Page 1

Improving the stability and accuracy of the Yb

optical lattice clock

Y. Y. Jiang1,2, A. D. Ludlow1, N. D. Lemke1, J. A. Sherman1,

J. von Stecher3, R. W. Fox1, L. S. Ma2, A. M. Rey3, C. W. Oates1

1NIST, 325 Broadway, Boulder, CO 80305, USA

2East China Normal University, 3663 North Zhongshan Road, Shanghai, 200062, China

3JILA, NIST and University of Colorado, Boulder, CO 80309, USA

Email: ludlow@boulder.nist.gov

Abstract—We report results for improving the stability and

uncertainty of the NIST

provements derive from a significant reduction of the optical Dick

effect, while the uncertainty improvements focus on improved

understanding and constraint of the cold collision shift.

171Yb lattice clock. The stability im-

I. INTRODUCTION

Optical lattice clocks have potential for achieving time and

frequency measurement at unprecedented levels of accuracy

and stability. However, to date these young systems are far

from reaching this potential. Here, we describe efforts to mit-

igate effects which, left unresolved, pose significant obstacles

to achieving these levels of performance. To improve the clock

stability, we reduce the optical Dick effect. To improve the

eventual accuracy of this system, we probe cold collisions

between the lattice-confined atoms.

II. REDUCING THE OPTICAL DICK EFFECT

The fundamental limit to the instability of an atomic fre-

quency standard is given by the quantum projection noise

(QPN). For an optical atomic clock that probes a large

ensemble of quantum absorbers, the QPN limit can be quite

low. For example, for a Yb or Sr lattice clock with 105atoms, a

1 Hz transition linewidth, and a cycle time of Tc= 1 second,

the QPN instability limit is below 10−17at 1 s. However,

while such clocks have resolved optical transition linewidths

approaching 1 Hz, the instability of these systems is much

higher than indicated above. Instead, the fractional frequency

instability is such that it would require significantly more than

104seconds to reach the 10−17level. This is because these

systems are usually limited by the Dick effect [1], i.e. as

the atoms are periodically interrogated by the local oscillator

(LO) with a period of Tcand for a probe duration of Tp, the

frequency noise of the LO is downsampled onto the transition

spectrum and contaminates the clock stability. In this way, the

frequency noise, the probe time Tp, and the cycle time Tcall

influence the magnitude and downconverted Fourier frequency

of the aliased noise and thus the stability degradation. The

previous operating conditions for our Yb lattice clock were

Tp= 0.08 s and Tc> 0.5 s. With a frequency noise of 0.5

Hz/√Hz at a Fourier frequency of 1 Hz, this led to a Dick-

limited instability of 1-2 × 10−15at 1 s.

In order to reduce this limitation, several improvements

could be made: reducing the LO frequency noise that is

aliased, achieving a higher duty cycle with longer probe times

or reduced dead time [2], or choosing a form of spectroscopy

which is less sensitive to the aliasing process (e.g. short-

pulse Ramsey spectroscopy). All of these are useful from a

practical perspective. However, by improving the LO laser

coherence and stability, we can achieve both reduction of

the LO frequency noise and longer probe times. In order

to improve the LO stability, the level of Brownian thermal

noise in the optical cavities used for laser stabilization must

be reduced. When stabilizing a laser to an optical cavity, the

thermal-noise limited laser instability dominated by the cavity

mirrors [3] is given by:

?

π3/2

Ew0L2

σtherm=

ln24kbT1 − σ2

?

φsub+ φcoat

2

√π

1 − 2σ

1 − σ

d

w0

?

(1)

Here, σ, E and φsubare Poisson’s ratio, Young’s modulus and

the mechanical loss for the mirror substrate, and φcoat and

d denote the mechanical loss and thickness of the thin-film

reflective coating. w0is the laser beam size on the mirror, T

is the mirror temperature (K), kBis Boltzmann’s constant and

L is the cavity length. In order to improve laser stabilization

by reducing the thermal noise, we designed a cavity with

length L = 29 cm, fused silica substrates with low mechanical

loss (φsub ≈ 10−6) and a somewhat large beam size using

mirrors with a somewhat longer radius of curvature (R = 1

m). For these parameters, the thermal-noise-limited fractional

frequency instability is 1.4 × 10−16.

To reduce acceleration-induced cavity length changes, the

optical cavity sits horizontally on four symmetrically placed

Viton hemispheres [4], [5]. The precise support position is

optimized to reduce the vertical acceleration sensitivity. Figure

1 shows the vertical acceleration sensitivity as a function

of support position, indicating both finite-element simulation

results as well as experimentally measured sensitivities. Simu-

lation results are also shown for cavity acceleration sensitivity

offset from the cavity optical axis. The measured sensitivity

reaches as low as 7 kHz/(ms−2) at the laser wavelength of

578 nm. The experimental measurement also includes weak,

incidental acceleration in the horizontal dimensions. During

U.S. Government work not protected by U.S. copyright2

Page 2

40 40

50

z/ms

n sensitivity (kH

vertical vibratio

-2)

20 20

30

0

10

2040 60 80

Support position d (mm)

10

z/√Hz)

uency noise (Hz

laser freq

0 10.1

1

0.1110

0.01

F Fourier frequency (Hz)if (H )

Fig. 1. top: Vertical acceleration sensitivity of the optical cavity. Experimental

measurement (blue diamonds), simulation results (red triangles), simulation

results for 250 µm removed from the cavity optical axis (black squares). The

support position, d, is measured from where the cavity taper begins. bottom:

Measured frequency noise spectrum for the laser locked to the fully-isolated

cavity. The solid red line gives the theoretical prediction of the Brownian

thermal noise.

normal operation, the reference cavities sat on vibration iso-

lators.

While the use of fused silica mirrors helps reduce Brownian

thermal-mechanical noise, it makes the cavity more susceptible

to thermal expansion. However, a balance between the thermal

expansion of the cavity components can be achieved, and we

have been able to demonstrate operation of these cavities at

the zero crossing of the coefficient of thermal expansion. This

is done at a temperature conveniently just above ambient [6].

By comparing two independent cavity systems, we mea-

sured the frequency noise spectrum of the cavity-stabilized

laser as shown in Figure 1. The red line is the thermal

noise limit for each reference cavity. Up to several Hz, the

laser frequency noise is close to the thermal noise limit.

This low level of frequency noise in turn reduces the aliased

noise contributing to the Dick effect. Furthermore, the reduced

frequency noise spectrum yields laser coherence times which

allow us to extend our clock probe time up to 1 second. For

a more conservative operating condition of Tp = 0.3 s, the

Dick instability is at 1.5 × 10−16/√τ, for measurement time

τ. This constitutes an order of magnitude improvement over

our previous Dick limit, and enables a significant improvement

of the clock stability. By using the narrow atomic transition

as a frequency discriminator, we have made measurements

consistent with a clock instability at the 5 × 10−16/√τ

fractional frequency level [6].

100100

mHz)

ency instability (m

frequ

10

10 100 1000

1

averaging time (s)

Fig. 2.

when the shift is cancelled to zero (see text).

Frequency instability from measurement of the cold collision shift,

III. COLD COLLISION SHIFT

While the presence of many atoms in the optical lattice is

desirable for low clock instability due to quantum projection

noise, another consequence of large atom number is high

number density which can lead to significant interactions

between the atoms. These interactions can shift the clock

transition frequency and in so doing can potentially compro-

mise the absolute uncertainty of the optical standard. Non-zero

interactions in a171Yb optical lattice clock were first observed

using one-pulse Rabi spectroscopy [7]. More recently, we have

studied the resulting cold collision shift of the clock transition

using two-pulse Ramsey spectroscopy, for atoms confined both

in a one- and two-dimensional optical lattice. The choice

of Ramsey spectroscopy was driven by simplification: the

interactions yielding the collision shift occur primarily dur-

ing the Ramsey dark time, when the atomic population is

not simultaneously being driven by the probing laser field.

By studying the collision shift as a function of excitation

fraction, sample inhomogeneity, and Ramsey dark time, we

have determined that the collisions responsible for the shift

are dominated by p-wave interactions between a ground and

excited state atom pair [8].

We have been able to identify regimes where the cold colli-

sion shift can be canceled, which is metrologically interesting

for clock operation. One such case is given by controlling the

excitation fraction just above 50%, where the shift on each

clock state is the same. By operating at these conditions, the

collision shift was measured to be consistent with zero at or

below the 10−17fractional frequency level. Figure 2 highlights

such a measurement, showing the frequency instability of the

measured collision shift. This data is taken by stabilizing the

probe laser to interleaved samples of high and low atomic

density, and measuring the frequency shift between the two

cases. Due to the clock stability improvements described in

section II, we are able to measure the shift at the 10−17level

with only several thousand seconds of measurement time. This

measurement emphasizes the potential of the Yb lattice clock

for very high measurement stability, as well as high accuracy

through control of the cold collision shift.

3

Page 3

ACKNOWLEDGMENT

The authors would like to thank T. Fortier, M. Kirchner, S.

Diddams, and D. Hume.

REFERENCES

[1] G. J. Dick, “Local oscillator induced instabilities in trapped ion frequency

standards,” Proc. Precise Time and Time Interval Meeting, p. 133–147,

1987.

[2] P. G. Westergaard, J. Lodewyck, and P. Lemonde, “Minimizing the Dick

effect in an optical lattice clock,” IEEE Trans. Ultra. Ferro. Freq. Cont.

57 623628, 2010.

[3] K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the

frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93

250602, 2004.

[4] J. Millo et al., “Ultrastable lasers based on vibration insensitive cavities,”

Phys. Rev. A 79 053829, 2009.

[5] S. A. Webster, M. Oxborrow, and P. Gill, “Vibration insensitive optical

cavity,” Phys. Rev. A 75 011801, 2007.

[6] Y. Y. Jiang et al., “Making optical clocks more stable with 10−16-level

laser stabilization,” Nature Photon. 5 158-161, 2011.

[7] N. D. Lemke et al., “Spin-1/2 optical lattice clock,” Phys. Rev. Lett. 103

063001, 2009.

[8] N. D. Lemke et al., “p-Wave cold collisions in a Yb lattice clock,”

arXiv:1105.2014, 2011.

4