固体フェムト秒光周波数コムの「再」開発と展開

東京大学大学院工学系研究科附属光量子科学研究センター 准教授
東京大学卓越研究員

吉岡 孝高
2017/11/17 第7回 可視赤外線観測装置技術ワークショップ 2017 @京都大学

超精密な周波数基準としてのレーザー光
クォーツ時計国際標準(1967-)

未来の標準(20XX-)

水晶振動子

マイクロ波発振器制御されたレーザー

Gunn

発振器

LETTERS
https://commons.wikimedia.org/wiki/File:InsideQuartzCrystal.jpg

周波数例

An optical lattice clock
http://www.miwavetechnoventures.com

http://micro.apitech.com 1
Masao Takamoto , Feng-Lei Hong3, Ryoichi Higashi1 & Hidetoshi Katori1,2

215 Hz = 32,768 Hz

9,192,631,770 Hz(例) 429,228,004,229,873 Hz

1秒の1/10,000

1秒の1/1,000,000,000

1秒の1/10,000,000,000,000

1秒の
刻み

誤差補正の
参照先

DRO

Vol 435|19 May 2005|doi:10.1038/nature03541

時報

The precision measurement of time and frequency is a prerequisite not only for fundamental science but also for technologies that
support broadband communication networks and navigation with
global positioning systems (GPS). The SI second is currently
realized by the microwave transition of Cs atoms with a fractional
uncertainty of 10215 (ref. 1). Thanks to the optical frequency comb
technique2,3, which established a coherent link between opticaland radio frequencies, optical clocks4 have attracted increasing
interest as regards future atomic clocks with superior precision.
To date, single trapped ions4–6 and ultracold neutral atoms in free
fall7,8 have shown record high performance that is approachingthat of the best Cs fountain clocks1. Here we report a different
approach, in which atoms trapped in an optical lattice serve as
quantum references. The ‘optical lattice clock’9,10 demonstrates alinewidth one order of magnitude narrower than that observed forneutral-atom optical clocks7,8,11, and its stability is better than thatof single-ion clocks4,5. The transition frequency for the Sr latticeclock is 429,228,004,229,952(15) Hz, as determined by an opticalfrequency comb referenced to the SI second.
atomicDownloaded from http://rsta.royalsocietypublishing.org/Accurate
on January
21,clocks
2017rely on the observation of a narrow atomic
resonance Dn at a transition frequency n 0 that is insensitive toexternal perturbations to the highest possible degree. An indicatorof clock performance is the fractional instability,
Ultracold atoms and time standards
4083 which is minimized
by repeatedly measuring the high-Q (Q ¼ n 0/Dn) transition. The
fractional instability is given by the Allan deviation12
pﬃﬃﬃﬃﬃﬃ(c)(a)ð1Þ
jy ðtÞ < Dn=ðn0 NtÞ

where N is the total number of oscillators (atoms or ions) measured
in unit time and t is the total measurement time. To improve thestability of the current Cs clock, the formula suggests the use of atransition with a higher frequency n 0 (that is, use of higher frequency
than that of microwaves), and this has led to active research towards
optical clocks4–8,11. The use of well-designed atom traps may further
increase the stability, since the extended coherent interaction time Dt
reduces the Fourier limit linewidth as Dn < 1/Dt, thus allowing a
2 microwave
2 higher effective
Q-factor.
(b)n = − d/2
A single
oscillator absorber held in a space smaller than the
1 quantum
1transition wavelength13 (that is, in the Lamb-Dicke regime) would
offer the ultimate system for ultra-precise spectroscopy, as such a trap
significantly decreases both atomic interactions and the Doppler
Vshifts that critically affect clock accuracy7,8. This system is actuallyembodied by an ion in a Paul trap, where the ion is trapped at the zerostate
n = + d/2
of a quadrupoleelectric field and is not perturbed by the trappingstate
selectionand this has provided the finest optical spectrum yetfield14, detectionVobtained4. However, strong Coulomb interactions between ionsprevent the use of more than a single ion in a trap, which severely
Figure 2. Fountain clocks. (a) Caesium atoms loaded from limits
a backgroundvapourarefirst cooled
clock stability
becauseof smallN in equation (1).
using six counter-propagating laser beams. (b) The cooledIn atoms
are neutral
launched
byweaker interactions7,8,11
this regard,
atomsupwards
with much
areAftersuitableterms ofa increasing
number of particles, anddetuning the frequency of the two vertical cooling beams. (c)theinlaunch,single spinthestate
thelaserstability.
A spatial
interference(|1⟩) is selected using a combination of optical pumping andtherefore
resonant
light.
The atoms
then pattern of lasers can
produce periodic trapping potentials for ultracold neutral atoms,
traverse a microwave cavity. The effect of the microwave field
is to put the atoms into a coherent
called an optical lattice15, as illustrated in Fig. 1a. This lattice potential

セシウム原子の超微細分裂
Phil. Trans. R. Soc. A
369, 4078 (2011).

物理実験で汎用測定の良質な発振器のメリット

様々な物理量の精密測定
相対性理論

can confine atoms in a submicrometre region, and its periodicity
allows the production of billions of micro-traps in a volume of
1 mm3. These features are indeed attractive for fine spectroscopy withenhanced stability.
In general, such a lattice-trapping field significantly modifies theinternal states of atoms by so-called light shifts, and so the system was
not seriously considered for atomic clocks until the demonstration of
the light shift cancellation technique16,17. The transition frequency n

原子の良質な
電子遷移
Nature 435, 321 (2005).
Figure 1 | Optical lattice clock. a, The spatial interference pattern of lasers
creates a lattice potential that confines atoms in a region much smaller thanthe optical wavelength, l L. b, Energy levels for Sr. The 1S0 and 3P0 states arecoupled to the upper respective spin states by an off-resonant laser toproduce an optical lattice with equal energy" shifts in "the clock transition at
l 0 ¼ 698 nm. Atoms are excited on the "1 S0 i^jni ! "3 P0 i^jni electronic–
vibrational transitions, where n denotes the vibrational states of atoms in thelattice potential. The clock transition is then monitored on the 1S0 2 1P1
cyclic transition with nearly unit quantum efficiency.

物理「定数」の恒常性？？？理論

superposition of state |1⟩ and state |2⟩. On the return trip, the atoms again traverse the cavity.
1
2
3
Engineering
Research transferred
Institute, The Universityof Tokyo
If the microwave frequency is on resonance, then the numberof atoms
to state|2⟩and PRESTO, Japan Science and Technology Agency, Bunkyo-ku, Tokyo 113-8656, Japan. National Metrology Instituteof Japan/National Institute of Advanced Industrial Science and Technology (NMIJ/AIST), Tsukuba, Ibaraki 305-8563, Japan.
is maximized. The number of atoms in state |2⟩ is detected using resonant laser light. (Online
version in colour.)321© 2005 Nature Publishing Group1caesium fountain clock, which realized the Zacharias proposal, was built in Parisby Clairon et al. [22]. Today, fountain clocks using optical molasses to first cool

周波数の測定精度の劇的な向上
Optical clock uncertainty through the years1.E)09!

From Chris Oates, NIST

IR
Optical!!

Frac2onal!Frequency!Uncertainty!

1.E)10!
1.E)11!

光周波数コムの登場

1.E)12!
1.E)13!
1.E)14!
1.E)15!

光の時計

state-of-the-art Cs microwave

4~10 x 1014 Hz

高周波の時計1.E)16!

(現在の秒の定義)

1.E)17!

9.2 x 109 Hz

1.E)18!
1970!

1975!

1980!

1985!

1990!

1995!

2000!

2005!

2010!

2015!

Year!

例：光格子時計

光周波数コムによって光の周波数を測れるようになった
セシウム原子時計が50年間の積算で積み上げてきた「秒」の正確さを
光領域の計測がここ数年で乗り越えてしまった。
光時計が「秒」の二次表現に採択された理由

レーザー共振器の共振周波数
p

!

p

!

w0
2x
2y
Hl
Hm
w(z)
w(z)
w(z)
 2
✓ 2
◆
2
2
x +y
x +y
⇥ exp
+
ik
+z
w2 (z)2R(z)Elm (r) = E0

z=z1

z=z2

⌘(z) = tan

1i(l + m + 1)⌘(z)✓z⇡w02 n

◆

= tan

✓

z
z0

◆

等位相面に一致する曲率半径のミラーを配置すると、その横モードのビームに対して共振器となる。
光が共振器を１周したとき、電場の位相が完全に一致すると共振する。
1周の光学長=波長の整数倍

これは半周で位相がπの整数倍だけ、ずれることと等価。

✓◆

z✓ (z) = kz (l + m + 1) tan✓l,m (z2 ) ✓l,m (z1 ) = N ⇡
✓ l,m
◆
z0
z
z
2
1
(L = z2
kN L (l + m + 1) tan 1
tan 1
= N⇡
z0
z0
c
fN +1 fN =N依存性(l, m固定)
2n(f )L✓◆1

l,m依存性(N固定)

1

c
1 z2
f=
(l, m) tan
2⇡nL
z0

tan

z1 )

1 z1

z0

共振周波数は離散的で、間隔は光が共振器を一周する時間で決まる。
しかし共振器内の分散(レーザー媒質やミラーのコーティング)を忘れてはならない。

マルチモード発振(cw発振)
発振モード
G
ロス

(飽和)
ゲイン

共振器モード !N = N•••

wq-2 wq-1 wq wq+1 wq+2 wq+3

⇡c
n(!)L

L

R1

•
•

R2

レーザー発振しているとき、ゲインとロスは釣り合っている。
余ったパワーがレーザー出力パワー。
共振器内でゲインが不足するモードでは発振しない。
• WALL ET AL
発振縦モード間隔は一般に等間隔ではない。
Titanium Sapphire Lasers
発振モード間の位相は時間的に変動している。

1.0

E
2-

Cil

0.8

c::

+"

Ti:Sapphireのレーザー遷移に対応する
発光バンド

c::

0.6

u

-E

Q)

0

U

c::

0.4

0

>,

C.
...

(fJ

c::

0

(fJ

.0

«

Q)
+"

Resid ual Absorption

0.2

c::

+

0.0
400

500

600

700

800

900

1000

1100

1200

Wavelength (nm)K. WALL and A. Sanchez, The Lincoln Laboratory Journal 3, 447 (1990).

FIGURE 4. The emission and absorption bands of Ti:AI 20 3. The absorption band, which peaks near 490 nm, occurs
in the blue-green region of the spectrum and allows Ti:AI 20 3 to be pumped by argon-ion lasers, frequency-doubled

モード同期もし縦モード間隔が一定ならば、マルチモード発振の出力電場は()
X
E(z, t) = ReẼm e i(!m t km z+ m )m!m = !0 + m !
(X
i!0 (t zc )E(z, t) = Re e
Ẽm e i[m !(tzc )+ mm])

かつ、各モードmの位相が相対的に固定されている場合＝モード同期(mode-locking)
例えば、すべてのφm=0で、電場振幅が同一である場合を考えると
(
)
!
z
N 2
t c
ML
i!0 (t zc ) sin
E(z, t)= Re Ẽ0 e
!
z
sin
t
2
c
ML
z=0ととり、I(t) / E(z, t)

I(t) / |Ẽ0 |

2 sin

2

sin2

N

2

!t
2
!t
2

を評価すると足し合わせるモードの数Nが増えると
周期2π/Δωのデルタ関数列に漸近する

モード同期の効果
4

モード間隔100MHz
N=2, 4, 10, 100

Intensity (N=2)

3

2

1

10000

0

20

40

60

80

100

Time (ns)16
14Intensity (N=4)

12Intensity (N=100)

8000

0

6000
4000
2000

10
0

8

0

6

20

40

60

80

100

Time (ns)

4
2
0
0

20

40

60

80

100

Time (ns)100

Intensity (N=10)8060

より多くの縦モードが位相ロックされるほど、より短いパルスが出力される。
(100 THz)-1=10 fs
ピーク強度はモード数の2乗で強くなる。

40

たくさんのcw発振達が強め合いの干渉で強力な光パルスを形成している。

20
0
0

20

40

60
Time (ns)80100

モード同期レーザーの成立条件
マルチモードレーザーは、自然にはモード同期を起こさない。
レーザーがモード同期を生じ、規則正しいパルスを発振するための条件は？
大まかには、2つの条件が満たされれば良い。
共振器を１周したときに、パルスが安定な解である必要がある。

1.0

1.0

0.5

0.5
Field amplitude

Field amplitude

条件1

0.0

レーザー中には分散があるため、何も工夫をしなければ光パルスは形状を保てない(「チャープ」)。

0.0

-0.5

-0.5

-1.0

-1.0
-20

0
Time (fs)

20

40

-40

-20

0
Time (fs)2040

プリズムやチャープミラーを用いた分散補償
条件2モード同期によってパルスを走らせる方が、連続波(cw)発振で定常的な光を発振させるよりもレーザーの中では得である必要がある。

カーレンズ効果や非線形偏波回転を用いた自己振幅変調を利用

非線形光学効果
物質の光応答は、光で励振された振動分極からの電気双極子放射で決まる。
P = "0 [ (1) E +

(2)

E2 +

(3)

E3 + · · · ]光電場が強くない場合：線形応答
入射光と同じ周波数で分極から放射：屈折率をもたらす。
平均パワー 1W、パルス幅20 fs、繰り返し100 MHz

第二高調波発生
ω -> 2ω

= ピークパワー 500 kW
直径 100 µmに絞ると I=6x109 W/cm2 2次の非線形光学効果が効いてくる
直径 10 µmに絞ると I=6x1011 W/cm2 3次の非線形光学効果が効いてくる

P (3) = "0 (3) E 2 E / "0 ·

(3)

I ·E

自分自身の光強度に比例して屈折率(位相)がダイナミックに変わる
自己位相変調-スペクトルの拡大効果

8さらに強度を上げると…
「再生増幅器」等で、パルス幅をキープしつつ
さらにパワー密度を6桁以上、上げることが出来る
原子核が電子を束縛する電場と同等の光電場では…
I=

1"0 cE 2 = 3.4 ⇥ 1016 W/cm2
21014 W/cm2あたりから、非摂動の領域に入る
Del Mar Photonics

プラトー

1015 W/cm2の光を希ガスに絞ると
高次高調波発生145 eV

カットオフ

J. Macklin et al., Phys. Rev. Lett. 70, 766 (1993).

I >1029 W/cm2

真空の非線形性 ~電子と陽電子の生成や光子光子相互作用~ が現れる

9

フェムト秒固体レーザーとフェムト秒ファイバーレーザー
モード同期固体レーザー (1990年代に成熟)
•
•
•
•
•
•
•

近赤外-可視 (700-1000 nm)
短パルス (数10 fs- 5 fs)
広帯域増幅無しで高出力 (数100 mW-数W)
繰り返し周波数が高い (<10 GHz)
線幅が細い
きれい

• 長期安定性に欠ける• 励起レーザーが高額
モード同期ファイバーレーザー (2000年代に成熟)• 近赤外 (1030 nm, 1560 nm)• 少しパルス幅が長い (40 fs- 200 fs)• 帯域はあまり広くない• パワーの増幅が得意• 繰り返し周波数が低い(<250 MHz)• 可動部が少なく長期安定性が良い• 線幅は太くなりがち
可視や紫外を出したいとき、究極の線幅の細さを目指したいとき= もし長期安定ならば固体レーザーが最適

10

RESEARCH ARTICLES

fcw = m × frep + fceo + Δ

tor to the beat to enhance the signal-to-noise
モード同期Ti:Sapphireレーザーの典型的スペクトルthe continuum (500 to 900 nm, containingf2n) is directed through one arm that contains
an acousto-optic modulator (AOM). The
near-infrared portion of the continuum (900
to 1100 nm, containing fn) traverses the otherarm of the apparatus, passing through a
4-mm-thick $-barium-borate frequency-doubling crystal. The crystal is angle-tuned toefficiently double at 1040 nm. The beams
from the two arms are then mode-matched
and recombined. The combined beam is filtered with a 10-nm bandwidth interference
filter centered at 520 nm and focused onto an
avalanche photo diode (APD). Approximately 5 %W are incident on the APD from thearm containing the AOM, whereas the frequency-doubling arm provides "1 %W. The
resulting RF beats are equal to &(# ! fAOM),
where fAOM is the drive frequency of the
AOM and is generated to be 7/8frep. The RFbeats are then fed into a tracking oscillator
that phase-locks a voltage-controlled oscilla-ratio by substantially reducing the noise
bandwidth. From the tracking oscillator output, we generate an error signal that is programmable to be (m/16)frep, thus allowing us
to lock the relative carrier-envelope phasefrom 0 to 2' in 16 steps of '/8.
Temporal cross correlation. Verificationof control of () in the time domain is obtained by interferometric cross correlation between two different, not necessarily adjacent,pulses in the pulse train (5). In fact, we
performed a time-averaged cross correlation
between pulses i and i * 2 using the correlator shown in Fig. 4. A multipass cell in one
arm of the correlator is used to generate therequired 20-ns delay. For the purpose of minimizing dispersion, the beam splitter is a2-%m-thick polymer pellicle with a thin gold
coating. To obtain a well-formed interferogram, we chose the mirror curvatures andtheir separations to mode-match the output

frep frep frep frep frep frep frep frep frep frep frep

x 40,000

Downloaded from www.sciencemag.org on May 16, 2012

k the repetimirror. Bepatially disof this mirhange withr the pulse),
petition rate
The maxi!4rad, subvergence, soble.
ncy of a sinexternal ine a full optiutput generhese experiwhereas thethat is, thefull octave.
is commonm of modear process of
the intrinsic
active index
ffers a small
g interaction
he width ofr, chromatic
pidly stretchowering theount of genspersion ophas existedorts a stable,
as zero disvailable only
employed aicrostructure
y dispersion
igh intensity
er generates
erent contin1125 nm (athrough fourinal spectrals transferred
As describedobtained by
2fn and f2n.

フェムト秒光周波数コムによる光周波数測定

D. J. Jones et al., Science 288, 635 (2000).

Fig. 2. Experimental setup for locking the carrier-envelope relative phase. The femtosecond laser isΔf

fn = n × frep + fceo
100万のオーダーの自然数

ともに10-1000 MHz程度で測定・制御可能光周波数間隔は原理的に等間隔。
2000年にフェムト秒光周波数コムが報告されて以来、高周波標準の精度で光周波数の測定が可能となった。
どれだけ動かない細い櫛になっているかが、
光周波数の測定能力を決める。
11

フォトニック結晶ファイバー
横モードのコアへの強い閉じ込め(数µm)と、ゼロ分散の伝搬
自己位相変調や4光波混合(3次の非線形)が効率良く起こる

Continuum

100fs input pulse“Supercontinuum”
J.K. Ranka et al., Opt. Lett. 25, 25 (2000).

従来SPM等で白色を得るためには、モード同期レーザーでは
ピークパワー不足であって、増幅器が必要であった。
モード同期レーザーの出力のみで、オクターブ以上のスペクトル広がりを得られるようになり、一種の革命となった。

f-2f 干渉計によるオフセット周波数の観測
全ての縦モードは

fn = n × frep + fceo

From Ti:S oscillator
950 mW

1 MHz
Free running
S/N: >~50 dB

750 mW
available for experiments
10 MHz

200 mW1064 nm → 532 nm“2f”

100-150 mW

フォトニック結晶ファイバーによる波長帯域の拡張“f”
13繰り返し周波数の基準の選択とコムの線幅
fn = n × frep + fceo
~400 THz

100 MHz0~50 MHz

4 x 106

frep frep frep frep frep frep frep frep frep frep frep①

fceoは高純度なRFを選定して基準にすれば良い。
何を基準にしてfrepを安定化するか？
f①安定なRF源からfrepを用意、それにコムの frepを直接安定化
基準RFの短期安定度が問題…
ルビジウム原子時計 (10 MHz) 2x10-11@1s: ~10 kHz
セシウム噴水時計 (9.2 GHz) 1x10-12@1s: ~1 kHz
水素メーザー (1.4 GHz) 1x10-13@1s: ~100 Hz②②安定な光周波数を用意、それにコムのn x frep を安定化
基準光周波数がそのままコムの精度と安定度を決定する。
②-A. 線幅1 Hzかつドリフトしないcwレーザー: 1 Hz (究極向け)②-B. 線幅1 kHzかつドリフトしないcwレーザー: 1 kHz (天文向け)
14

②-A
光格子時計を用いた光周波数コムの周波数安定化

15光格子時計M. Takamoto et al., Nature 435, 321 (2005).

周波数シフトにつながる原因を完全に制御した上で、多数の中性原子の遷移周波数を測定し、短い測定時間でも周波数の不確定さを減らすという発想

omic
e to
cator
mized
The

the
ould
trap
ppler
ually
zero
ping
yet
ions
erely

s7,8,11
and
can
oms,
ntial

f
p
f0 N ⌧

Sr光格子時計・光格子を使ってLamb-Dicke regimeでトラップすると、原子間相互作用やドップラーシフトを劇的に落とすことができ、本来持っている自然幅を観測できる。
・「魔法波長」で光格子を作ることで、時計遷移の
NATURE PHOTONICS DOI: 10.1038/NPHOTON.2015.5
LETTER
上準位と下準位の光シフトの差をなくすことができる。
a

a

1.0
0.8
0.6

Δν (Hz)

ured
e the
of a
ency
wards
rther
me Dt
ng a

Excitation probability

ð1Þ(⌧ ) ⇡

Allan分散

0
−1
−2
−3

0
4,000 8,000
0.4Time (s)296spatial
K
95 K of lasers
Figure 1 | Optical lattice clock. a, Theinterference patterncreates a lattice potential that confines atoms in a region much smaller than-14
. b, Energy levels for Sr. The 1S0 and 3P0 states are
the optical wavelength, l L0.2
coupled to the upper respective spin states by an off-resonant laser toproduce an optical lattice 0.0
with equalclock transition at-16 energy"1 shifts in "the" S0 i^jni ! "3 P0 i^jni electronic–l 0 ¼ 698 nm. Atoms are excited −6on the−4
−2
0
2
4
6
8
10
vibrational transitions, where n denotes the vibrational states of atoms in the
1
Clock laseronfrequency
lattice potential. The clock transition is then monitored
the 1S0 2(Hz)P1cyclic transition with nearly unit quantum efficiency.

2005年の発表当時は1秒間の積算で10
今や1秒間で10、数千秒の積算で18桁に到達している。

ence and Technology Agency, Bunkyo-ku, Tokyo 113-8656, Japan. 3National Metrology Institute
IJ/AIST), Tsukuba, Ibaraki 305-8563, Japan.

10−16

10−17

10−18

100

101

102

103

104

Averaging time (s)10Residubの不確かさ。

Allan standard deviation

hing
rent
ve as
tes a
d for
that
ttice
tical

b

I. Ushijima et al., Nat. Photon. 9, 185 (2015).
10−17全縦モードの超高精度な安定化
全ての縦モードは fn = n · frep +(δは0.1 mHzのレベルで安定化済み)
数百万本の「歯」が用意されている
等間隔ではあるものの、線幅がついておりまた間隔も時々刻々変化している

光原子時計に安定化された超狭線幅レーザーとコムの「歯」1本が正確な周波数間隔を持つように繰り返し周波数frepを制御する

Δ

全ての「歯」が同等の超狭線幅になり、しかもそれらの絶対周波数が現在の国際標準よりも高い精度で定まることになる

Δ’
コムはどの波長域でも同じ線幅を持つ計算になるため、それを参照すれば
あらゆる波長で絶対周波数の定まった超狭線幅レーザーを用意できる

17

functions were fitted to the recorded modes as afunction of pixel position and identified with theabsolute comb frequencies, fn, which are referenced
to the atomic clock (10). The dense grid of modes
allows the spectrograph’s calibration function (Fig.
3A) to be determined to very high accuracy; evena simple, second-order polynomial fit to the pixelversus-frequency distribution has only 9 m s−1
root mean square (RMS) residual deviations aroundit (Fig. 3B), and this remains almost unchanged
with higher-order polynomial modeling (10).
With traditional calibration techniques, suchas thorium comparison lamps, I2 gas absorption
cells or Earth’s atmospheric absorption lines forcalibration achieve ~10 m s−1 absolute precision
per calibration line at best (30). Thus, even withthese “first light” comb recordings, we alreadydemonstrate superior absolute calibration accuracy. Because more than 104 modes will be available

and then mitigate and/or model and remove such
systematics. Because the VTT spectrograph is
not stabilized (i.e., temperature-, pressure- andvibration-isolated), instrument drifts are expected
and the VTT LFC spectra can already be used to
track them accurately. From a time series of exposures, we derive a drift in the spectrograph oftypically 8 m s−1 min−1 (5 MHz min−1) (10).
Much lower drift rates have been demonstrated
with suitably stabilized instruments [e.g., ~1 m s−1
over months with HARPS (13)]; although the
VTT is not optimized for stability, this does notaffect its usefulness to test calibration procedures.
Indeed, different modes are observed to drift atdifferent rates, with neighboring modes having
highly correlated drift rates (10). Also, as the
comb modes drift across the detector, higherorder distortions are evident, which are the combined result of many effects, such as intrapixel

Downloaded from www.sciencemag.org on September 9, 2008

omical spectrohigh-resolution
t corresponds
ilicon atom instatistics of anes can the revided that syscordingly (10).
lized, vacuumnical drifts will
the CCD. Alto first order,
ixel sensitivity
gher precision.
entually modelcrucial for theation; tests ofspectrographs,
tive.
mical LFC test
Telescope (24)able rubidium
5 parts in 1011
rate clocks aree absolute unen comb mode.
infrared waveely simple andd. The erbium0 MHz which,g higher resolvor 1.2 km s−1)phs, is too low
ltering out unot cavity (FPC)
ggested as one
ective (28, 29).
separated by ay length so that> 1), are interlower panel).
er ratio, m, byonic servo syscings, m × frep,
e to which thes an importantfunction falls
ode frequencies②-B
繰り返し40 GHz固体天文コムの試作

sensitivity variation
Fig. 2. Spectra of theshow an importantsolar photosphere (backThe dense grid of h
ground image) overlaid
by a LFC with 15-GHz modetion allows the disco
spacing (white, equallyplex effects correlat
spaced vertical stripes).
The first light f
Spectra are dispersed hornomical spectrogra
izontally, whereas the verprecision beyond
tical axis is a spatial crossopportunity now issectionof GHzthe Sun’sphoand remove system
15
spacing
tosphere. The upper panthe ~1 cm s−1 lonel shows a small section
accuracy, and repeaof the larger portion ofredshift drift experi
the spectrum below. The
brighter mode labeled
References andwith its absolute frequen1. A. G. Riess et al., A
cy is additionally super2. S. Perlmutter et al
3. D. N. Spergel et al.,imposed with a CW laser
4. J. A. Peacock et al.
used to identify the mode
5. D. J. Eisenstein et
number (Fig. 1). The fre6. A. Sandage, Astropquencies of the other
7. A. Loeb, Astrophys.
modes are integer mul8. J. Liske et al., Mon.
9. L. Pasquini et al.,tiples of 15 GHz higher
P. Whitelock, M. D
(right) and lower (left) in(Cambridge Univ. P
frequency. Previous calipp. 193–197.
bration methods would
10. Materials and meth
use the atmospheric abmaterial on Scienc
sorption lines (dark vertical
11. M. Mayor, D. Quel
Fig. 1. Sketch of our experimental setup at the VTT. By superimposing the frequency
comb
withinter12. G. W. Marcy, R. P. B
bands labeled“Atm”
13. C. Lovis et al., Natlight from a celestial body—in this case, the Sun—one can effectively calibrate
its withemissionorleavedthe Fraunhofer
14. C. Lovis et al., in P
absorption spectrum against an atomic clock. An erbium-doped fiber LFC withabsorption
250-MHzmode
lines), which are comparably few and far between. Also shown in the upper panel is the only
I. Masanori, Eds. (20T. Steinmetz,etal.,Science321,
1335
thoriumemissionline
lying
in this(2008).
wavelength range from a typical hollow-cathode calibration lamp. 1815. J. N. Bahcall, E. E. S
spacing (pulse repetition rate) is filtered with a FPC to increase
the effectivemode
spacing,requiredallowing it to be resolved by the spectrograph. The latter has a resolution Recordingof ~0.8it GHz
at an integration time of 30 min, compared with the LFC exposure time of just 10 ms. 16. J. K. Webb, V. V. Flam

Fig. 1. Left: the dense modes of a low-repetition-rate frequency comb can be filtered in a
Fabry-Pérot etalon to provide a wider mode spacing. If the group delay dispersion of the etalon
is not zero then unwanted modes can be insufficiently or asymmetrically suppressed(exaggerated for effect). Right: a false-color CCD image of the 15-GHz astrocomb deployed at
the Southern African Large Telesecope [13].

天文コムとFabry-Perot共振器
コムへの要求①視線速度の変化 1 cm/s
500 nmにおいて20 kHzのシフト
コムの線幅は数kHzで良い:
原子遷移にロックしたcwを基準にする(後述)②R=50,000, 500 nmで観測したいとすると
Df=12 GHzなので、繰り返しは40 GHzくらい欲しい

Fig. 2. Illustration of different astrocomb architectures. FPC, Fabry-Pérot cavity; SHG, second
harmonic generation; PCF, photonic crystal fiber; AMP, amplifier; EOM; electro-optic
modulator; AOM, acousto-optic modulator. See text in §2.1 for further details.

Fabry-Perot共振器等による「間引き」が必要• FP共振器の縦モード間隔が光周波数コ
ムに合うように制御が必要• 線幅が細いFP共振器ほど• 分散の制御が完璧でないとコムと合わない• 擾乱に敏感、その制御は精緻かつ高速である必要R. A. McCracken et al., Opt. Exp. 25, 15058 (2017).

Fig. 1. Left: the dense modes of a low-repetition-rate frequency comb can be filtered in a

19

PCF(長さ10 cm)によるスペクトル拡大
𝑓"#$ = 1 GHz, 2 GHz における白色スペクトル (ポンプレーザーパワー：5.5 W)

Si検出器の
感度不足

𝑓*)

SHG結晶
𝑓'#( ビート信号𝑓)20

参考：紫外への拡張
𝑓"#$ = 1 GHzにおける白色スペクトル↓• 第二高調波を取るだけで250 nm程度までの短波長を得る事もできる--- Ti:Sapphireコムの大きなメリット
21原子遷移に対するコム1本のロック
87Rb

Fg=2

Fe=1

Fe=2

Fe=3

Fe=3

87Rbの

85Rb

Fg=3

Fe=2

飽和吸収スペクトル@ 780 nm
(線幅：数MHz)Fe=4,! = 1×10/ MHz"! = 0.060 2 GHz

cwレーザー

fn = n × frep + fceo!

frep frep frep frep frep frep frep frep frep frep frep

・原子遷移にロックしたcwレーザー
・コム1本

数kHzの線幅で固定

周波数差が一定になるように
レーザー共振器長を制御
f

22

まとめ
長期安定なモード同期チタンサファイアレーザーによる周波数コムの構築
1. 繰り返し周波数120 MHzの超高精度フェムト秒光周波数コム••

光格子時計に対する1秒間あたり10-18の追従度で数百万本の縦モードが安定化された
東京大学内の光ファイバー網を通じた時計レーザーの受信と光周波数コムの安定化

2. 40 GHzを超える繰り返し周波数の天文コムの試作••••繰り返し周波数1 GHz - 3.2 GHzのモード同期レーザーの製作繰り返し周波数1.5 GHzでコムとしての周波数安定化
ファブリーペロー共振器を用いて40.5 GHz-67.5 GHzの繰り返しを達成(750-850 nm)
可搬な500-600 nmの40 GHz天文コムを構築中
23