Measurements of the ion velocity distribution in an ultracold neutral plasma derived from a cold, dense Rydberg gas

0.65 MB·

by  S. D. Bergeson

Submitted to J. Phys. B Special issue on Rydberg atom physics
Measurements of the ion velocity distribution in an ultracold neutral plasma derived
from a cold, dense Rydberg gas
S. D. Bergeson1 and M. Lyon2
1 Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA and
2 Joint Quantum Institute and Department of Physics,
University of Maryland, College Park, Maryland 20742, USA
6
We report measurements of the ion velocity distribution in an ultracold neutral plasma derived
1
fromadense,coldRydberggasinaMOT.TheRydbergatomsareexcitedusingaresonanttwo-step
0
excitation pathwaywithlasers of 4nsduration. Theplasmaforms spontaneouslyand rapidly. The
2
rms width of the ion velocity distribution is determined by measuring laser-induced fluorescence

n (LIF)oftheions. ThemeasuredexcitationefficiencyiscomparedwithaMonte-Carlowavefunction
a calculation, and significant differences are observed. We discuss the conditions for blockaded Ryd-
J
bergexcitation andthesubsequentspatial orderingof Rydbergatom domains. Whiletheblockade

7 interaction is greater than the Rabi frequency in portions of the atomic sample, no evidence for
2 spatial ordering is observed.

]
h
I. INTRODUCTION regime [22, 29, 30].
p
-
m The Rydberg blockade [1–5] occurs when a laser ex- Achieving spatial order in the laboratory for mm-
o cites oneatomto aRydbergstate inthe presenceofsev- sized atomic samples requires careful manipulation of
at eral ground-state atoms. Under certain conditions, the the many-body wavefunction. The ground state of
. subsequent interactions between the Rydberg atom and the ordered Rydberg crystal has one excited atom sur-
s
c neighboring ground-state atoms shifts the energy levels rounded by severalatoms in the groundelectronic state.
i in such a way that none of the surrounding atoms can As discussed, for example, in Ref. [4], the many-
s
y be excited by the laser. This blockade effect occurs over body wavefunctionfor Nb blockadedatoms has the form
h a characteristic distance scale given by the details of the |Wi = (Nb)−1/2 Ni=b1|g1,g2,g3,...,ei,...gNi. The adi-
p atom-atom interaction. abatic transitionPto this low-energy and highly-ordered
[ In an atomic sample where the nearest-neighbor dis- state from one in which all atoms are initially in the
1 tance between atoms is much smaller than the blockade electronic ground state requires a shaped chirped pulse
v radius, the excitation blockade can lead to spatialorder- [6, 30]. However, even when the excitation pulse is not
9 ing of the Rydberg atoms in the gas [6–13]. A spatially- specifically tailored, blockading still occurs [31] and this
3 ordered atomic system has many potential applications, changes the spatial distribution of excited-state atoms
4
not only in massively parallelquantum logic, but also in [6].
7
probingthe behaviorofmany-bodysystems,engineering
0
. synthetic gauge fields, enhancing fusion in high-energy- Modifications in the initial nearest-neighbor distribu-
1
density plasmas,and generating high brightness charged tion in an ultracold neutral plasma can lead to a signifi-
0
particle beam sources [3–5, 14–16]. cant reduction in the resulting disorder-induced heating
6
The connection between dense Rydberg systems and [24]. This suggests that straight-forward excitation to
1
: plasma physics is very close. A number of experiments Rydberg states using ns-duration pulsed lasers [31], fol-
v
havereportedthatdenseRydbergsystemsspontaneously lowedbyrapidionization,couldleadtoanultracoldneu-
i
X convert into plasmas [17–24]. Although the initial atom tralplasmainwhichtheiontemperatureislowerthanin
r temperature can be a few mK, the subsequent ion tem- a plasma created by direct excitation to the continuum.
a perature is typically hundreds of times higher because
of unbalanced forces between the ions [11, 23, 25, 26]. In this paper, we explore the possibility of creating an
This process is called disorder-induced heating (DIH), ultracold neutral plasma with reduced temperature by
and it can severely limit the degree of strong coupling exciting laser-cooled calcium atoms in a MOT to Ryd-
in the plasma. A plasma generated from an initially or- berg states. The conditions under which blockading is
dered system would circumvent disorder-induced heat- expected to occur are presented. The Rydberg atom in-
ing, which is the largest source of heating in ultracold teractions lead to rapid ionization, as in Ref. [32, 33],
plasmas. The resulting ultracold system could become as well as ion heating. We report measurements of the
a robust platform for transport and kinetic studies near ionvelocitydistributionintheplasmaderivedfromthese
the plasma/solid interface [27], with interesting applica- interacting Rydberg atoms. While the blockade interac-
tions for warm dense matter experiments [28]. It may tionisgreaterthantheRabifrequencyinportionsofthe
be possibleto generateanorderedplasmasystemfroma atomic sample, no evidence for blockaded excitation is
coldRydberggasthatisexcitedintheRydbergblockade observed.
2
II. BLOCKADE DISCUSSION where e is the electron charge and is the electric field
2
E
from the 390 nm laser. For excitation to n = 40 and
Excellent treatments of the Rydberg blockade have a laser intensity of 108 mW/cm2, the Rabi frequency is
been reported in the literature [3–5]. The blockade en- Ω2 = 2π 300 MHz. As discussed in Ref. [4], when
×
ergy is there are Nb atoms in a blockade sphere, then the Rabi
frequency is increased by a factor of N1/2 and also by a
C b
U = 6, (1) coordinationnumberthatincludestheinfluenceofneigh-
6 r6 bors beyond the nearest one.
whereristhedistancebetweenground-stateatoms. The TheRabifrequencycanalsobewrittenintermsofthe
C coefficients have been calculated for the 4sns 1S Ry- laser intensity,
6
dberg series in calcium [34]. In atomic units, the coeffi-
I
cients are calculated using the expression Ω=2π ∆ν , (4)
× Nr2I
sat
C6 =n11 an2+bn+c , (2) where ∆ν = (2πτ)−1 is the natural linewidth, τ is the
N
(cid:0) (cid:1)
excited state lifetime, I is the laser intensity, and I is
wherenistheprincipalquantumnumberoftheRydberg sat
stateanda= 1.793 10−3,b=0.3190,andc= 1.338. the saturation intensity. A large Rabi frequency power-
− × − broadens the atomic transition so that the full-width at
This expression is valid for 30 n 70. Conversion
≤ ≤ half-maximum (FWHM) is,
from atomic units is accomplished using the expression
C (GHz µm6)=1.4448 10−19(a.u.). Foranatomsep-
ar6ationo·f2µm,excitatio×nton=45givesaninteraction δν =2π ∆ν I =√2Ω. (5)
× NrI
energy of 33 MHz. This energy is a strong function of sat
n, so exciting to n= 55 increases the interaction energy This power-broadened linewidth sets the time-scale for
by an order of magnitude. This energy also scales with the blockade. The assumption in all Rydberg blockade
density-squared. work is that the interaction energy is much greater than
The time-scale for Rydberg excitation depends on the Rabi frequency, or U /¯h Ω.
6
≫
laser intensity, principle quantum number, and den- As discussed previously, the interaction energy de-
sity. Similar to most other currentRydberg experiments pends on the nearest-neighbor distance. In our ther-
[22, 35, 36], we use a two-step process to excite Ryd- mal sample, these distances have a distribution. Con-
berg levels. Our experiment uses laser pulses at 423 and sequently, depending on the excitation parameters, por-
390 nm (see Fig. 1). The Rabi frequency for the 390 tionsoftheatomicsamplemaybeintheblockaderegime,
nmexcitation,the secondstepinourexperiment,canbe as discussed below.
calculated if the transition matrix element is known. In
calcium it is probably similar to the rubidium 5p ns
value [5], r =0.014 (50/n)3/2a . The Rabifrequ→ency III. NEAREST-NEIGHBOR DISTRIBUTION IN
0
h i × A MOT
is calculated as
Ω =e r /¯h, (3)
2 2 For a thermal gas at constant density, the nearest-
| | E h i
neighbordistributionisgivenbytheErlangdistribution,
a) b) r 2 r3
4sns1S
0 m P1(r)=3(cid:18)aws(cid:19) exp(cid:18)−a3ws(cid:19), (6)
n
093 W2 4p2P3/2 where aws =(3/4πn0)1/3 is the Wigner-Seitz radius and
4s4p1P1 l =2 D 4p2P1/2 mn sni0anisotfhethdeenfosirtmy. Inn(ra)M=OnT0,ewxhpe(−rert2h/e2σd2e)n,sitthyeisnGeaaruesst-
m 0 neighbor distribution changes. At small values of r, it
5
n 324 W1 mn 7 8 3d2D3/2 bhuastionneafralyllsthoeffsmamucehfomrmoreasslPo1w(lry).wHhoenwerve>r,σthebedciastursie-
= 93 the density falls off gradually and the average nearest-
1
4s21S l 4s2S neighbor distance increases.
0 1/2
In ultracold neutral plasmas, most of the disorder-
induced heating (DIH) comes from ions that are much
FIG. 1. a) Partial energy level diagram of our two-step Ry-
dberg excitation scheme in neutral Ca. Pulsed lasers at 423 closer to each other than the average distance. If
and390nmdrivethetransition fromthegroundstatetothe the nearest-neighbordistribution could be suppressedat
Rydberg level. b) Partial energy level diagram in Ca+. We short distances, the DIH temperature would be reduced
use a cw laser at 397 nm to excite the s−p transition and [24]. If the initial order matched the close-packed con-
measurefluorescenceatthissamewavelength. Alaserat850 figuration of a strongly-coupled plasma, DIH would be
nm is used to depopulatethe metastable state. eliminated [37].
3
broadened linewidth is 350 MHz, approximately equal
to the bandwidth of the laser. The corresponding Rabi
frequency for this transition is Ω =2π 250 MHz.
1 ×
The4p nstransitionisdrivenusingapulse-amplified
−
frequency-doubled ti:sapphire laser near 390 nm. An
AOMis alsoused in this laserbeam to turn the cw laser
on 100 ns before the pump laser arrives at the dye cell.
Aswiththe423nmlaser,thislaserisalsoaperturedand
imagedintotheMOTsothattheintensityisintherange
of 109 mW/cm2. The two lasers counterpropagate each
other in the MOT and arrivesimultaneously. The inten-
sity of this laser is adjusted so that the Rabi frequency
ranges from 1 to 300 MHz, similar to other ns-pulsed
experiments [38, 39].
Laser pulses with durations in the 1 µs range are
∼
FIG.2. Aplotofthenearest-neighbordistributionasafunc- typically used in blockade experiments. Unfortunately
tion distancebetween atoms,r,forarangeofpeakdensities, forus,the atomsinourMOTmoveontheµstime scale.
n0. Theverticallinesindicatethenearest-neighbordistances At a typical density of 3 1010 cm−3 and a tempera-
×
at which the U6 energy is equal to 300 MHz. The relative tureof1mK,theaveragetimebetweennearest-neighbor
numberofblockadedatomscanbedeterminedbyintegrating collisions is only 2 µs. This motion results in collisions,
thedistribution up to theblockade radius.
placing µs-duration pulsed laser experiments in Ca out-
side of the “frozen gas” assumption used in all blockade
experiments (see Fig. 1). Unless the atoms are much
Dependingontheexperimentalconditions,portionsof
colder or the atoms tightly confined to short distances,
the atomic cloud are found to be in a regime in which
ns-duration laser pulses are required.
blockadedexcitationis expected to occur. We derivethe
Rydberg excitation efficiency is measured using MOT
nearest-neighbor distribution in the MOT by generat-
loss measurements. A weak, resonant cw 423 nm laser
ing a three-dimensionalrandom-normaldistribution and
beam passes through the MOT. When the MOT is
computing the distance from each atom to its first near-
loaded, the transmission of this laser beam is typically
est neighbor. In Fig. 2 we plot this distribution for a
1%. When the MOT atoms are excited to Rydberg
few different peak MOT densities. Also shown in Fig. 2
states, they no longer interact with this laser beam and
areverticallinesthatindicatetheradiusatwhichtheU
6 the transmission increases. Using Beer’s law we are able
interactionenergyisequalto300MHzforarangeofprin-
to convert this transmission into atomic density. In a
ciple quantum numbers. This value is chosen because it
typical measurement, we measure the changes in trans-
matches the measured frequency width (FWHM) of our
mission of this probe laser beam as the 390 nm laser
laserpulses. Becausethe interactionenergyscalesasthe
frequency is scannedacrossthe Rydberg excitationreso-
nearest-neighbor distance to the sixth power, atoms to
nance. To avoidEITeffects,the probelaseristurnedoff
theleftoftheverticallinesshouldbestronglywithinthe
while the excitation lasers are on.
blockaded excitation regime. We therefore expect the
Theatomicspectroscopyisperformedbyoffset-locking
leading edge of the nearest-neighbor distribution to be
the lasers to a partially-stabilized frequency comb [40].
suppressed in these systems [24].
This provides long-term stability, accurate determina-
tions of the absolute frequencies, and convenient fre-
quency scanning of the lasers. The comb uses a pas-
IV. EXPERIMENTAL DETAILS
sively mode-locked ti:sapphire laser with a repetition
rate, f = 978MHz. Its spectrum is nominally Gaus-
rep
Calcium atoms in a thermal beam (T = 750 K) are sian, 35 nm FWHM, and centered at 815 nm. Without
slowed and captured into a MOT (T 0.001 K). The broadening,thespectrumgivesstrongbeatnoteswithall
∼
Rydberg atoms are excited using a two-step process, as of the cw lasers used in this experiment (>25 dB above
showninFig. 1. Thefirststepisnearly-resonantwiththe the technical noise, 30 kHz measurement bandwidth).
423nmlaser-coolingtransition,with∆=2π 150MHz. Onemode ofthe combisoffset-lockedtoa 780nmdiode
A cw laser beam at 423 nm is pulse-amplified×in a single laser that is itself locked to the 87Rb F = 2 F = 2/3
→
transverse-pumped dye cell. An AOM is used to turn cross-over transition. The offset lock feeds back to the
the cw laser beam on 100 ns before the pump laser ar- ti:sapphire laser cavity length. The absolute frequency
rives at the dye cell. The pump laser pulse width is 4 of one comb mode is therefore known with a precision
ns FWHM. The pulse-amplified 423 nm laser beam is of a few kHz. The repetition rate of the laser is not
expanded, apertured to a few mm diameter, attenuated, controlled. However repeated measurements of the rep-
andimagedintotheMOT.Theresultingintensityprofile etition rate in a 1-second measurement duration show
is relatively flat, with I/I = 100 so that the power- drifts of approximately 1 Hz/s. Therefore, counting the
sat
4
repetition rate during our experiments allows us to de- 0.7
100
termine laser frequencies with sub-MHz precision.
50
0.6
20
10
V. PULSED EXCITATION MEASUREMENTS 0.5 5
d
e
cit0.4
In Fig. 3 we show the fraction of MOT atoms ex- ex
lcaitseedr ftroeqtuheen4csy3.0Tsh1eSd0asttaatsehoawssaifnucnrcetaisoinngofexthcieta3t9io0nnams action 0.3
fr
Ω increases. For excitation to this level, we expect no
2 0.2
blockading to occur. The peak density in the MOT is
n0 =4 1010 cm−3. As the Ω2 increases, the excitation 0.1
×
fraction grows, and the line center is Stark shifted and
broadened. The signal-to-noise ratios in these data are 0
30 35 40 45 50 55 60 65 70
compromised by shot-to-shot fluctuations in the excita-
principle quantum number
tionlasers,densityfluctuationsintheMOT,andbytech-
nical noise in the strongly-attenuated probe laser beam.
FIG. 4. The fraction of MOT atoms excited to Rydberg
We have collected data like this for n = 30,40,50,60,
states as a function of the principle quantum number. The
and 70. As the excitation proceeds to greater values of legend indicates the peak intensity in the 390 nm laser pulse
n, the lines are significantly broadened even at low ex- in units of 107 W/cm2.
citation fractions. At n = 70, for example, the line is
broadened beyond 800 MHz.
InFig. 4weplotthepeakexcitationfractionasafunc-
tionofprinciplequantumnumberforarangeofdifferent
390nmlaserpowers. Forthehighestlaserpowers,theex-
citationfractionnevervariesfarfrom0.5. This indicates
thatthereisrelativelylittleionizationorotherlossonthe
time scale of the Rydberg excitation pulse. The highest
laser power probably power-broadens the Rydberg tran-
0.6 170 MHz
80 MHz
40 MHz
0.5 16 MHz
8 MHz
d0.4
e
cit
x
n e0.3
o FIG. 5. The calculated excitation fraction in the Rydberg
fracti0.2 sthtaeteprainftceirpltehqeulaanseturmpunlsuemsbaerre(o3v0ertofo7r0)aarnadngaeroafngvealoufes39o0f
nm laser intensities (2 to 100×107 mW/cm2). The greatest
0.1
excitation occurs when thelasers produceasingle π-rotation
in the wavefunction. This calculation was performed on res-
0 onance (∆=0) and averaged over 1000 runs(see Eq. 7).
-300 -200 -100 0 100 200 300
frequency (MHz)
FIG.3. Measurements ofthefraction ofMOT atomsexcited sition so that it exceeds the U6 energy. At higher values
to the 4s30s 1S state vs. the 390 nm laser frequency for a of n, the ns and (n 1)d states are only a few hundred
0
−
numberof different laser intensities. Thepeak density in the MHz apart, and the transitions are not well separated.
MOTisn0 =4×1010 cm−3. Theexcitedfractioniscalculate
Twofeaturesstandoutinthisfigure. Wewillconsider
based on the transmission of a weak probe laser beam that
the red trace for a laser intensity of 50 107 W/cm2.
passesthroughtheMOT,inresonancewiththe423nmMOT
×
transition. As the 390 nm Rydberg excitation laser intensity The excitation fraction increases with increasing n from
increases, agreaternumberofatomsareexcitedintotheRy- 30to40. Athighervaluesoftheprinciplequantumnum-
dbergstate,saturatingatroughly50%excitation. Increasing ber, the excitation fraction falls slowly. This behavior is
intensity also Stark shifts and broadens the transition. The also observed for most of the other intensities, although
legend indicates the Rabi frequency, Ω2/2π. For these mea- the value of n above which the excitation fraction falls
surements, Ω1 =2π×250 MHz. appears to be greater at lower intensities.
5
VI. MONTE-CARLO WAVEFUNCTION
40 0 µs 1 µs 2 µs 5 µs 10 µs
CALCULATION
30
s)
µ
To understand the excitation process, as well as the me (20
possible influence of blockading on the excitation dy- ti
namics, we have constructed a three-level model based 10
on the Monte-Carlo wave function (MCWF) method
0
[41, 42]. This method is appropriate for calculating
-150 0 150 -150 0 150 -150 0 150 -150 0 150 -150 0 150
excitation amplitudes in the presence of radiative de- frequency (MHz)
cay. We begin with a single-atom wavefunction ψ =
| i FIG.6. Acountourplotofthelaser-inducedfluorescencesig-
a(t) g + b(t) e + c(t) r where g , e , and r rep-
resen|tithe 4s1|1iS , 4s4p| i1P◦, and|4isn|si1S lev|elis and nal. The atoms are excited into the state n = 50. After a
0 1 0 delaytimerangingfrom0to10µs,the397nmprobelaseris
a(t),b(t), and c(t) are their time-dependent amplitudes.
rapidlyswitchedon. Foreachoftheseplots,thelaser-induced
The Schr¨odinger equation is used with a rotating-wave
fluorescence is measured as a function of time at a given 397
approximation to find the time-evolution of the eigen- nm laser frequency. Measurements are repeated for a range
state amplitudes. In the nth time interval dt, these am- of 397 nm laser detunings. A collection of measurements are
plitudes change according to then used to produce these countour plots. The 850 nm re-
pumplaserisusedtopreventatomsfromaccumulatinginthe
dcn =bn−1iΩ22dt metastable state.
dbn =an−1iΩ21dt+bn−1 −Γ2 −i∆ dt+cn−1iΩ22dt
dan =bn(cid:0)−1iΩ21dt, (cid:1) (7) resulting in loweroverallexcitation after the laserpulses
are over.
whereΓ=1/τ =(4.5ns)−1[43,44]. Thisisequivalentto These differences may be partly due to collective ex-
treating both transitions in a rotating frame, with each citation and interactions of the Rydberg levels, effects
frame rotatingindependently ofthe other. The Rydberg that are omitted from the simulation. However, other
state is assumed to be stable. factorsmayalsobeimportant. Intheexperiment,weob-
Decayoftheintermediate e stateiscalculatedproba- servesignificantshot-to-shotvariationinthelaserpower.
| i
bilistically. InthestandardMCWFmanner,wecalculate Thepulsedlaseramplifiersuseamulti-longitudinal-mode
a probability dp = b Γdt and compare it to a random Nd:YAG laser. The fast temporal structure in these
n n
| |
number ǫ generated with uniform probability between 0 pulses can produce broad wings in the spectral profile,
and 1. If ǫ<dp , then the state e has decayed and we whereas the simulation is performed on resonance for a
n
| i
set the amplitudes a,b, and c to 1,0, and 0 and proceed single frequency. Finally, interactions between the Ryd-
withthecalculation. Toensurepropernormalization,we berg atoms beyond collective excitation could be impor-
calculate (a 2+ b 2+ c 2)1/2 atevery time step and tant.
n n n
dividethis|int|othe|am| plit|ud|es. Becausedt Ω−1,Ω−1,
≪ 423 390
thisamplitudecorrectionissmallandisequivalenttothe
normalization method used in Refs. [41, 42]. VII. ION VELOCITY DISTRIBUTION
The calculated value of c(t∞)2 is plotted in Fig. 5. MEASUREMENTS
| |
Thiscorrespondstotheprobabilityoffindinganatomin
the Rydberg state after the laser pulses are over As ex-
After the Rydberg atoms are created, they sponta-
pected, the simulation shows the population in the Ry-
neously ionize. A recent study in Ref. [32] proposed
dberg state oscillating at the frequency 1 Ω2+Ω2 1/2 amany-atomionizationmechanism. Ina dense Rydberg
2 1 2
during the laser pulse. The greatest excit(cid:0)ation occ(cid:1)urs gas, the configuration with all individual atoms in the
whenathe pulseintensity anddipole momentproduce a well-defined Rydberg state is not necessarily an eigen-
single π-rotation. state ofthe many-bodysystem. The authorsofRef. [32]
ThesimulationinFig. 5qualitativelyreproducessome suggest that the excited Rydberg atoms make a series
features observed in the experiment. For example, it of transitions to nearby excited states and that some of
capturesthe low-amplitude excitationfor lowervaluesof these atoms eventually end up in the continuum. This
theprinciplequantumnumber,andincreasingexcitation state diffusion is predicted to be the major ionization
with n at a given laser intensity. However, the profiles mechanismwhenn=50atadensityof1011cm−3. Ifthe
in Fig. 4, which correspondto horizontalcuts acrossthe Rydberg atoms transitionfrom the initial Rydberg state
data in Fig. 5, depend differently on laserintensity. The to nearby states that are dipole-coupled, the mechanical
experimental data of Fig. 4 shows that excitation de- force on the atoms can collisionally ionize the atoms in
creases with lower laser power. The simulation data of the 100 ns time scale noted in their experiment. A re-
Fig. 5 shows that excitation increases with decreasing cent simulation of the experiment could not reproduce
laser intensity. In the simulation, this happens because the prompt ionization of the experiment [33]. However,
the higher intensities produce multiple Rabi oscillations, electroncollisionsandcollisionswithfastatomswerenot
6
included in the simulation. Those effects may boost the 700
ionization signal at early times. 0 µs
1 µs
A calculation in Ref. [45] suggests that the avalanche 600 2 µs
ionizationrateperatomatadensityof4 1010cm−3and 5 µs
a principle quantum number of 50 is onl×y 104 s−1. This 500 10 µs
is far too slow to explain ionization. Direct collisional z)
H
ionization of the Rydberg atoms due to thermal motion M400
occurs on the 1 µs time scale [46]. M (
∼ H300
The mechanical forces between Rydberg atoms has W
F
beendocumentedinanumberofpublications. Thishap-
200
penswhensomemechanismtransfersatomsfromtheini-
tial Rydberg state to some other state. This can occur
100
throughcollisions[47],interactionsatF¨orsterresonances
orcollisionalresonances[3,7,10,47],throughblackbody
0
radiation [48], or transitions induced using microwaves
0 5 10 15 20 25 30 35 40
[49–51]. When present, these mechanical forces will ac- time (µs)
celerate Rydberg atoms towards (or away from) one an-
other. If this Rydberg gas is converted into an ultracold FIG. 7. The measured FWHM of the data from Fig. 6. The
plasma, the ions will inherit the velocity distribution of lineshapes are complicated and asymmetric. However, the
the Rydberg atoms. FWHMgivessomeindicationoftheapproximatevelocitydis-
tribution. Atomicinteractionsgiverisetotheselargewidths.
In our experiment, similar to Ref. [32], we observe a
The contour lines correspond to 90%, 80%, etc., levels of the
rapid rise in the ion signal following excitation to Ry-
maximum fluorescence signal in thefigure.
dberg states. However, complete conversion of the Ry-
dberg system into a plasma seems to occur over a few
microseconds.
laser. Atthesetimes,the Rydbergatomshavebeencon-
Usinglaserspectroscopy,weprobetheRydbergsystem
vertedinto ionsordiffused into highangularmomentum
after it has been excited. We use a cw laser at 397 nm
states in which the 397 nm probe laser beam does not
to drive the 4s 4p transition, as in our previous ultra-
− significantly perturb the velocity distribution.
coldneutralplasmaexperiments[52]. WhentheRydberg
atomsareinstateswithlowangularmomentum,this“in- In Fig. 7 we measure the FWHM as a function of
nercore”excitationleadstoextremelyfastionization. A time for all of the data in Fig. 6. While it could be
recentstudyonsimilarstatesinSrshowedthatthewidth argued that the 0 and 1 µs data are strongly perturbed
of this auto-ionizing resonance is measured in THz [53], by the 397 nm laser, it appears that the longer delay
suggesting that autoionization occurs in less than one data are not. The width of the fluorescence signal rises
ps. The Rydberg atomis instantly convertedinto an ion to several hundred MHz, corresponding to velocities on
when the inner electronis excited. That ioninitially has the order of 200 m/s. This occurs with and without the
the same velocity as the Rydberg atom. The combined presence of the 397 nm laser. The nearly linear rise in
motion of the Rydberg atoms before ionization and also thefluorescencewidthindicatesthattheionacceleration
themotionoftheionsafterionizationbothcontributeto is approximately 4 107 m/s2.
×
the width of the laser-induced fluorescence signal at 397 The central question in this investigation is whether
nm. or not the excitation of the Rydberg atoms is blockaded
In Fig. 6 we present contour plots of the ion fluo- by the Rydberg-Rydberg interaction, and if that block-
rescence signal as a function of frequency and time. In aded excitation would lead to a spatial ordered Rydberg
these measurements we introduce a delay between the system. The primary manifestation of that blockading
timewhentheRydbergstatesareinitiallypopulatedand andorderingshouldbetheslowexpansionoftheplasma.
when the 397nmprobe laser turns on. This providesin- Data previously published by us on the expansion of ul-
sightintothetime-scalefortransferringatomsoutofthe tracold neutral plasmas shows characteristic post-DIH
initial Rydberg state by collisions or other mechanisms. broadeningofthevelocitydistributionofroughly2 107
Foreachofthe measurements,arepumplaserat850nm m/s2[23],dependingonelectrontemperature. This×value
is used to prevent population from accumulating in the issameorderofmagnitudeasthevaluederivedfromFig.
metastable d-state (see Fig. 1). 7. We therefore must conclude that the Rydberg block-
For time delays of 0 and 1 µs, the fluorescence is de- ade is likely not significant in these data.
pleted when the 397 nm laser is on resonance. In addi- It is possible that blockading and ordering is present
tion, the entire fluorescence signal vanishes in less than but that it is masked by some other effect. The plasma
10 µs. For these measurements, autoionization of Ry- expansion is driven by the electrons. Anything that
dberg atoms is the dominant loss mechanism when the heats the electrons will contribute to faster plasma ex-
laser is on resonance. At later delay times, the fluores- pansion. Energy-poolingcollisionsbetweenfreeelectrons
cence signal is less strongly perturbed by the 397 nm and excited-state ions and auto-ionization from the ex-
7
cited inner-shell electron, for example, could contribute that the initial Rydberg state is rapidly scrambled by
significantly to electron heating. interactionswithotherparticles. Thiswouldleadtolarge
mechanical forces, as mentioned previously, that could
produce ions rapidly.
VIII. CONCLUSION It would be better to excite these Rydberg atoms us-
ingalongerlaserpulse,perhaps50nsindurationwitha
We have explored evidences of blockaded Rydberg ex- smoothtemporalprofile. Suchanexcitationpulse would
citation of laser-cooled Ca atoms in a MOT using ns- place less stringent constraints on the Rabi frequency.
duration laser pulses. The energy scales set by the Rabi One could even imagine tailoring the frequency and in-
frequency and the U interactionseem to be appropriate tensity of such a laser pulse. However, all laser issues
6
for blockaded excitation and spatialordering in portions aside,theuncontrollednearest-neighbordistributionina
oftheatomsample. However,ourvelocitymeasurements MOTwouldundoubtedlycomplicatetheblockademech-
provide no indication that this effect is present. anism, producing an uncontrollednumber of Rabi cycles
The presence of charged particles in our MOT would and resulting in low excitation probability (see Fig. 5)
preventrealizationoftheblockade. Itispossiblethatthe and weak blockading.
transitionfromaRydbergatomtoanionoccursontime
scales shorter than the 4 ns laser pulse. Under certain
IX. ACKNOWLEDGEMENTS
conditions, we measure ions emitted from our MOT. We
have minimized these in the present work by applying a
constant electric field until 100 ns before the laser pulse This research is supported in part by the Air Force
arrives,effectivelysweepingallchargedparticlesfromthe Office of Scientific Research (Grant No. FA9950-12-
MOT when the Rydberg excitation occurs. 0308) and by the National Science Foundation (Grant
Itisalsopossiblethatblockadedexcitationoccurs,but No. PHY-1404488).
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