Fabrication of a centimeter-long cavity on a nanofiber for cavity QED

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by  Jameesh Keloth

Fabrication of a centimeter-long cavity on a nanofiber for cavity QED
Jameesh Keloth, K. P. Nayak, and K. Hakuta
Wereport thefabrication of a1.2 cm long cavitydirectly on ananofiberusingfemtosecond laser
ablation. Thecavitymodeswithfinessevalueintherange200-400canstillmaintainthetransmission
between40-60%,whichcanenable“strong-coupling”regimeofcavityQEDforasingleatomtrapped
200 nm away from the fiber surface. For such cavity modes, we estimate the one-pass intra-cavity
transmission to be 99.53%. Other cavity modes, which can enable high cooperativity in the range
3-10, show transmission over 60-85% and are suitable for fiber-based single photon sources and
quantumnonlinear optics in the“Purcell”regime.
7
Efficient quantum state transfer between single pho- spectively,whereη isthechannelingefficiencyofsponta-
1
tons and single atom is a key challenge towards real- neous emission of atom into the nanofiber guided modes
0
2 ization of quantum networks [1]. Interaction of a sin- without a cavity, γ is the atomic spontaneous emission
gle atom with strongly confined photons in an optical rate near the nanofiber, c is the speed of light in vac-
n
cavity leading to cavity QED effects, is a promising ap- uum, L is the optical length of the cavity and F is
a
J proach to realize a quantum interface [1–3]. A crucial the finesse of the cavity mode. From this one can get,
4 requirement to achieve strong interaction between single C = (2g0)2/(κγ0) 4ηF/π. One should notice that the
≃
2 photon and single atom, is that the single atom coop- C is independent of L and mainly depends on F and
erativity parameter C = (2g0)2/(κγ0) >> 1, where 2g0 the transverse confinement of the optical mode through
] is the single photon Rabi frequency, κ is the cavity de- η. The effective mode waist of the nanofiber or other
h
p cay rate (linewidth) and γ0 is the atomic spontaneous nanophotonic structures can be less than 1 µm which is
- emission rate in vacuum. Even with C >> 1, there are one order smaller comparedto the typical mode waistof
nt tworegimeswithdifferentdynamics,a)“Purcell”regime, 10 - 30 µm for free space FP cavities. As a result high
a when κ>2g0,γ0 andb) “strong-coupling”regime,when cooperativity can be achieved even for moderate finesse
u 2g0 > κ,γ0. The “strong-coupling” regime has been of50-100. Furthermoreincaseofnanofibercavitiesone
q investigated using free-space Fabry-Perot (FP) cavities, can independently control the cavity length to reach the
[
wherethecoherentquantumphenomenalikesingle-atom “strong-coupling”regimesincetheκvaluereducesfaster

1 lasing and vacuum Rabi oscillations have been demon- than the 2g0 value as the cavity length increases.
v strated[3–5]. However,itrequiresextremelyhighfinesse
9 of0.3to0.5million,whichistechnicallychallenging. Al- Fabrication of cavity structures on the nanofiber us-
1 ing the focused ion beam milling has been demonstrated
though high quality mirrors with transmission and scat-
7 [11]. Also fabrication of the photonic crystal nanofiber
tering loss less than 2 ppm has been reported, but the
6 (PhCN) cavity using the femtosecond laser ablation has
overall cavity transmission may drop to 10-20% [3, 6].
0
already been demonstrated [12, 13]. A composite pho-
. Followingthedevelopmentoffree-spaceFPcavities,var-
1 tonic crystal nanofiber cavity is also demonstrated by
ious designs of nanophotonic cavities have also been de-
0 mounting a nanofiber on a nanofabricatedgrating struc-
velopedandinvestigated. Inparticular,the designs have
7
ture and using single quantum dot on such a cavity,
1 focusedonthe“Purcell”regime,forapplicationslikesin-
Purcell enhancement factor of 7 has been demonstrated
: glephotongeneration,singlephotonswitchingandquan-
v [14, 15]. In the abovecases,the cavity is formeddirectly
tumnonlinearoptics,wherehightransmissionisessential
i onthe nanofiber and designedfor operationin “Purcell”
X [3, 7].
regime with high transmission of up to 80%. The cav-
r
a In the vision of a quantum network, efficient integra- ity lengths ranged from 30 µm to few mm, depending
tion of the quantum interface to the existing fiber net- onthe cavitydesignandmainlylimitedbythe nanofiber
workisalsoanessentialrequirement. Inthiscontext,op- length of few mm. On the other hand, extremely long
tical nanofiber based cavities offer a flexible alternative nanofibercavitieswithcavitylengthof10-33cmarealso
platform [8]. The nanofiber is the subwavelength diam- realized by splicing two conventional single mode fiber
eter waist of a tapered single mode optical fiber. Using Bragg gratings to the tapered fiber [16, 17]. In this type
adiabatic tapering condition [9], efficient mode coupling ofcavities,thepresenceofthetaperedsectionwithinthe
tonanofiberregioncanberealized[10],enablingefficient cavity may induce intra-cavity loss and limit the achiev-
integration to fiber networks. Strong transverse confine- ablefinesseandon-resonancetransmission. Theone-pass
ment of guided fields down to wavelength scale can be intra-cavitytransmissionreportedinref. [16]and[17]are
realized in the nanofiber. Moreover a major part of the 98.3% and 94%, respectively. Hence for a finesse in the
guidedfieldpropagatesoutsidethefiberenablinginterac- range 50 - 100 the total cavity transmission may reduce
tionwiththesurroundingmedium. Inordertogetinsight to 10% in ref. [16] and below 5% in ref. [17]. Neverthe-
abouttheinteractiondynamicsinananofiberbasedcav- less, using such extremely long nanofiber cavity, strong-
ity we follow the formalism developed in ref. [8]. Based couplingbetweensingletrappedCs-atomsandthecavity
onthe formalism,2g0 =2pηγc/Landκ=πc/(FL),re- guided photons have been demonstrated [17].
2
a) Nanofiber
PhCN
b) Y X
Z
c) 1 µm
2.0 0.20
m]
µ m]
eter [1.5 PhCN1 0.16 er [µ
m et
a 0.12 m
Di a
r 1.0 Di
ofibe PhCN2 0.08 ater
an Cr
N0.5 0.04
-10 -8 -6 -4 -2 0 2 4 6 8 10
Length [mm]
FIG. 1. (a) Schematic diagram of the long nanofiber cavity.
(b) SEM image of a typical fabricated PhCN sample. (c)
Diameterprofilesofthenanofiber(bluecircles)andthenano-
craters(greencircles)fabricatedonit. Theredcurvesarethe
Gaussianfittothenano-craterprofiles. Thebluelineisguide FIG. 2. Transmission (black lines) and reflection (red lines)
to theeyes. spectra of the nanofiber after the fabrication of the (a) first
and (b) second PhCNs. The spectra are measured for one of
theprincipal polarizations (X-pol).
Inthisletter,wereportthefabricationofacentimeter-
long cavity directly on the nanofiber, which can operate
mentthelinearlyincreasinghot-zonetechnique[18]. The
both in “Purcell” and “strong-coupling” regimes of cav-
profile of the tapered fiber and the pulling parameters
ity QED. We demonstrate the fabrication of a 1.7 cm
are designed based on the adiabatic tapering guidelines
long nanofiber with highly uniform diameter of 500 2
detailed in ref. [9, 18]. By optimizing the parameters
±
nm over the entire length and maintaining high trans-
we have realized >99% transmission for tapered fibers
mission of >99%, which is a crucial requirement for this
with a total length of 7 to 8 cm, with a nanofiber waist
approach. Furthermore, we fabricate two photonic crys-
diameter of 500 nm and waist length of 1.5 to 2.5 cm.
tal structures separated by 1.2 cm on such a nanofiber
The uniformity of the diameter over the entire length
using femtosecond laser ablation, thus forming a long
of the nanofiber is 2 nm which is measured using a
nanofiber cavity. The cavity modes with finesse value nondestructive and ±in situ method detailed in ref. [19].
in the range 200-400 can still maintain the transmission
Thephotoniccrystalstructuresarefabricatedatthetwo
between 40-60%, enabling “strong-coupling” regime for
endsofthenanofiberusingthefemtosecondlaserablation
a single atom trapped 200 nm away from the fiber sur-
[12, 13], thus forming a long nanofiber cavity. The scan-
face [8]. For such cavity modes, we estimate the one-
ning electron microscope image of a typical part of the
pass intra-cavity transmission to be 99.53%. Other cav-
PhCN is shown in Fig. 1(b). One can see that periodic
ity modes, which can enable high cooperativity in the
nano-crater structures with a period of 350 nm are fab-
range 3-10,show transmission over 60-85%and are suit-
ricated on the nanofiber [12, 13]. Figure 1(c) shows the
ableforquantumnonlinearopticsinthe“Purcell”regime.
diameter profile of a long nanofiber cavity whose optical
Moreover, placing solid-state quantum emitters directly
properties are discussed in the following paragraphs. It
on the nanofiber surface such cooperativity will be fur-
shows the diameter profile of the nanofiber (blue circles)
ther enhanced by a factor of 5, which will be promising
and that of the nano-craters (green circles) fabricated
for fiber-based single photon sources.
on it. The nanofiber diameter is 500 nm and it is uni-
Figure 1(a) shows the schematic diagram of the form over a length of 1.7 cm. The two PhC structures
nanofibercavity. Thenanofiberisfabricatedbytapering (indicated as PhCN1 and PhCN2) are fabricated on the
a standard single mode optical fiber using heat-and-pull nanofiber with a separation of 1.2 cm. The PhCN1 is
technique [18]. The nanofiber is located at the waist of fabricated first and the PhCN2 is fabricated later. Each
thetaperedopticalfiber. Inordertoextendthenanofiber PhCN structure consists of thousands of periodic nano-
lengthfromfewmillimeterstofewcentimeters,weimple- craters[12,13]. Thediameterprofilesofthenano-craters
3
showapeak-likestructure. Thediametersatthepeakof
the profiles for the PhCN1 and PhCN2 are 140 nm and
190 nm, respectively. The red curves show the Gaus-
sianfits tothe diameterprofilesyieldingthe 1/e2-widths
of 0.9 mm and 1.7 mm for the PhCN1 and PhCN2, re-
spectively. Thissuggeststhatthesecondfabricationwas
stronger than the first one.
The transmission and reflection spectra of the long
nanofiber cavity are measured using a tunable, narrow
linewidth diode laser (Newport TLB6700). The laser is
coupled to the tapered fiber through a 99:1 fiber-inline
beam splitter. The input light is launched through the
1% port and the transmission is measured after the ta-
pered fiber, whereas the reflection is measured through
the 99% port in the reverse direction. The spectra are
recorded by monitoring the power in the transmission
and reflection ports using photodiodes while the laser
frequency is being scanned. The polarization control is
achievedusing a fiber-inline polarizer before the tapered
fiber. Figure 2(a) shows the transmission (black curve)
and reflection (red curve) spectra after the fabrication
of the PhCN1 for the polarization perpendicular to the
nano-crater faces (X-pol). One can see that the stop-
band extends over 845 nm to 848 nm, where the light is
strongly reflected back. Also one can notice that sharp
cavity modes appear in the red-side of the stopband.
The mode spacing is 95.5GHz correspondingto a cavity
length of 1.3 mm. As discussed in the ref. [12, 13], those
cavity modes are due to the apodized index variation
along the PhCN1. Figure 2(b) shows the transmission
(black curve)and reflection(red curve) spectra after the
FIG. 3. (a) A typical part of the transmission (black curve)
fabricationofboththe PhCN1andPhCN2. One cansee
andreflection(redcurve)spectraofthelongnanofibercavity
that the width of the stopband increased and extends forX-pol,showingperiodicallyspacedcavitymodes. (b)The
over 844 nm to 850 nm. Moreover many closely spaced transmission(blackcircles)andreflection(redcircles)spectra
cavity modes appeared. This suggests that the second for four typical cavity modes (i-iv) shown individually. The
fabricationwasstrongerandconfirmsproperoverlapbe- green and blue curvesare thecorresponding Lorentzian fits.
tween the stopbands of PhCN1 and PhCN2 to form a
long nanofiber cavity.
3(b). Thedataforthemeasuredtransmissionandreflec-
In order to properly resolve the cavity modes and
tionspectrafor the cavitymodes areshowninblackand
precise normalization of the on-resonance transmission
redcircles,respectively. The greenandblue curvesshow
and reflection values, we use a CW Ti-sapphire laser
the Lorentzian fits. The linewidths (κ) for the modes
source (MBR-110, Coherent Inc.). In this measurement
marked as i, ii, iii and iv are 59, 41, 33 and 27 MHz
the laser frequency is locked to a reference cavity and
corresponding to the finesse (F = ∆ν /κ) values of
the linewidth is 100 kHz. The spectra are recorded by FSR
175, 252, 314 and 384, respectively. One can notice that
monitoring the power in the transmission and reflection
the on-resonance transmission (T0) and reflection (R0)
ports while stretching the tapered fiber. The details of
is increasing and decreasing, respectively as the cavity
such a technique was reported in ref.[13]. Although we
linewidth is increased.
chose this method to be more reliable, we must mention
The amplitudes of the field transmission (t) and re-
that the spectra measured using laser frequency scan-
flection (r) of a two-sided cavity can be formulated [20]
ningtechniqueyieldedsimilarresultswithonlymarginal
as
differences. A typical part of the transmission (black
curve) and reflection (red curve) spectra for X-pol is
shown in Fig. 3(a). One can see periodically spaced √κ1κ2 21(κ1 κ2 κs) i∆̟
t= ; r= − − − (1)
sharpcavitymodes. Themodespacing(∆ν )is10.36
FSR κ/2+i∆̟ κ/2+i∆̟
GHz. Fromthe∆ν valueweestimateacavitylength
FSR
(l = L/n = c/(2n ∆ν )) of 1.2 cm, where n where∆̟ isthe detuningbetweenthe laserfrequency
eff eff FSR eff
( 1.2)istheeffectiveindexofthenanofiberguidedmode. andthe cavityresonance, κ is the intra-cavityloss rate,
s
≃
Four typicalcavity modes are shownindividually in Fig. κ1 and κ2 are the coupling rates of the input and out-
4
a) 1.0 thetotaloutcouplingrate(2κ )andtheintra-cavityloss
c
rate (κ ) balance each other and one can get κ =κ/2.
s s
er0.8 Figure 4(a) shows the T0 (blue circles) and R0 (red
w
o circles) values for the selected cavity modes (along with
P0.6 the modes showninFig. 3(b)) plotted againstthe corre-
d T
e 0 sponding κ values. In the selection process we have cho-
aliz0.4 R0 sfoerntthheeccoarvrietyspmonoddiensgthκavtahluavese.thTehheigbhlueestatnrdanrsemdislsinioens
m
r0.2 are the fits using Eq. 2. From the fits we estimate the
o
N lowestκs valuetobe15 1MHz. Alsoonecanclearlysee
±
0.0 fromtheplotthattheT0 andR0 valuesareequalaround
50 100 150 200 30 MHz. From this κs value, we estimate the one-pass
intra-cavity transmission to be 99.53%. We have fabri-
κ [MHz]
cated severalcavitysamples and measuredthe lowestκ
s
b) Cooperativity (C)
value tobe inthe range15-20MHz. Thissuggeststhat
5 10 15 20 25
thefabricationprocessisreproducible. Wemustmention
250
thatwe havealsomeasuredthe cavity characteristicsfor
Measured κ
theorthogonalpolarization(Y-pol). We havefoundthat
200 Estimated 2g0 the cavity transmissionfor Y-pol is smaller comparedto
the X-pol, resulting in higher κ value.
s
] 150
z Based on the optical characteristics of the cavity we
H
M nowestimatethepotentialofthecavityinthecontextof
[ 100 cavity QED and quantum information application. Fig-
ure4(b)summariesthemeasuredκvaluescorresponding
50 totheF values. TheestimatedC and2g0 valuesarealso
shown assuming a single Cs-atom trapped 200 nm away
from the fiber surface [8]. This shows that for the mea-
100 200 300 400 500
sured cavity modes we can achieve high cooperativity
Finesse (F) ranging from 3 to 25. For cavity modes having κ values
smallerthan50MHz(i.e. finesseintherange200to400),
”strong-coupling” regime can be realized. As shown in
FIG. 4. (a) The measured on-resonance transmission, T0 Fig. 4(a), the on-resonance transmission for such cavity
(blue circles) and reflection, R0 (red circles) values vs the modescanbeashighas40%to60%. Ontheotherhand,
cavity linewidths (κ) for typical cavity modes. The blue and forthe cavitymodes havingκ valuesbetween50MHz to
red lines are the fits using Eq. 2. (b) The black circles show
170MHz,theon-resonancetransmissionrangefrom60%
the measured cavity linewidths (κ) vs the finesse (F) values
to 85%, while maintaining a cooperativity of 3-10. We
for the typical cavity modes. The green line is a fit showing
must mention that using solid-state quantum emitters
the inverse relation. The red line shows the estimated single
like quantum dot or color centers in nanodiamonds, the
photon Rabi frequency (2g0), assuming a Cs-atom trapped
200 nm away from the fiber surface. The corresponding sin- emitter can be placed directly on the nanofiber surface
gle atom cooperativity (C) is shown in the top axis. leading to much higher cooperativity in the range 15-
50 [8]. Hence such cavity modes can be implemented for
fiber-basedsinglephotonsourcesandquantumnonlinear
optics in ”Purcell” regime.
put side mirrors, respectively and κ = κ1 +κ2 +κs is
In conclusion, we have demonstrated the fabrication
the cavity linewidth. The power transmission (T) and
2 of a 1.7 cm long nanofiber with highly uniform diameter
reflection (R) from the cavity are given by T = t and
2 | | of 500 2 nm over the entire length and maintaining
R = |r| . Assuming a symmetric cavity (κ1 = κ2 = κc) high tra±nsmission of >99%. Furthermore, we fabricate
the on-resonance (∆̟ = 0) transmission and reflection
two photonic crystal structures separated by 1.2 cm on
can be written as
such a nanofiber using femtosecond laser ablation, thus
formingacentimeter-longnanofibercavity. Thehighop-
ticalqualityofsuchacavityshowspromisingavenuesfor
2
T0 =(cid:12)(cid:12)(cid:12)(cid:12)2κκc(cid:12)(cid:12)(cid:12)(cid:12) =(cid:12)(cid:12)(cid:12)1− κκs(cid:12)(cid:12)(cid:12)2; R0 =(cid:12)(cid:12)(cid:12)κκs(cid:12)(cid:12)(cid:12)2. (2) fibTerh-ibsasweodrkquwanatsusmupinptoerrtfeadcebayndthseinJgalepapnhoStocniensoceuracnesd.
TechnologyAgency(JST)asoneoftheStrategicInnova-
From the above equation it is clear that the T0 and R0 tion projects. KPN acknowledges support from a grant-
valueswillincreaseanddecrease,respectivelyastheκin- in-aid for scientific research (Grant no. 15H05462) from
creases. Moreover,when the T0 andR0 values areequal, the Japan Society for the Promotion of Science (JSPS).
5
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