were trapped by Coulomb attraction to the ions
and formed a neutralizing background with over-
all nonneutrality on the order of a few percent
( 14 , 15 ).
Immediately after plasma formation, counter-
propagatings+ands−polarized beams near res-
onance with the 5s^2 S1/2–5p^2 P3/2transition at
408 nm (g= 22.4 MHz) illuminated the plasma,
forming a one-dimensional optical molasses ( 4 )
for laser cooling along thexdirection (Fig. 1).
The single-beam peak intensity wasI=100mW/
cm^2 (1/e^2 -intensity radiusw= 9 mm, and satu-
ration parameters 0 = 2.3). Lasers at 1092 and
1033 nm repumped ions from long-lived^2 D3/2
and^2 D5/2states, returning them to the cooling
cycle. Reductions in cooling efficiency caused by
coherent coupling of the^2 S1/2and^2 D5/2states
and resulting electromagnetically induced trans-
parencies ( 35 ) were minimized by rapid velocity-
changing collisions in the plasma ( 25 ). After laser
cooling, spatially resolved measurements of ion
temperatureanddensitywereperformedbyusing
laser-induced fluorescence (LIF) on the^2 S1/2–
(^2) P
1/2transition at 422 nm (^36 ). The LIF laser il-
luminated a central slice of the plasma (z≈0),
providing transverse spatial resolution of 13mm
and resolution along the imaging axis equal to
the tight dimension of the LIF light (wz= 2 mm).
Unless otherwise specified, temperature was mea-
sured along the laser-cooling axis (Fig. 1).
Figure 2, A to C, shows temperature measure-
ments, spatially resolved along the laser-cooling
axis, for three different laser-cooling parameters:
no cooling light (yellow), detuning from reso-
nance ofD=−20 MHz [cooling (red)], andD=
+20 MHz [heating (blue)]. By 5ms after plasma
formation, cooling and heating beams had little
effect. Temperature variation across the sample
reflected variation in density and the resulting DIH
temperatureðTDIHºn
1 = 3
i Þ.By60ms, the ion tem-
perature was substantially altered by the lasers.
In the center of the plasma (x≈0),Tidoubled in
the heating configuration and was reduced by
half for cooling compared with no cooling light.
The trend continued for 135msofheatingor
cooling, with the lowest temperature observed,
Ti= 50(4) mK, providing clear evidence of laser
cooling.
Cooling was effective only in the central region
(jxj≲1 mm), which illustrates the role of plasma
expansion. Immediately after plasma formation,
the density gradient and electron thermal energy
created a radially directed force that drives ex-
pansion ( 14 ). Although electron-ion thermaliza-
tion has noticeable effects ( 37 ) and the plasma
used in this work was slightly asymmetric, an
analytic expansion model for a collisionless,
spherically symmetric, Gaussian plasma is a sat-
isfactory approximation for developing an intui-
tive explanation of laser-cooling results. In this
model ( 14 , 15 ), expansion creates a hydrodynamic
plasma-velocity fieldv
→
expðr;tÞ¼½t=ðt^2 þt^2 expÞr
→
(whereris the displacement from the plasma
center,tis time, andtexp=[mis(0)^2 /kBTe(0)]1/2is
a characteristic time for the expansion). The
velocity increases withtime and distance from
the plasma center, saturating at an RMS value
for the entire plasma of
ffiffiffiffiffiffiffiffiffiffiffiffi
hv^2 expi
q
¼sð 0 Þ=texpon
a time scale oftexp. Cooling is effective only in
regions for which the expansion velocity along the
cooling-laser axis remains less than or comparable
to the velocity capture range½jx^v
→
expðr
→
;tÞj≲vcfor
an appreciable time.
For these experiments,s(0)/texp≈40 m/s ex-
ceeded the velocity capture range, andtexp≈ 75 ms
was on the order of the minimum time required
to scatter enough photons to substantially cool
the ions ( 4 ). Thus, cooling was most effective for
jxj≲1 mm, where the expansion velocity stayed
relatively small. Analogous statements can be
made for the heating configuration. To observe
substantial laser cooling, it was essential to
create very large plasmas compared with those
in previous UNP experiments ( 14 , 15 ), which in-
creasedtexpand gave more time for laser cooling.
Figure 2D shows the evolution of the ion
temperature for the center of the plasma, where
cooling and heating were most effective. Fits
from an approximate kinetic model ( 14 , 37 ) ac-
counting for DIH, electron-ion heating, adiabatic
cooling, and laser cooling describe the data rea-
sonably well ( 36 ). The natural dynamics, seen in
the data for no laser cooling, was an increase to
Ti~ 0.4 K within the first few microseconds,
owing to DIH, followed by cooling caused by
adiabatic expansion. In the presence of the cool-
ing lasers, however, the ion temperature dropped
much farther than that for no 408-nm light. Even
more notable is the increase ofGito 11(1) after
135 ms (Fig. 2E), which is comparable to condi-
tions of interest in white dwarf stars ( 6 , 17 ), for
example. It is also much deeper into the strong
coupling regime than has previously been re-
ported with these systems. A value ofGi= 4 was
obtained ( 38 ) in a UNP with relatively high den-
sity and low electron temperature, which in-
duces substantial screening of ion-ion interactions
[screening parameterk=a/lD= 1 for Debye
screening lengthlD=(kBTee 0 /nee^2 )1/2] and re-
duces the effects of strong coupling. For our con-
ditions,k≤0.7, and the screening was weaker.
Although laser-cooling was applied only along
one axis, all three degrees of freedom were ef-
fectively cooled because of the high collision rate
in the plasma. Molecular dynamics simulations
( 39 ) show that local thermal equilibrium is es-
tablished on the time scale of a few times the
inverse of the ion plasma oscillation frequency,
wpi^1 ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
e 0 mi=nie^2
p
≲ 2 ms. We confirmed cross-
thermalization by measuring the temperature
transverse to the cooling axis ( 36 ). Lasers along
a single axis also produce three-dimensional
cooling in trapped ions ( 1 , 2 ),butthisisnottrue
for neutral atoms ( 4 ) and molecules ( 10 ), which
have much lower collision rates. Collisions did
not damp the hydrodynamic expansion velocity
transverse to the laser-cooling axis because of
conservation of momentum during each collision.
Langinet al.,Science 363 ,61–64 (2019) 4 January 2019 2of4
Fig. 2. Ion temperature and coupling variation.Shown are the data for laser detuningD=−20 MHz
[red (cooling)],D= 20 MHz [blue (heating)], and no 408-nm laser (yellow). (AtoC) Temperature at
three different times after plasma creation (as indicated in each panel). Each measurement corresponds
to a region withDx=260mmandDy= 4.5 mm centered aty= 0. Cooling and heating were ineffective
at large displacement from the plasma center because the plasma expansion Doppler-shifted these
ions out of resonance with the lasers. (D) Temperature versus time in the central region (|x|≤0.5 mm).
(E) Coulomb coupling parameterGiversus time in the central region. Solid lines in (D) and (E) were
calculated by using coupled ion and electron kinetic equations ( 36 ). We do not display results from
the model for the heating data because the density perturbation was too severe for the model to
be applicable (Fig. 3A). Error bars indicate SD.
RESEARCH | REPORT
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