An Atomic-Array Optical Clock with Single-Atom Readout

Ivaylo S. Madjarov,

Alexandre Cooper,

Adam L. Shaw ,

Jacob P. Covey,

Vladimir Schkolnik ,

Tai Hyun Yoon ,

†

Jason R. Williams ,

and Manuel Endres

Division of Physics, Mathematics and Astronomy, California Institute of Technology,

Pasadena, CA 91125, USA

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

(Received 4 September 2019; revised manuscript received 23 October 2019; published 11 December 2019)

Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an

ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system

based on an array of individually trapped neutral atoms with single-atom readout, merging many of the

benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum

simulation and computing with neutral atoms. We evaluate single-site-resolved frequency shifts and short-

term stability via self-comparison. Atom-by-atom feedback control enables direct experimental estimation

of laser noise contributions. Results agree well with an

ab initio

Monte Carlo simulation that incorporates

finite temperature, projective readout, laser noise, and feedback dynamics. Our approach, based on a

tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively

simple experimental setup suited for transportable operation. These results establish the foundations for a

third optical clock platform and provide a novel starting point for entanglement-enhanced metrology,

quantum clock networks, and applications in quantum computing and communication with individual

neutral atoms that require optical-clock-state control.

DOI:

10.1103/PhysRevX.9.041052

Subject Areas: Atomic and Molecular Physics, Optics,

Quantum Physics

I. INTRODUCTION

Optical clocks

—

based on interrogation of ultranarrow

optical transitions in ions or neutral atoms

—

have surpassed

traditional microwave clocks in both relative frequency

stability and accuracy

–

. They enable new experiments

for geodesy

[2,5]

, fundamental physics

[6,7]

, and quantum

many-body physics

[8]

, in addition to a prospective

redefinition of the SI second

[9]

. In parallel, single-atom

detection and control techniques have propelled quantum

simulation and computing applications based on trapped

atomic arrays; in particular, ion traps

[10]

, optical lattices

[11]

, and optical tweezers

[12,13]

. Integrating such tech-

niques into an optical clock would provide atom-by-atom

error evaluation, feedback, and thermometry

[14]

; facilitate

quantum metrology applications, such as quantum-

enhanced clocks

[15

–

18]

and clock networks

[19]

; and

enable novel quantum computation, simulation, and com-

munication architectures that require optical-clock-state

control combined with single-atom trapping

[20

–

22]

As for current optical clock platforms, ion clocks already

incorporate single-particle detection and control

[23]

,but

they typically operate with only a single ion. Research

towards multi-ion clocks is ongoing

[24]

. Conversely,

optical lattice clocks (OLCs)

[1,2,4]

interrogate thousands

of atoms to improve short-term stability, but single-atom

detection and control remains an outstanding challenge.

An ideal clock system, in this context, would thus merge

the benefits of ion and lattice clocks, namely, a large array

of isolated atoms that can be read out and controlled

individually.

Here, we present a prototype of a new optical clock

platform based on an atomic array, which naturally incor-

porates single-atom readout of currently about 40 individu-

ally trapped neutral atoms. Specifically, we use a magic-

wavelength 81-site tweezer array stochastically filled with

single strontium-88 (

Sr) atoms

[25]

. Employing a repetitive

imaging scheme

[25]

, we stabilize a local oscillator to the

optical clock transition

[26,27]

with a low dead time of

approximately 100 ms between clock interrogation blocks.

We utilize single-site and single-atom resolution to

evaluate the in-loop performance of our clock system in

terms of stability, local frequency shifts, selected systematic

mendres@caltech.edu

†

Present address: Department of Physics, Korea University,

Seoul 02841, Republic of Korea.

Published by the American Physical Society under the terms of

the

Creative Commons Attribution 4.0 International

license.

Further distribution of this work must maintain attribution to

the author(s) and the published article

’

s title, journal citation,

and DOI.

PHYSICAL REVIEW X

041052 (2019)

Featured in Physics

2160-3308

9(4)

041052(14)

041052-1

Published by the American Physical Society

effects, and statistical properties. To this end, we define an

error signal for single tweezers, which we use to measure

site-resolved frequency shifts at otherwise fixed parame-

ters. We also evaluate statistical properties of the in-loop

error signal, specifically, the dependence of its variance on

atom number and correlations between even and odd sites.

We further implement a standard interleaved self-

comparison technique

[28,29]

to evaluate systematic

frequency shifts with changing external parameters

—

specifically, trap depth and wavelength

—

and find an

operational magic condition

[30

–

32]

where the dependence

on trap depth is minimized. We also demonstrate a proof of

principle for extending such self-comparison techniques to

evaluate single-site-resolved systematic frequency shifts as

a function of a changing external parameter.

Using self-comparison, we evaluate the fractional short-

term instability of our clock system to be

−

ffiffiffi

To compare our experimental results with theory predic-

tions, we develop an

ab initio

Monte Carlo (MC) clock

simulation

[33]

(Appendix

), which directly incorporates

laser noise, projective readout, finite temperature, and

feedback dynamics, resulting in higher predictive power

compared to traditionally used analytical methods

[1]

.Our

experimental data agree quantitatively with this simulation,

indicating that noise processes are well captured and

understood at the level of stability we achieve here.

Based on the MC model, we predict a fractional instability

–

−

ffiffiffi

for single-clock operation, which

would have shorter dead time than that in self-comparison.

We further demonstrate a direct evaluation of the

ffiffiffiffiffiffiffi

dependence of clock stability with atom number

,ontop

of a laser-noise-dominated background, through an atom-by-

atom system-size-selection technique. This measurement

and the MC model strongly indicate that the instability is

limited by the frequency noise of our local oscillator. We

note that the measured instability is comparable to OLCs

using similar transportable laser systems

[34]

We note the very recent, complementary results of

Ref.

[35]

that show seconds-long coherence in a tweezer

array filled with approximately 5

Sr atoms using an

ultralow-noise laser without feedback operation. In this and

our system, a recently developed repetitive interrogation

protocol

[25]

, similar to that used in ion clocks, provides a

short dead time of approximately 100 ms between inter-

rogation blocks, generally suppressing the impact of laser

noise on stability stemming from the Dick effect

[36]

Utilizing seconds-scale interrogation with such low dead

times, combined with the feedback operation and realistic

upgrade to the system size demonstrated here, promises a

clock stability that could reach that of state-of-the-art OLCs

[2,4,37,38]

in the near-term future, as further discussed

in Sec.

Concerning systematic effects, the demonstrated atomic

array clock has intrinsically suppressed interaction and

hopping shifts: First, single-atom trapping in tweezers

provides immunity to on-site collisions present in one-

dimensional OLCs

[39]

. While three-dimensional OLCs

[37]

also suppress on-site collisions, our approach retains a

short dead time as no evaporative cooling is needed.

Furthermore, the adjustable and significantly larger inter-

atomic spacing strongly reduces dipolar interactions

[40]

and hopping effects

[41]

. We experimentally study effects

from tweezer trapping in Sec.

and develop a corre-

sponding theoretical model in Appendix

, but we leave a

full study of other systematics, not specific to our platform,

and a statement of accuracy to future work. In this context,

we note that our tweezer system is well suited for future

investigations of blackbody radiation shifts via the use of

local thermometry with Rydberg states

[14]

The results presented here and in Ref.

[35]

provide the

foundation for establishing a third optical clock platform

promising competitive stability, accuracy, and robustness,

while incorporating single-atom detection and control

techniques in a natural fashion. We expect this to be a

crucial development for applications requiring advanced

control and readout techniques in many-atom quantum

systems, as discussed in more detail in Sec.

II. FUNCTIONAL PRINCIPLE

The basic functional principle is as follows. We gen-

erate a tweezer array with linear polarization and

site-to-site spacing in an ultrahigh-vacuum glass cell using

an AOD and a high-resolution imaging system [Fig.

1(a)

]

[25]

. The tweezer-array wavelength is tuned to a magic

trapping configuration close to 813.4 nm, as described

below. We load the array from a cold atomic cloud and

subsequently induce light-assisted collisions to eliminate

higher trap occupancies

[25,42]

. As a result, approxi-

mately 40 of the tweezers are stochastically filled with a

single atom. We use a recently demonstrated narrow-line

Sisyphus cooling scheme

[25]

to cool the atoms to an

average transverse motional occupation number of

≈

, measured with clock sideband spectroscopy

(Appendix

). The atoms are then interrogated twice

on the clock transition, once below (

) and once above (

)

resonance, to obtain an error signal quantifying the

frequency offset from the resonance center [Figs.

1(b)

and

1(c)

]. We use this error signal to feedback to a

frequency shifter in order to stabilize the frequency of the

interrogation laser

—

acting as a local oscillator

—

to the

atomic clock transition. Since our imaging scheme has a

survival fraction of greater than 0.998

[25]

, we perform

multiple feedback cycles before reloading the array, each

composed of a series of cooling, interrogation, and readout

blocks [Fig.

1(d)

For state-resolved readout with single-shot, single-atom

resolution, we use a detection scheme composed of two

high-resolution images for each of the

and

inter-

rogation blocks [Fig.

1(e)

]

[25]

. A first image determines

if a tweezer is occupied, followed by clock interrogation.

IVAYLO S. MADJAROV

et al.

PHYS. REV. X

041052 (2019)

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