Quantum Logic Spectroscopy and Precision Measurements

Quantum Logic Spectroscopy and Precision Measurements

Piet O. Schmidt

Bad Honnef, 4. November 2009

PTB Braunschweig and Leibniz Universität Hannover

OverviewOverview

• 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?What is Quantum Metrology?

Beat standardquantum limitBeat standardquantum limit

Combineproperties of

similar/differentsystems

Combineproperties of

similar/differentsystems

SqueezingSqueezing Quantum LogicQuantum LogicEntanglementEntanglement

One of the first „real“ application of QIPOne of the first „real“ application of QIP

Quantum Metrology ApplicationsQuantum Metrology Applications

• Interferometry & gravitational wave detection

• Quantum imaging

• Phase & frequency measurements

• Designer atoms frequency & atomic properties

• Quantum Logic Spectroscopy:– precision spectroscopy

– optical clocks

Quantum Metrology ApplicationsQuantum Metrology Applications

• Interferometry & gravitational wave detection

• Quantum imaging

• Phase & frequency measurements

• Designer atoms frequency & atomic properties

• Quantum Logic Spectroscopy:– precision spectroscopy

– optical clocks

need efficient techniques to create entangled statesneed efficient techniques to create entangled states

Why Trapped Ions?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 Logicwith Trapped IonsQuantum Logic

with Trapped Ions

RF

EC

CE

RF (radio frequency): V0cos(Ωtt)EC (end caps): +U0

CE (center electrodes): GND

Linear Ion TrapsLinear Ion Traps

3D harmonic trap

The Innsbruck Ion TrapThe Innsbruck Ion Trap

dion-electr ∼ 0.8 mmωz ∼ 1 MHzωr ∼ 3 MHz

Innsbruck

Ion BilliardIon Billiard

String of Mg+ ions in linear Paul trapBraunschweig

State detection using electron shelvingState detection using electron shelvingAux

detectionspectroscopy/coherent operations

time (s)

fluor

esce

nce

inte

nsity |↓i

|↑i

Innsbruck

continuous excitationcontinuous excitation

• observe quantum jumpsonline

State detection using electron shelvingState detection using electron shelvingAux

detection

0 20 40 60 80 100 1200

1

2

3

4

5

6

7

8

Zählrate pro 9 ms

D-Zustand besetzt S-Zustand besetzt

Anza

hl d

er M

essu

ngen

detection efficiency: >99.85%

|↑i state occupied |↓i state occupied

counts per 9 ms

# of

mea

sure

men

ts

Innsbruck

pulsed excitationpulsed excitation

• record number of detectedphotons per experimentand build histogramm

spectroscopy/coherent operations

spectroscopy: carrier and sidebands

Laser detuning

Quantized MotionQuantized Motion

BSB:Δn = 1

RSB:Δn = -1

CAR:Δn = 0

2-level-atom harmonic trap

.. .

n = 0 1 2

ω

excitation: various resonances

coupled system

.. ... .

......

coupled system

Γáω

Coherent State ManipulationCoherent State Manipulation

carriercarrier

sidebandsideband

time (µs)

time (µs)

Rabi frequencies:CAR:

BSB:

Lamb-Dickeparameter:

π-Pulse: |↓⟩ → |↑⟩

Innsbruck

Quantum LogicQuantum Logic• Idea by:

J. I. Cirac P. Zoller

Collective motion of ions describedby normal modes

4091

I2I2I2*

Creation of a Bell StateCreation of a Bell State

I1I1*I1*

n=0n=1

n=0n=1

I2I1

|↑i

I2I1 I2I1 I2I1

X

initial state BSB π/2 on Ion 1 RSB π on Ion 2 final state

|↓i1 |↓i2 |0i |↓i1 |↓i2 |0i+|↑i1 |↓i2 |1i

|↓i1 |↓i2 |0i+|↑i1 |↑i2 |0i

|↓i1 |↓i2 ±|↑i1 |↑i2 also:|↓i1 |↑i2 ±|↑i1 |↓i2

|↓i

Bell-State SpectroscopyBell-State Spectroscopy

1st Example:

Christian Roos, University of Innsbruck(Blatt group)

Time evolution of the Bell state |↓↑i−|↑↓iTime evolution of the Bell state |↓↑i−|↑↓i

ΔE

Let ion 1 and ion 2 havedifferent energy shifts:

time

Ene

rgy

Measurement of phase evolution rate

yields information about differential

energy shift !

Measurement of phase evolution rate

yields information about differential

energy shift !

C. F. Roos et al., Nature 443, 316 (2006)

Sources for ΔESources for ΔE• Magnetic Fields: Zeeman Shift

• Electric Field Gradient: Quadrupole Shift

Problem for ion-based optical clocksProblem for ion-based optical clocks

D5/2

P

S1/2

detection397 nm

729 nm

|↓i

|↑i

Electric Quadrupole ShiftElectric Quadrupole Shift

Electric quadrupole shift of the D5/2 level (j=5/2):

D5/2

S1/2

m = -5/2 -3/2 -1/2 1/2 3/2 5/2

+ +

InnsbruckC. F. Roos et al., Nature 443, 316 (2006)

Solution: “Designer Atoms”Solution: “Designer Atoms”Prepare the two-ion Bell state

D5/2m = -5/2 -3/2 -1/2 1/2 3/2 5/2

sensitive to quadrupole shift

10 Hz

C. F. Roos, quant-ph/0508148

insensitive to linear Zeeman shift

D5/2m = -5/2 -3/2 -1/2 1/2 3/2 5/2

5 MHz

Quadrupole shift measurement:Measure phase evolution as a function of time

Innsbruck

more generally: with m1+m2 = m3+m4

40Ca+ Quadrupole Shift Measurement40Ca+ Quadrupole Shift Measurement

oscillation frequency: Δ1 =(2π) 33.35(3) Hz

electric field gradient:

InnsbruckC. F. Roos et al., Nature 443, 316 (2006)

40Ca+ Quadrupole Measurement40Ca+ Quadrupole Measurement

Innsbruck

Quadrupole shift versus electric field gradient

(2nd order Zeeman effect)

C. F. Roos et al., Nature 443, 316 (2006)

Heisenberg Limited SpectroscopyHeisenberg Limited Spectroscopy

2nd Example:

Didi Leibfried, NIST Boulder(Wineland group)

Measurement LimitsMeasurement Limits• Classical: N independent measurements

uncertainty decreases as

• Heisenberg limit: ΔE Δt ∼ ~

Ene

rgy

Phase evolution:

N=1 N=2 N=3

uncertainty decreases as Boulder Innsbruck

Creating GHZ StatesCreating GHZ States

Encoding (Phase Gate)

Encoding (Phase Gate)

Decoding (Phase Gate)

N qubits

Boulder InnsbruckD. Leibfried et al., Science 304, 1476 (2004)

Heisenberg Limited SpectroscopyHeisenberg Limited Spectroscopy

Encoding (Phase Gate)

Decoding (Phase Gate)

N qubits

Boulder

InnsbruckD. Leibfried et al., Science 304, 1476 (2004)

Results with 3 QubitsResults with 3 Qubits

D. Leibfried et al., Science 304, 1476 (2004) Boulder

• 45 % better than perfect experiment with unentangled atoms

• method scalable to arbitrary number of qubits

Scaling up…Scaling up…

Contrast: 97%

Contrast: 84%

Contrast: 69%

Contrast: 52%

Contrast: 42%

D. Leibfried et al., Nature 438, 639 (2005)

0

S/N gain: 45%

S/N gain: 38%

S/N gain: 16%

S/N gain: 3%

BoulderNeed better gates!Need better gates!

The Aluminum Ion Optical Clock(NIST Boulder/PTB Braunschweig)

The Aluminum Ion Optical Clock(NIST Boulder/PTB Braunschweig)

3rd Example:

Principle of Optical ClocksPrinciple of Optical Clocks

Laser Oscillator

Single Ion

fs-comb

10:33am

State Detector

frequencyfeedback

500 THz

I(f)

ν0

Laser

Aluminum as Optical Clock ReferenceAluminum as Optical Clock Reference

•• Hans Hans DehmeltDehmelt 1992 (NP 1989)1992 (NP 1989)

•• AlAl++ Features:Features:– narrow optical transition

– no electric quadrupole shift

– small black-body shift

– But: no accessible cooling transition

1S0

3P0+

1P1

λ=167 nm (!) clock transitionλ = 267.43 nmΓ ≈ 2π×8 mHz

27Al+ (I=5/2) partial level scheme

Spectroscopy of 27Al+Spectroscopy of 27Al+

D.J. Wineland et. al.,Proc. 6th Symposium on FrequencyStandards and Metrology, 361 (2001)

Use additional ion (9Be+) and quantum logic for…

• sympathetic cooling

• internal state preparation

• internal state detection

n=0n=1

n=0n=1

Be+Al+|↓i

|↑i

Be+Al+ Be+Al+ Be+Al+

X

Be+Al+

X

initial state Al+ spectroscopy RSB transfer pulse RSB transfer pulse detection

Quantum Logic State TransferQuantum Logic State Transfer

Frequency Scan Time Scan

contrast ≈ 93% coherence ≈ 5 flops

1S0

3P1

27Al+

Be+

Al+

P.O. Schmidt et al., Science, 309, 749 (2005) Boulder

Single Pulse Rabi SpectroscopySingle Pulse Rabi Spectroscopy

Al+ Clock TransitionAl+ Clock Transition

T. Rosenband et al., PRL 98, 220801 (2007)

-20 -15 -10 -5 0 5 10 15 200

0.2

0.4

0.6

0.8

1

frequency detuning (Hz)

exci

tatio

npr

obab

ility

8.4 Hz

Boulder

Spectroscopy of 27Al+Spectroscopy of 27Al+

D.J. Wineland et. al.,Proc. 6th Symposium on FrequencyStandards and Metrology, 361 (2001)

Alternative approach:

⇒ use additional ion (9Be+) and quantum logic for…

• sympathetic cooling

• internal state preparation

• internal state detection

mF= -5/2 -3/2 -1/2 +1/2 +3/2 +5/2

Deterministic clock state preparationDeterministic clock state preparation

• probe mF=± 5/2 transitions to eliminate linear magnetic field shift

• conventional optical pumping is slow(≈ 20 s excited state lifetime!)

3P0

1S027Al+

Al CARπ-pulseπ-pol.

⇒ use Be+ assisted state preparation

SB coolingon Be+

(non reversible)

Al RSBπ-pulseσ−−pol.

Fieldindependent

1 kHz / gauss

Boulder

Applications in Ground StateCooling of Molecular Ions!

Applications in Ground StateCooling of Molecular Ions!

Spectroscopy of Zeeman Statesusing Deterministic PreparationSpectroscopy of Zeeman Statesusing Deterministic Preparation

1S0

3P1

27Al+mF= -5/2 -3/2 -1/2 +1/2 +3/2 +5/2-7/2 +7/2

P.O. Schmidt et al., Science, 309, 749 (2005)

Boulder

Al+ Laboratory @ NIST/BoulderAl+ Laboratory @ NIST/Boulder

February 2005

Principle of Optical ClocksPrinciple of Optical Clocks

Laser Oscillator

Single Ion

fs-comb

10:42am

State Detector

frequencyfeedback

500 THz

I(f)

Al+/Hg+ ComparisonAl+/Hg+ Comparison

T. Rosenband et al., Science 319, 1808 (2008)

First comparison of frequency standards

at the 17th digit

First comparison of frequency standards

at the 17th digit

μ-wave clock

SQL Al +100ms probe

Boulder

Al+: 2.3×10−17 systematic uncertainty

What does 10-17 mean?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

• 1st 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

1970 1980 1990 2000 2010 202010

-18

10-16

10-14

10-12

year

unce

rtain

ty

HHg+

Yb+Ca

Hg+

Sr

Sr

Al+@NISTHg+

Caesium

optical(neutral)

optical(ions)

History of Clock UncertaintiesHistory of Clock Uncertainties

courtesy: T. Rosenband, NIST

Al+@PTB

Sr+

goal

The Al+ Clock Project @ PTBThe Al+ Clock Project @ PTB

Goals:– more synergies with quantum logic

(e.g. entangled ions, new traps)– quantum sensors Geodesy– clocks in space?– tests of fundamental theories

Goals:– more synergies with quantum logic

(e.g. entangled ions, new traps)– quantum sensors Geodesy– clocks in space?– tests of fundamental theories

improved clock laser improved systematics

portabel

entangled ions

Clock ComparisonClock Comparison

|e2⟩

|g2⟩

α

|g1⟩hω1(α)

|e1⟩

hω2(α)

Does α change?Does α change?

α/α = (-1.6± 2.3)×10-17/yearα/α = (-1.6± 2.3)×10-17/year•

T. Rosenband et al., Science 319, 1808 (2008)

Direct Frequency Comb Spectroscopyusing Quantum Logic

Direct Frequency Comb Spectroscopyusing Quantum Logic

4th Example:

(PTB Braunschweig)

MotivationMotivation

Quasar absorption spectra suggest αmay have changed in cosmological time

More accurate laboratory spectra needed!

Physics beyond the Standard Model?

Goals: indirect, direct; me/mp in molecules, …Goals: indirect, direct; me/mp in molecules, …

Direct Frequency Comb SpectroscopyDirect Frequency Comb Spectroscopy

• frequency comb emits many colors• get complete level structure in one sweep• absolute frequency reference

can be used for many species

FrequencyComb Laser

also: Ye JILA/Boulder, Hollberg/Diddams NIST/Boulder, Eikema group Amsterdam, Hänsch MPQ and others

Ca+, Ti+, Fe+,…

Quantum Logic DetectionQuantum Logic Detection

spectroscopyion: Ca+

logic ion: 25Mg+

Red Sideband PulseState detection

Ions initially in motional ground state

StatusStatus

• First try:• Lamb-Dicke η ∼ 0.32• Limited by inefficient repumping

Raman laser driven Rabi oscillationsafter side-band cooling

F=2, mF=2

F=3, mF=2

Mg+

Quantum Logic SpectroscopyQuantum Logic Spectroscopy

• logic ion is a sensor for spectroscopy ion• spectroscopy ion controlled through logic ion• combine advantages of atomic species

universal technique

transfer state information

spectroscopyion

logic ion

Other Systems: NV Color CentersOther Systems: NV Color Centers

Jiang et al., Science 326, 267 (2009)

Other Systems: NV Color CentersOther Systems: NV Color Centers

Jiang et al., Science 326, 267 (2009)

Other Systems: CQED & MoleculesOther Systems: CQED & Molecules

André et al., Nat. Phys. 2, 636 (2006)

The Team @ PTBThe Team @ PTB

C. Bleuel, O. Mandel, I. Sherstov, D. NiggP.-C. Carstens, S. Ludwig, P. Schmidt, S. Klitzing, B. Hemmerling

Master & PhD

STARTProgram

€

SummarySummary

• Strong synergies betweenQIP and metrology:– Heisenberg limited spectroscopy

– „Designer“ Atoms

– Quantum Logic Optical Clock

– Direct Frequency Comb Spectroscopy

Quantum enhanced metrologyhas a bright future!

Quantum enhanced metrologyhas a bright future!