Physics 301: Physics Today Seminar - March 6th, 2018

Building clocks out of atoms and nanoscale probes out of diamond

Shimon Kolkowitz University of Wisconsin - Madison

Optical lattice clocks: Color centers in diamond:

The Kolkowitz Lab today:

The Kolkowitz Lab in August:

4

1st Solvay conference in 1911:Standing (L-R): R. Goldschmidt, M. Planck, H. Rubens, A. Sommerfeld,

F. Lindemann, M. de Broglie, M. Knudsen, F. Hasenöhrl, G. Hostelet, E. Herzen, J.H. Jeans, E. Rutherford, H. Kamerlingh Onnes, A. Einstein, P. Langevin.

Seated (L-R): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz, E. Warburg, J. Perrin, W. Wien, M. Skłodowska-Curie, H. Poincaré.

100 years of quantum mechanics

Image credit: wikipedia.org

5

5th Solvay conference in 1927:Standing (L-R): A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder,

E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin Seated 2nd row(L-R): P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers,

P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. BohrSeated 1st row(L-R): I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz,

A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson

16 years later…

Image credit: wikipedia.org

6

Applications

Atomic clocks and GPS:

NMR and MRI: The laser:

Understanding and controlling the internal quantum states of atoms gave rise to a number of fundamental

technologies:

These generally involve many billions of atoms.

Image credit: wikipedia.org

7

Last 30 years: Isolated quantum systems

Neutral atoms Quantum dots

Crystal defectsSC qubits

Trapped ions

Monroe group, UMD Eriksson group

McDermott groupBellini group, Florence

Single photons

Saffman group

8

Last 30 years: Isolated quantum systems

Neutral atoms Quantum dots

Crystal defectsSC qubits

Trapped ions

Monroe group, UMD Eriksson group

McDermott groupBellini group, Florence

Single photons

Saffman group

9

Quantum science

Idea: Harness quantum “weirdness” (i.e. entanglement, superpositions, Heisenberg uncertainty, no-cloning theorem…)

Potential Applications:Quantum computing/simulation - Harness quantum mechanics to solve problems that are intractable on a classical computer.

Quantum communication - Communicate privately by sending information using quantum bits.

Quantum sensing/metrology - Use quantum systems and states to improve sensitivity, accuracy, and resolution of clocks and sensors.

Requires well isolated quantum systems with controllable, coherent interactions.

Research in the Kolkowitz Lab:Optical lattice clocks: Color centers in diamond:

Research in the Kolkowitz Lab:Optical lattice clocks: Color centers in diamond:

Many condensed matter systems with features of interest at the nanometer length scale:

Johansen group, Oslo1 Jacques group, CNRS2 Westervelt group, Harvard3

Motivation

500 nm

1Goa et al., Rev. Sci. Inst. (2003), 2Tetienne et al., Science (2014), 3Topinka et al., Nature (2001)

1 micron

Vortices in high Tc SCs:

Magnetic domains:

Electron transport in 2DEGS:

McDermott group, UW-Madison1

Lukin & Loncar groups, Harvard3

Motivation

500 nm

1Sendelbach et al., PRL (2008), 2Deslauriers et al., PRL (2006), 3Burek et al., Nano Letters (2012)

500 nm 500 nm

SQUIDs and flux qubits: Ion traps:

NVs in nanophotonic structures:

Monroe group, University of Maryland2

In addition, quantum systems are now becoming limited by surface noise:

McDermott group, UW-Madison1

Lukin & Loncar groups, Harvard3

Motivation

500 nm

1Sendelbach et al., PRL (2008), 2Deslauriers et al., PRL (2006), 3Burek et al., Nano Letters (2012)

500 nm 500 nm

SQUIDs and flux qubits: Ion traps:

NVs in nanophotonic structures:

Monroe group, University of Maryland2

“God made the bulk; the surface was invented by the devil.” -Wolfgang Pauli

In addition, quantum systems are now becoming limited by surface noise:

MotivationProbing materials with single spin qubits:

Idea: Use shallow NV centers as probe of local fields near materials of interest.

See also: Work of Yacoby, Degen, Jacques, Jayich, Budker groups, amongst others

Thin diamond

(Super)conductorSpin clusters

Optical path

d ~ 10 nm

Single shallow implant NVs

e-

Electron motionVortex

Nitrogen-vacancy centers in diamond

See e.g. Childress et al., Science (2006)

=

Δ−2.87 GHz

ms = ±1

ms = 0

1042 nm532 nm 637+ nm

g

e

s

Nitrogen-vacancy centers in diamond

2gμBBz

2.88 GHz

+1

1

ms = 0 💡

💡

💡

~2.87

Nitrogen-vacancy centers in diamond

19

NV advantages and applicationsGood system for Quantum information applications: • Easy optical initialization and readout of electronic spin state • Long electronic spin coherence times at room temperature (~1 ms T2) • Access to quantum register of well-isolated nuclear spins (>1 sec T2)

Solid State System: • No trapping required • Highly stable • Scalable

Key Challenge: • Long range coupling

Opportunities: • Unique applications in biology,

nanoscience • Highly sensitive probe of local

magnetic fields • Robust from <1-600 Kelvin

Yacoby group, Harvard2

Walsworth group, Harvard3 Lukin, Park groups, Harvard4

Hanson group1

1Hensen et al. Nature (2015), 2Maletinsky et al., Nature Nano (2012), 3Le Sage et al. Nature (2013), 4Kucsko et al., Nature (2013)

Many condensed matter systems with features of interest at the nanometer length scale:

Johansen group, Oslo1 Westervelt group, Harvard3

Motivation

1Goa et al., Rev. Sci. Inst. (2003), 2Tetienne et al., Science (2014), 3Topinka et al., Nature (2001)

1 micron

Vortices in high Tc SCs:

Electron transport in 2DEGS:

Jacques group, CNRS2

500 nm

Magnetic domains:

Many condensed matter systems with features of interest at the nanometer length scale:

Jayich group, UCSB1 Jacques group, CNRS2 Hollenberg group, Melbourne3

Motivation

500 nm

1Pelliccione et al., Nat. Nano (2016), 2Tetienne et al., Science (2014), 3Tetienne et al., arXiv:1609.09208 (2016)

200 nm

5 μm

Vortices in high Tc SCs:

Electron transport in 2DEGS:

Magnetic domains:

• Thermally induced electron currents in a metal generate field noise nearby

• Johnson noise can limit the spin lifetimes of atoms on atom chips, quantum dots, and NVs used as sensors or qubits1,2

• Noise above the Johnson noise limit is observed in the heating rates of ions in chip traps3,4

• NVs provide probe of Johnson noise in unexplored regime

Johnson-Nyquist noise next to conductors

1Henkel et al., App. Phys. B (1999), 2Lin et al., PRL (2004), 3Hite et al., PRL (2012), 4Brownnutt et al., arXiv (2014)

L

e-

z BAC

Conductor

Spin

NVs as a probe of Johnson noise

NVs as a probe of Johnson noise

NVs as a probe of Johnson noise

NVs as a probe of Johnson noise

NVs as a probe of Johnson noise

Silver'

20 μm

τ532 nm excitation

620-750 nm collection

Polarization Readout

Meas. Ref.

2gμBBz

2.88 GHz

+1

1

ms = 0

Measuring NV spin relaxationkBT >> !ω

Single NV under silver film

Impact of 100 nm thick silver film on single NV spin lifetime:

-25

-20

-15

-10

-5

0

% c

hang

e in

fluo

resc

ence

1.00.80.60.40.20.0Relaxation time (ms)

NV T1 before silver: 4 ms

1SK, A. Safira et al., Science (2015)

Single NV under silver film

NV T1 before silver: 4 msNV T1 with silver: 160 us

Impact of 100 nm thick silver film on single NV spin lifetime:

-25

-20

-15

-10

-5

0

% c

hang

e in

fluo

resc

ence

1.00.80.60.40.20.0Relaxation time (ms)

1SK, A. Safira et al., Science (2015)

Single NV under silver film

NV T1 before silver: 4 msNV T1 with silver: 160 μs

NV T1 after silver: 4 ms

Impact of 100 nm thick silver film on single NV spin lifetime:

-25

-20

-15

-10

-5

0

% c

hang

e in

fluo

resc

ence

1.00.80.60.40.20.0Relaxation time (ms)

1SK, A. Safira et al., Science (2015)

Quantitative analysis of noise dependence

Fermi’s golden rule:

Fluctuation dissipation theorem + conductivity:

See e.g. Henkel et al., App. Phys. B (1999), or Langsjoen et al., PRB (2014)

Γ0→1 =1!2

0 µα 1 1 µβ 0 Sαβ

B (r,ω)α,β=x,y,z∑

Γ =1T1=3g2µB

2µo2

32!2π(1+ 1

2sin2(θ ))×σ kBT

z

Distance dependence of Johnson noise

Silver

Diamond Single NVs

Optical Path

SiO2 Ramp

150

100

50

0 R

amp

heig

ht (n

m)

1.51.00.50.0 Lateral position (mm)

1SK, A. Safira et al., Science (2015)

Distance dependence of Johnson noise

Silver

Diamond Single NVs

Optical Path

SiO2 Ramp

No free parameter theory prediction1/T1,max measured at each position

Γ=1T1∝σ kBTz

1SK, A. Safira et al., Science (2015)

Distance dependence of Johnson noise

Atomic spin lifetime, Vuletic group1:

1Lin et al., PRL (2004), see also Harber et al., Journal of Low Temp. Phys. (2003)

Atom lifetime above copperAtom lifetime above dielectric

Distance dependence of Johnson noise

No free parameter theory predictionMax T1 measured at each position

This work

Atomic spin lifetime, Vuletic group1:NV spin lifetime

Atom lifetime above copperAtom lifetime above dielectric

1Lin et al., PRL (2004), see also Harber et al., Journal of Low Temp. Phys. (2003)

Temperature and conductivity dependence

Fit with depth as only free parameterNV inverse lifetime

vs temperature for NV under silver:Γ

z = 31 ± 2 nm7

6

5

4

3

2

1

Rel

exat

ion

rate

Γ 1

/ms

30025020015010050 Temperature (K)

Temperature dependence for 100 nm thick silver film:

Γ=1T1∝σ kBTz

1SK, A. Safira et al., Science (2015)

Temperature and conductivity dependence

Fit with depth as only free parameterNV inverse lifetime

vs temperature for NV under silver:Γ

z = 31 ± 2 nm7

6

5

4

3

2

1

Rel

exat

ion

rate

Γ 1

/ms

30025020015010050 Temperature (K)

Temperature dependence for 100 nm thick silver film:

1T1∝kBTz×σ (T )

σ vs temperature for silver film on diamond:

4-pt measured conductivity

700 nm

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Con

duct

ivity

(S/m

x 1

0-8)

300250200150100500 Temperature (K)

1SK, A. Safira et al., Science (2015)

Temperature and conductivity dependence

Fit to high temperature data

σ vs temperature for silver samples: vs temperature for NV under silver:Γ

Polycrystalline silver conductivitySingle crystal silver conductivity

700 nm

14

12

10

8

6

4

2

Con

duct

ivity

(S/m

x 1

0-8)

25020015010050 Temperature (K)

Temperature dependence for 1.5 micron thick single crystal silver:

NV inverse lifetime

1T1∝kBTz×σ (T )

1SK, A. Safira et al., Science (2015)

Breakdown of Ohm’s lawPreviously, we used the Drude model to equate the dissipation in the film

to it’s bulk conductivity1:

z ~30 nm

Polycrystalline silver

l ~ 10 nm

1Henkel et al., App. Phys. B (1999)

1T1∝kBTz×σ (T )

e-

z

z

NV spin

Diamond

1T1∝kBTz×σ (T )

Breakdown of Ohm’s lawNow, the mean free path is much larger than the distance from the NV to

the silver1,2:

ε(ω)→ε(ω,!k )

Single crystal silver

l ~ 1 micron

1Beenakker et al., Solid State Physics 44 (2004), 2Langsjoen et al., PRB (2014)

z ~30 nm

e-

z

z

NV spin

Diamond

Effects of non-local dielectric function

Local fit to high temperature data

vs temperature for NV under silver:Γ

NV inverse lifetime

1SK, A. Safira et al., Science (2015)

Effects of non-local dielectric function

Local fit to high temperature data

vs temperature for NV under silver:Γ

NV inverse lifetime

z = 36 ± 1 nm

Non-local fit

1SK, A. Safira et al., Science (2015)

Effects of non-local dielectric functionvs temperature for NVs under silver:Γ

NV inverse lifetime

z = 33 ± 2 nm

Non-local fit

z = 141 ± 4 nm

NV inverse lifetime

Non-local fit

1SK, A. Safira et al., Science (2015)

T1 vs distance for NVs under silver at 103 K:

Consistency of non-local model

Predicted lifetime from local theory, 103 KPredicted lifetime as a function of distance, 103 K

NVs in regions of increasing distance to the film

1SK, A. Safira et al., Science (2015)

e-

z

z

NV spin

Ballistic transport in macroscopic samples

Silver'

1Mattioli, Palacios, Nano Letters (2015)

Implications

Hanson group2Eriksson group1

Fundamental limits to quantum dot and NV coherence times and sensitivities in certain architectures:

Non-contact probe of local temperature or resistance:Yacoby, Degen, Jayich groups3

1Kim et al. Nature (2014), 2Hensen et al. Nature (2015), 3Maletinsky, et al., Nature Nano (2012)

Recent results building on our work“Nanoscale electrical conductivity imaging using a nitrogen vacancy

center in diamond1”

1Ariyartne et al., arXiv:1712.09209 (2017)

Research at UW-Madison:

NV

Thin diamond

Laser

Spin clustersMagnetic impuritySample of interest

1/f flux noise in Josephson circuits2: Kondo effect1:

1Domenicali, Christenson, Journal of App. Phys. (1961), 2Sendelbach et al., PRL (2008)

Resi

stan

ce

Temperature (K)

Nanoscale metrology with solid-state defects

Si

NV decoherence near surfaces1:

1Myers et al., PRL (2014)

UW-Madison Physics Intro Grad Seminar 2017

Research in the Kolkowitz Lab:Optical lattice clocks: Color centers in diamond:

g

Lθ

Components of a mechanical clock

Local oscillatorCounter Frequency reference

Image credits: wikipedia.org

Principles of an atomic clock

Local oscillator (LO) Frequency reference

g

e

T ~100 picoseconds

ν = 9 GHz

hν

Counter

LO frequency

Pe

Local oscillator (LO) Frequency reference

g

e

T ~100 picoseconds

ν = 9 GHz

hν

Counter

LO frequency

Pe

Principles of an atomic clock

Why is an atomic clock better?

g

ehν

Better frequency reference:

vs

Clock ticks faster:

vs

t

T ~1 second

t

T ~0.1 nanosecond

Ammonia maser Cs beam Cs fountain

Atomic clock progress, 1949 - 2012

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laser cooling

Image credit: wikipedia.org/International Bureau of Weights and Measures

Applications

Global Positioning System Unit definitions

Laser frequency comb

Image credits: nist.gov

2005 Nobel prize Hänsch and Hall

“optical escapement”

1 mHz linewidthQ ~ 1018

160 s lifetime

87Strontium

1S0mF=-9/2

-7/2 -5/2 -3/2 -1/2 1/27/25/2 9/2

3/2

See Ludlow et al., Reviews of Modern Physics (2015) for other species of optical clocks

1 mHz linewidthQ ~ 1018

160 s lifetime

T = 800 KT = 2 mKT = 2 μK

1 mHz linewidth

Laser cooling

1 mHz linewidth

Laser cooling

T = 2 μK

Δν = 40 kHzStill too broad!

Optical lattice trap

The solution?

nz = 0nz = 1

nz = 2

M. Martin, PhD Thesis, 2013

Resolved sideband and Lamb-Dicke regimes:

nz = 0g

enz = 0

nz = 1nz = 2

nz = 1nz = 2

Optical lattice trap

A magic wavelength trap

M. Martin, PhD Thesis, 2013

3P0 polarizability1S0 polarizability

Optical lattice clock

Local oscillator (LO) Frequency reference

T ~ 2 femtoseconds

ν = 430 THz

Counter

LO frequency

Pe

?1 mHz linewidth

40 cm ultrastable ULE cavity

Martin, et al., Science, (2013)

115

-2x10-12

0x10-12

2x10-12Fr

ac.y

sens

. (1/

ms2

)

-4 -2 0 2 4

Position along mirror (mm)

-2x10-10

0x10-10

2x10-10 Frac.xsens. (1/m

s 2)

a

b c

Figure 4.11: The Big ULE cavity and Zerodur support structure. (a) The final design of the BigULE removed the teflon legs in favor of a Zerodur support shelf. The cavity rests on Viton hemi-spheres (not pictured). (b) Exaggerated cavity deformation in response to a vertical accelerationand when held at the optimal points via finite element analysis (FEA). (c) FEA-predicted mirrordisplacement per acceleration as a function of vertical (left) and horizontal (right) displacementalong the mirror surface when the cavity is supported optimally.

116

60

50

40

30

20

10

0Vacu

um c

ham

ber t

emp

(C)

600x1034002000

Time (s)

3000

2500

2000

1500

1000

500

0

Drift rate (H

z/sec)

86420

Time (days)

Figure 4.12: The double-layer vacuum system for the Big ULE. The inner vacuum chamber isactively temperature stabilized by Peltier elements (visible at right) to the level of several mK(sub-mK) per day (hour). The outer vacuum is kept below 10 Torr to provide thermal isolationfrom the outside world and promote temperature homogeneity over the surface of the inner vacuumchamber. A vacuum level of 2 ⇥ 10�8 Torr is maintained in the inner chaber with a 75 L/s ionpump. The measured time constant between the inner vacuum chamber and the cavity is 1.6 days.Inset: Measurement of the thermal time constant of the system. A large temperature change wasapplied to the system and the optical beat of the laser stabilized to the Big ULE was measuredwith a second stable laser system.

40 cm ultrastable ULE cavity

Martin, et al., Science, (2013)

116

60

50

40

30

20

10

0Vacu

um c

ham

ber t

emp

(C)

600x1034002000

Time (s)

3000

2500

2000

1500

1000

500

0

Drift rate (H

z/sec)

86420

Time (days)

Figure 4.12: The double-layer vacuum system for the Big ULE. The inner vacuum chamber isactively temperature stabilized by Peltier elements (visible at right) to the level of several mK(sub-mK) per day (hour). The outer vacuum is kept below 10 Torr to provide thermal isolationfrom the outside world and promote temperature homogeneity over the surface of the inner vacuumchamber. A vacuum level of 2 ⇥ 10�8 Torr is maintained in the inner chaber with a 75 L/s ionpump. The measured time constant between the inner vacuum chamber and the cavity is 1.6 days.Inset: Measurement of the thermal time constant of the system. A large temperature change wasapplied to the system and the optical beat of the laser stabilized to the Big ULE was measuredwith a second stable laser system.

Linewidth: 26 mHzQ ~ 2 x 1016

ΔL ~ 10-16 m (1/10th rproton)

rproton

∆L=0.05 fm

Coherent for ~10 round trips

Optical lattice clock

Local oscillator (LO) Frequency reference

T ~ 2 femtoseconds

ν = 430 THz

Counter

LO frequency

Pe

1 mHz linewidth

Clock performance: statistical uncertainty

Bloom et al., Nature (2014)

σ ≈1

νo naTτ=3.4×10−16

τ

Clo

ck fr

actio

nal f

requ

ency

dev

iatio

n σ

Averaging time (s)

Systematic evaluation

Nicholson et al., Nature Communications, (2015)

Shifts and Uncertainties in Fractional Frequency Units × 10-18

First Evaluation Second Evaluation

Systematic Effect Shift Uncertainty Shift Uncertainty

BBR Static -4962.9 1.8 -4562.1 0.3

BBR Dynamic -346 3.7 -305.3 1.4

Density Shift -4.7 0.6 -3.5 0.4

Lattice Stark -461.5 3.7 -1.3 1.1

Probe AC Stark 0.8 1.3 0.0 0.0

1st Order Zeeman -0.2 1.1 -0.2 0.2

2nd Order Zeeman -144.5 1.2 -51.7 0.3

Line pulling and tunneling 0.0 <0.1 0.0 <0.1

DC Stark -3.5 2 0.0 0.1

Background gas collisions 0.0 0.6 0.0 <0.6

AOM Phase Chirp -1 1 0.6 0.4

2nd-Order Doppler 0.0 <0.1 0.0 <0.1

Servo Error 0.4 0.6 -0.5 0.4

Total -5923.1 6.4 -4924.0 2.1

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Ammonia maser Cs beam Cs fountain Ion optical clock Sr optical lattice clock

Atomic clock progress, 1949 - 2016

optical clocks

Novel applications of optical lattice clocks

1Huntemann et al. PRL (2014), 2Dereviako, Pospelov, Nature Physics (2014), 3SK et al., Nature (2016),4Bromley, SK, et al., Nature Physics, 2018, 5SK et al. PRD (2016), 6Arms, Serna, arXiv (2016),

Tests of GR6

Dark matter detection2

Variation of fundamental constants1

Gravitational wave detection5

Image credit: R. Hurt/Caltech-JPL 🌎🔥

🍎g

a

🍎

Quantum simulation3,4

A multiplexed optical lattice clock

Gravitational redshift at the mm scale

Latti

ce 1

Latti

ce 2

Clo

ck b

eam

1

Clo

ck b

eam

2

g

Δh

δ ff GR

≈gΔhc2

Gravitational red shift:

Chou et al., Science (2010)

Test of general relativity with Al+ ion clock

Equivalence principle test

Latti

ce 1

Latti

ce 2

Clo

ck b

eam

1

Clo

ck b

eam

2

g

Δh

δ ff GR

≈gΔhc2

Gravitational red shift:

🌎 🔥

🍎g

a

🍎

Equivalence principle test

Latti

ce 1

Latti

ce 2

Clo

ck b

eam

1

Clo

ck b

eam

2

g

Δh

δ ff GR

≈gΔhc2

Δl

Lattice 1

Lattice 2Clock beam 1

Clock beam 2g a

Gravitational red shift:

Acceleration analogue:

δ ff SR

≈aΔlc2

🌎 🔥

🍎g

a

🍎

Other long term directions

1S0, g

3P0, e

698 nm clock

5s50s 3S1, r

317 nm Rydberg

Δ

Introduce Rydberg interactions: Spin squeezing:

Entangled clock networks:

1Gil et al., PRL (2014), 2Komar et al., Nature Physics (2014)

Thank you for your attention!

My thanks also to the Lukin group, Ye group, Eugene Demler, Maxim Vavilov, Robert Joynt, Amrit Poudel, and Luke Langsjoen.

Johnson noise:Soonwon Choi Robert Devlin

Alex High David Patterson

Arthur Safira Quirin Unterreithmeier

Alexander Zibrov Vladimir Manucharyan

Hongkun Park Mikhail Lukin

Sr-1 optical lattice clockToby Bothwell Sarah Bromley Dhruv Kedar

Colin Kennedy Andrew Koller

Ed Marti Michael Wall Xibo Zhang

Ana Maria Rey Jun Ye

Acknowledgements:

Questions?Optical lattice clocks: Color centers in diamond:

Room for grad and undergrad students! Interested? Please email: kolkowitz@wisc.edu