Nonlocal control of dissipation with entangled photons

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by  Charles Altuzarra

Nonlocal Control of Dissipation with Entangled Photons
Charles Altuzarra 1,2, Stefano Vezzoli1, Joao Valente3, Weibo
Gao1, Cesare Soci1, Daniele Faccio4, Christophe Couteau1,2,5,∗
1 Centre for Disruptive Photonic Technologies, TPI,
Nanyang Technological University, 637371, Singapore
2 CINTRA, CNRS-NTU-Thales, CNRS UMI 3288, Singapore
3 Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, Southampton, UK
4 Institute for Photonics and Quantum Sciences and SUPA,
Heriot-Watt University, Edinburgh EH14 4AS, UK
5 Laboratory for Nanotechnology, Instrumentation and Optics,
ICD CNRS UMR 6281, University of Technology of Troyes, Troyes, France
* Corresponding author: [email protected]
7 (Dated: January 20, 2017)
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Quantumnonlocality,i.e. thepresenceofstrongcorrelationsinspatiallyseparatedsystemswhich
0
2 areforbiddenbylocalrealism,liesattheheartofquantumcommunicationsandquantumcomputing.
Here, we use polarization-entangled photon pairs to demonstrate a nonlocal control of absorption
n oflightinaplasmonicstructure. Throughthedetectionofonephotonwithapolarization-sensitive
a
device, we can almost deterministically prevent or allow absorption of a second, remotely located
J
photon. We demonstrate this with pairs of photons, one of which is absorbed by coupling into
9 a plasmon of a thin metamaterial absorber in the path of a standing wave of an interferometer.
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Thus,energydissipationofspecificpolarizationstatesonaheat-sinkisremotelycontrolled,promis-

ing opportunities for probabilistic quantum gating and controlling plasmon-photon conversion and
]
s entanglement.
c
i
t
p Introduction.— One of the quintessential aspects of gledphotons. Wepreviouslydemonstratedthatthelevel
o quantum mechanics is the existence of entangled states of dissipation of a thin absorber placed in a single pho-
s. whereby the classical description of a particle being in toninterferometercanbevariedfromnearly0%(’perfect
c a well-defined state is replaced with a quantum descrip- transmission’) to 100% (’perfect absorption’), depending
i
s tion based on superposition of states. Moreover, quan- on the position in the standing wave, whereas only 50%
y tum entanglement provides a unique route for nonlocal absorption is observed, when the standing wave is not
h
correlations between remote particles such as photons. formed[16]. Therefore,byenablinginterferenceandcon-
p
Beyond the relevance to the fundamental questions of trolling the resulting standing wave, one can nonlocally
[
quantum physics [1–4], nonlocality is a resource for a select the level of dissipation of photons of certain polar-

1 number of applications such as quantum teleportation, ization states in the absorber.
v quantum erasure, and interaction-free measurements [5–
7
10]. In addition to demonstrating a new application of The concept.— In a simplified Sagnac interferometer,
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nonlocality, our work presented here is also relevant to an input beamsplitter creates two optical paths A and B
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5 the field of quantum plasmonics. This rather recent field (see Fig.1). To render the device polarization-sensitive
0 emerged when Altewischer et al. [11] showed that light weintroducea half-waveplateonlyinpathA andorient
. passing through a metallic nanohole array conserved the itsmain axisto be 45◦ tothe planeofthe interferometer
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quantum state of entangled photons. In parallel, Lukin [17]. In what follows we will refer to light linearly po-
0
7 et al. demonstrated that single plasmons can be gener- larized in the plane of the interferometer as horizontally
1 ated from single photons as a process that can be deter- polarized (H-polarized) light and light polarized perpen-
: ministic [12, 13]. More recently, Hong-Ou-Mandel two- dicular to the plane as vertically polarized (V-polarized)
v
photon quantum interference experiments were carried light. Suchaninterferometercreatesstandingwavesonly
i
X outwithplasmons[14,15],therebyprovidingexperimen- for light polarized along the fast and slow axis of the
r tal proof that propagating plasmons retained the quan- waveplate. Input linear polarizations of +45◦ or −45◦
a
tum coherency of the photons that launched them. to the plane of the interferometer will not be affected by
thewave-plateandwillevolvethroughbothpathsAand
In this work, we demonstrate that nonlocal interac- B as identically polarized traveling waves forming two
tions of entangled photons can be used to achieve non- standing waves in the interferometer with the antinode
local control of light’s absorption through the excitation for+45◦correspondingtothenodefor−45◦. Conversely,
of plasmonic modes. In order to demonstrate the non- the half-wave plate converts a vertical polarization into
local control of dissipation with polarization-entangled a horizontal one, and vice versa: so if vertically or hori-
photons, we constructed a polarization-sensitive ’quan- zontallypolarizedlightislaunchedintheinterferometer,
tum eraser’ interferometer for which we show that the optical paths A and B will contain counter-propagating
conditions for interference can be non-locally controlled orthogonal that do not interfere: a standing wave is not
through a polarization-sensitive detection of the entan- formed in the interferometer.
2
Now, with polarization-entangled photon pairs (de- cidence with the idler photon PD within a 10 ns time
i
notedidleriandsignalsphotonsforeachpair,seeFig.1) window.
it is possible to nonlocally control the state of the signal The SPDC source creates a quantum superposition of
photons inside the interferometer, through a measure- polarized photons of orthogonal basis. The wavefunc-
ment on the idler photons outside (and that never en- tions general form for polarization entangled states of
ter) the interferometer. This is achieved by adding a this type is [20]:
polarizer on the idler channel. When the idler polar-
izer is set to either an angle of +45◦ or −45◦ to the
1
plane of the interferometer, the polarization state of the |Ψ(cid:105)= √ (|H(cid:105) |V(cid:105) −|V(cid:105) |H(cid:105) ) (1)
i s i s
polarization-entangled signal photon will be polarized at 2
−45◦ or+45◦ correspondingly. Thesignalphotonspath-
whereindicesiandsdenotetheidlerandsignalphotons
entangled wavefunction will form a standing wave in the
respectively and |H(cid:105) and |V(cid:105) denote the horizontal and
interferometer and strong dissipation in the ’coherent
vertical polarization states respectively.
absorption’ regime and zero dissipation in the ’coher-
The path entanglement wavefunction of a single pho-
ent transmission’ regime can be observed. Conversely,
ton that enables interference has the general form:
whenthepolarizerintheidlerchannelissetverticallyor
horizontally, the polarization state of the signal photon |Ψ(cid:105)= √1 (cid:0)|1(cid:105) |0(cid:105) −eiφ|0(cid:105) |1(cid:105) (cid:1) (2)
will be necessarily projected to the horizontal or vertical A B A B
2
polarization, correspondingly. Therefore, due to distin-
guishability of optical paths [7, 8], no standing wave will By integrating the path entanglement wavefunction
be formed in the interferometer and coherent control of Eq.(2) into the polarization entanglement wavefunction
the absorption process is removed. Eq.(1), in representation of our optical scheme, we ob-
Therefore, the scheme described here is a dissipative tain:
form of a ’quantum eraser’. The idler polarizer installed
at+45◦ or−45◦ totheplaneoftheinterferometererases |Ψ(cid:105)= 21(cid:2)|H(cid:105)i(cid:0)|H(cid:105)A|0(cid:105)B −eiφ|0(cid:105)A|V(cid:105)B(cid:1) (3)
the ”which-path information to the absorber and thus −|V(cid:105) (cid:0)|V(cid:105) |0(cid:105) −eiφ|0(cid:105) |H(cid:105) (cid:1)(cid:3)
restoresthestandingwaveintheinterferometerandthus i A B A B
the coherent absorption regime.
Andbyexpanding,wearriveatthepathentanglement
Theexperiment.—Theexperimentalsetupisshownin of two polarization wavefunctions:
Fig.1. Wegeneratedpairsofpolarization-entangledpho-
tons at the wavelength of 810 nm by spontaneous para- 1
|Ψ(cid:105)= [(|H(cid:105) |H(cid:105) −|V(cid:105) |V(cid:105) )|0(cid:105)
metric down-conversion (SPDC). A 200-mW laser diode 2 i A i A B (4)
with emission centered at the wavelength of λp = 405 −eiφ|0(cid:105)A(|H(cid:105)i|V(cid:105)B −|V(cid:105)i|H(cid:105)B)(cid:3)
nm was used to pump a 2mm-thick type-II beta-barium
borate (BBO) nonlinear crystal producing non-collinear, We first measured the degree of polarization entangle-
degenerate photon pairs. Polarization entanglement is ment of the generated photons . These measurements
achieved by adding 1mm-thick BBO compensation crys- were performed for two different polarization basis sets,
talsandhalfwaveplatessetat45◦. Thephotonpairscol- |H,V(cid:105) and ±45(cid:105) which correspond to 1) horizontal and
lected from the areas of intersections of phase-matching vertical polarizations and 2) polarizations at +45◦ and
cones were coupled to single-mode fibres with collima- −45◦ totheplaneoftheinterferometer. TheBellparam-
√
tion lenses. A 10-nm bandpass filter centered at 810 nm eterwasthenfoundtobeS = 2(V +V )=2.66±0.01
1 2
was used to block the pump radiation and select ’twin’ where V were visibilities calculated from the correla-
1,2
SPDC photons. As detailed in Fig.1, the idler channel tion curves for the two basis sets. Here, according to the
was connected to a photon counting avalanche photo- Clauser-Horne-Shimony-Holt inequality [20–22], a value
diode detector and a coincidence counter (IDQuantique of S greater than 2 implies nonlocal quantum correla-
ID800). It was used to control the presence of the signal tions. We note that our measured value of the Bell pa-
photon within the interferometer. The signal photons rameter of S = 2.66, is close to the maximum value of
√
were coupled to the interferometer. A variable retarder S =2 2≈2.88 that is expected for perfectly entangled
was used to compensate for the polarization change in states.
the signal fiber. The photons enter the interferometer The plasmonic metamaterial absorber made of split
through a lossless (50:50) non-polarizing beam splitter. ring resonators was designed to provide a nearly 50%
Thethinmetamaterialabsorberwasplacedatthecentre traveling wave absorption, similarly to work reported
of the interferometer between two x10 microscope objec- in Ref.[18]. We fabricated a freestanding gold film
tives producing a spot size of ≈10 µm in diameter. The of subwavelength thickness nanostructured to create
absorbers position was scanned using a piezoelectrically polarization-independent plasmonic absorption at the
actuatedlineartranslationstageoverafewopticalwave- operational wavelength of 810 nm.
lengths. The sum of the photon counts were detected by Todemonstratethenonlocalcontrolofdissipationwith
the two avalanche detectors (PD and PD ) in coin- polarization-entangledphotons,weintroduceonephoton
A B
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FIG. 1. Nonlocal dissipation management with entangled photons. Polarization-entangled photon pairs are generated by a
typeIIspontaneousparametricdownconversionprocess(laserat405nmimpingingaBBOnonlinearcrystal). Onephotonof
thepairisintroducedintheinterferometer(thesignalphotonatthe50/50beamsplitter)andcantaketwopaths(AandB)with
a fiber link and a compensator for synchronization issues. Hwp is a half waveplate in arm A. A thin metamaterial plasmonic
absorber is introduced in the polarization-sensitive interferometer. By detecting the idler photon outside the interferometer
with the help of a polarizer (ξ), one can non-locally prevent or allow deterministic absorption of the signal entangled photon
thatdissipatesthroughcouplingintoaplasmonoftheabsorberplacedintheinterferometer. PD ,PD andPD arephoton
A B i
detectors.
of the entangled pair (signal) in the polarization sensi- or form a standing wave in the interferometer: coher-
tive interferometer where it interacts with the plasmonic ent control of absorption is lost and photons entering
metamaterial absorber. We placed the absorber on a the metamaterial film suffer probabilistic absorption of
piezo-driven actuator in the center of the interferome- approximately50%. Asmalldifferenceinthelevelofab-
ter (see Fig.1). We then detected the level of light in- sorption between curves for vertical and horizontal po-
tensity at the interferometer output by taking the sum larizations is explainable by residual anisotropy of the
of the photon counts registered by photodetectors PD plasmonic absorber.
A
and PD that are heralded by the detection events of On the contrary, if heralding is performed with the
B
the idler photons on PD . We then normalized these idler polarization set to +45◦ with respect to the plane
i
to the total level of photon counts when the absorber is of the interferometer, we observe a clear oscillation of
removed from the interferometer and recorded the nor- absorptionasafunctionoftheabsorber’spositioninthe
malized level as a function of absorbers position along standing wave (curve with red circles in Fig.2-a). The
the standing wave. The results of these measurements which-path information has been erased and the path-
are presented in Fig.2. entangled single photon wavefunction forms a standing
No dependence of photon counts jointly registered by wave in the interferometer:
photodetectors PD and PD on the position of the
plasmonic metamatAerial were Bseen if the heralding was (cid:104)+45|Ψ(cid:105)= 1(cid:0)|−45(cid:105) |0(cid:105) −eiφ|0(cid:105) |−45(cid:105) (cid:1) (6)
2 A B A B
performed with an idler polarization set (with polarizer
ξ inFig.1)toverticalorhorizontal(curveswithblackdi- The corresponding modulation of the absorp-
amonds for V and green squares for H in Fig.2-a). This tion/transmission is shown in Fig.2-a. We note
measurement and distinguishability of which-path infor- that when absorption is achieved for +45◦, transmission
mation derived from Eq.(4) can be described by: is correspondingly observed for −45◦. Each entangled
photon entering the interferometer is therefore deter-
(cid:104)H|Ψ(cid:105)= 1(cid:0)|H(cid:105) |0(cid:105) −eiφ|0(cid:105) |V(cid:105) (cid:1) (5) ministically absorbed and converted into a plasmon in
2 A B A B
the nanostructure.
Thus, the single photon wavefunction does not interfere Finally, in order to underline the role of polarization
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to the fundamental differences in polarization proper-
a) 1 “Perfect transmission” ties of the generated photons. The regime of high Bell
s
tn +45 parameter implies that photons traveling in the same
u
o0.8 direction, but emerging from the intersections of two
c
e phase-matchingconesoftheparametricdownconversion
c
n
ed0.6 V crystal can create arbitrary superpositions of vertically
ic and horizontally polarized states defined by the nonlin-
n
io ear down-conversion process. As a result entangled, or-
c d0.4 thogonally polarized pairs of photons are generated with
e
zila H arbitrary polarization basis. In contrast, in the regime
m0.2 of low values of the Bell parameter, quantum superpo-
r
oN sitions of vertically and horizontally polarized states are
“Perfect absorption” not formed and the parametric device generates orthog-
0
onally polarized photons where idler and signal photons
-0.5 0 0.5
can either be horizontally or vertically polarized. This
Sample position (units of λ)
b) 1 mixed state produced is thus not sufficient to produce
interferences, unlike an entangled state.
s
tn S = 2.66 Conclusion.— In conclusion, we have demonstrated a
uoc0.8 regime of nonlocal control of dissipation of polarization-
e
c heraldedphotons. Byselectingtheidlerphotonpolariza-
n
ed0.6 tionthatneverenteredtheinterferometer,wecanswitch
icn S = 2.09 the metamaterial from the regime of travelling-wave ab-
ioc d0.4 sorptiontotheregimeofcoherentabsorption. Wethere-
e foredemonstratedanewtypeofquantumgateforwhich
z
ila the output signal can be switched nonlocally in the ’co-
m0.2
r herenttransmission’regimefromunitarytransmissionto
o
N a probabilistic 50% transmission. Alternatively, in the
0 ’coherent absorption’ configuration, the system can be
-0.5 0 0.5 switched nonlocally from zero transmission to a proba-
Sample position (units of λ) bilistic 50% transmission.
It should be noted that control of dissipation of
FIG. 2. Normalized transmission of the plasmonic thin ab- polarization-heralded photons does not imply that the
sorberplacedintheinterferometer,a)registeredfordifferent total dissipation of light energy on the absorber can be
polarizationstatesofthephotonsdetectedintheidlerchannel nonlocally controlled. Indeed, photons with other polar-
withverticalpolarization(blackdiamonds),horizontalpolar-
izationstatesarealwayssimultaneouslypresentandalso
ization (green squares) and with polarization at 45◦ to the
entertheenergybalancemakingthetotaldissipationin-
plane of interferometer (red circles). b) presents the photons
dependent from the heralding or nonlocal control.
detected in the idler channel with polarization at 45◦ to the
Theapproachshownherecanbeusednotonlyfornon-
planeofinterferometerfortwodifferentlevelsofpolarization
entanglement of the idler and signal photons: ’strong’ entan- localcontrolofcouplingofphotonstolocalizedplasmons,
glement with S=2.66 (red circles) and ’weak’ entanglement but can also be exploited for the nonlocal control of cou-
with S=2.09 (blue triangles). pling of photons to plasmon polaritons in polarization-
sensitive schemes where photon-plasmon entanglement
can be envisaged.
entanglement,wecomparedtheresultsfromexperiments Following a period of embargo, the data from
performed with two levels of polarization entanglement. this article can be obtained from the Univer-
We adjusted our photon source from the regime when it sity of Southampton ePrints research repository,
generatedentangledstatesclosetomaximumBellparam- http://dx.doi.org/10.5258/SOTON/xxxxx
eterS =2.657±0.004,toaratherlowdegreeofentangle- Acknowledgements. The authors acknowledge the
mentwithS =2.087±0.004. Thesourceofphotonswith support of the Singapore MOE Grant MOE2011-
alowerdegreeofentanglementyieldedabsorptionmodu- T3-1-005, EPSRC (U.K.) grants EP/M009122/1 and
lationofapproximately14%(seeFig.2-b,curvewithblue EP/J00443X/1 and EU Grant ERC GA 306559. C.C.
triangles) compared to the 80% (see Fig.2-b, curve with would like to thank the Champagne-Ardenne region,
red circles) attainable with strongly entangled photons. the French LABEX Action and the EU COST Action
The reduction of the absorption modulation visibility Nanoscale Quantum Optics. Authors acknowledge N.
in the experiments performed with photon pairs with Zheludev for inspiring and supporting this work and T.
high and low values for the Bell parameter is relevant Rogers and G. Adamo for useful discussions.
5
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