Table Of ContentLaser-Ranging Long Baseline Differential Atom Interferometers for Space
Sheng-wey Chiow, Jason Williams, Nan Yu∗
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109
(Dated: February 3, 2015)
Highsensitivitydifferentialatominterferometersarepromisingforprecisionmeasurementsinsci-
ence frontiers in space, including gravity field mapping for Earth science studies and gravitational
wave detection. We propose a new configuration of twin atom interferometers connected by a laser
ranging interferometer (LRI-AI) to provide precise information of the displacements between the
two AI reference mirrors and a means to phase-lock the two independent interferometer lasers over
long distances, thereby further enhancing the feasibility of long baseline differential atom interfer-
5 ometers. We show that a properly implemented LRI-AI can achieve equivalent functionality to
1 the conventional differential atom interferometer measurement system. LRI-AI isolates the laser
0 requirementsforatominterferometersandforopticalphasereadoutbetweendistantlocations,thus
2 enabling optimized allocation of available laser power within a limited physical size and resource
budget. A unique aspect of LRI-AI also enables extended dynamic range of differential signals and
n
the highest possible effective data rate.
a
J
PACSnumbers: 03.75.Dg,06.30.Gv,07.87.+v
1
3
Atom interferometry exploits the wave nature of neu-
]
h tralatoms,whichallowseachatomtointerferewithitself (a)!
p resulting in modulation of the probability of populating Apparatus
- a discrete state, associated with the environment that Mirror!
m AI 2! AI 1!
the atom traverses [1]. In a light-pulse atom interferom- !!
o AI laser!
eter (AI), an atomic matter wave is split, reflected, and
t
a recombinedbylaserpulses,andduringeachpulsetheop-
x x x
. M 2 1
s tical phase is registered by the atom. The output phase
c
of the AI, the probability distribution among possible (b)!
i
s states, depends on the optical phases and the evolution
y Platform 2 Platform 1
h of the atomic wave under the influences of environmen- Double mirror! Double mirror!
p tal perturbations, including electromagnetic fields, grav- AI 2! AI 1!
!! !!
[ ity, etc. Due to the inherent stability and identicality of AI2 laser! Laser ranging! AI1 laser!
atomicproperties,theaccuracyofanAIisfundamentally
1
v limitedbythestabilityoftheinterrogatinglaser,andthe x2 xM2 xM1 x1
7 understandingandcontroloftheenvironment. Thisisin
4 contrast to classical sensors, which drift over time and
0 possessbulkeffectsthatdependontheirshapeandcom-
0 FIG.1: (a)ConventionaldifferentialAIshostedinoneappa-
position. The repeatability and thorough understanding
0 ratus. xi is the position of the corresponding element. The
. of the atomic systems make them ideal candidates for instrumentbaselineL=x1−x2. (b)TwinAIslinkedwitha
2
precision measurements, including: local gravity accel- laserranginginterferometer(LRI-AI).Adoublemirrorhasa
0
eration g [2], photon recoil frequency (cid:126)/m and the fine reflective surface serving as the retroreflection mirror for AI
5
1 structure constant α [3], rotation [4], the gravitational on one side and serving as the retroreflection mirror for LRI
on the other side.
: constant G [5, 6], etc. The power of AI-based precision
v
measurements is illustrated in Ref [2]: An AI gravimeter
i
X notonlysurpassestheshort-termsensitivityofastate-of-
r the-art classical falling corner cube gravimeter, but also largely common to the two AIs, thanks to the relatively
a
agrees with global/regional gravity models over 4 years, short propagation delay for a laser pulse to go from one
thusrestrictinglocalLorentzvarianceingravityandelec- AItotheother[11]. Commonmodenoisesuppressionof
tromagnetism to unprecedented levels. vibrationsisdemonstratedtoexceed140dB[12]. Differ-
The applicability of atom interferometry is further ex- entialmeasurementsallowinstrumentsensitivitybeyond
tended by a widely used technique, differential measure- theabilitiesofsystematicerrorreductions. Inparticular,
ments between two simultaneous AIs [7–10] as depicted AI gravity gradiometers [5, 6, 10, 13] are constructed for
in Fig. 1(a). In this scheme, two AIs are interrogated by terrestrialandspaceorientedapplications. Furthermore,
a common laser, using either the same or different spec- spacebornegravitationalwavedetectionusingdifferential
tralcomponentsofthebeam. Thevibrationsofopticsin AIs are proposed for frequency bands and sensitivities
the laser beam path, as well as the laser phase noise, are unachievable on Earth [14–19].
2
Here we propose an alternative approach for differen- may be a concern [23, 24]. Larger optics lead to larger
tial AI measurements, which further enhances the fea- optical and electrical power requirements, which lead to
sibility of long baseline differential AIs. As depicted in much heavier payload and an astronomical price tag for
Fig. 1(b), instead of a common interrogation laser for ambitiousscientificexplorations. Ontheotherhand,the
both AIs, twin local AIs driven by independent lasers AI laser beams in LRI-AI can be tailored for the local
arelinkedwitha laserranginginterferometer(LRI)[20]. atomicsamplesize. Higherintensityforlargemomentum
AsimilarconceptusingindependentAIforgravitational transfer beam splitters will be more affordable in LRI-
wave detection was previously proposed [21]. Concep- AI[25–29]. ThelaserrequirementsforLRIarelessstrin-
tually, LRI-AI uses phase-locked lasers to replace the gentthanthoseforAI,particularlyinthathighintensity
common laser in the conventional differential AI con- is not necessary and that wavefront aberrations do not
figuration, thus the fundamental measurement concept significantly impact LRI operations. Furthermore, the
is the same for both: atomic motions are interrogated relative Doppler shift between distant spacecrafts could
by a coherent classical light field. In the conventional be on the order of MHz [20], which prevents simulta-
configuration, the readout phase of a Mach-Zehnder AI neous operation of distant AIs while LRI-AI would have
is φ = k (x¨ −x¨ )T2 + φ , where i = (1,2), k localAIrelativelystationarytothespacecraft. Thelarge
i eff i Mi Li eff
the effective wavenumber, T the pulse separation time, Doppler shifts will be removed by heterodyne measure-
M and L indicate mechanical reference points and ments in LRI.
i i
AI lasers. Differential acceleration experienced by dis- Recent technology advancements of laser ranging in-
tant atoms is revealed by taking the phase difference: terferometry have made LRI-AI feasible [20]. Theoret-
φ1−φ2 =keff(x¨1−x¨2)T2+(φL1−φL2)[7,8],wherethe ically, δφ (cid:39) 0.001 for an AI with 106 signal atoms
mechanical motions of reference points are removed As- for a projection noise limited phase measurement. As-
suming that the noise o√f each AI is atom number shot suming keff = 4π/780 nm, the acceleration sensitivity
noi√se limited, δφ ∝ 1/ N, the combined uncertainty is 6.21 × 10−11/T2 m/s2 per shot, where T is in sec-
is 2×δφ per shot. In LRI-AI, the readout phase of onds. Practically, terrestrial AIs with laser cooled atom
each AI is ψi = keff(x¨i−x¨Mi)T2. Neglecting propa- sources (thermal AI) typically have T < 1 s and rep-
gation delay, LRI provides L¨ = x¨M1 −x¨M2 to the de- etition rates ∼ 0.5 Hz while achieving fringe contrast
sired accuracy. The combination ψ1 −ψ2 +keffL¨T2 = ≤ 0.5. State-of-the-art√AI accelerometers have sensitiv-
keff(x¨1−x¨2)T2+(φL1−φL2). A proper phase locking ities of ∼ 10−7 m/s2/ Hz√[2], whereas AI gradiome-
between the two AI lasers with the LRI lasers can elim- ters reach 3 × 10−8 m/s2/ Hz in differential acceler-
inate the laser phase noise difference, yielding identical ation (with T = 160 ms) [6]. Using ultracold atoms
differential phase to that of the conventional configura- from a Bose-Einstein condensate atom source (BEC AI)
√
tionwhenthepropagationdelayisignored. Intheregime and T = 1.15 s, a sensitivity of 3 × 10−10 m/s2/ Hz
wherethenoisecontributionofLRIisnegligible,thecom- has been demonstrated [30]. On the other hand, LRI
bined uncertainty is the quadrature sum of individual has also been demonstrated in lab, and will be imple-
AIs, thus identical to that of the conventional configu- mentedintheGravityRecoveryandClimateExperiment
ration. With very long baselines for gravitational wave follow-on mission (GRACE-FO), scheduled for launch in
detection, the time delayed interferometer technique can 2017[20]. Theperformanceofthisimplementationisex-
√
be used [22]. pected to reach 80 nm/ Hz (in the frequency range of
LRI-AI is advantageous over the conventional configu- 2 mHz <f < 100 mHz) over a distance up to 270 km,
ration in several aspects. As the instrument baseline L corresponding to an acceleration nois√e with power spec-
increases for demanding sensitivity requirements, asso- traldensityof 3.16×10−6 m/s2 (f2/ Hz). Thus, asim-
ciated technical challenges may become prohibitively ex- ilar LRI system would support twin thermal AIs at time
pensivetoovercomefortheconventionalconfiguration,if scales longer than 10 s, and would support twin BEC
atallpossible. Forinstance,asdiscussedindetailin[17], AIs at time scales longer than 100 s. Shorter time scales
theRayleighrangez =πw2/λofaGaussianbeamwith can be expected with more advanced LRIs, such as that
R 0
waistw andwavelengthλshouldbelargerthanLtoef- demonstrated for the LISA mission with 1000× better
0
ficiently deliver optical power from one site to the other. performance [20].
√ √
To support larger beams of waist ∼ 2 w ∝ L, larger As an example, the combination of a terrestrial state-
0
optics with vanishing curvature are required. To main- of-the-art thermal AI and the GRACE-FO LRI with
tainthesameintensityatz forAIs,therequiredoptical a baseline of 200 km will have a gravity gradient sen-
R √
powerisproportionaltoL. Moreover,ifthetwinAIsare sitivity of 150 µE/ Hz, where E is E¨otv¨os=10−9/s2.
hosted inside one single vacuum chamber, the baseline The achievable sensitivity can be further enhanced with
is limited to (cid:28) 1 km even with the help of a boom sys- longer T available under microgravity. This gravity gra-
tem[18];iftheAIsarehousedindifferentspacecraftsand diometer measurement concept can build on the well
the common laser passes through free space and addi- developed LRI concepts, and could be incorporated in
tionaloptics, staticandstochastic wavefront aberrations GRACE-likemissionsinthenearfuture. TheAIoneach
3
Ranging
!!
AI 2!
AI2 laser! laser!
MA! MA! !!
!!
Ranging AI1 laser!
AI 1!
laser! !!
Platform 2! Phasemeter!
Platform 1!
and tilt sensor!
FIG. 2: Schematic of LRI-AI with key components. Local forces measured by a mechanical accelerometer (MA) are used to
feedbackontheAIlaserphasetocompensateforexcessiveexcursionsandmaintaintheAIphasenearzero, wheresensitivity
is optimized.
platform will serve as an ideal drag-free reference in the AI sensors, with greatly extended dynamic range intrin-
presence of spacecraft self-gravity gradient when the in- sictostateoftheartMAs. TheAIdifferentialphasecan
terrogationtimeiskeptrelativelyshort,whichisessential be easily calculated while LRI provides satelite ranging
for gravity measurement missions. The performance of with high stability and sensitivity to accommodate shot-
GRACE, for instance, relies on the on-board accelerom- to-shot variation of differential signal, including Doppler
eters, which are sensitive to influences on the spacecraft shifts on the order of MHz. This scheme is easily imple-
other than gravity. The acceleration information is then mentable with local AIs using independent lasers, even
used to calculate the gravity distribution that yields the under harsh conditions such as sign changing of the rel-
spacecraft orbit best matching the orbit observed with ative velocity.
the positioning systems. Uncertainty in the scale factor In summary, we propose a new method for long base-
calibration and variations are issues associated with the line atom interferometers with laser ranging in space
mechanical accelerometers, whereas unprecedented sta- (LRI-AI). This method adapts the state-of-the-art ac-
bility has been demonstrated with AI [2, 4]. curate atomic accelerometer technology and the techni-
cal advancement of laser ranging interferometer, allow-
Current methods of differential phase extraction be-
ing > 100 km baseline differential AIs with low optical
tween AIs rely on the constancy of the phase differ-
power and a compact apparatus. With the assistance of
ence [7, 8] relative to the duration of data acquisition.
mechanical accelerometers to keep the AIs operating at
Thisrequirementreducesthespatial-temporalresolution
their most sensitive phase points, LRI-AI exhibits large
of an instrument in a dynamic environment such as in
dynamic range, fast data extraction, and low aliasing for
low Earth orbit, where high frequency signals behave as
high resolution spatial-temporal mapping. This method
noiseindataprocessing(aliasing), potentiallyincreasing
will be applicable in atom interferometer based space-
the instrument noise budget and thus impacting instru-
borne gravity measurements as well as in gravitational
mentsensitivity. ThesituationinLRI-AImayappearto
wave detection.
be worse in that the phase difference between AIs also
This work was carried out at the Jet Propulsion Lab-
depends on the LRI phase, which could vary while the
oratory, California Institute of Technology, under a con-
acceleration difference between two locations is station-
tract withthe NationalAeronautics andSpace Adminis-
ary. On the contrary, a mitigation unique to LRI-AI
tration. (cid:13)c 2015CaliforniaInstituteofTechnology. Gov-
greatlyenhancestheusefuldatarate(Fig.2): Eachlocal
ernment sponsorship acknowledged.
AI is operated near a phase zero-crossing (equal proba-
bility between two output ports) by controlling the AI
beam splitter phase based on the reading of a mechani-
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