Quantum Logic Spectroscopy and Precision Measurements · Quantum Logic Spectroscopy and Precision...
Transcript of Quantum Logic Spectroscopy and Precision Measurements · Quantum Logic Spectroscopy and Precision...
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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
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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?
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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
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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
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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
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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
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Quantum Logicwith Trapped IonsQuantum Logic
with Trapped Ions
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RF
EC
CE
RF (radio frequency): V0cos(Ωtt)EC (end caps): +U0
CE (center electrodes): GND
Linear Ion TrapsLinear Ion Traps
3D harmonic trap
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The Innsbruck Ion TrapThe Innsbruck Ion Trap
dion-electr ∼ 0.8 mmωz ∼ 1 MHzωr ∼ 3 MHz
Innsbruck
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Ion BilliardIon Billiard
String of Mg+ ions in linear Paul trapBraunschweig
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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
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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
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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
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Coherent State ManipulationCoherent State Manipulation
carriercarrier
sidebandsideband
time (µs)
time (µs)
Rabi frequencies:CAR:
BSB:
Lamb-Dickeparameter:
π-Pulse: |↓⟩ → |↑⟩
Innsbruck
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Quantum LogicQuantum Logic• Idea by:
J. I. Cirac P. Zoller
Collective motion of ions describedby normal modes
4091
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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
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Bell-State SpectroscopyBell-State Spectroscopy
1st Example:
Christian Roos, University of Innsbruck(Blatt group)
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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)
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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
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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)
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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
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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)
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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)
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Heisenberg Limited SpectroscopyHeisenberg Limited Spectroscopy
2nd Example:
Didi Leibfried, NIST Boulder(Wineland group)
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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
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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)
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Heisenberg Limited SpectroscopyHeisenberg Limited Spectroscopy
Encoding (Phase Gate)
Decoding (Phase Gate)
N qubits
Boulder
InnsbruckD. Leibfried et al., Science 304, 1476 (2004)
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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
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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!
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The Aluminum Ion Optical Clock(NIST Boulder/PTB Braunschweig)
The Aluminum Ion Optical Clock(NIST Boulder/PTB Braunschweig)
3rd Example:
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Principle of Optical ClocksPrinciple of Optical Clocks
Laser Oscillator
Single Ion
fs-comb
10:33am
State Detector
frequencyfeedback
500 THz
I(f)
ν0
Laser
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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
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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
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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
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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
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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
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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
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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!
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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
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Al+ Laboratory @ NIST/BoulderAl+ Laboratory @ NIST/Boulder
February 2005
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Principle of Optical ClocksPrinciple of Optical Clocks
Laser Oscillator
Single Ion
fs-comb
10:42am
State Detector
frequencyfeedback
500 THz
I(f)
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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
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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
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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
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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
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Clock ComparisonClock Comparison
|e2⟩
|g2⟩
α
|g1⟩hω1(α)
|e1⟩
hω2(α)
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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)
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Direct Frequency Comb Spectroscopyusing Quantum Logic
Direct Frequency Comb Spectroscopyusing Quantum Logic
4th Example:
(PTB Braunschweig)
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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, …
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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+,…
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Quantum Logic DetectionQuantum Logic Detection
spectroscopyion: Ca+
logic ion: 25Mg+
Red Sideband PulseState detection
Ions initially in motional ground state
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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+
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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
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Other Systems: NV Color CentersOther Systems: NV Color Centers
Jiang et al., Science 326, 267 (2009)
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Other Systems: NV Color CentersOther Systems: NV Color Centers
Jiang et al., Science 326, 267 (2009)
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Other Systems: CQED & MoleculesOther Systems: CQED & Molecules
André et al., Nat. Phys. 2, 636 (2006)
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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
€
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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!