantum tunneling over barrier

23 Trap lifetime Trap lifetime (ms) vs intensity and detuning Representative trap parameters (Cs, Q=10 7 ): Lifetime: 20 ms Distance to surface: 15 nm Δx: 1.2 nm Classical depth: 6 mk Quantum binding energy: 5 mk

24 Application to photonic crystals? Major differences between Drude materials and photonic crystal membranes ε(ω) x PhC Drude Resonances via: geometry material Achievable Q: 10 7 (Si PhC s) 10 2 (silver) Decoherence: minimal (?) huge magnetic, electric field noise

25 Going to PhC s ω e x ω g x + Γ 0 k 0 x 3 Q Δ d ε(ω) Γ x Γ 0 k 0 x 3 Q Δ d 2 + Γ 0 e g ω 0 ω g x 3Γ k 0 x 3 Only the spatial functions change Should enable engineering of trap shapes and dimensionalities

26 Photonic crystal experiments Experiments now couple atoms to 1D beams and cavities Painter, Kimble (Caltech)

27 Toward leveraging Casimir forces Learning how to tailor vacuum forces in photonic crystal structures First step: hybrid optical-casimir trap Casimir forces trap in 1D, optical in other 2D Atom-PhC coupling A. Goban et al., arxiv: (2013)

28 Outlook Atom-nanophotonics interfaces can provide fundamentally new tools for atomic physics! Surface & vacuum forces Dimensionality & dispersion Large perphoton forces Strong atom-photon interactions New paradigms Quantum information processing Many-body physics Single-photon nonlinear optics Atom trapping

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