Experimental demonstration of interaction-free all-optical switching via the quantum Zeno effect

0.75 MB·English

by  Kevin T. McCusker

Experimental demonstration of interaction-free all-optical switching via the quantum
Zeno effect
Kevin T. McCusker,∗ Yu-Ping Huang, Abijith Kowligy, and Prem Kumar
Center for Photonic Communication and Computing, EECS Department,
Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3118, USA
(Dated: February 1, 2013)
We experimentally demonstrate all-optical interaction-free switching using the quantum Zeno
effect,achievingahighcontrastof35:1. Theexperimentaldatamatchesazero-parametertheoretical
model for several different regimes of operation, indicating a good understanding of the switch’s
characteristics. We also discuss extensions of this work that will allow for significantly improved
performance, and the integration of this technology onto chip-scale devices.
3 Interaction-free measurement [1–4] allows observation
1 tobemadeinaregimethatisimpossibleclassically, i.e.,
0
without the interaction actually occurring. Incorporat-
2
ingthequantumZenoeffect,suchmeasurementcaneven

n be done with arbitrarily high efficiency [5], allowing for
a
exoticexperimentssuchascounterfactualquantumcom-
J
putation [6]. In this Letter, we describe implementation
1
ofarecently-proposedprotocol[7,8]andforthefirsttime
3
demonstrate high-contrast all-optical switching based on

] the quantum Zeno effect.
h
p All-optical switching will allow for fast, efficient net-
-
works with ultrahigh data capacity [9]. However, com-
t
n
mon switches involving nonlinear optical devices employ
a
direct coupling between the signal and the pump, which FIG. 1: (a) The electric fields at various points through-
u
q causes photon loss and possibly, in a quantum system, out the cavity (see text for details). (b) The experimental
setup. EDFA: Erbium-doped fiber amplifier. EOM: Electro-
[ decoherence as well. In contrast, a Zeno-based switch
opticmodulator. PBS:polarizingbeam-splitter. FR:Faraday
mediated via an interaction-free process has no direct
1 rotator (so the light reflected from the cavity is transmitted
v coupling, so the loss is minimized and the decoherence throughthePBSinsteadofreflected). D:detectorsforpump,
1 from signal-pump coupling is eliminated, making it suit- transmitted signal, and reflected signal.
3 able for working with quantum as well as classical sig-
6
nals. In addition, by using a microresonator instead of
7
bulkoptics(seediscussionattheendofthisLetter),such is converted to the DF field, so constructive interference
.
1 a switch can operate with ultra-low energies (potentially is inhibited, and the photon is prevented from entering
0
down to the single-photon level) and can even act as an the cavity. From the Zeno perspective, the pump is con-
3
1 optical transistor, i.e., a lower-energy pulse can switch a stantly measuring if the photon is in the cavity, which
: higher-energy pulse. guarantees that the photon will not enter the cavity (or
v
even ever interact with the pump!), and instead will be
i The prototype switch presented in this letter is based
X reflected by the cavity.
onaFabry-Pérotdesign(seeFig.1(a))withanintracav-
ar ity crystal phase-matched for difference-frequency (DF) Besides our χ(2)-based implementation, other pro-
generation (other interactions such as sum-frequency tocols for Zeno-based all-optical switching have also
generation would work as well). The cavity is resonant been proposed, employing, e.g., cavity-enhanced two-
with a high finesse at both the signal and the difference photonabsorption(TPA)byrubidiumatomicvapor[10]
frequencies (but not at the pump frequency for this im- or inverse-Raman scattering in silicon-based microres-
plementation;ahighfinesseforthepumpwoulddecrease onators [11] (which has been demonstrated for modu-
the required pump power). In the normal operation of lation only, not switching [12]). Initial evidence of the
the Fabry-Pérot, i.e., with the pump off, when a signal TPA-induced switching has been recently observed with
photon(orpulse)reachesthecavity,asmallportionofits verylowcontrast, wherethesignaltransmissionthrough
amplitudeinitiallyentersthecavity,and,uponsuccessive theswitchwasshowntobeaffectedbyabout3%[13,14].
round-trips, constructively interferes with the incoming TheimplementationpresentedinthisLetterisamodi-
amplitude, allowing the entire photon to pass through fiedversionoftheproposaldevelopedin[8]. Theprimary
cavity, with only a small overall reflection. With the difference is that we use a continuous-wave (CW) sig-
pump on, however, the signal field that enters the cavity nalbeamforexperimentalconvenience(thepumpisstill
2
pulsed). The switch is modeled here using quasi-static
1
analysis, similar to the usual classical description of a ut −4−2φS,0° 2 4 −4−2φS,0° 2 4
Fabry-Pérot cavity, which is valid if all of the input in- np0.8
tensitiesvaryslowlywithrespecttothecavityround-trip o i 0.2 0.2
e t0.6
time. Let the fields of the signal and the DF in the cav- v
ifiteyldbseadtetnhoetefidrsbtymAirSroarnadreArDe,larteesdpevcitaiv(esleye. FTihg.e1v(aar)iofuosr er, relati0.4 00−4−T2ime0,µs2 4 00−4−T2im0e,µs2 4
a pictorial representation of the location of these fields) w0.2
o
P
A0S(t) = AS(t)rS +AI(t)tS, AR(t) = AS(t)tS −AI(t)rS, 0
andA0 (t)=A (t)r , wherer (r )andt (t )referto 0 10 20 30 40 50 60
D D D S D S D Time, ns
the reflection and transmission coefficients, respectively,
at the signal (difference) frequency, and AI(t) and AR(t) FIG. 2: Experimental switching performance when both the
are the signal fields at time t for the incident light and signal and DF fields are on resonance (φ = φ = 0). Red
S D
thereflectedlight,respectively(fortheDF,onlythefield dots: transmitted signal (measured). Red line: transmit-
inside of the cavity is considered). After the first mir- ted signal (theory). Blue pluses: reflected signal (measured).
ror,thefieldsundergothree-wavemixinginthenonlinear Blue line: reflected signal (theory). Black line: pump pulse
(measured and then used to predict the transmitted and re-
crystal, which—assuming a single-mode regime, perfect
flectedsignals). Greendashedline: (theoretical)signallostto
phase-matching, and an undepleted pump—gives:
DFgeneration. Notethetheorycurvesarenotfits,butzero-
A00(t)=A0(t)cos(gpI )+(ωS)1/2A0 (t)sin(gpI ), ptoarsacmaleetreerlaptrievdeictotiotnhse.inAplultposiwgenrasl(peoxwceepr.tPfourmthpeppuulsmepw)idatrhe
S S P ω D P
D is 20ns with a peak power of 17W. Insets: Transmitted sig-
A00(t)=A0 (t)cos(gpI )−(ωD)1/2A0(t)sin(gpI ). nal as the piezo-mounted mirror is scanned while the pump
D D P ωS S P pulsesareperiodicallyapplied. Whenthescanisasymmetric
(left), φ 6=0, and when it is symmetric (right), φ =0.
Here, ω (ω ) is the signal (difference) frequency and D D
√ S D
g I is the strength of the interaction, which depends
P
on the nonlinear coefficient of the crystal, the focusing
just the temperature of the crystal, which changes the
conditions, the crystal length, and the time-dependent
frequency-dependent path length (the phase matching is
pump power I . After the crystal, there is some loss
P also affected, but not significantly).
from, e.g., scattering or absorption in the crystal or
mirrors, followed by a frequency-dependent phase shift, Inordertopredicttheswitchingbehavior,wefirstneed
whichtakesintoaccountthevariableopticalpath-length to determine the experimental values for the parameters
of the cavity, giving A0S00(t) = A0S0(t)ηSeiφS and A0D00(t) = in the above equations. The values of the cavity finesse
A0D0(t)ηDeiφD. The fields then reach the second mirror, (ratio of the free-spectral range to the bandwidth) are
where we can determine the output of the cavity by ap- 28.3 and 276 at the signal and difference frequencies,
plying similar transformations as the first mirror. After respectively, and the mirror reflectivity is measured to
propagating back through the cavity following the same be 0.938 at the signal frequency. From this, we can
loss and phase transformations, the fields return to the determine r = 0.968, t = 0.250, and η = 0.977.
S S S
first mirror for the start of the next round-trip, complet- Since it does not matter where in the cavity the DF
ing the cycle, and yielding AS(t+∆t) = A0S00(t)rSηSeiφS is lost, we need to only determine the overall trans-
and AD(t+∆t)=A0D00(t)rDηDeiφD, where ∆t is the cav- mission coefficient for this frequency for one round-trip
ity round-trip time. The parameters in these equations through the cavity, which is found to be r2η2 = 0.989.
D D
can be directly measured, leaving no free parameters for The single-pass depletion of the signal is measured to
describing the experimental performance of the switch. be 0.65% at a peak pump power of 13W, correspond-
√
Our experimental setup is shown in Fig. 1(b). We use ing to g = 0.022/ W. Measuring the light transmit-
the output from a CW Helium-Neon laser at 633nm as ted through the cavity with the pump off as we scan
the signal with a 1550-nm pulse created by chopping the thepiezo-mountedmirrorallowsustodetermineφ , but
S
output of a CW laser with an electro-optic modulator finding φ is more difficult. To determine this parame-
D
and then amplifying it with an erbium-doped fiber am- ter, we send in pump pulses every µs while scanning the
plifier. The cavity is made up of two curved mirrors cavitymirrorataspeedtotraversethecavitybandwidth
(radiiofcurvatureof75mm, separatedbyabout25mm) inabout20µs. Thisallowsustoseetheswitchingbehav-
arounda5-mm-longlithium-niobatecrystal,whichispe- ior for several different values of φ and φ . The values
S D
riodically poled for quasi-phase-matched DF generation ofφ canbedirectlymeasured,whereasthevaluesofφ
S D
at 1070nm. The position of one mirror can be scanned arerevealedrelativetoeachotheruptoasingleabsolute
with a piezo-electric actuator, giving us one of the two offset, since no other phase shifts from sources such as
degreesoffreedomnecessarytotunethecavityresonance mechanical vibrations or thermal drift occur on the µs
for two different frequencies. For the other, we can ad- time scale. The switching behavior (both theoretically
3
and experimentally) is asymmetric for this scan around
φ = 0 unless φ is also 0 at the same mirror position (a) φS = 2◦, φD = 9◦
S D 0.6
(see Fig. 2 insets). Tuning the crystal temperature until
the switching behavior becomes symmetric during this 0.4
scan allows us to set φ =0.
D
TypicalswitchingperformanceisshowninFig.2,along 0.2
withthetheoreticalpredictions,whicharebasedonmea-
0
surements discussed above with no free parameters for 0 10 20 30 40
the switching behavior itself. We start out at t=0 with put (b) φS = −2◦, φD = 6◦
n
the pump off, so most of the signal light is transmitted o i
by the cavity. There is still some reflected light since e t0.4
v
the signal is under coupled to the cavity owing to in- ati
taralocwaveirt-yrelfloescsti(vtihtyisficrosutldmibrerocr)o.mTpehnesalotessdifnorthbeycuasviintyg wer, rel0.02
o 0 10 20 30 40
is also why we observe that T +R 6= 1. As the pump P
turns on, some of the signal light is converted into the (c) φS = 0◦, φD = 73◦
DF field, which changes the cavity conditions so as to
inhibit the signal light from entering the cavity, causing 0.4
thetransmissiontofallandthereflectiontoincrease. As
0.2
one can see from the plots in Fig. 2, the theory and ex-
periment agree well. The ratio between the transmitted 0
0 10 20 30 40
power when the pump is off to that when it is on is 35,
Time, ns
showing high-contrast operation of our switch.
In addition to studying the switch performance with
both the signal and the difference frequencies on reso- FIG. 3: Switching behavior when off resonance. When
nance, we explored off-resonant conditions. When the slightlyoff-resonanceatthesignalfrequency,thepumpcanef-
cavityisdoublyresonant,theorypredictsthatthetrans- fectivelyshiftthecavityresonance,eitherincreasing(a)orde-
creasing (b) the cavity transmission, depending on the phase
missionofthecavityisnotjustloweredatthesignalfre-
shift of the DF. When significantly off resonance at the DF
quency, but in fact it is shifted to a different frequency.
(c),thereiseffectivelynochangeinthecavitybehaviorwhen
We can observe this shift by slightly detuning the cav-
the pump is turned on. All theory curves have no fitting pa-
ity. For determining φ when it is 6= 0, we observe the rameters. Pumppulsewidthandpeakpowerarethesameas
D
signal output while moving the mirror position by sev- in Fig. 2 (20 ns and 17 W, respectively).
eral multiples of the free-spectral range of the cavity at
the signal frequency. Since we know at what position
φ = 0, and that ∆L = λ ∆φS = λ ∆φD, the value
D S 2π D 2π
of φD can be determined at any position near the signal theory predicts that much more pump power is required
resonance (because φS can always be directly measured for switching, and the cavity resonance at the signal fre-
when near resonance). In Fig. 3, we show evidence of
quency is destroyed (rather than shifted) [8]. To investi-
such resonance shifting. We slightly detune the cavity
gatethisregimeofoperation,weinsertafilter(Semrock,
at the signal frequency, equivalent to the signal being
modelFF01-640/14-25,transmission<10−4 at1070nm)
slightly off-resonant with the cavity. When the DF de-
into the cavity to reflect the DF light out. With this
tuning is in the same direction as the signal, the res-
filter in the cavity, η drops to 0.951, and η ≈ 10−2
S D
onance is shifted towards the signal, allowing more of
(when η (cid:28)r η , its precise value is not relevant). The
D S S
the light to enter and be transmitted through the cavity
observed switching contrast is much worse at 1.6:1 (see
(Fig. 3(a)). Conversely, when the DF is shifted in the
Fig.4),asexpected,evenatthemuchhigherpeakpump
opposite direction as the signal, the resonance is shifted
power of 150W compared to 17W in Fig. 2. While the
further away from the signal, allowing less of the light
absolute value of φ is difficult to measure in this case,
D
to pass through (Fig. 3(b)). If we significantly detune
nevertheless we are able to look at different relative val-
the cavity at the DF, then almost no switching is ob-
uesofφ andverifythattheswitchingcontrastdoesnot
D
served, as can be seen in Fig. 3(c). This is due to the
change, as predicted.
multiplepassesofDFgenerationdestructivelyinterfering
with eachother, allowing forverylittle overall frequency One feature of this device is that the switching is not
conversion. very dependent on the pump power. Taking the pump
√
The fact that the cavity is low loss at the DF has a power to be constant in time and letting g0 = g I , we
P
significant effect on the performance of the switch. If cansolveforthesteady-statetransmissionandreflection
the cavity is instead very lossy at this frequency, the coefficients of the cavity when on double resonance, i.e.,
4
powerisrequiredtoswitchthelightifthecavityishigh-
1
Signal transmitted loss at the DF; the regime in which it is expected to sat-
ut
np0.8 Signal reflected urate is not accessible with the components used. Note
o i Signal lost to DFG that the switching takes more power to turn on than
e t0.6 Pump
v is predicted with our zero-parameter single-spatial-mode
elati0.4 model. One possible explanation for this discrepancy is
er, r the presence of spatial mismatches between the various
w0.2 modes,i.e.,thesignalmodethatisdepletedbythepump,
o
P
ortheDFmodethatiscreated, isnotperfectlymatched
0
0 10 20 30 40 50 to the mode of the cavity. Such spatial mismatch is also
Time, ns
a possible explanation for the ∼3% residual transmitted
light when the model predicts a value much closer to
FIG. 4: Switching behavior when the cavity is very lossy at
the DF. Even with a significantly higher peak pump power zero. Resolving these discrepancies will be one goal of
(150W compared to 17W in Fig. 2), the switching contrast our future investigation.
is significantly lower (1.6:1 compared to 35:1). In this plot In summary, we have demonstrated, for the first time,
the pump pulse duration is 15ns. Note the peak transmis- interaction-free all-optical switching with high contrast
sionofthesignalthroughthecavityislowerduetoincreased
(35:1). Such switching occurs without the need for di-
intracavity loss from the filter.
rect interaction between the control and the signal light
waves. Using DF generation in a χ(2)-nonlinear Fabry-
Pérot cavity, we have performed systematic studies of
1
this switching mechanism in three separate operational
regimes, corresponding to where the intracavity DF is
0.8 resonant with the cavity, detuned from the cavity reso-
on 1 nance, and subjected to high intracavity loss. All three
si
s cases lead to interaction-free switching, which was ob-
mi0.6 0.5
s served by measuring the signal power present in both
n
a
e tr 0 the reflected and the transmitted ports of the device.
v0.4 0 2 4 Thebestperformance,however,wasachievedwhenboth
ati
el Low loss at DF, theory the signal and the DF fields are in cavity resonance. All
R
High loss at DF, theory ofourexperimentaldataareingoodagreementwiththe
0.2
Low loss at DF, data predictionsofthetheorywithouttheneedforanyfitting
High loss at DF, data
parameter.
0 Our results highlight a new approach to realizing all-
0 20 40 60 80 100 120
Peak pump power (W) optical logic operations that overcomes several funda-
mental constraints as well as practical difficulties as-
FIG. 5: Relative transmission of the signal light vs. pump sociated with the existing devices. Applying this ap-
power. The switching does not depend on pump power be- proach to nonlinear microresonators of high Q-factor,
yond a certain threshold, making the device less sensitive to
high-performance switching devices can be constructed
pump fluctuations. When the cavity is lossy at the DF, the
that will manifest large switching contrast, low loss,
pump power required for switching is much higher. Inset: A
low switching power, and ultralow energy dissipation.
closer look at the switching behavior for low pump powers.
In addition, due to the ultralow in-band noise intro-
duced by such devices, they can potentially operate on
φ =φ =0: quantum-optical signals as well. For example, using a
S D
lithium-niobate microdisk with a 1-mm diameter and
t = t2SηS(cosg0−rD2ηD2) , Q > 107, whose fabrication and operation has been well
cavity 1−r2η2cosg0−r2η2 cosg0+r2r2η2η2 demonstrated [15, 16], low loss (<10%) switching can be
S S D D S D S D
−r (1−η2cosg0−r2η2 cosg0+r2η2η2) achieved with pump-pulse energy on the order of 10pJ.
rcavity = 1−S r2η2cSosg0−r2ηD2 cDosg0+r2rD2ηS2ηD2 . Byusingtailoredpumppulses,togetherwithsmallermi-
S S D D S D S D crodisks and higher Q, the pump-pulse energy could be
The experimental measurement and theoretical predic- further reduced to single-photon energy, leading to de-
tion for the relative power of the transmitted light are terministic quantum logic gates for single-photon signals
showninFig.5. Asthepumppowerincreases,thecavity [17].
rapidlybecomeshighlyreflective,andthensaturates(un- ThisresearchwassupportedinpartbytheDefenseAd-
til g0 approaches 2π, at a pump power of about 80kW). vanced Research Projects Agency (DARPA) Zeno-based
Thisisclearlydemonstratedinthefigureforthedoubly- Opto-Electronics program (grant W31P4Q-09-1-0014).
resonant case. As predicted, significantly more pump We acknowledge Amar Bhagwat for the construction of
5
the crystal mount. 79.063830.
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