The Importance of Atomic Clocks in Modern Technology
Hg
+
ion
Single-atom optical clocks
D. J. Wineland, NIST, Boulder
Hg
+
ion
Summary
•
Why precise clocks?
•
Atomic clock basics
•
Optical atomic clocks
- atomic ion examples
(neutral atoms good too)
•
Why single atoms?
•
State of play
•
Future
Single-atom optical clocks
D. J. Wineland, NIST, Boulder
pulse emitted at t
0
pulse received at t
1
ℓ = c x (t
1
– t
0
)
error:
ℓ = c
t
for
t = 10
-9
s,
ℓ
30 cm
(
t)/(1 day) = 10
-14
f/f
0
Why precise clocks?
Navigation: e.g. satellite navigation (GPS)
Global positioning system GPS
satellite network
gives 3 space
dimensions
+ time
Clocks
Traditional periodic event-generators,
or frequency references:
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.:
Atomic energy state superpositions act like pendulum clock
superposition
of
electron energy levels,
wave function:
= |1
+ exp(-i2
f
0
t) |2
oscillating electric dipole
plot of electron density vs. time
Planck’s constant
at frequency f
0
= (E
2
– E
1
)/h
center
of atom
plot of electron density vs. time
Practical mode of operation
:
1. Start atom in |1
.
3. Measure probability of
| 2
.
Maximum
| 1
| 2
transition probability when f
L
= f
0
.
2. Apply radiation at frequency f
L
for short time.
center
of atom
superposition
of
electron energy levels,
wave function:
= |1
+ exp(- i2
f
0
t) |2
oscillating electric dipole
Planck’s constant
at frequency f
0
= (E
2
– E
1
)/h
Atomic energy state superpositions act like pendulum clock
detector
counter
Atomic clock recipe
f
f
0
transparent cell (“trap”)
containing atoms
absorption
Why atomic clocks?
Pendulum:
ℓ
f = [g/ℓ]
1/2
/2
gravitational
acceleration
Reproducibility:
f
0
depends on:
manufacturing tolerances (ℓ)
local value of g
wear
Atoms:
Reproducibility:
all atoms of a particular kind
(e.g.,
133
Cs ) are
identical!
atoms don’t wear out!
-wave cavity
(Ramsey method)
-waves
atomic beam
f ~ 1/(2T
transit
)
e.g., Cesium beam clock (hyperfine trans.)
f
0
≡ 9 192 631 770 Hz (microwaves)
e.g., NBS-6 (~ 1976)
L = 3.75 m,
f
30 Hz (T
transit
~ 16 ms)
state detection
(e.g., state-dependent
fluorescence)
state preparation
(e.g. laser optical pumping)
count
atoms
f
0
absorption
Atomic beam spectrometer
f = 1/(2T
transit
)
-waves
state detection
(e.g., state-dependent
fluorescence)
state preparation
(e.g. laser optical pumping)
atomic beam
-waves
atom cooling,
state preparation & detection
Atomic fountain
Atomic beam spectrometer
f
0
absorption
f = 1/(2T
transit
)
NIST F-1
-wave cavity
(Ramsey method)
count
atoms
T
transit
1 s
•
tick rate can be fast; e.g., for
199
Hg
+
(
2
S
1/2
2
D
5/2
)
f
0
=
1 064 721 609 899 144.94 (97)
Hz
•
absorption range very narrow
e.g., for
199
Hg
+
,
f
0
1.6 Hz
Why optical atomic clocks?
199
Hg
+
1 mm
2
S
1/2
“trap” electrodes
282 nm
= 0.1 s
Hg
+
ion optical clock experiments at NIST
(1981
)
1 mm
2
S
1/2
“trap” electrodes
= 0.1 s
Why just one ion?
(single ions
smallest systematic errors)
for two ions,
quadrupole shift ~ 1 kHz
Single Hg
+
ion optical clock experiments at NIST
,
1981
199
Hg
+
1 mm
2
S
1/2
“trap” electrodes
282 nm
= 0.1 s
Single Hg
+
ion optical clock experiments at NIST
,
1981
1 mm
2
S
1/2
2
D
5/2
2
P
1/2
“trap” electrodes
194 nm
cooling
and detection!
Hg
+
Detection:
199
Hg
+
1 mm
2
S
1/2
2
D
5/2
2
P
1/2
“trap” electrodes
194 nm
Hg
+
Detection:
“trap” electrodes
•
suppresses ion loss (T
storage
~ 6 months)
•
suppresses heating, perturbations
from collisions
•
reduces blackbody radiation shifts
trap
imaging
lens
Ion “trap” in vacuum at liquid Helium temperature ( 4 K)
averaging time
= 20 s
proximity sensors
laser stabilization:
= 563 nm
2-mirror resonant cavity:
distance = integer number of
half- wavelengths
Brendt Young, Flavio Cruz, Wayne Itano,
Jim Bergquist , PRL 82, 3799 (1999) + ICOLS ‘99
t
E
(
t
)
synchronize carrier
phase with pulse phase
Frequency domain
f
f
r
0
I
(
f
)
f
1
f
2
f
2
= 2 f
1
f
1
= M f
r
X 2
feed back on
laser to make
f
beat
0
f
beat
Mode-locked laser
T. Hänsch, J. Hall
et al.
Frequency counters, > 2000
•
trapping
first-order Doppler shift
0
•
laser cooling
time dilation small
•
trapping in high vacuum at 4 K
small environmental perturbations (collisions, black body shifts, etc.)
Single
199
Hg
+
ions for (optical) clocks:
J. C. Bergquist et al., (NIST)1981
first clock with systematic uncertainly (7x10
-17
) below Cesium
- W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006)
Jim Bergquist
trapping
first-order Doppler shift
→
0
laser cooling
time dilation small
trapping in high vacuum at 4 K
environmental perturbations (collisions, black body shifts, etc.) small
Jim Bergquist
first clock with systematic uncertainly (7x10
-17
) below Cesium
- W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006)
Single
199
Hg
+
ions for (optical) clocks:
J. C. Bergquist et al., (NIST)1981
Plus several other ion species:
88
Sr
+
,
171
Yb
+
,
27
Al
+
,
40
Ca
+
,
115
In
+
see, e.g., A. Ludlow et al., arXiv:1407.3493
229
Th
3+
(PTB, UCLA
Kuzmich group)
Al
+
“quantum-logic clock”
(T. Rosenband, D. Lebrandt et al.)
laser-cooled Mg
+
keeps Al
+
cold
Mg
+
helps to calibrate
B
2
from all sources
collisions observed by ions switching places
……
Till Rosenband
|
Al
+
|
Al
motion superposition
|
Mg
+
|
Mg
David Leibrandt
trap at
~ 300 K
= 280 nm
P. O. Schmidt et al.,
Science
309, 749 (2005)
Example
:
relativistic effects in measurement
v
/c
: (“first-order” Doppler shift)
•
for
f/f
0
= 10
-18
|
v
| = 0.3 nm/s
trap vs. probe laser? Remove as in spacecraft ranging
(Bob Vessot, Ed Mattison
et al.
, PRL 45, 2081 (1980))
– ½
v
2
/c
2
:
(time dilation shift)
•
suppressed with laser cooling
gravitational-potential red shift
f/f
0
=
grav
/mc
2
= g
local
h/c
2
2
nd
twin paradox
Systematic frequency shifts
Doppler shifts
:
f/f
0
=
v
/c – ½
v
2
/c
2
with all systematic errors,
uncertainty (
27
Al
+
) = 8.0 x 10
-18
after 80 years, your twin (at sea level)
would be 1/1000 second younger
Some fun science:
Clocks and “relativity”
James Chou with “portable” Al
+
clock (clock #1)
(reference clock in adjacent room, clock #2)
clock #1 raised 33 cm (~ 13 inches)
f
1
/f
2
= 1.000 000 000 000 000 041(16)
Jun Ye’s group (JILA), Sr neutral atoms in optical lattice
:
f/f
0
(systematic) =
6.4 x 10
-18
(B. J. Bloom et al.,
Nature
506, 71 (2014))
T
30 mK
PTB, Braunschweig, Germany
f/f
0
(systematic) =
3.3 x 10
-18
(unpublished)
weak (octupole) transition, laser Stark shifts, …
H. Katori group (Riken) Sr neutral atoms in optical lattice
f/f
0
(systematic) =
7.2 x 10
-18
(arXiv:1405.4071)
Moving target!
2.4
Future?
* “Navigation” at < 1 cm scale:
- Measure earth strain – earthquake prediction
- geodesy: map earth via gravitational red shift
* Fundamental science:
- are the strengths of the basic forces really
constant in time?
- possible deviations from Einstein’s
general relativity?
Shlomi Kotler, Dustin Hite, Katie McCormick ,Susanna Todaro, Leif Waldner, Yiheng Lin, Daniel Slichter, James Chou, David Allcock, Didi Leibfried, Jwo-Sy Chen, Sam Brewer, Kyle McKay
David Hume Ting Rei Tan
Jim Bergquist, John Bollinger, Joe Britton, Justin Bonet, Ryan Bowler, John Gaebler, Andrew Wilson, Dave Wineland, David Leibrandt, Peter Burns, Raghu Srinivas, Shon Cook, Robert Jordens
Not pictured: Brian Sawyer, Till Rosenband, Wayne Itano, Dave Pappas, Bob Drullinger
NIST “IONS” June 2014
Explore the significance of precise timekeeping provided by atomic clocks, the fundamentals of atomic clocks, the advancements in single-atom optical clocks by experts like D. J. Wineland from NIST Boulder, the role of atomic energy state superpositions, and the practical operation of atomic clocks. Understand why atomic clocks are crucial for precise global navigation systems like GPS and how they outperform traditional clocks in accuracy and reliability.
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Presentation Transcript
Single-atom optical clocks D. J. Wineland, NIST, Boulder Hg+ ion
Single-atom optical clocks D. J. Wineland, NIST, Boulder Summary Why precise clocks? Atomic clock basics Optical atomic clocks - atomic ion examples (neutral atoms good too) Why single atoms? State of play Future Hg+ ion
Why precise clocks? Navigation: e.g. satellite navigation (GPS) pulse emitted at t0 pulse received at t1 = c x (t1 t0) error: = c t for t = 10-9 s, 30 cm ( t)/(1 day) = 10-14 f/f0
Global positioning system GPS satellite network gives 3 space dimensions + time
Clocks periodic-event generator Traditional periodic event-generators, or frequency references: pendulum clock counter
Atomic energy state superpositions act like pendulum clock |2 Energy superposition of electron energy levels, wave function: = |1 + exp(-i2 f0t) |2 oscillating electric dipole at frequency f0 = (E2 E1)/h |1 center of atom Planck s constant plot of electron density vs. time
Atomic energy state superpositions act like pendulum clock Energy |2 superposition of electron energy levels, wave function: = |1 + exp(- i2 f0t) |2 oscillating electric dipole at frequency f0 = (E2 E1)/h |1 center of atom Planck s constant plot of electron density vs. time Practical mode of operation: 1. Start atom in |1 . 2. Apply radiation at frequency fL for short time. |2 3. Measure probability of | 2 . Maximum | 1 | 2 transition probability when fL = f0 . |1
Atomic clock recipe electronic feed back servo absorption f f0 radiation source frequency f detector 2 transparent cell ( trap ) containing atoms 1 counter
Why atomic clocks? Pendulum: f = [g/ ]1/2/2 Atoms: gravitational acceleration Environmental sensitivity: (e.g. temperature T) Environmental sensitivity: (e.g. temperature T) relativistic time dilation: (f0(T) f0(T = 0))/f0 = - (v/c)2 -1.4 x 10-13 T/M(u) f/f0 = - ( T) coefficient of thermal expansion: = ( T) low expansion materials: ~ 10-8/ C For M = 133 u (e.g., 133Cs Cesium) f/f0 -1 x 10-15/ C f/f0 -5 x 10-9/ C Reproducibility: Reproducibility: f0 depends on: manufacturing tolerances ( ) all atoms of a particular kind (e.g., 133Cs ) are identical! local value of g atoms don t wear out! wear
f = 1/(2Ttransit) Atomic beam spectrometer absorption -waves f0 -wave cavity (Ramsey method) count atoms atomic beam state detection (e.g., state-dependent fluorescence) state preparation (e.g. laser optical pumping) f ~ 1/(2Ttransit) e.g., Cesium beam clock (hyperfine trans.) f0 9 192 631 770 Hz (microwaves) e.g., NBS-6 (~ 1976) L = 3.75 m, f 30 Hz (Ttransit ~ 16 ms)
f = 1/(2Ttransit) Atomic beam spectrometer absorption -waves f0 -wave cavity (Ramsey method) count atoms atomic beam state detection (e.g., state-dependent fluorescence) state preparation (e.g. laser optical pumping) Atomic fountain NIST F-1 Ttransit 1 s -waves atom cooling, state preparation & detection
Why optical atomic clocks? tick rate can be fast; e.g., for 199Hg+ ( 2S1/2 2D5/2) f0 = 1 064 721 609 899 144.94 (97) Hz absorption range very narrow e.g., for 199Hg+ , f0 1.6 Hz From 1879 text written by Thompson (Lord Kelvin) and Tate, (Idea attributed to Maxwell) ``The recent discoveries indicate to us natural standard pieces of matter such as atoms of hydrogen or sodium, ready made in infinite numbers, all absolutely alike in every physical property. The time of vibration of a sodium particle corresponding to any one of its modes of vibration is known to be absolutely independent of its position in the universe, and it will probably remain the same so long as the particle itself exists." W. F. Snyder, Lord Kelvin on atoms as fundamental natural standards (for base units) IEEE Trans. Instrum. Meas., 99, 1973.
Hg+ ion optical clock experiments at NIST(1981 ) = 0.1 s trap electrodes 2D5/2 2S1/2 282 nm 199Hg+ 1 mm
Why just one ion? (single ions smallest systematic errors) = 0.1 s trap electrodes 2D5/2 2S1/2 for two ions, 1 mm quadrupole shift ~ 1 kHz
Single Hg+ ion optical clock experiments at NIST,1981 2P1/2 trap electrodes Hg+ 2S1/2 Laser cooling 194 nm 194 nm 199Hg+ 1 mm Single Hg+ ion
Single Hg+ ion optical clock experiments at NIST,1981 = 0.1 s trap electrodes 2D5/2 2S1/2 282 nm 199Hg+ 1 mm
Detection: 2P1/2 trap electrodes 2D5/2 Hg+ 2S1/2 cooling and detection! 194 nm 1 mm
Detection: 2P1/2 trap electrodes 2D5/2 Hg+ 2S1/2 194 nm 199Hg+ 1 mm
2P1/2 trap electrodes 2D5/2 Hg+ 2S1/2 atom in 2S1/2state atom in 2D5/2state 1 mm
Ion trap in vacuum at liquid Helium temperature ( 4 K) suppresses ion loss (Tstorage ~ 6 months) suppresses heating, perturbations from collisions reduces blackbody radiation shifts imaging lens trap
2-mirror resonant cavity: laser stabilization: distance = integer number of half- wavelengths averaging time = 20 s proximity sensors = 563 nm Brendt Young, Flavio Cruz, Wayne Itano, Jim Bergquist , PRL 82, 3799 (1999) + ICOLS 99
Frequency counters, > 2000 Mode-locked laser E(t) synchronize carrier phase with pulse phase t Frequency domain I(f) fr f 0 f1 f2 feed back on laser to make fbeat 0 f2 = 2 f1 f1 = M fr ! X 2 fbeat T. H nsch, J. Hall et al.
Single 199Hg+ ions for (optical) clocks: J. C. Bergquist et al., (NIST)1981 2P1/2 2D5/2 Hg+ Jim Bergquist 2S1/2 trapping first-order Doppler shift 0 laser cooling time dilation small trapping in high vacuum at 4 K small environmental perturbations (collisions, black body shifts, etc.) first clock with systematic uncertainly (7x10-17) below Cesium - W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006)
Single 199Hg+ ions for (optical) clocks: J. C. Bergquist et al., (NIST)1981 2P1/2 2D5/2 Hg+ Jim Bergquist 2S1/2 Plus several other ion species: 88Sr+, 171Yb+, 27Al+, 40Ca+, 115In+ trapping first-order Doppler shift 0 laser cooling time dilation small trapping in high vacuum at 4 K environmental perturbations (collisions, black body shifts, etc.) small first clock with systematic uncertainly (7x10-17) below Cesium - W. H. Oskay et al., Phys. Rev. Lett. 97, 020801 (2006) see, e.g., A. Ludlow et al., arXiv:1407.3493 229Th3+ (PTB, UCLA Kuzmich group)
Al+quantum-logic clock (T. Rosenband, D. Lebrandt et al.) Coulomb interaction 1P1 trap at ~ 300 K 2P3/2 3P0 Till Rosenband David Leibrandt = 280 nm Al+ (F=2, mF = -2) = 167 nm 2S1/2 25Mg+ (F=3, mF = -3) 1S0 | Al + | Al motion superposition | Mg + | Mg laser-cooled Mg+ keeps Al+ cold Mg+ helps to calibrate B2 from all sources collisions observed by ions switching places P. O. Schmidt et al.,Science 309, 749 (2005)
Systematic frequency shifts Example: relativistic effects in measurement Doppler shifts: f/f0 = v /c v2 /c2 v /c: ( first-order Doppler shift) for f/f0 = 10-18 | v | = 0.3 nm/s trap vs. probe laser? Remove as in spacecraft ranging (Bob Vessot, Ed Mattison et al., PRL 45, 2081 (1980)) v2 /c2 : (time dilation shift) suppressed with laser cooling with all systematic errors, uncertainty (27Al+) = 8.0 x 10-18 gravitational-potential red shift f/f0 = grav/mc2 = glocal h/c2 2nd twin paradox after 80 years, your twin (at sea level) would be 1/1000 second younger
Some fun science: Clocks and relativity single Al+ ion clock (pre-wristwatch model)
James Chou with portable Al+ clock (clock #1) (reference clock in adjacent room, clock #2)
clock #1 raised 33 cm (~ 13 inches) f1/f2 = 1.000 000 000 000 000 041(16)
Moving target! Jun Ye s group (JILA), Sr neutral atoms in optical lattice: 2.4 f/f0(systematic) = 6.4 x 10-18 (B. J. Bloom et al., Nature 506, 71 (2014)) T 30 mK PTB, Braunschweig, Germany f/f0(systematic) = 3.3 x 10-18 (unpublished) weak (octupole) transition, laser Stark shifts, H. Katori group (Riken) Sr neutral atoms in optical lattice f/f0(systematic) = 7.2 x 10-18 (arXiv:1405.4071)
Future? * Navigation at < 1 cm scale: - Measure earth strain earthquake prediction - geodesy: map earth via gravitational red shift * Fundamental science: - are the strengths of the basic forces really constant in time? - possible deviations from Einstein s general relativity?
NIST IONS June 2014 Jim Bergquist, John Bollinger, Joe Britton, Justin Bonet, Ryan Bowler, John Gaebler, Andrew Wilson, Dave Wineland, David Leibrandt, Peter Burns, Raghu Srinivas, Shon Cook, Robert Jordens David Hume Ting Rei Tan Shlomi Kotler, Dustin Hite, Katie McCormick ,Susanna Todaro, Leif Waldner, Yiheng Lin, Daniel Slichter, James Chou, David Allcock, Didi Leibfried, Jwo-Sy Chen, Sam Brewer, Kyle McKay Not pictured: Brian Sawyer, Till Rosenband, Wayne Itano, Dave Pappas, Bob Drullinger
