Efficient routing of single photons by one atom and a microtoroidal cavity

0.32 MB·English

by  Takao Aoki

Efficient routing of single photons by one atom and a microtoroidal cavity
TakaoAoki,†a A.S.Parkins,b D.J.Alton,† C.A.Regal,† BarakDayan,†c E.Ostby,‡ K.J.Vahala,‡ andH.J.Kimble†
†Norman Bridge Laboratory of Physics 12-33, ‡T. J. Watson Laboratory of Applied Physics,
California Institute of Technology, Pasadena, California 91125, USA
(Dated: January 7, 2009)
Single photons from a coherent input are efficiently redirected to a separate output by way of a
fiber-coupled microtoroidal cavity interacting with individual Cesium atoms. By operating in an
overcoupledregimefortheinput-outputtoataperedfiber,oursystemfunctionsasaquantumrouter
withhighefficiencyforphotonsorting. Singlephotonsarereflectedandexcessphotonstransmitted,
asconfirmedbyobservationsofphotonantibunching(bunching)forthereflected(transmitted)light.
Our photon router is robust against large variations of atomic position and input power, with the
observed photon antibunching persisting for intracavity photon number 0.03(cid:46)n¯ (cid:46)0.7.
9
PACSnumbers:
0
0
2
Cavity quantum electrodynamics (cQED) offers sys-

n tems in which the coherent interaction between matter
a and light can dominate irreversible channels of dissipa-
J
tion [1, 2, 3, 4]. Diverse systems based upon radiative
7
interactions in cQED are thereby promising candidates

] for the physical implementation of quantum networks,
h where, for example, atoms in optical cavities (quantum
p
nodes) are linked by photons in optical fiber (quantum
-
t channels) [4]. Although many important capabilities for
n
quantum nodes have been demonstrated within the set-
a
u ting of cQED with single atoms in Fabry-Perot cavi-
q ties [5, 6, 7, 8, 9, 10], an outstanding challenge is high
[ efficiencytransportofquantumfieldsintoandoutofop-

1 tical cavities [4], as is required to link large numbers of
v quantum nodes.
6
In this regard, the coupling rate κ of photons to and
3 FIG. 1: (a) Simple depiction of one atom coupled to a
8 fromthequantumchannelshoulddominatetheratesfor toroidal cavity, together with fiber taper and relevant field
0 anyotherinput-outputmechanisms. Onewaytoachieve modes, with rates (g ,κ ,κ,h) as defined in the text. (b-
tw ex i
. thisistooperatethenodesinanovercoupledregime[11], d) Theoretical plots for the parameters of our experiment,
1
0 whereexternalcouplingdominatesinternalsystemlosses. (gtw,κex,κi,h)/2π = (50,300,20,10) MHz, with ωA = ωC.
(b, c) Transmission and reflection spectra T(∆),R(∆) for
9 In the microwave domain, “circuit QED” systems rou-
a ,b as functions of probe detuning ∆ = ω −ω with
0 tinely operate in the overcoupled regime [3] for high ex- out out C p
: and without the atom. (d) Theoretical intensity correlation
v ternal efficiency. functions versus ∆ for the transmitted (g(2)(τ = 0)) and re-
i T
X In this Letter, we realize a cQED system in the op- flected (g(2)(τ =0)) fields. (e) Schematic of our experiment.
R
r tical domain with efficient input-output coupling while A Cesium MOT is formed in a separate chamber, and atoms
a still maintaining high internal efficiency for coupling to are transfered to the main chamber via an optical conveyor
a single atom. We use a microtoroidal cavity interacting belt. Atomsarethendroppedontoatoroid,whichiscoupled
with single Cesium atoms [12, 13, 14], with coupling to toataperedfiberasin(a). Aprobebeamain isinjectedinto
the taper, and the transmitted a and reflected b fields
and from the cavity implemented with a tapered optical out out
aremeasuredwithtwopairsofsingle-photondetectorsD .
fiber in an overcoupled regime [11]. As a proof of princi- 1−4
ple,wedemonstrateanefficientandrobustphotonrouter
for which single photons are extracted from an incident
the cavity supports two counter-propagating modes a,b
coherent state and redirected to a separate output with
of frequency ω . These cavity modes have intrinsic loss
C
efficiency ξ (cid:39)0.6.
rate κ and are coupled to each other at rate h (e.g., due
i
To model photon transport for the atom-cavity sys- to internal scattering)[11]. Input to and output from the
tem, we consider the interaction of one atom with the internal modes of the cavity are provided by a tapered
evanescent fields of a microtoroidal cavity, as shown in fiber with external coupling rate κ , where the fields of
ex
Fig. 1(a), with g the rate of coherent atom-cavity cou- the tapered fiber are denoted by {a ,a ,b ,b } in
tw in out in out
pling [15]. Near the atomic resonance at frequency ω , Fig. 1(a). For single-sided excitation as in our current
A
2
experiment, the input modes have coherent amplitudes Hence the reflected light exhibits sub-Poissonian photon
statistics and photon antibunching. Similarly, photon
(cid:104)ain(cid:105)=−iE√pe−iωpt, (cid:104)bin(cid:105)=0. (1) detection for the transmitted light aout results in atomic
2κex projection that depends on Ep and C [19], with then aout
displaying photon bunching and super-Poissonian statis-
The Hamiltonian, master equation, and input-output
tics. The net effect is the routing of single photons into
relations for the system depicted in Fig. 1(a) can be
the backward direction b and remaining excess pho-
found in Refs. [13, 14, 16]. When the total cavity decay out
tons into the forward field a .
rate, κ=κ +κ , is much larger than any other rate in out
i ex
Figures1(b-d)presenttheoreticalresultsfortransmis-
the system, the cavity modes can be adiabatically elim-
sion and reflection spectra T(∆), R(∆) and intensity
inated from the system dynamics [17]. The system can
thenbedescribedbyeffectiveopticalBlochequationsfor correlations gT(2)(0), gR(2)(0) in the weak-driving limit for
a two-level atom with the cavity-enhanced atomic decay the parameters of our experiment: (gtw,κex,κi,h)/2π =
rate Γ = γ(1+2C), where C = 2|gtw|2κ is the cooper- (50,300,20,10) MHz. Although not deeply in the over-
γ(κ2+h2) coupled regime, efficient transmission and reflection can
ativity parameter for a single atom and γ is the rate of
beachieved,withT ≈0.005,R ≈0.7withanintracav-
atomic decay to modes other than a,b. 0 0
ity atom, and T ≈0.8, R ≈0.003 without the atom.
In the overcoupled regime of toroid-taper coupling, 0 0
AschematicofourexperimentisshowninFig.1(e)and
κ (cid:29) (κ,h), the analytic expressions for steady-
ex i issimilartothatdescribedinRefs.[13,14]. However,our
state transmitted I = (cid:104)a† a (cid:105) and reflected I =
T out out ss R new apparatus has two major improvements that allow
(cid:104)b† b (cid:105) fluxes, and for the second-order correlation
out out ss us to reproducibly tune κex to the desired overcoupled
functions, gT(2)(τ) = (cid:104)a†outa†out(τ)aout(τ)aout(cid:105)ss/IT2 and value and to maintain a small κi. Firstly, the silicon
g(2)(τ) = (cid:104)b† b† (τ)b (τ)b (cid:105) /I2, can be greatly chip supporting an array of SiO toroidal cavities and
R out out out out ss R 2
simplified. Specifically,atzerodetuning(i.e.,ω =ω = the tapered fiber for input-output coupling are mounted
A C
ω ) and in the weak driving limit, the transmission and on piezoelectric-driven stages that are placed inside the
p
reflection coefficients are given by [16] mainchamber. Thecombinationofcompact,rigiddesign
andgoodpassivevibration-isolationenableustotunethe
1
T(∆=0)≡I (0)/I (∆(cid:29)κ)≡T (cid:39) , (2) separation between the taper and toroid and to achieve
T T 0 (2C+1)2 stablecouplingbetweentheevanescentfieldsofthetaper
(cid:18) 2C (cid:19)2 and toroid without having the taper contact the surface
R(∆=0)≡I (0)/I (∆(cid:29)κ)≡R (cid:39) (,3)
R T 0 2C+1 of the toroid.
Secondly, in order to avoid degradation of quality fac-
whilesecond-orderintensitycorrelationsatzerotimede- tor for the toroids caused by Cesium contamination, our
lay are found to be new apparatus has a separate “MOT chamber” where
Cesiumatomsaremagneto-opticallycooledandtrapped,
g(2)(τ =0) (cid:39) (4C2−1)2, (4)
T then loaded into an optical conveyor belt [20] and trans-
g(2)(τ =0) (cid:39) 0. (5) ferred into the “cQED chamber” through a differential
R
pumping tube. The optical conveyor is formed by two
The physical interpretation of these results is as fol- counter-propagating beams red detuned 100 GHz below
lows. In steady state and with C (cid:29)1, the field radiated the D2 line of Cesium to form a standing-wave dipole-
by the atomic polarization σSS interferes destructively force trap. By independently shifting the frequencies of
−
with the intracavity field from ain, resulting in small each beam with acousto-optic modulators, atoms loaded
transmission T0 (cid:28)1. But σ−SS also coherently drives the from the MOT are conveyed 25 cm from MOT to cQED
intracavityfieldb,therebygeneratingabackwardpropa- chamberandpositioneddirectlyaboveaparticulartoroid
gatingfieldbout,leadingtoreflectionR0 →1[18]. Onthe on the silicon chip.
other hand, the overcoupled cavity without the atomic The resonance frequency ω of the toroid is tuned
C
polarization (i.e., C =0) has T0 (cid:39)1 and R0 (cid:39)0. Strong via the chip temperature near the frequency ωA of the
optical nonlinearity of the atom-toroid system gives rise 6S ,F = 4 → 6P ,F(cid:48) = 5 transition of Cesium,
1/2 3/2
to a dynamical switching between these two limits con- with |ω − ω |/2π (cid:46) 30 MHz. The frequency ω of
A C p
ditioned upon photon detection. (1) T0 (cid:39)0, R0 (cid:39)1 due the probe beam Ep is locked to coincide with ωA, with
to the field from σ−SS, and (2) T0 (cid:39) 1, R0 (cid:39) 0 due to |ωA − ωp|/2π (cid:46) 1 MHz. The probe is sent into the
the conditional atomic polarization σC following photon taper via the 1% port of 99/1 fiber beamsplitter (Fig.
−
detection [19]. 1(e)). The 99% port of this beamsplitter is connected
This description is substantiated by examination of to a 50/50 beamsplitter followed by two single-photon
g(2) . Detection of a ‘first’ photon for the reflected field counting-modules (SPCMs), D ,D , to detect the re-
T,R 1 2
b projects the atom to the ground state, which pre- flected field b . Similarly, the transmitted field a
out out out
cludesthedetectionofa‘second’photonforb [14,19]. in the taper is detected with another pair of SPCMs,
out
3
FIG. 2: (a,b) Average atom transit signals for (a) transmis-
sionT (t)and(b)reflectionR (t)oftheprobefield. Asshown
0 0
in the inset in (a), the transit selection criteria are set to be FIG. 3: (a) False detection ratio F, (b) transmitted signal
Cth =4,5,6, where in all cases, ∆tatom =4µs. (c,d) The in- T0(t=0)atthecenterofanatomictransit,and(c,d)intensity
tensitycorrelationfunctionsgT(2,)R(τ)forthetransmittedfield correlation functions gT(2,)R(τ = 0) at zero time delay for
a andthereflectedfieldb . For(a-d),n¯ =0.093photons. the transmitted T and reflected R light as functions of the
out out
Solid lines are a theoretical calculation using the parameters threshold Cth for the selection of atom transits. In all cases,
(gtw,κex,κi,h)/2π = (50,300,20,10) MHz. Dashed lines are ∆tatom =4µs and n¯ =0.093.
the same calculation with 4% background counts.
S ≡ (cid:80)tj+∆tatom[C (t )+C (t )], to be equal or greater
j ti=tj 1 i 2 i
D3,D4. Photoelectric events from the four SPCMs are thanathresholdcountCth. Afterapplyingthisselection
time stamped and recorded for analysis. criterion to C1,2(t), we determine the time origin t = 0
The physical properties of the new toroids for our foreachtransiteventbythetemporalmeanofthecounts
current experiment are similar to those in Ref. [14]. in ∆tatom and extract counts in a time window of ±6µs
The major diameter D ≈ 25µm and minor diameter around t=0 for further analysis.
d ≈ 6µm, leading to an effective atom-cavity coupling Figure2(a,b)showthetransmittedT0(t)andreflected
rate of geff/2π ≈ 70 MHz (gtw/2π ≈ 50 MHz) [13, 15]. R0(t)signalsaveragedovertransiteventswithtransitse-
Combined with the measured values for (κex,κi,h) and lection criteria of Cth = 4,5,6 and ∆tatom = 4µs, where
with γ/2π = 5.2 MHz, we calculate the single-atom co- T0(t) and R0(t) are normalized to the resonant trans-
operativity parameter C = 3.0 and the cavity-enhanced mission of the empty cavity, T0 (cid:39) 0.83. Atom-cavity
atomicdecayrateΓ/2π =36.4MHz. Notethatforlarge coupling results in reduced transmission and increased
toroid-taper separation with κ (cid:39) κ , our system is in reflection [22]. The second-order correlation functions
ex i
the strong coupling regime of cQED with g >κ,γ. g(2) (τ) for the transmitted and reflected fields a ,b
eff T,R out out
About 107 atoms with temperature T ≈ 100µK are arecalculatedinthesamemannerasinRefs.[14,16]and
dropped from a height of 0.5 mm above the toroid by plotted in Fig. 2(c,d). Photon bunching and antibunch-
turningoffthedipoletrapbeams. AsshowninFig.1(c), ing are clearly observed for a ,b in the forward and
out out
the reflected intensity I associated with b should be backward directions, respectively. The recovery time τ
R out R
near zero when there is no atom in the cavity. A falling to steady state is set by the cavity-enhanced atomic de-
atomthatinteractswiththeevanescentfieldsofthecav- cay rate Γ=γ(1+2C), with τ ∼1/Γ [14, 16].
R
ity generates an increase in I for the duration of the These observations are consistent with the theoretical
R
atomictransitandenablessingletransiteventstobeob- predictions in Fig. 1(b-d) for ∆ = 0, thereby demon-
served with high signal-to-noise ratio [21]. While tran- stratingafunctionalphotonrouter. Notethatthetraces
siting atoms are sufficient for these experiments due to with larger threshold C show more significant effects
th
ourinsensitivitytoatomicposition, inthefuturewerec- of atom-cavity coupling. This is because we have fewer
ognize the need to trap and localize single atoms near “falsely detected transits” (i.e., time windows that have
the toroid to allow continuous operation of the system no atom but nevertheless satisfy the selection criterion
[7, 8, 9, 10]. S ≥C because of background light) and reduced con-
j th
We first fix the probe power |E |2 such that the intra- tributions from transits with smaller g.
p
cavity photon number n¯ = 0.093 for the empty cavity. To explore this point further, in Fig. 3(a) we plot
Atom transit events are extracted from the records of the ratio F of false to total atomic transit events, F ≡
photoelectriccountsC (t)fromb atdetectorsD ,D Rno(t=0)/R (t=0), where Rno is the measured tran-
1,2 out 1 2 0 0 0
by the following procedure. For an atom transit event, sit signal for the reflected field as in Fig. 2(b), but now
we require the sum of the counts over a time ∆t , with no atoms present. Clearly, F decreases as C in-
atom th
4
atomic azimuthal position kx around the major circum-
ference of the toroid. Curves for particular values of kx
would be indistinguishable on the scale of the plot. This
insensitivity to kx is due to the small coupling between
the counterpropagating modes a and b, characterized by
the ratio h/κ(cid:39)0.03(cid:28)1, that limits the formation of a
standing wave [16].
To account for background light, the dashed lines in
Fig. 4 include background counts at a level of 4% of the
signal. Thisleadstogoodagreementforthebackground-
sensitive parameter g(2)(τ = 0) in Fig. 4(b). There still
R
remains a discrepancy for T in Fig. 4(a) given the sta-
0
tistical error bars, even when we account for variation in
FIG. 4: (a) Transmitted signal T (t = 0) at the center g by averaging over a range of values around g =50
0 tw tw
of an atomic transit and (b) intensity correlation function MHz ( g =35 MHz to g =65 MHz). Thus, we must
tw tw
g(2)(τ =0) at zero time delay for the reflected light for vari- attribute the discrepancy in (a) to a systematic uncer-
R
ousvaluesofintracavityphotonnumbern¯. Pointsareexper- tainty in the experiment.
imental data averaged over individual transit events. Solid
In summary, we have realized a photon router using
lines are from a theoretical calculation with the parameters
(gmin,gmax,κ ,κ,h)/2π = (35,65,300,20,10) MHz where single Cesium atoms coupled to a microtoroidal cavity
tw tw ex i
instead of a single value of g we use an average over gmin in the overcoupled regime. In comparison to our previ-
tw tw
togmax. Dashedlinesarethesamecalculation, butwiththe ous photon turnstile [14], this photon router is robust
tw
assumption of background counts of 4% of the signal. against azimuthal position of the atom (kx) and taper-
toroiddistance(κ ),inadditiontotheatom-cavitycou-
ex
→−
pling strength (g(r)). The current system already has
creases. Correspondingly, in (b) - (d), T , g(2), and g(2) throughputefficiencyforsinglephotonsofξ ≈0.6andit
0 T R
showmoresignificanteffectsofatom-cavitycouplingwith is projected to reach ξ > 0.999 through use of smaller
increasing C , albeit with larger error bars due to the toroid diameter [23] and improvement of the intrinsic
th
diminishingnumberoftransitevents. ThevalueC =5 qualityfactorofthecavitytoQ≈1010 [24]. Therealiza-
th
(F (cid:39) 0.025) provides a reasonable compromise between tion of strong interactions of single photons and atoms
decreasing signal-to-noise ratio and reduced contamina- togetherwithefficientinput-outputprovidesanenabling
tion from false transit events. capability for the realization of quantum networks and
Finally, in order to investigate the saturation behav- investigationsofquantummany-bodysystemsbuiltcom-
ior of our photon router, we vary the intracavity pho- ponent by component.
ton number by way of the probe intensity |E |2. Fig- WegratefullyacknowledgethecontributionsofS.Kel-
p
ure 4 displays the measured values of T (t = 0) and ber and E. Wilcut-Connolly. This work is supported
0
g(2)(τ = 0) as functions of n¯. For each value of n¯, we by the NSF PHY-0652914, by IARPA via ARO, and by
R
settheselectionthresholdC sothatthefalsedetection NGST. ASP thanks the Marsden Fund of the Royal So-
th
ratio F < 0.05. The point for the lowest value of n¯ for ciety of New Zealand for support.
g(2)(τ =0) is omitted from (b) due to its poor signal-to- Permanent addresses: a TA - Department of Physics, Kyoto Uni-
R versity, Kyoto, Japan, and PRESTO, Japan Science and Technology
noiseratio. In(a),thetransmissionT (t=0)showsclear Agency, Saitama, Japan; b ASP - Department of Physics, University
0
ofAuckland,Auckland,NewZealand;c BD-DepartmentofChemical
saturation of the atom-cavity coupling, from T ≈0.2 at
0 Physics,WeizmannInstituteofScience,Rehovot,Israel.
n¯ ≈ 0.01 to T ≈ 0.8 at n¯ ≈ 0.7. Importantly, in (b)
0
g(2)(τ = 0) < 1 over a wide range of intracavity photon
R
number, 0.01(cid:46)n¯ (cid:46)0.7.
From the measured T and known parameters
0 [1] K. J. Vahala, Nature 424, 839 (2004).
(g ,κ ,κ,h), we estimate the efficiency ξ for single-
tw ex i [2] G. Khitrova et al., Nature Physics 2, 81 (2006).
photon throughput and obtain ξ ≈ 0.6 for the lowest
[3] R. J. Schoelkopf and S. M. Girvin, Nature 451, 664
n¯ ≈ 0.012, with ξ → 0.7 for n¯ → 0. This is consistent (2008).
with the value ξ ≈ 0.5±0.2 directly inferred from the [4] H. J. Kimble, Nature 453, 1023 (2008).
distribution of R for the individual transits. As evi- [5] Q.A.Turchetteet al.,Phys.Rev.Lett.75,4710(1995).
0
denced in Fig. 2(a, c), multiple photons are efficiently [6] T. Wilk et al., Science 317, 488 (2007).
[7] J. McKeever et al., Science 303, 1992 (2004).
transmitted into the output channel a .
out [8] M. Hijelkema et al., Nature Physics 3, 253 (2007).
The solid lines in Fig. 4 are from a simplified theoret-
[9] M. Keller et al., Nature 431, 1075 (2004).
ical model based on adiabatic elimination of the cavity [10] A. D. Boozer et al., Phys. Rev. Lett. 98, 193601 (2007).
[16]. The curves are obtained from an average over the [11] S.M.Spillaneetal.,Phys.Rev.Lett.91,043902(2003).
5
[12] D. K. Armani et al., Nature 421, 925 (2003).
[13] T. Aoki et al., Nature 443, 671 (2006).
[14] B. Dayan et al., Science 319, 1062 (2008).
[15] The rate of coherent interaction between the atom and
themodesa,bisgivenbyg =gtwf(ρ,z)e±ikx,whereρ
tw 0
istheatom-toroidradialdistance,xistheatom’sposition
around the toroid circumference, and z is the vertical
coordinate.
[16] Supporting Online Material accompanying Ref. [14].
[17] C. W. Gardiner and P. Zoller, Quantum Noise, 2nd Ed.
(Springer-Verlag, Berlin, 1999).
[18] J. T. Shen and S. Fan, Opt. Lett. 30, 2001 (2005).
[19] H. J. Carmichael, Phys. Rev. Lett. 70, 2273 (1993).
[20] S. Kuhr et al., Science 293, 278 (2001).
[21] Forourpreviouswork[13,14],thetaperandtoroidwere
critically coupled with the taper in contact mode. Atom
transitsweredetectedasincreasesinthetransmittedin-
tensity I for the field a .
T out
[22] TheasymmetryevidentinFig.2(a,b)isarobustfeature
of our observations. We have no definitive explanation,
but are investigating various possible causes, including
surface forces.
[23] S. M. Spillane et al., Phys. Rev. A 71, 013817 (2005).
[24] D. W. Vernooy et al., Opt. Lett. 23, 247 (1998).