Nitzan Akerman

Trapped ions group (Roee Ozeri)

Weizmann Institute of Science

Optical atomic clock with trapped ions

QTC Workshop 28/10/2020

Optical Ion Clock

𝑄 =𝜔0

∆𝜔

+

𝜔0: 1010 → 1015 𝐻𝑧

Principle of optical atomic clock :

Counter Oscillator Reference

The quality factor

Optical clock outperform microwave due to the much higher frequency

Height resolution due to gravitational red shift

1 m

10 cm

1 cm

The Ion Clock Setup

Stable laser @ 1560 nm with ~1Hz linewidth

Ion reference

Optical frequency comb (modelock laser)

+

Trapped Ions as Reference

Trap RF

• Are atoms and identical by their nature

• The charge allows trapping to be decouple from

the internal electronic state

• Deep trapping and strong confinement

• Can be well isolated from the environment

Advantages of trapped ions and clock reference

Disadvantages of trapped ions

• Micromotion needs to be controlled

• Trapping many ions is challenging due to the

strong Coulomb repulsion

The Strontium Ion Setup

Lasers breadboard

Compact vacuum system

5 2P1/2

5 2P3/2

5 2S1/2

4 2D3/2

4 2D5/2

422 nm

1092 nm

1033 nm

674 nm

t ≈ 8 ns

t ≈ 0.4 s

The Strontium Ion Setup

Lasers breadboardSr+ energy levels

Comparison to GPS

Optical frequency comb) locked to stable laserGPS receiver

• Comparing the stable laser to GPS clock through the frequency comb

• At short time scale stability is limited by GPS

• At times > 1 hour the cavity (linear) drift become apparent

The Ion Clock Setup

Ion reference

Optical frequency comb) locked to stable laser

+

GPS receiver• Comparing the stable laser to GPS clock through the frequency comb

• At short time scale stability is limited by GPS

• At times > 1 hour the cavity (linear) drift become apparent

• With calibration of the drift using the ion (3 measurements) the Allen div. keeps improving

Clock interrogation schemes

Two ions Rabi spectroscopy (60ms)

Magnetic field gradient(~60 μG)• Cancelling the DC magnetic field with a single

“magnetic Echo” in a Ramsey sequence Two ions Ramsey spectroscopy (100ms)

• 88Sr+ ions have first order sensitivity to magnetic field.

• For single ion solved by averaging opposite Zeeman states

• For many ions homogeneity matters

• There is advantage in coherent averaging

𝛿f

𝑓= 5 × 10−15 ൗ1 𝜏 (estimation for single ion)

Two entangled ions clock

Another solution is using two ions in entangled state:

• The 𝛿B drops out because of the opposite Zeeman states in each part of the superposition

• The signal is acquired twice faster (however also the dephasing)• Required single ion addressing capability

ȁ ൿ𝑆+1/2 ȁ ൿ𝑆−1/2 + 𝑒𝑖 2𝛿𝑙𝑎𝑠𝑒𝑟 𝑡ȁ ൿ𝐷+3/2 ȁ ൿ𝐷−3/2

+

Δ𝜈𝑆1/2,𝐷5/288,86 = 570,264,063.435(5)(8) (stat)(sys) [Hz]

T. Manovitz et al, Phys. Rev. Lett. 123, 203001 (2019).

88Sr+ 86Sr+

ȁ ൿ𝑆+1/2 ȁ ൿ𝑆−1/2 ȁ ۧ0 ↔ ȁ ൿ𝐷+3/2 ȁ ൿ𝑆−1/2 ȁ ۧ1

ൿห𝐷88

ൿห𝑆86

Τ𝜋 2BSB

𝜋RSB

Τ𝜋 2

ൿห0𝜈 ൿห0𝜈

Τ𝜋 2

Initializing Entangling Interrogating Detecting

Two Isotope entangled clock

Time [us]

ȁ ൿ𝑆+1/2 ȁ ൿ𝑆−1/2 + 𝑒𝑖 2𝛿𝑙𝑎𝑠𝑒𝑟 𝑡ȁ ൿ𝐷+3/2 ȁ ൿ𝐷−3/2

Time [us]

ȁ ൿ𝐷+3/2 ȁ ൿ𝑆−1/2 ȁ ۧ1 ↔ ȁ ൿ𝐷+3/2 ȁ ൿ𝑆−1/2 ȁ ۧ0

Parity=P ȁ ۧ𝑆𝑆 ȁ + P ȁ𝐷 ۧ𝐷− P ȁ ۧ𝑆𝐷 − P ȁ ۧ𝐷𝑆

Two Isotope entangled clock

ȁ ൿ𝑆+1/2 ȁ ൿ𝑆+1/2 + 𝑒𝑖 2𝛿𝑙𝑎𝑠𝑒𝑟+2𝛿B 𝑡ȁ ൿ𝐷+3/2 ȁ ൿ𝐷+3/2

ȁ ൿ𝑆+1/2 ȁ ൿ𝑆−1/2 + 𝑒𝑖 2𝛿𝑙𝑎𝑠𝑒𝑟 𝑡ȁ ൿ𝐷+3/2 ȁ ൿ𝐷−3/2

GHZ :

DFS :

• Here the 50Hz feedforward compensation was off in order to emphasize the difference

Roee Ozeri (PI) Tom ManovitzYotam ShapiraMeirav PinkasOr KatzLee Peleg

Weizmann Institute Trapped-ions group

David SchwerdtHaim NakavSapir CohenAbraham Gross Vidyut Kaushal

Michal GoldenshteinBen Yamin