Lecture II: Precision quantum metrology

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1 Lecture II: Precision quantum metrology Jun Ye JILA, NIST & Univ. of Colorado ICAP Summer School, Paris, July 20, 202 $ Funding $ NIST, NSF, AFOSR, DARPA DOE, ONR

2 Clocks are everywhere Space exploration, Defense & Homeland security ESA satellite to satellite comm Fiber-Laser Comb Telecommunications Transmit Fiber Standards for Industry Length Metrology Fundamental and Applied Science

3 Optical atomic clocks Oscillator Ultrastable laser Sr atoms Counter optical comb optical frequency counter

4 Ultracold Matter Precise control of a quantum system The most precise measurements, e.g., clocks Quantum information Quantum sensors Control: A tool for understanding complexity Strongly correlated many-body quantum systems Superfluidity & Superconductivity Quantum magnetism (Fully-)Quantum chemistry

5 Quantum metrology in optical lattice P 0 S 0 ω trap Atomic confinement << l (e ikx ~, k = 2p/l probe ) Trap potential identical for S 0 and P 0 Precision improvement by N /2 Long coherence time; Zero Doppler shift, Zero recoil shift No light shift from the trap; but, Interaction effects? Accuracy?

6 An interacting many-body quantum system U U U ~ Hz ~ 50 x 0-2 K

7 Strontium Quality factor > 0 7 Once set, it swings during the entire age of the universe

8 Alkali Polarization Gradient Stimulated Raman VSCPT Limited to Low Densities Alkaline Earth versus Alkali All-Optical Cooling to Ultra-Low Temperatures Cold / Ultra-Cold Collisions Alkaline Earth High Density Intercombination line sub-recoil Sideband Cooling in Dipole Traps Low Transfer Efficiency High Collision Rates Feshbach Resonances Hyperfine structure BEC / FDG Quantitative Studies Diverse polar molecules Low Collision Rates Ground-State Magnetic Traps Tunable Interactions Only two Fermions: 40 K, 6 Li Time / Frequency Metrology Diversity of Bose, Fermi Isotopes Optical Feshbach resonance Structure Free Ground State Microwave Clocks Small Optical Line Q High Optical Line Q Second-Stage Cooling Required

9 Strontium: first stage cooling 5s6s 5s6s large dipole moment mostly closed transition J=0 to J= diode laser with frequency doubling 5s5p 5s4d 5s5p 5s4d 5s 2 S 0 P D S 2 P J D J

10 Strontium: Narrow Line Laser Cooling 5s6s 5s6s smaller dipole moment closed transition J=0 to J= 5s5p 5s4d 5s5p 2 0 5s4d 2 0 diode laser accessible 5s 2 S 0 P D S 2 P J D J

11 Bad things about motion Short observations; Relativity (Doppler) shifts

12 The Doppler Problem Frequency landscape

13 Cooling atoms using lasers Always pushing atoms against their motions

14 Force (x0-2 N) Stop the moving atom Detuning Dependent Mechanical Dynamics P billionth (0-9 ) of room temperature 2 0 v X ( or v Y ) (m/s) d (khz) = -20 khz T ~ 0.5 photon recoil ~ 220 nk.2 mm = -800 khz g 46nm (2 MHz) -2 s = nm (7.4 khz) P - 0 x (or y) Position (mm) = -800 khz 2 S = khz mm

15 Strontium: Clock Transition 5s6s 5s6s HFI provides S 0 - P 0 clock ( ~ mhz) field insensitive states 5s5p 5s4d 5s4d 2 0 diode laser accessible Starkfree confinement wavelength 5s5p 2 0 clock states J=0 5s 2 S 0 P D S 2 P J D J

16 Alkaline earth A tale of Twin Electrons JILA, Tokyo, Paris, NIST, PTB, Florence, NICT, NPL, NIM, NRC Science 4, 40 (2006). PRL 98, (2007). Science 9, 805 (2008). P 46 nm (~ 5 ns) P 0 Metastable state quality factor 698 nm (~ 50 s) Q > 0 7 S 0

17 Trapping atom with light l l 2 Ye, Kimble, & Katori, Science 20, 74 (2008). 2> > P nm S 0 l magic

18 Sr energy levels 5snd D,2, 5snp P 5snp S 5s6s S 2 5p P0,,2 ~ 490 nm 5s5d D,2, 5s5p P ~ 680 nm λ trap ~ 480 nm 5s4d D,2, ~ 460 nm ~ 2.7μm 5s5p P0,,2 2 5s S0 λ trap Porsev, Ludlow, Boyd, Ye, Phys. Rev. A 78, (2008).

19 p 0 a 0 (a. u.) Crossing of polarizabilities P 0 S Optical trap wavelength ( m)

20 Stark I 0 (khz) It s a mess if J S 0, pol. = p, +, - P 0, pol. = p, +, - P (m = 0), pol. = p P (m = +/- ), pol. = p; (m=0), pol. = + P (m = +/- ), pol. = +/- P (m = +/- ), pol. = -/ Optical trap wavelength ( m)

21 Important Regimes for Spectroscopy trap well-resolved sideband Lamb-Dicke trap recoil uniform confinement

22 Atomic recoil P 0 No recoils S 0 photon

23 Spectroscopy at the magic wavelength Ludlow et al., Phys. Rev. Lett. 96, 000 (2006). Photon counts Clock probe S/N ~ N /2 S 0 P 0 ω trap N atoms tr a p tr a p r e c o il No Doppler, No Recoil No Stark shift Red sideband Carrier Blue sideband Optical frequency (khz)

24 Photon Counts Zoom into the carrier of 87 Sr S 0 P Q ~ x 0 4 FWHM: 4.6 Hz Clock Laser Detuning (Hz) Single trace without averaging S0 - P 0 Linewidth (Hz) 80 Magnetic Broadening Magnetic Field (mg)

25 Differential Landé g-factor ' P0 P0 c P c2 P P P HFI P 0 P 0 S 0 I = 9/2 S 0-9/2 m f +9/2 P 0 g-factor different from S 0 due to hyperfine Zeeman-shift; vector & tensor light shifts All are determined with high-resolution measurement

26 P0 Signal (Norm.) Optical Measurement of Nuclear g-factor Boyd, Zelevinsky, Ludlow, Foreman, Blatt, Ido, & Ye, Science 4, 40 (2006). P0 S0 S /2-9/ / / / / P NMR-like No net electronic experiment angular in the momentum optical domain Resolved Dg = -08.4(4) transitions Hz/(G with < m F ) Gauss Small P 0 lifetime B-field does 40(40) not perturb s hyperfine mixing 2 π 2 2 +/ / /2 -/ Laser Detuning (Hz)

27 Scalar, vector, tensor polarizabilities Boyd et al., PRA 76, (2007). Westergaard et al. PRL 06, 2080 (20). P0 S0 p mf π 0 Dg mf 0 S 2 2 B T F Itrap ( D D F ) ( D V F T 2 F m D m ) Hyperpolarizability ~ (I trap ) 2 : <E-7 P. Lemonde, SYRTE D : differential polarizability : polarization ellipticity I trap Clock frequency st order Zeeman Scalar + Tensor polarizability Vector +Tensor polarizability

28 S0 Coherent optical manipulation of nuclear spins P p Quantum computing Quantum register Quantum simulations 2 2 Spectral resolution P0 Populatin (arb) m F = -9/2 m F = +9/ Detuning (Hz) Two stable spin systems, separately manipulated or entangled. Nuclear spins for information storage & accessed via electronic qubits. Electronic states for state-dependent lattice & control. SU(N) symmetry; spin orbital coupling dynamics. Deutsch et al., PRL 98 (2007); PRL 99, (2007). Daley et al., PRL 0 (2008). Gorshkov et al., PRL. 02 (2009); Nature Phys. 6, 289 (200).

29 Coherent spectroscopy Q ~ x 0 5 Boyd et al., Science 4, 40 (2006); PRL 98, (2007). June, 202 Sr linewidth: 0.5 Hz Instability ~ 2 x 0-6 / Near the quantum projection noise

30 total deviation JILA Sr atomic clock Science 4, 40 (2006); Science 9, 805 (2008); Science 20, 74 (2008); Science 24, 60 (2009); Science, 04 (20). 0, 000, 000, 000, 000, 000 ± (0-6 ) 0-5 Sr Yb standards Definition of SI SECOND Ludlow / Time & Freq time (s)

31 Collision is a big deal for Sr Systematics

32 Measurement of frequency shift (0-6 ) for spin-polarized fermions G. Campbell et al, Science 24, 60 (2009) K K Fraction of atoms de-excited

33 Interactions between identical Fermions () Particles behave like waves (T -> 0) (2) Angular momentum is quantized s p d 0 ħ 2ħ () Quantum statistics matter 0 0 Fermions c L =, p-wave collisions

34 Lattice clock: an interacting quantum system e g n 2 n Triplet Singlet state s-wave interaction shift. Triplet states can also have p-wave interactions. Rey et al PRL (2009), Gibble PRL (2009), Yu & Pethick, PRL (200). Swallows et al., Science, 04 (20). 2W 2W Shifted singlet u eg DW

35 p-wave interactions Two-particle: Many-particle: J=N/2 Lemke et al. PRL 07 (20); Bishof et al. PRA 84, (20). 2W J= J=0 Triplet p-wave v ee Singlet s-wave u eg In a strongly interacting system: s-wave suppressed (contributing as sidebands) p-wave dominant (acting on the carrier) s-wave 2W v eg DW p-wave

36 Spin model (Ana Maria Rey et al.) Pseudo-spin S and W: laser detuning and Rabi freq. Micheli, A., Jaksch, D., Cirac, J., & Zoller, P. (200). Physical Review A, 67() (200)

37 Competition between W and V V Interaction energy: Elastic & Inelastic mapping to bosons GPE (mean field + loss) Rabi frequency ee

38 zˆ W Competition between W and V yˆ V xˆ U () W >> V mean-field shift W Rabi frequency V (2) W < V Correlated spin spectrum Interaction energy

39 2-s optical/atomic coherence D lattice spectroscopy P 0 2 s S 0 Fourier Limit

40 Linear response regime (Rabi spectroscopy) 2 uk sample temperature High density Low density Experiences shift (N -) DE µ v eg V e g

41 Rabi spectroscopy with strong interactions D Non-trivial eigenvalue spectrum of correlated states. etc. g Structure due to interactions (both elastic & inelastic). excitation blockade at increasing density or probe time.

42 Excitation Ramsey spectroscopy under interactions p / 2 p / 2 Interaction dominates over optical dephasing 0 ms 200 ms Laser detuning (Hz)

43 Density shift in Ramsey Collisional shift has a linear dependence on the tipping angle. CS z

44 Shift Beyond mean field Interaction & Poissonian distribution Ramsey fringe decay 5p 6 D p 2 p 6 Tipping angle dependence Ramsey fringe decay vs. the spin tipping angle Excitation fraction

45 Fractional shift Cavity-Enhanced Lattice System Retroreflected Lattice: Cavity Lattice: k axial radial N Retro-Refl. 80 khz 450 Hz 0 Pierre Lemonde SYRTE Cavity 90 khz 00 Hz Density shift: 0-7 Uncertainty: 5 x s 0 s 00 s 000 s

46 Special thanks M. Swallows M. Martin M. Bishof T. Nicholson B. Bloom J. Williams M. Swallows (JPL/Caltech) S. Blatt (Harvard) A. Ludlow (NIST) Y. Lin (NIM, Beijing) G. Campbell (U. Maryland) M. Boyd (AO Sense) J. Thomsen (U. Copenhagen) T. Zelevinsky (Columbia U.) T. Zanon (Univ. Paris ) S. Foreman (Stanford U.) X. Huang (WIPM) T. Ido (Tokyo NICT) T. Loftus (AO Sense) X. Xu (ECNU) Ana M. Rey (theory)

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