1 of 36

Strontium Molecular Lattice Clock in the THz Frequency Regime

Brandon Iritani

February 3, 2025

1

2025/02/03

OCP-TAP

1

2 of 36

Atomic Clocks – background and Applications

2

2025/02/03

OCP-TAP

2

3 of 36

Atomic clocks

Microwave

Optical

3

2025/02/03

OCP-TAP

3

4 of 36

Atomic Clocks - Progress

Significant progress since invention of optical frequency comb

N. Poli, C. W. Oates, P. Gill and G. M. Tino (2014)

4

2025/02/03

OCP-TAP

4

A frequency comb allows a direct link from radio frequency standards to optical frequencies. Current frequency standards such as atomic clocks operate in the microwave region of the spectrum, and the frequency comb brings the accuracy of such clocks into the optical part of the electromagnetic spectrum. A simple electronic feedback loop can lock the repetition rate to a frequency standard.

There are two distinct applications of this technique. One is the optical clock, where an optical frequency is overlapped with a single tooth of the comb on a photodiode, and a radio frequency is compared to the beat signal, the repetition rate, and the CEO-frequency (carrier–envelope offset). Applications for the frequency-comb technique include optical metrology, frequency-chain generation, optical atomic clocks, high-precision spectroscopy, and more precise GPS technology.

5 of 36

Atomic clock applications

Zheng, X., …S. Kolkowitz. Nature 602, 425–430 (2022).

Bothwell, T., Kennedy, C.J., Aeppli, …J. Ye. Nature 602, 420–424 (2022).

Gravitational Redshift across mm-scale sample

McGrew, W.F., Zhang, X.,… Ludlow, A. Nature 564, 87–90 (2018).

Geodesy below the cm level

Resolve Gravitational Redshift at 1 cm

Dark Matter Constraints

Colin J. Kennedy, … Jun Ye, Phys. Rev. Lett. 125, 201302 (2020)

5

2025/02/03

OCP-TAP

5

TAI

GPS

Fundamental physics

General relativity

Time variation of fundamental constants

Dark matter searches

Geodesy

The Global Positioning System (GPS) operated by the United States Space Force provides very accurate timing and frequency signals. A GPS receiver works by measuring the relative time delay of signals from a minimum of four, but usually more, GPS satellites, each of which has at least two onboard caesium and as many as two rubidium atomic clocks.

Geodesy (/dʒiˈɒdəsi/^[1] jee-OD-ə-see) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity.^[2] The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as planetary geodesy). Geodynamical phenomena, including crustal motion, tides and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and coordinate systems.

6 of 36

Why make a molecular clock?

2025/02/03

OCP-TAP

6

7 of 36

Quantum Chemistry

⁸⁸Sr₂ Molecular Clock – Motivation

THz Frequency Standard

Access long coherence times in molecules

7

2025/02/03

OCP-TAP

7

8 of 36

⁸⁸Sr₂ Molecular Clock – Motivation

Time variation of fundamental constants

Tests of Non-Newtonian gravity or fifth forces at nm-scale distances

T. Zelevinsky, S. Kotochigova, J. Ye, PRL 100, 043201 (2008)

8

2025/02/03

OCP-TAP

8

First I will talk about the motivation for using Sr2.

Theories predict the time variation of the proton to electron mass ratio, mu. The molecular clock, based on a vibrational transition rather than an electronic transition, is sensitive to the proton-to-electron mass ratio. By monitoring the frequencies of transitions in the molecular clock we could constrain the temporal variation of this fundamental constant.

Additionally, we hope to perform tests of non-newtonian gravity or fifth forces at nm-scale distances. These forces are often represented using this Yukawa parametrization, where alpha is the strength of the force relative to gravity and lambda is the length scale at which it acts. Shown on this plot is the length scale lambda on the x axis and strength alpha on the y axis. We hope to set constraints on yukawa forces at 0.1-1 nm length scales.

By monitoring the frequencies of transitions with weak and strong differential sensitivity to the proton-electron mass ratio we could constrain the temporal variation of this fundamental constant.

9 of 36

Experimental Scheme

2025/02/03

OCP-TAP

9

10 of 36

Clock Scheme

32 THz Raman transition spanning ground state potential

K. H. Leung, B. Iritani, E. Tiberi, I. Majewska, M. Borkowski, R. Moszynski, and T. Zelevinsky Phys. Rev. X 13, 011047 (2023)

10

2025/02/03

OCP-TAP

10

11 of 36

Magic Wavelength Lattice

Lattice Wavelength (nm)

Utilize X(0,0) -> 1u(9,1) transition to tune ground state polarizability

11

2025/02/03

OCP-TAP

11

12 of 36

Clock Laser Locking Scheme

12

2025/02/03

OCP-TAP

12

13 of 36

Referencing an atomic clock to absolute frequency (conventional method)

Lab Frequency Synthesizers and Counters

GPS Receiver

Local Time Base (Rb Clock)

13

2025/02/03

OCP-TAP

13

14 of 36

Referencing Molecular Clock to absolute frequency

14

2025/02/03

OCP-TAP

14

15 of 36

Referencing Molecular Clock to absolute frequency - Solution

GPS signal from NIST atomic clock
Local time base – Free-running Rb clock
Compare pps signals between GPS receiver and free-running Rb Clock
Correct differences in post-processing

15

2025/02/03

OCP-TAP

15

FIG. 5. (a) Absolute frequency of the clock transition mea-�sured over 10 trials (filled black circles) with all known fre-�quency offsets corrected, including that of the local timebase�(see main text for details). Blue error bars are 1σ statistical�uncertainties, dominated by the determination of the comb�repetition rate rather than the stability of the scanned molec-�ular clock lines. Red error bars are 1σ systematic uncertain-�ties due to the molecular clock only (see Table I). Black error�bars are 1σ total uncertainties, where the uncertainties of�the local timebase calibrations are added in quadrature with�the statistical and molecular clock systematic uncertainties.�The black horizontal line shows the weighted average, and the�shaded grey area shows the associated ±1σ standard error of�the mean (χ2�red = 0.57). (b) Histogram of all clock frequency�measurements in the 10 trials, relative to the weighted average�of fclock. The solid red line is a Gaussian fit to the histogram.

16 of 36

Referencing Molecular Clock to absolute frequency

16

2025/02/03

OCP-TAP

16

17 of 36

Improved timing precision

In the future, different local time base such as cesium clock/hydrogen maser

Rb Clock

2 x 10^-11

Cs clock

5 x 10^-13

Hydrogen maser

6 x 10^-14

Carrier phase work

Tracking exact phase of GPS signal, including fractional wavelength (down to 2 mm accuracy)

Two-way time transfer

17

2025/02/03

OCP-TAP

17

18 of 36

Recent Clock Evaluation

2025/02/03

OCP-TAP

18

19 of 36

Systematic Evaluation

Absolute Frequency = 31 825 183 207 592.8(5.1) Hz (1.6 x 10^-13)

Total Systematic Uncertainty = 4.6 x 10^-14

K. H. Leung, B. Iritani, E. Tiberi, I. Majewska, M. Borkowski, R. Moszynski, and T. Zelevinsky Phys. Rev. X 13, 011047 (2023)

19

2025/02/03

OCP-TAP

19

20 of 36

Lattice Stark Shift - Hyperpolarizability

K. H. Leung, B. Iritani, E. Tiberi, I. Majewska, M. Borkowski, R. Moszynski, and T. Zelevinsky Phys. Rev. X 13, 011047 (2023)

Lattice Detuning (MHz)

*

*R. C. Brown, N. B. Phillips, … A. D. Ludlow, Phys. Rev. Lett. 119, 253001 (2017)

Lattice Stark Shift (Polarizability) = 100.1(3.4)*10^-14

Lattice Stark Shift (Hyperpolarizability) = -50.8(1.9)*10^-14

20

2025/02/03

OCP-TAP

20

While evaluating this we observed hyperpolarizability, which is this quadratic dependence of the lightshift on trap depth. In order to characterize the lattice light shifts, we fit the clock shifts with this equation, where alpha is the linear polarizability and beta is the quadratic hyperpolarizability.

Plotted here is the lightshift vs. trap depth at many frequencies, as well as the linear polarizability coefficient of the light shift vs. lattice frequency. We tune alpha and beta so that the curve is flattest at operational trap depth, which was around 500 recoil energies, and we are insensitive to lattice power fluctuations. This is our operational magic wavelength.

The hyperpolarizability could be due to some kind of two-photon process.

Crucially, the polynomial form of Eq. (5.38) hinges on a linear scaling of the sample temperature with 𝑈0, which we verify to hold true for our molecules using Raman carrier thermometry [Fig. 5.15].

21 of 36

BBR Shift Systematic

BBR shift uncertainty will limit at 10^-15-10^-16 level (after Stark shifts)

K. H. Leung, B. Iritani, E. Tiberi, I. Majewska, M. Borkowski, R. Moszynski, and T. Zelevinsky Phys. Rev. X 13, 011047 (2023)

21

2025/02/03

OCP-TAP

21

22 of 36

Measure polarizability at 1.95 μm using stark shift spectroscopy

B. Iritani, E. Tiberi, W. Skomorowski, R. Moszynski, M. Borkowski, and T. Zelevinsky, Phys. Rev. Lett. 131, 263201 (2023)

BBR Shift Systematic

Differential Polarizability (a.u.)

V

In good agreement with ab initio theory

22

2025/02/03

OCP-TAP

22

23 of 36

BBR Shift Systematic

Measure polarizability at 1.95 μm using stark shift spectroscopy
In good agreement with ab initio theory

Ab initio calculation of polarizability at a range of wavelengths from DC to 1.25 μm

Differential Polarizability (a.u.)

V

B. Iritani, E. Tiberi, W. Skomorowski, R. Moszynski, M. Borkowski, and T. Zelevinsky, Phys. Rev. Lett. 131, 263201 (2023)

23

2025/02/03

OCP-TAP

23

24 of 36

BBR Determination

B. Iritani, E. Tiberi, W. Skomorowski, R. Moszynski, M. Borkowski, and T. Zelevinsky, Phys. Rev. Lett. 131, 263201 (2023)

Characterize BBR to <5*10^-16

24

2025/02/03

OCP-TAP

24

25 of 36

Q factor limit - lifetime of clock states

Current Limitation - Coherence Time

Off-resonant Lattice Scattering

Kondov, S.S., Lee, CH., Leung, K.H. et al. Nat. Phys. 15, 1118–1122 (2019)

Lattice Wavelength (nm)

25

2025/02/03

OCP-TAP

25

26 of 36

Q factor limit - lifetime of clock states

K H Leung et al 2021 New J. Phys. 23 115002

2-body collisional loss

1-body scattering loss

Limitation - Collisional Loss

Current Limitation - Coherence Time

Off-resonant Lattice Scattering

Kondov, S.S., Lee, CH., Leung, K.H. et al. Nat. Phys. 15, 1118–1122 (2019)

26

2025/02/03

OCP-TAP

26

27 of 36

Future Work: Constraining New Mass-dependent Fifth forces with Isotope Shifts

2025/02/03

OCP-TAP

27

28 of 36

28

Isotope shifts as test of fundamental interactions

Ab initio quantum chemistry - <10^-13 too challenging for heavy molecule
Remove Born Oppenheimer terms via isotope shifts - only ~10^-6 needed for mass-dependent terms

Isotope shift = “Mass shift” + “Field shift”
With enough isotopes, can remove “Field shift”
Any non-linearities in King plot result from unknown atomic/nuclear physics or new electron-neutron interactions

J. J. Lutz and J. M. Hutson, JMS 330, 43 (2016), I. Counts et al., PRL 125, 123002 (2020)

88

86

84

2025/02/03

OCP-TAP

28

29 of 36

Projected Constraints

Assuming:

~5 Hz resolution in experiment
Theory matches experiment to ~1 Hz

Yukawa Potential

We project improved constraints for ranges less than 1.3 nm.

29

2025/02/03

OCP-TAP

29

30 of 36

Second Generation Molecular Lattice Clock

2025/02/03

OCP-TAP

30

31 of 36

Difficulty - Relative Abundance

⁸⁸Sr

82.6% abundance
Molecules produced and v = 0 -> 62 transition measured

⁸⁶Sr

9.86% abundance
Photoassociative spectroscopy, least bound state measured¹

⁸⁴Sr

0.56% abundance
Molecules produced via STIRAP, weakly bound binding energies measured²

¹J. A. Aman, J. C. Hill, R. Ding, Kaden R. A. Hazzard, T. C. Killian, and W. Y. Kon, Phys. Rev. A 98, 053441 (2018)

²Simon Stellmer, Benjamin Pasquiou, Rudolf Grimm, and Florian Schreck, Phys. Rev. Lett. 109, 115302 (2012)

31

2025/02/03

OCP-TAP

31

32 of 36

Second generation setup

AOSense Sr source

Recessed MOT coil viewports

Gate valve for future extension

ZnSe viewports coated for 10 μm for precise BBR determination

Vertical lattice

32

2025/02/03

OCP-TAP

32

33 of 36

Vertical build-up lattice cavity

Recessed viewport for high NA imaging

g

K. Kim, A. Aeppli, T. Bothwell and J. Ye Phys. Rev. Lett. 130, 113203 (2023)

Longer coherence times:

Lower lattice intensity – less scattering
Larger lattice waist – less density and collisional loss

33

2025/02/03

OCP-TAP

33

34 of 36

34

Interleaved measurement in Gen I experiment

⁸⁸Sr MOT

⁸⁶Sr MOT

34

2025/02/03

OCP-TAP

34

35 of 36

Outlook

measured a V = 62 -> 0 transition to 10^-14 in ⁸⁸Sr
Constrained BBR uncertainty to 10^-16
Plan to measure an isotope shift between ⁸⁸Sr₂-⁸⁶Sr₂ in order to constrain mass-dependent Yukawa forces at the nm scale
Second-Generation Apparatus:

Improved atomic flux
In-vacuum buildup cavity

Direct frequency standard with mixed isotopologues?

35

2025/02/03

OCP-TAP

35

36 of 36

36

Theory Collaborators: Robert Moszynski, Wojciech Skomorowski, and Iwona Majewska

Debayan

Mitra

Wenwei

Xu

Jingjing

Huang

36

2025/02/03

OCP-TAP

36