Table Of ContentEfficient all-optical switching using slow light within a hollow fiber
M. Bajcsy,1 S. Hofferberth,1 V. Balic,1 T. Peyronel,2 M. Hafezi,1 A. S. Zibrov,1 V. Vuletic,2 and M.D. Lukin1
1Harvard-MIT Center for Ultracold Atoms, Department of Physics, Harvard University, Cambridge, MA 02138
2Harvard-MIT Center for Ultracold Atoms, Department of Physics, MIT, Cambridge, MA 02139
(Dated: January 3, 2009)
We demonstrate a fiber-optical switch that is activated at tiny energies corresponding to few
hundredoptical photonsper pulse. This is achieved bysimultaneously confining both photons and
asmalllaser-cooledensembleofatomsinsidethemicroscopichollowcoreofasingle-modephotonic-
crystal fiber and using quantum optical techniques for generating slow light propagation and large
nonlinear interaction between light beams.
PACSnumbers:
9
0
0
In analogy with an electronic transistor, an all-optical wavemixing[16],aswellasobservationsofEIT[17]. Re-
2
switch is a device in which one light beam can fully con- cently,bothroom-temperatureandultra-coldatomshave
n
trol another. Realization of efficient all-optical switches successfully been loaded into PCFs [18, 19, 20, 21] and
a
J is along-standinggoalin opticalscience andengineering observations of EIT with less than a micro-Watt control
[1]. If integrated with modern fiber-optical technologies, field have been reported [18, 21].
3
suchdevicesmayhaveimportantapplicationsforoptical Ourapparatus(Fig. 1a)makesuseofa3cm-longpiece
] communication and computation in telecommunication ofsingle-modehollow-corePCFverticallymountedinside
h
networks. Optical switches operating at a fundamental an ultra-high vacuum chamber. A laser cooled cloud of
p
- limit of one photon per switching event would further 87Rb atoms is collected into a magneto-optical trap, fo-
nt enable the realizationof key protocols fromquantum in- cused with a magnetic guide, and loadedinto the hollow
a formation science [2]. coreofthePCF.Onceinside,theatomsareradiallycon-
u
Typically,interactions of light beams in nonlinear me- fined by a red-detuned dipole trap formed by a single
q
dia are very weak at low light levels. Strong interac- beam guided by the fiber itself. The small diameter of
[
tions between few-photon pulses require a combination theguidedmodeallowsforstrongtransverseconfinement
1 of large optical nonlinearity, long interaction time, low (trapping frequencies ω /2π ∼ 50−100kHz) and deep
t
v
photon loss, and tight confinement of the light beams. trapping potential (∼10mK) at guiding light intensities
6
Here, we present a fiber-optical switch that makes use of a few milliwatts.
3
3 of an optically dense medium containing a few hundred Toprobethe atomsinthe fiber, wemonitorthe trans-
0 cold atoms trapped inside the hollow core of a photonic missionofaverylowintensity(∼1pW)probebeamcou-
1. crystal fiber (PCF) [3] within dimensions d of a few mi- pled into the single mode PCF (Fig. 1a). The signature
0 crometers. Near atomic resonance, the interaction prob- of atoms inside the PCF are absorption profiles associ-
9 ability p between a single atom and a single photon of atedwithatomicresonancelines. Iftheatomsareprobed
0 wavelength λ, which scales as p ∼ λ2/d2, approaches a inside the dipole trap,we observea unique profile shown
:
v fewpercent. Inthissystemthepropertiesofslowlyprop- in figure 1d. The dipole trap introduces a power depen-
Xi agating photons under conditions of electromagnetically dent, radially varying AC-Stark shift, which results in
induced transparency(EIT)[4, 5,6]canbe manipulated broadening and frequency shift of the absorption profile
r
a by pulses containing p−1 ∼100 photons [7, 8, 9, 10]. (reddatapointsinFig. 1d). Comparisonwiththecalcu-
Simultaneous implementation of all requirements for latedprofile based onthe dipole trapparametersverifies
few-photonnonlinearopticshas untilnow onlybeen fea- thattheatomsareloadedinsidethefiber. Fortheexper-
sible in the context of cavity quantum electrodynamics iments described below, we avoid the broadening of the
(QED)[11],withseveralexperimentsdemonstratingnon- atomic transition by synchronous square-wave modula-
linearopticalphenomenawithsingleintracavityphotons tionofthedipoletrapandtheprobebeamwithopposite
[12, 13, 14]. However, these experiments remain tech- phase (Fig. 1e) at a rate much higher than the trap-
nologically challenging and must compromise between ping frequency. When using this technique andscanning
cavity bandwidth, mirrortransmissionandatom-photon the probelaser overa particularhyperfine transition, we
interaction strength. Consequently, large nonlinearities observe a typical absorption profile as shown in figure
in these systems are accompanied by substantial losses 1d (black data points). The shape of this resonance is
at the input and output of the cavity. Our alternative completely determined by the natural line profile of the
cavity-free approach uses propagating fields in a PCF. transition T = exp(−OD/(1+4(δp)2)), where Γ is
nat Γe e
Hollow-core PCF filled with molecular gas have been the lifetime of the excited atomic state andδ =ω −ω
p p 0
used for significant enhancements of efficiency in pro- is the detuning of the probe laser from resonance. The
cessessuchasstimulatedRamanscattering[15]andfour- optical depth is defined as OD = 2N (σ /A), where
eff eg
2
(a) cswonittcrhoiln fige lfide ld (a) |4> , 5P3/2(F'=3) n1.0 (b)
HWP single mode fiber (b) ssio0.8
bfialntderpsa ss to photon counter 87Rb cloud probe |3> , 5P1/2(F'=2) ansmi0.6
MOT B dipole 2 1 e tr0.4
ltaraseprpsi ng trap beam |2> , pump Prob0.2
hfiborlleo w core mguaigdne ewtiicres 5S1/2(F=2) |1> , 5S1/2(F=1) 0.00 500 1000 1500 2000
coupling BS
lens (90:10) PBS fiber tip Switching photons
control field
switching field
probe dipole (c) 10μm FIG.2: (a)Four-stateatomicsystemfornonlinearsaturation
(d) trap laser based on incoherent few-photon controlled population trans-
fer. (b)Transmissionoftheprobeasafunctionofthenumber
160
ns of incident pumpphotons. 50% reduction of probe transmis-
to120 sion is achieved with ∼300 pump photons. The dashed grey
o
h line represents an exponential fit to thedata.
p 80
d
tte 40 (e)
mi
ns 0 dipole trap to a cycling atomic transition, |2i → |4i, is controlled
a
Tr -50 0 50 100 150 probe via an additional pump beam transferring atoms from
Frequency [MHz] an auxiliary state |1i into |2i (Fig. 2a). Initially, the
state |2i is not populated, and the system is transparent
FIG. 1: (a) Schematic of the experimental setup. (b) for the probe beam. The incident pump beam, resonant
Schematic detail of the fiber loading. Inside the fiber, the with the |1i → |3i transition, is fully absorbed by the
atoms are transversely trapped by an optical trap formed by
optically dense atom cloud, thereby transferring atoms
a single beam guided by the fiber. After exiting the top
into the |2i state, where they then affect the propaga-
end of the fiber the divergent beam creates an additional
tion of the probe beam. As demonstrated in Fig. 2b, we
funnel potential guiding the atoms into the fiber core from
a distance up to ∼ 100µm. The atomic cloud is moved achieve a 50% reduction of the probe transmission with
into this region while being focused with a magnetic guide only 300pump photons. The efficiency ofthe incoherent
consisting of four current-carrying wires that fan out from population transfer is limited by the branching ratio of
the fiber tip. (c) Scanning electron microscope image of the atomic decayfromthe excitedstate |3i. In this case,
the fiber cross section. The diameter of the central hollow
∼ 150 atoms are transferred into the |2i state, which is
region is 7µm. (d) Transmission through the fiber loaded
sufficient to cause the observed absorption of the probe
with ∼ 3000 atoms as a function of probe detuning from the
′ beam.
(5S1/2,F =1)→(5P1/2,F =2)transition. Redpointsshow
the absorption profile with the dipole trap on continuously. Next, we demonstrate coherent interaction between
Comparisontothecalculatedprofilebasedonthedipoletrap few atoms and photons in our system. First, we demon-
parameters(solidredline)confirmsthattheatomsareloaded
strate EIT [4, 5], where atomic coherence induced by a
inside the fiber. Black points show the observed absorption
controlbeam changes the transmissionof a probe beam.
profile when probe and dipole trap are modulated as shown
For this we consider the three-state Λ-configuration of
in (E). Here, a homogeneous broadening is caused solely by
thelarge optical depth of thesystem. atomic states shown in Fig. 3a. In the presence of a
strong control field, the weak probe field, resonant with
the|1i→|3itransition,istransmittedwithoutloss. The
N is the effective number of atoms in the fiber (cor- essence of EIT is the creation of a coupled excitation
eff
responding to all atoms localized on the fiber axis – see of probe photons and atomic spins (”dark-state polari-
Supplementary Information), σ is the atomic absorp- ton”) [22] that propagates through the atomic medium
eg
tioncrosssectionfortheprobedtransition,andA=πw2 at greatly reduced group velocity [6].
0
isthebeamarea. Notethatthe opticaldepthforagiven In the absence of the control beam, our medium is
number of atoms inside the fiber does not depend upon completely opaque at resonance (Fig. 3c, black data
thelengthoftheatomiccloud. Themeasuredbeamwaist points). In contrast, when the co-propagating control
ofguidedlightinsidethefiberisw0 =1.9±0.2µm. This field is added, the atomic ensemble becomes transparent
means that ∼ 100 atoms inside the fiber create an op- neartheproberesonance(Fig. 3c,reddatapoints). Fig-
tically dense medium (OD = 1). The profile shown in ure 3d shows the profile of individual pulses and their
figure 1d yields OD = 30, which corresponds to ∼ 3000 transmissionand delay due to reduced groupvelocity v
g
atoms loaded into the fiber. inside the atomic medium. For probe pulses with rms
We first consider nonlinear saturation based on inco- width t ∼150ns we observe a groupdelay t approach-
p d
herent population transfer in our mesoscopic atomic en- ing 100ns, corresponding to reduction of group velocity
semble. The transmission of the probe beam, coupled tov ≈3km/s. Remarkably,figure3Eshowsthatcontrol
g
3
(a) |3>, 5P1/2(F'=1 ) (a) |4>, 5P3/2(F'=3) 1.2 switch photons per λ2/2π
control (d)
probe s (d) switch |3>, 5P1/2(F'=1) 1.0
n0.06 n
|2>, 5S1/2(F=2) |1>, 5S1/2(F=1) n>/30ph00..0024 |2>, 5S1/2(F c=o2n)trolprobe nsmissio 00..68
(b) probe <0.00 |1>, 5S1/2(F=1) Tra 0.4
(b) probe 0.2
control 1μs 300 t6i0m0e [n90s0] 1200 control 1μs 0.0
time switch 500ns 0 500 1000 1500 2000
1.4 time Switch photons (500ns pulse)
1.2 (c) n (e) 1.4 (c) (e)
Transmission000001......024680 EIT transmissio Transmission000011......246802 Pro1001beSw1100itch time [ns] 0000000.......00000000202022 <n><n><n>
-30 -20 -10 0 10 20 30 0.0 0.00 <n>
Frequency [MHz] control field (photons/pulse) -20 -10 0 10 20 300 600 900
Frequency [MHz]
FIG. 3: (a) Three-level lambda scheme used for EIT in
the mesoscopic atomic medium. (b) Both probe and con- FIG.4: (a)Four-levelsystemfornonlinearopticalswitching.
trol field are broken into a set of ∼ 100 synchronized pulses The transmission of the EIT probe by a switch field reso-
sentthroughthefiberduringtheoff-timesofthedipoletrap. nant with an additional transition from level |2i. (b) Timing
The probe pulses have Gaussian envelopes with rms width sequences for probe, control, and switch fields. (c) Probe
t ∼ 150ns. (c) Probe transmission through the fiber with- transmission through thefiberwithout (red) andwith (blue)
p
out (black data points) and with (red data points) control the switch field present. Solid lines are fits of equation (2).
field (each data point corresponds to 100 individual pulses. (d) Observed transmission versus average number of switch
Solidlinesarefitsofequation(2). (d)Individualprobepulse photonsperpulse. Thesolidgreylineisthepredictionbased
shape and delay. The EIT pulse (red) is delayed by ∼100ns on equation (2). The transmission is normalized to the EIT
compared to the reference pulse (black), for control pulses transmission in theabsence of the switch photons. (e) Truth
containing ∼ 3500 photons. Here, hn i represents the av- tableoftheswitch, showingthedetectedphotonsintheout-
ph
erage number of photons detected in a 30ns time bin. (e) put port of the switch system. Data are presented for probe
Observed transmission of the probe pulses on resonance as a pulses containing on average ∼2 photons and ∼1/e attenu-
functionofaveragenumberofphotonsinthe1µscontrolfield ation of transmission in the presenceof theswitch photons.
pulse and theprediction (grey line) based on eq. (2)
.
pulses containing as few as ∼ 104 photons are sufficient
observebest switching results for switch pulses of length
toachievealmostcompletetransparencyoftheotherwise
t ≈t +t . Wefinda50%reductionoftheinitialtrans-
opaque system. s p d
mission for a total number of ∼ 700 switch photons per
The sensitive nature of the quantum interference un-
pulse. Figure 4e presents the truth table of our switch
derlying EIT enables strong nonlinear coherent interac-
for ∼1/e attenuation of probe transmission in the pres-
tionbetweenthedark-statepolaritonandadditionallight
ence of the switch photons. As seen from figure 4d, a
fields,whichcanbeviewedasaneffectivephoton-photon
contrast of over 90% between the ”on” and ”off” state
interaction[7,8,10]. Anefficientnonlinearopticalswitch
of the switch, desirable for practical applications, can
can be realized by adding to the EIT Λ-system a switch
be achieved with a moderate increase of the number of
field coupling the state |2i to an excited state |4i (Fig.
switch photons.
4a) [9]. In this scheme, the switching photons interact
withflippedatomicspins(state|2i)withintheslowdark-
We now analyze the nonlinear behavior of our
state polariton, causing a simultaneous absorption of a
atomic medium. When the resonant control and
probeandaswitchphoton[23,24]. Switchingisachieved
switching pulses are longer than the weak probe
when all three light fields involved (probe, control and
pulse, the effect of the atomic medium on such
switching field) are overlapping within the atomic cloud
probe pulses with carrier frequency ω is given by
(Fig. 4b). In the absenceofthe switching field(reddata p
in figure 4c), we observe high transmission of the probe Eout(t) = √12π dωEin(ω)eıO2Df(ω)e−ıωt, where Ein(ω)
beam on resonance due to EIT. When the switch field is the Fourier Rtransform of the slowly varying enve-
is turned on, this transmission is reduced. The strength lope Ein(t) of the probe pulse, normalized such that
of the reduction depends on the number of photons con- N = dt |E (t)|2, with N being the number of in-
in in in
tained in the switch pulse (Fig. 4d). Experimentally, we put phoRtons. The frequency dependent atomic response
4
to probe light f(ω)is given by [8, 9] photon storage with spin-flipped atom interrogation via
the cycling transition. Further improvements in nonlin-
γ13 |Ωs|2−4δ12δ24 earopticalefficiencyarepossiblebyeithersimultaneously
f(ω)= (cid:16) (cid:17) . (1)
slowing down a pair of pulses to enable long interaction
δ 4δ δ −|Ω |2 −δ |Ω |2
24 12 13 c 13 s time[27]orusingstationary-pulsetechniques[28,29]. In
(cid:16) (cid:17)
the former case, the thresholdnumber of switch photons
Here,Ω the Rabifrequenciesofthe switchandcontrol
s,c wouldbereducedtoN ∼ 1 A. [27],whileinthelat-
fields The complex detunings δij are defined as δij = s √ODλ2
δ +ıγ ,withγ beingthecoherencedecayratesbetween tercasethe probabilityofinteractionbetweentwosingle
lepvelsiij,j, whiliej δ = ω + ω − ω , where ω is the photons scales as ∼ ODλ2 [29]. Thus, with a relatively
p p 13 13 A
frequency of the |1i→|3i transition. We consider input modest improvement of atom loading resulting in opti-
t2 cal depth OD > 100, achieving nonlinear interaction of
pulses with Gaussian envelope Ein(t) ∼ e−4t2p, in which two guided photons appears within reach. Finally, the
case the transmission through our atomic medium is
present demonstration opens up the possibility to create
stronglyinteractingmany-bodyphotonstates[30],which
T(ωp,OD)= NNoiunt =rπ2 tpZ dωe−2t2pω2e−ODImf(ω). mstraoynggilvyecnoerwreilnatseigdhstyssitnetmost.hephysicsofnon-equilibrium
(2)
Wefitexpression(2)toobservedabsorptionprofilessuch
We thank Yiwen Chu and David Brown for their con-
as the ones shown in figures 3c and 4c to extract the
tributiontotheexperiment. Thisworkwassupportedby
control and switch Rabi frequencies, optical depth, and
Harvard-MITCUA,NSF,DARPAandPackardFounda-
groundstatedecoherencerate. Wenextusetheseparam-
tion.
eterstocompareourobservedEITandnonlinearoptical
switchdatatothetheoreticalpredictioninfigures3eand
4d. In both cases, we find excellent agreement between
our experimental data and the theoretical model. In the
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