Quantum Logic Spectroscopy and Precision Measurements

Quantum Logic Spectroscopy and Precision Measurements Piet O. Schmidt PTB Braunschweig and Leibniz Universität Hannover Bad Honnef, 4. November 2009

Overview What is Quantum Metrology? Quantum Logic with Trapped Ions Designer Atoms (Innsbruck) Heisenberg Limited Spectroscopy (NIST Boulder) Quantum Logic Optical Clock (NIST Boulder/PTB Braunschweig) Direct Frequency Comb Spectroscopy (PTB Braunschweig) Other systems?

What is Quantum Metrology? Beat standard quantum limit Combine properties of similar/different systems Squeezing Entanglement Quantum Logic One of the first real application of QIP

Quantum Metrology Applications Interferometry & gravitational wave detection Quantum imaging Phase & frequency measurements Designer atoms frequency & atomic properties Quantum Logic Spectroscopy: precision spectroscopy optical clocks

Why Trapped Ions? well isolated from environment long coherence times coherent control of internal and external deg. of freedom high fidelity quantum computing toolbox available near 100% internal state detection efficiency

Quantum Logic with Trapped Ions

Linear Ion Traps CE EC RF RF (radio frequency): V 0 cos(ω t t) EC (end caps): +U 0 CE (center electrodes): GND 3D harmonic trap

The Innsbruck Ion Trap d ion-electr 0.8 mm ω z 1 MHz ω r 3 MHz Innsbruck

Ion Billiard String of Mg + ions in linear Paul trap Braunschweig

Aux State detection using electron shelving detection spectroscopy/ coherent operations continuous excitation observe quantum jumps online fluorescence intensity time (s) i i Innsbruck

Aux State detection using electron shelving detection spectroscopy/ coherent operations detection efficiency: >99.85% pulsed excitation record number of detected photons per experiment and build histogramm Anzahl # of measurements der Messungen 8 7 6 5 4 3 2 1 i state occupied i state occupied D-Zustand besetzt 0 0 20 40 60 80 100 120 counts Zählrate per pro 9 ms S-Zustand besetzt Innsbruck

Quantized Motion 2-level-atom Γáω harmonic trap... coupled system............ excitation: various resonances spectroscopy: carrier and sidebands RSB: Δn = -1 CAR: Δn = 0 BSB: Δn = 1 ω n = 0 1 2 Laser detuning

Coherent State Manipulation π-pulse: carrier Rabi frequencies: CAR: BSB: Lamb-Dicke parameter: sideband time (µs) time (µs) Innsbruck

Quantum Logic Idea by: J. I. Cirac P. Zoller Collective motion of ions described by normal modes 4091

Creation of a Bell State I1I1* I1* I2I2* initial state BSB π/2 on Ion 1 RSB π on Ion 2 final state i n=1 n=0 X i n=1 n=0 I1 I2 I1 I2 I1 I2 I1 I2 i 1 i 2 0i i 1 i 2 0i+ i 1 i 2 1i i 1 i 2 0i+ i 1 i 2 0i i 1 i 2 ± i 1 i 2 also: i 1 i 2 ± i 1 i 2

1 st Example: Bell-State Spectroscopy Christian Roos, University of Innsbruck (Blatt group)

Time evolution of the Bell state i i Let ion 1 and ion 2 have different energy shifts: time ΔE Energy Measurement of phase evolution rate yields information about differential energy shift! C. F. Roos et al., Nature 443, 316 (2006)

Sources for ΔE Magnetic Fields: Zeeman Shift Electric Field Gradient: Quadrupole Shift P i D 5/2 detection 397 nm 729 nm i Problem for ion-based optical clocks S 1/2

Electric Quadrupole Shift m = -5/2-3/2-1/2 1/2 3/2 5/2 D 5/2 + + S 1/2 Electric quadrupole shift of the D 5/2 level (j=5/2): C. F. Roos et al., Nature 443, 316 (2006) Innsbruck

Solution: Designer Atoms Prepare the two-ion Bell state insensitive to linear Zeeman shift sensitive to quadrupole shift 5 MHz 10 Hz D 5/2 m = -5/2-3/2-1/2 1/2 3/2 5/2 D 5/2 m = -5/2-3/2-1/2 1/2 3/2 5/2 more generally: with m 1 +m 2 = m 3 +m 4 Quadrupole shift measurement: Measure phase evolution as a function of time C. F. Roos, quant-ph/0508148 Innsbruck

40 Ca + Quadrupole Shift Measurement electric field gradient: oscillation frequency: Δ 1 =(2π) 33.35(3) Hz C. F. Roos et al., Nature 443, 316 (2006) Innsbruck

40 Ca + Quadrupole Measurement Quadrupole shift versus electric field gradient (2nd order Zeeman effect) C. F. Roos et al., Nature 443, 316 (2006) Innsbruck

2 nd Example: Heisenberg Limited Spectroscopy Didi Leibfried, NIST Boulder (Wineland group)

Measurement Limits Classical: N independent measurements uncertainty decreases as Heisenberg limit: ΔE Δt ~ Energy N=1 N=2 N=3 Phase evolution: uncertainty decreases as Boulder Innsbruck

Creating GHZ States N qubits Encoding (Phase Gate) Encoding (Phase Gate) Decoding (Phase Gate) D. Leibfried et al., Science 304, 1476 (2004) Boulder Innsbruck

Heisenberg Limited Spectroscopy N qubits Encoding (Phase Gate) Decoding (Phase Gate) D. Leibfried et al., Science 304, 1476 (2004) Boulder Innsbruck

Results with 3 Qubits 45 % better than perfect experiment with unentangled atoms method scalable to arbitrary number of qubits D. Leibfried et al., Science 304, 1476 (2004) Boulder

Scaling up Contrast: 97% S/N Contrast: gain: 45% 84% S/N Contrast: gain: 38% 69% S/N Contrast: gain: 16% 52% S/N Contrast: gain: 3% 42% Need better gates! 0 D. Leibfried et al., Nature 438, 639 (2005) Boulder

3 rd Example: The Aluminum Ion Optical Clock (NIST Boulder/PTB Braunschweig)

Principle of Optical Clocks I(f) Laser Oscillator 500 THz fs-comb frequency feedback 10:33am State Detector Single Ion Laser ν 0

Aluminum as Optical Clock Reference Hans Dehmelt 1992 (NP 1989) Al + Features: narrow optical transition no electric quadrupole shift small black-body shift But: no accessible cooling transition 1 P 1 + 1 S 0 3 P 0 λ=167 nm (!) clock transition λ = 267.43 nm Γ 2π 8 mhz 27 Al + (I=5/2) partial level scheme

Spectroscopy of 27 Al + Use additional ion ( 9 Be + ) and quantum logic for sympathetic cooling internal state preparation internal state detection D.J. Wineland et. al., Proc. 6th Symposium on Frequency Standards and Metrology, 361 (2001)

Quantum Logic State Transfer initial state Al + spectroscopy RSB transfer pulse RSB transfer pulse detection i n=1 n=0 i n=1 n=0 Al + Be + X Al + Be + Al + Be + Al + Be + X Al + Be +

Single Pulse Rabi Spectroscopy 3 P 1 1 S 0 27 Al + Frequency Scan Time Scan Be + Al + contrast 93% coherence 5 flops P.O. Schmidt et al., Science, 309, 749 (2005) Boulder

Al + Clock Transition 1 excitation probability 0.8 0.6 0.4 0.2 0-20 -15-10 -5 0 5 10 15 20 frequency detuning (Hz) 8.4 Hz T. Rosenband et al., PRL 98, 220801 (2007) Boulder

Alternative approach: Spectroscopy of 27 Al + use additional ion ( 9 Be + ) and quantum logic for sympathetic cooling internal state preparation internal state detection D.J. Wineland et. al., Proc. 6th Symposium on Frequency Standards and Metrology, 361 (2001)

Deterministic clock state preparation probe m F =± 5/2 transitions to eliminate linear magnetic field shift conventional optical pumping is slow ( 20 s excited state lifetime!) use Be + assisted state preparation 3 P 0 1 khz / gauss 27 Al + Al CAR π-pulse π-pol. Al RSBcoolingField π-pulse on Be + independent (non σ pol. reversible) 1 S 0 m F = -5/2-3/2-1/2 +1/2 +3/2 +5/2 Applications in Ground State Cooling of Molecular Ions! Boulder

Spectroscopy of Zeeman States using Deterministic Preparation P.O. Schmidt et al., Science, 309, 749 (2005) 3 P 1 m F = -7/2-5/2-3/2-1/2 +1/2 +3/2 +5/2 +7/2 1 S 0 27 Al + Boulder

Al + Laboratory @ NIST/Boulder February 2005

Principle of Optical Clocks I(f) Laser Oscillator 500 THz fs-comb frequency feedback 10:42am State Detector Single Ion

Al + /Hg + Comparison μ-wave clock SQL Al + 100ms probe Al + : 2.3 10 17 systematic uncertainty First comparison of frequency standards at the 17 th th digit T. Rosenband et al., Science 319, 1808 (2008) Boulder

What does 10-17 mean? 1:100,000,000,000,000,000 50x better than Cs fountain clocks 1 s deviation in 3 billion years 1 st order Doppler shift: 3 nm/s or 300 μm/jahr Distance measurement earth-sun to 1/100 of the diameter of a hair 150 million kilometer 100 μm

History of Clock Uncertainties 10-12 Caesium uncertainty 10-14 10-16 10-18 H Hg + optical (ions) 1970 1980 1990 2000 2010 2020 year Ca Yb + Sr + Sr goal Hg + Hg + optical (neutral) Sr Al + @NIST Al + @PTB courtesy: T. Rosenband, NIST

The Al + Clock Project @ PTB improved clock laser improved systematics portabel Goals: more synergies with quantum logic (e.g. entangled ions, new traps) quantum sensors Geodesy clocks in space? tests of fundamental theories entangled ions

Clock Comparison e 1 hω 1 (α) g 1 hω 2 (α) e 2 g 2 α

Does α change? α/α = (-1.6± 2.3) 10-17 /year T. Rosenband et al., Science 319, 1808 (2008)

4 th Example: Direct Frequency Comb Spectroscopy using Quantum Logic (PTB Braunschweig)

Motivation Quasar absorption spectra suggest α may have changed in cosmological time More accurate laboratory spectra needed! Physics beyond the Standard Model? Goals: indirect, direct; m e /m p in molecules,

Direct Frequency Comb Spectroscopy Frequency Comb Laser Ca +, Ti +, Fe +, frequency comb emits many colors get complete level structure in one sweep absolute frequency reference can be used for many species also: Ye JILA/Boulder, Hollberg/Diddams NIST/Boulder, Eikema group Amsterdam, Hänsch MPQ and others

Quantum Logic Detection Ions initially in motional ground state spectroscopy ion: Ca + logic ion: 25 Mg + State detection Red Sideband Pulse

Status Raman laser driven Rabi oscillations after side-band cooling F=2, m F =2 F=3, m F =2 First try: Lamb-Dicke η 0.32 Limited by inefficient repumping Mg +

Quantum Logic Spectroscopy spectroscopy ion logic ion transfer state information logic ion is a sensor for spectroscopy ion spectroscopy ion controlled through logic ion combine advantages of atomic species universal technique

Other Systems: NV Color Centers Jiang et al., Science 326, 267 (2009)

Other Systems: CQED & Molecules André et al., Nat. Phys. 2, 636 (2006)

The Team @ PTB START Program Master & PhD C. Bleuel, O. Mandel, I. Sherstov, D. Nigg P.-C. Carstens, S. Ludwig, P. Schmidt, S. Klitzing, B. Hemmerling

Strong synergies between QIP and metrology: Summary Heisenberg limited spectroscopy Designer Atoms Quantum Logic Optical Clock Direct Frequency Comb Spectroscopy Quantum enhanced metrology has a bright future!