Lecture II: Precision quantum metrology Jun Ye JILA, NIST & Univ. of Colorado http://jila.colorado.edu/yelabs ICAP Summer School, Paris, July 20, 202 $ Funding $ NIST, NSF, AFOSR, DARPA DOE, ONR
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
Optical atomic clocks Oscillator Ultrastable laser Sr atoms Counter optical comb optical frequency counter
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
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?
An interacting many-body quantum system U U U ~ Hz ~ 50 x 0-2 K
Strontium Quality factor > 0 7 Once set, it swings during the entire age of the universe
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
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 2 0 2 0
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
Bad things about motion Short observations; Relativity (Doppler) shifts
The Doppler Problem Frequency landscape
Cooling atoms using lasers Always pushing atoms against their motions
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) -2 0 2 d (khz) -20-800 -800-2800 = -20 khz T ~ 0.5 photon recoil ~ 220 nk.2 mm = -800 khz g 46nm (2 MHz) -2 s = 248 689 nm (7.4 khz) P - 0 x (or y) Position (mm) = -800 khz 2 S 0 2 0 = -2800 khz 0-2 0 2-5.6 mm
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
Alkaline earth A tale of Twin Electrons JILA, Tokyo, Paris, NIST, PTB, Florence, NICT, NPL, NIM, NRC Science 4, 40 (2006). PRL 98, 08002 (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
Trapping atom with light l l 2 Ye, Kimble, & Katori, Science 20, 74 (2008). 2> > P 0 698 nm S 0 l magic
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, 02508 (2008).
2000 000 4p 0 a 0 (a. u.) Crossing of polarizabilities 0-000 -2000 P 0 S 0 0.2 0.4 0.6 0.8 2 4 Optical trap wavelength ( m)
Stark Shift @ I 0 (khz) It s a mess if J 0 0-50 -00-50 -200 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. = -/+ -250 0.7 0.8 0.9.0..2 Optical trap wavelength ( m)
Important Regimes for Spectroscopy trap well-resolved sideband Lamb-Dicke trap recoil uniform confinement
Atomic recoil P 0 No recoils S 0 photon
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 500 000 tr a p tr a p r e c o il No Doppler, No Recoil No Stark shift 2500 2000 500 000 500 Red sideband Carrier Blue sideband -60-40 -20 0 20 40 60 Optical frequency (khz)
Photon Counts Zoom into the carrier of 87 Sr S 0 P 0 200 000 2800 2600 2400 2200 2000 800 600 400 Q ~ x 0 4 FWHM: 4.6 Hz 200-20 -0 0 0 20 0 Clock Laser Detuning (Hz) Single trace without averaging S0 - P 0 Linewidth (Hz) 80 Magnetic Broadening 70 60 50 40 0 20 0-40 -0-20 -0 0 0 20 0 40 Magnetic Field (mg)
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
P0 Signal (Norm.) Optical Measurement of Nuclear g-factor Boyd, Zelevinsky, Ludlow, Foreman, Blatt, Ido, & Ye, Science 4, 40 (2006). P0 S0 S 0 0.0 +9/2-9/2 9 2 7 2 +7/2 5 2-7/2 0.08 2 +5/2 2 2-5/2 0.06 0.04 9 2 0.02 0.00 7 2 P 0 5 2 2 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 2 5 2 5 2 +/2 7 2 7 2 -/2 -/2-400 -200 0 200 400 9 2 9 2 Laser Detuning (Hz)
Scalar, vector, tensor polarizabilities Boyd et al., PRA 76, 02250 (2007). Westergaard et al. PRL 06, 2080 (20). P0 S0 p mf 9 2 9 2 7 2 7 2 5 2 5 2 2 2 2 2 2 2 π 0 Dg mf 0 S 2 2 B 5 2 5 2 T 7 2 7 2 9 2 9 2 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
S0 Coherent optical manipulation of nuclear spins P0 9 2 9 2 7 2 7 2 5 2 - p 5 2 2 0 2 2 2 2 2 Quantum computing Quantum register Quantum simulations 2 2 Spectral resolution 5 2 5 2 7 2 7 2 9 2 9 2 P0 Populatin (arb).0 0.8 0.6 0.4 0.2 0.0 m F = -9/2 m F = +9/2-00 0 00 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).
Coherent spectroscopy Q ~ x 0 5 Boyd et al., Science 4, 40 (2006); PRL 98, 08002 (2007). June, 202 Sr linewidth: 0.5 Hz Instability ~ 2 x 0-6 / Near the quantum projection noise
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 0-6 0-7 Ludlow / Time & Freq. 0 00 000 0000 time (s)
Collision is a big deal for Sr Systematics
Measurement of frequency shift (0-6 ) for spin-polarized fermions G. Campbell et al, Science 24, 60 (2009). 2.0.5 K K.0 0.5 0.0-0.5 0. 0.2 0. 0.4 0.5 0.6 0.7 0.8 Fraction of atoms de-excited
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
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
p-wave interactions Two-particle: Many-particle: J=N/2 Lemke et al. PRL 07 (20); Bishof et al. PRA 84, 05276 (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
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)
Competition between W and V V Interaction energy: Elastic & Inelastic mapping to bosons GPE (mean field + loss) Rabi frequency ee
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
2-s optical/atomic coherence D lattice spectroscopy P 0 2 s S 0 Fourier Limit
Linear response regime (Rabi spectroscopy) 2 uk sample temperature High density Low density Experiences shift (N -) DE µ v eg V e g
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.
Excitation Ramsey spectroscopy under interactions p / 2 p / 2 Interaction dominates over optical dephasing 0 ms 200 ms Laser detuning (Hz)
Density shift in Ramsey Collisional shift has a linear dependence on the tipping angle. CS z
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
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 0 5 0-6 0-7 Density shift: 0-7 Uncertainty: 5 x 0-9 0-8 0-9 s 0 s 00 s 000 s
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)