Quantum teleportation from a telecom-wavelength photon to a solid-state quantum memory

5 MB·

by  Felix Bussieres

Quantum teleportation from a telecom-wavelength photon to a solid-state quantum
memory
F´elix Bussi`eres,1,∗ Christoph Clausen,1,† Alexey Tiranov,1 Boris Korzh,1 Varun B. Verma,2
Sae Woo Nam,2 Francesco Marsili,3 Alban Ferrier,4 Philippe Goldner,4 Harald
Herrmann,5 Christine Silberhorn,5 Wolfgang Sohler,5 Mikael Afzelius,1 and Nicolas Gisin1
1Group of Applied Physics, University of Geneva, CH-1211 Gen`eve 4, Switzerland
2National Institute of Standards and Technology, Boulder, Colorado 80305, USA
3Jet Propulsion Laboratory, California Institute of Technology,
4800 Oak Grove Drive, Pasadena, California 91109, USA
4Chimie ParisTech, Laboratoire de Chimie de la Mati`ere Condens´ee de Paris,
CNRS-UMR 7574, UPMC Univ Paris 06, 75005 Paris, France
5Applied Physics / Integrated Optics Group, University of Paderborn, 33095 Paderborn, Germany
(Dated: January 28, 2014)
4
1 In quantum teleportation [1], the state of a single quantum system is disembodied into classical
0 information and purely quantum correlations, to be later reconstructed onto a second system that
2 has never directly interacted with the first one. This counterintuitive phenomenon is a cornerstone
ofquantuminformationscienceduetoitsessentialroleinseveralimportanttasks[2–4]suchasthe
n
long-distance transmission of quantum information using quantum repeaters [5]. In this context, a
a
J challenge of paramount importance is the distribution of entanglement between remote nodes, and
tousethisentanglementasaresourceforlong-distancelight-to-matterquantumteleportation. Here
7
wedemonstratequantumteleportationofthepolarizationstateofatelecom-wavelengthphotononto
2
the state of a solid-state quantum memory. Entanglement is established between a rare-earth-ion

dopedcrystalstoringasinglephotonthatispolarization-entangledwithaflyingtelecom-wavelength
]
h photon [6, 7]. The latter is jointly measured with another flying qubit carrying the polarization
p state to be teleported, which heralds the teleportation. The fidelity of the polarization state of
- thephotonretrievedfromthememoryisshowntobegreaterthanthemaximumfidelityachievable
t
n withoutentanglement,evenwhenthecombineddistancestravelledbythetwoflyingqubitsis25km
a of standard optical fibre. This light-to-matter teleportation channel paves the way towards long-
u distance implementations of quantum networks with solid-state quantum memories.
q
[

Quantum teleportation [1] allows the transfer of a for entanglement distribution, but it requires the flying
1
quantumstatebetweenremotephysicalsystemsthrough qubits to have a suitable telecom wavelength (i.e. with
v
8 the use of quantum entanglement and classical commu- minimal absorption). Satisfying this requirement using
5 nication. The combination of quantum teleportation the aforementioned emissive quantum memories is diffi-
9 with quantum memories provides scalable schemes for cult,becausethewavelengthoftheflyingqubitisstrictly
6 quantum computation [2], quantum repeaters [3, 5] and determined by the discrete energy levels of the quan-
.
1 quantum networks [4]. Light-to-matter quantum tele- tum memory, and this wavelength is typically far away
0 portation was demonstrated by use of quantum memo- from the low-loss region of standard optical fibre. More-
4 ries based on warm [8] or cold [9] atomic ensembles, or over, the spectral widths obtained with resonant emis-
1
a quantum dot spin qubit [10]. In these demonstrations, sion in atomic ensembles are very narrow (a few MHz
:
v the memory emits a flying qubit (i.e. a qubit encoded in at most), which effectively reduces the rate at which
i a photon) with whom it is entangled, and the photon is the flying qubits can be generated, and thus the rate at
X
usedtodistributetheentanglementnecessarytoperform which quantum teleportation can be attempted. Finally,
r
teleportation. these memories typically have a low multimode capac-
a
Inordertoachievelong-distancelight-to-matterquan- ity [12], which limits the entanglement distribution rate
tumteleportation,andmoregenerallytoexchangequan- in a long-distance configuration [5]. To overcome these
tuminformationbetweendistantnodesofaquantumnet- limitations,anapproachbasedonsourcesofphotonpairs
workinascalableway,werequireefficientandmultimode combined with multimode quantum memories was pro-
quantum memories with on-demand read-out, as well as posed [13]. The essential idea is that the sources create
a practical and efficient method to distribute entangle- pairs comprised of one telecom-wavelength photon that
ment [5, 11]. Optical fibre is a naturally suited media is used to distribute entanglement between remote sta-
tions, while the other photon other is stored in a nearby
quantum memory. In this context, quantum memories
based on rare-earth doped crystals are promising candi-
∗ [email protected] dates due to their large storage bandwidths and multi-
† Current address: Present address: Vienna Center for Quantum modecapacity[11]. Intherecentyears,theywereusedto
Science and Technology, TU Wien - Atominstitut, Stadionallee demonstrate high-efficiency storage [14], long coherence
2,1020Vienna,Austria.
2
times [15], multimode storage [16], on-demand readout viously shown to faithfully store arbitrary polarization
atthesingle-photonlevel[17],storageofphotonicentan- statesofsinglephotonswithauniformefficiency[20–22].
glement [6, 7] and heralded entanglement between two The absorption bandwidth of the quantum memory is of
crystals [18]. Here we demonstrate quantum teleporta- theorderof600MHzandstoresphotonsfor50nswithan
tion of the polarization state of a telecom-wavelength overall efficiency of 5% using the atomic frequency comb
photon onto the state of a single collective excitation (AFC)storageprotocol[12]. Thequbitstatetoteleport,
stored in a rare-earth-ion doped crystal. For this, a pair henceforth denoted the input state, is encoded in the po-
ofbroadbandpolarization-entangledphotonsisfirstgen- larizationofaphotonfromaweakcoherentstate(WCS)
erated from spontaneous parametric downconversion in at 1338 nm that is created through difference-frequency
nonlinear waveguides, and one photon from the pair is generationinaseparatenonlinearwaveguide. Thisauto-
stored in a nearby rare-earth-ion doped crystal. The maticallyyieldsthesamecentralwavelengthfortheWCS
othertelecom-wavelengthphotonfromtheentangledpair andidlerphotons(seetheSI).Theindistinguishabilityof
is sent to a Bell-state analyzer where it is jointly mea- theWCSandtheidlerphotonwascheckedindependently
sured with a photon that is carrying the polarization of the quantum teleportation through the observation of
qubitstatetobeteleported. Thepolarizationstateofthe aHong-Ou-Mandeldipof81%visibility(seetheSI).The
photon retrieved from the quantum memory is then an- Bell state measurement (BSM) between the idler photon
alyzed with quantum state tomography, and the fidelity and the input state is done by sending them through a
of several teleported states is shown to outperform the 50/50 beam splitter, projecting their joint state on the
classical benchmark. We also performed teleportation in Bell state |Ψ−(cid:105) = √1 (|HV(cid:105)−|VH(cid:105)) when they are de-
2
aconfigurationwherethecombineddistancetravelledby tected in different output modes [23]. Two polarizers re-
both telecom-wavelength photons is 25 km in standard spectively selecting horizontal and vertical polarizations
opticalfibrewhilestilloutperformingtheclassicalbench- on those output modes remove accidental coincidences
mark, demonstrating the long-distance capability of our of photons with identical polarizations. The photons are
approach. Of crucial importance to achieve this is the then coupled in single mode optical fibres and detected
use of highly-efficient superconducting nanowire single- using tungsten-silicide superconducting-nanowire single-
photon detectors [19], which significantly improves the photon detectors [19, 24, 25] (SNSPDs), shown as D
1
success rate of the teleportation. and D on Fig. 1. These SNSPDs were specifically de-
2
The experiment is represented on Fig. 1, and details signedtooperateat2.5K,whichishigherthanprevious
aregiveninthemethodsandinthesupplementaryinfor- demonstrations (operating at around 1 K or less). This
mation (SI). A pair of entangled photons at 883 nm (the means the detectors could for the first time be operated
signal photon)and1338nm(theidler photon)iscreated in a simple two-stage closed-cycle cryocooler. Their effi-
from spontaneous parametric downconversion (SPDC). ciencydependsonthebiascurrentandreached75%with
For this, 532-nm light is coherently pumping two non- a temporal resolution (jitter) of ∼ 500 ps. The jitter of
linear waveguides such that the photon pair is in su- the detectors is smaller than the coherence time of the
perposition of being created in a first waveguide (with photons, meaning that coincidences on the SNSPDs for
horizontal polarizations |HH(cid:105)) and in a second waveg- which the WCS and idler photons overlap can be tem-
uide(withverticalpolarizations|VV(cid:105)). Recombiningthe porally resolved and post-selected. The teleportation is
output modes of the waveguides on two polarizing beam completed by retrieving the stored signal photon from
splitters(PBS)yieldstwoopticalmodesrespectivelycon- the quantum memory and sending it into a polarization
taining the signal and idler photons prepared in an en- analyzer, where it is detected by single-photon detector
tangled state that is very close to √12(|HH(cid:105)+eiϕ|VV(cid:105)). D3orD4. Thequbitstateoftheretrievedphoton,hence-
The spectra of the idler photon is afterwards filtered to forth denoted the retrieved state, requires a unitary cor-
a 240 MHz spectral width, corresponding to a coherence rection [1] that is included in the polarization analyzer.
time τ = 1.4 ns. Similarly, the signal photon is filtered Inafirstseriesofmeasurements,theWCSphotonand
to a width of 600 MHz with an etalon. However, due the idler photon both travelled a few meters before the
to energy conservation in SPDC, detection of the idler BSM (see Fig. 1), and their detection occurred while the
photon projects the signal’s spectrum to a width that signal photon was stored in the quantum memory. To
nearly reaches 240 MHz as well. This spectral width is post-select the threefold detections with the correct tim-
more than five times larger than previous experiments ing, we plot the temporal distribution of the measured
with the same type of quantum memory [6, 18], which threefold coincidences as a function of the delays δt
j1
considerably increases the intrinsic repetition rate of our and δt between a detection at D (j = 3 or 4) and
j2 j
experiment. detections at D and D . The results for the telepor-
1 2
Following the creation of a pair, the signal photon is tation of the state |−(cid:105) = √1 (|H(cid:105)−|V(cid:105)) are shown as
2
directly sent to a 14 mm-long quantum memory con- two-dimensionalhistogramsonFig.2-a(withD project-
3
sisting of two inline neodymium-doped yttrium orthosil- ing on |−(cid:105)), and 2-b (with D projecting on |+(cid:105)). Off-
4
icatecrystalsinterspacedwithahalf-waveplate(HWP). sets on the detection times are chosen such that events
This configuration compensates for the polarization- at the vicinity of the centre of the histograms (i.e. for
dependent absorption of a single crystal, and was pre- δt ,δt <τ =1.4 ns) correspond to the actual telepor-
j1 j2
3
Polarization
WSi SN2.S5P DKs D2 D1 WCSm5e0a/s5Bu0erellm steantet12.4 km VBG Etalon SignalVmBQGuamnetumomr2.y6 KC1 C2 analyzer DD43
Input state preparGatrion12.4 km C(Id1a3lev3ri8 t ynm) M DM883 n PPSKwTP (8pL8irg3et pnham rfoa)tri omne mory
53828 3n mnmDM PPKTP 1338 nm Lens PBS QWP HWPEntanglement sourceD PPLN 532 nm
FIG.1. Experimental setup. Thesystemcomprisesthesourceofpolarization-entangledphotonsat883nm(thesignal)and
1338nm(theidler)usingfilteredspontaneousparametricdownconversionfromtwononlinearwaveguides(PPLNandPPKTP)
coherently pumped with 532 nm light. After the waveguides, the signal and idler modes are separated using dichroic mirrors
(DM)andarethenindividuallymanipulatedtoobtaingoodoverlapafterrecombinationattwopolarizingbeamsplitters(PBS),
as well as high transmission through the filtering cavity and etalon. A single pair of energy-correlated spectral modes of the
signal and idler photons are selected using volume Bragg gratings (VBG). The signal photon is sent to a neodymium-based
polarization-preserving quantum memory that was priorly prepared as an atomic frequency comb (AFC) using 883 nm light
(see Methods). A switch (Sw) selects either the preparation light or the signal photons. The weak coherent state (WCS) at
1338 nm is created through difference-frequency generation from 532 and 883 nm light. The WCS is then selected using a
grating (Gr) and coupled in an optical fibre. The input state to be teleported is prepared using wave plates and sent towards
a50/50beamsplitter(BS)whereitismixedwiththeidlerphotontoperformtheBellstatemeasurement. Theoutputmodes
oftheBSarepolarizationfilteredandsenttowardstwohigh-efficiencydetectorsbasedonWSisuperconductingnanowires(D
1
and D ) operated at 2.5 K in a closed-cycle cryocooler that is 10 m away from the quantum memory. A coincidence detection
2
at D and D heralds a successful Bell state measurement. The signal photon retrieved from the quantum memory is sent to
1 2
apolarization-stateanalyzerwhereitisdetectedonD orD . TheidlerandWCSphotonsareeachtransmittedovereithera
3 4
short distance, or 12.4 km of single mode optical fibre.
tation (see SI). Fig. 2-a shows an increased number of purity P = Tr(ρ2) of the retrieved state, where P = 1
countsatthecentre,whereasFig.2-bhasadip,whichis for a pure state, P = 1/2 for a completely mixed state,
expected if the retrieved state is close to the input state and 1 <P <1 otherwise. Since the input state is effec-
2
|−(cid:105). This is more easily visualized on Fig. 2-c (or 2-d), tively pure, P is related to the amount of depolarization
which shows a horizontal slice of 2-a (or 2-b) centred on caused by the teleportation process, which includes the
δt =0 (or δt =0). storageofthesignalphoton. Here,themaincauseofthis
31 41
depolarization is noise coming from multi-pair emission
The fidelity of the retrieved state ρ with respect to fromthesourceandofmultiplephotonsintheWCS;see
the input state |ψ(cid:105) (which here is effectively pure), is the SI. The measured purity with the input state |−(cid:105) is
F = (cid:104)ψ|ρ|ψ(cid:105). It is equal to one if the teleportation is 94±6%. This value allows us to find an upper bound
√
perfect, which implies that ρ = |ψ(cid:105)(cid:104)ψ|. For the tele- F = 1(1+ 2P −1) = 97±3% on the observable
max 2
portation of the state |−(cid:105) discussed above, the fidelity fidelity, assumingthelatterisaffectedbynoiseonly, and
of the retrieved state can be readily be estimated from notbyanadditional(andundesired)unitaryrotationon
the number of events observed at the centre of Fig. 2-c the Bloch sphere.
(δt = 0) and at the minimum of Fig. 2-d (δt = 0),
32 42
after a bias due to the different coupling and detection The fidelity and the purity of the retrieved state was
efficiencies of D and D is removed (see SI). The values also evaluated with other input states, and the results
3 4
that we used for the calculation of the fidelity are shown are listed in table 1 (see the SI for the histograms). The
asthesoliddiamondson2-cand2-d(seeSIforanexpla- expected fidelity of an arbitrary state is F¯ = 23F¯e+ 13F¯p,
nationofhowthesepointshavebeenselected). Themea- where F¯ and F¯ are the average fidelities measured
e p
suredfidelityis92±4%. Toobtaincompleteinformation on the equator and the pole, respectively. We find
about the state ρ, we performed quantum state tomog- F¯ =89±4%, which is larger than the maximum fidelity
raphy [26] by measuring in the {|R(cid:105),|L(cid:105)} and {|H(cid:105),|V(cid:105)} of66.7%achievablewithaprepare-and-measurestrategy
bases (see the SI for the histograms of these measure- that does not use entanglement [27]. The fidelities for
ments). With this information, we can also calculate the states on the equator of the Bloch sphere (|+(cid:105),|−(cid:105),|R(cid:105))
4
a c e f h
Counts nts Teleportation of Counts
u
o
d c
b d detecte g i
of
n
o
Counts Fracti Counts
Angle of the analyzer’s HWP (°)
FIG. 2. Experimental results. The results of the teleportation of the input state |−(cid:105) are shown on a through d. a is a
two-dimensional histogram showing the number of threefold coincidences between detectors D , D and D as a function of
1 2 3
the delays δt and δt between detections at D and D and D . b is the same as a with D instead of D . Each histogram
31 32 3 1 2 4 3
indicates on which polarization state the retrieved photon was projected onto (|−(cid:105)(cid:104)−| for a and |+(cid:105)(cid:104)+| for b). Each pixel
correspondstoasquaretimewindowwhosesideisof486psduration. Thisissmallerthanthecoherencetimeofthephotons,
which is necessary to temporally resolve the detection events correspond a successful BSM. c and d are horizontal slices of a
and b (centred on δt =0 and δt =0, respectively), and show the respective peak and dip in number of detections at the
31 41
centre. The black diamonds shown are the points that have been used to estimate the fidelity of the teleportation. e shows
the detected fraction of counts on D and D of the analyzer with input state |+(cid:105), when the retrieved state is measured in
3 4
a basis that is rotated around the equator of the Bloch sphere. Solid lines show the values expected from the quantum state
tomography. f through i show the results of the teleportation of |+(cid:105) when the combined distance travelled by the idler and
WCS photons is 25 km of standard optical fibre.
configuration where the WCS photon and the idler pho-
TABLE I. Measured fidelities and purities for all input
ton each travelled through 12.4 km of standard single
states. TheuncertaintiesareobtainedfromMonteCarlosim-
modeopticalfibresbeforetheBSM,yieldingacombined
ulations assuming a Poisson distribution of the number of
travel distance of 24.8 km. The histograms show a dip
threefold events. Also shown is the upper bound on the fi-
(Fig. 2-f-h) and a peak (Fig. 2-g-i), which are indicatives
delity F that is obtained from the measured purity.
max
of the teleportation. The fidelity of this measurement is
Input state Fidelity (%) Purity (%) F (%)
max 81±4%, i.e. the same as the one measured without the
|H(cid:105) 94±3 93±3 96±3
fibres. This is consistent with the fact that the added
|−(cid:105)= √1 (|H(cid:105)−|V(cid:105)) 92±4 94±6 97±3
2 lossisroughlysamefortheWCSandidlermodes,which
|R(cid:105)= √12(|H(cid:105)+i|V(cid:105)) 84±4 73±5 84±4 keepstheirrelativecontributionstothenoiseatthesame
|+(cid:105)= √1 (|H(cid:105)+|V(cid:105)) 82±4 83±9 91±6 level as without the fibres (see the SI).
2
|+(cid:105) (12.4 km) 81±4 — —
Our experiment demonstrates the feasibility of long-
distance teleportation of a single quanta of light onto a
solid-state quantum memory. The fundamentals of our
are all smaller than for |H(cid:105) which is consistent with the experiment could be used to demonstrate a small-scale
factteleportationofthelatterisunaffectedbyslowdrifts network of remote quantum memories, or a real-world
of the phase ϕ of the entanglement, and by the finite jit- quantum repeater based on an optical-fibre architecture.
ter of the detectors (see SI). However, the main factor In this context, we require a quantum memory with on-
limiting of the measured fidelities is the noise due to the demand readout based on storage on spin levels. Such
creation of several pairs of photons and/or the presence levels are currently being used for spin-wave storage at
ofmorethanonephotonintheWCS(seeSI).Moreover, the single-photon level in europium-doped crystals [17],
the observed differences in the purities indicate that this and are a promising avenue towards fulfilling require-
noise fluctuated from state to state. Finally, for the tele- ments of a quantum repeater [11]. Alternatively, the
portation of |+(cid:105), we show on Fig. 2-e the variation of need for on-demand readout (in time) could be allevi-
the number of threefold coincidences when the measure- ated by exploiting spectral multimode storage in rare-
mentbasisisgraduallyrotatedaroundtheequatorofthe earth crystals [28], which however needs to be comple-
Bloch sphere. The horizontal offset in the fitted curve is mented with a large increase in the number of other re-
due to an additional rotation of the Bloch vector that, sources. In a broader context, our experiment could be
in addition to the purity-reducing noise, further reduces useful to transfer quantum information between remote
the observed fidelity below the Fmax upper bound. quantum network nodes made of rare-earth crystals cou-
Wealsoperformedateleportationofthe|+(cid:105)stateina pled to superconducting qubits embedded in microwave
5
resonators [29, 30], which could ultimately lead the real- by the European project QuReP and the Swiss NCCR
izationofdeterministictwo-qubitgates[31]insolid-state QSIT. Part of the research was carried out at the Jet
network nodes. Propulsion Laboratory, California Institute of Technol-
ogy, under a contract with the National Aeronautics
and Space Administration. F.B. and C.C. contributed
ACKNOWLEDGMENTS equally to this work.
We thank Rob Thew, Pavel Sekatski and Hugo
Zbinden for useful discussions. We acknowledge support
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6
METHODS both photons having horizontal polarization) and in the
PPKTP waveguide (with both photons having vertical
WSi superconducting nanowire detectors polarization). The pair creation probability is set to be
lowenough(atabout1%withinatimewindowof500ps)
suchthatthecreationofmorethanonepairismuchless
The W Si detectors optimized for maximum ab-
x 1−x likely (with a probability 10−4). The output modes of
sorption at a wavelength of 1340 nm were fabricated on
the waveguides a collimated, and the signal and idler
a 3 inch Silicon wafer. A gold mirror was fabricated by
modes are separated using dichroic mirrors. This yields
depositing 80 nm of gold on top of Ti using electron-
four spatial modes whose transverse profiles are individ-
beam evaporation and photolithographically patterned
uallymanipulatedwithtelescopes,whosenecessityisde-
using a lift-off process. A space layer between the gold
scribed below. The two spatial modes of the signal pho-
mirror and WSi detector consisting of 195 nm of SiO
2 ton are then recombined in a single one using a PBS.
wasthendepositedbyplasma-enhancedchemicalvapour
Similarly, the modes of the idler are also recombined us-
deposition (PECVD). A 4.5 nm-thick W Si layer
x 1−x inganotherPBS.AfterthetwoPBS,wehavetwospatial
(x≈0.8) was deposited by DC magnetron co-sputtering
modes containing a pair of photons prepared in a state
from separate W and Si targets at room temperature,
that is very close to √1 (|HH(cid:105)+eiϕ|VV(cid:105)) (see the SI).
andcappedwith2nmofamorphousSitopreventoxida- 2
tion. Electron-beam lithography and etching in an SF The telescopes are necessary to obtain a good overlap
6
plasma were used to define nanowire meanders with a when recombining the two modes of the signal photon
width of 130 nm and pitch of 260 nm. An antireflection (likewise for the idler photon), and also to adjust the
coating was deposited on the top surface consisting of modeoftheidlerphotontomatchthemodeoftheFabry-
225 nm SiO2, 179 nm SiN , 231 nm SiO , and 179 nm PerotcavitythatcomesafterthePBS.Thespectraofthe
x 2
SiN . A keyhole shape was etched through the Si wafer idler (or signal) photon is filtered to a Lorentzian line
x
around each SNSPD, which could then be removed from width of 240 MHz (or 600 MHz) using the combination
the wafer and self-aligned to a single mode optical fi- of a Fabry-Perot cavity (or an etalon) and a highly re-
bre [19]. The size of the SNSPD is 16×16 µm2, larger flectivevolumeBragggrating(VBG).Severalprocedures
than the 10 µm mode field diameter of a standard sin- are implemented to monitor and stabilize the properties
gle mode fibre, to allow for slight misalignment. When of the source, which list here. Firstly, the pump light
cooledto2.5K,theSNSPDshaveanoptimalsystemde- at 532 nm is continuously stabilized in frequency using a
tectionefficiencyof75%withadarkcountrateoftheor- feedbackmechanismbasedondifference-frequencygener-
derof300countspersecond. Duringtheexperiment,the ationoflightat1338nmfrommixingthe532and883nm
temperature of the cryostat could fluctuate and the bias preparationlightinthePPLNwaveguide,asdescribedin
current would need to be adjusted accordingly to keep it Ref. [6]. Thisensuresthattheenergyofapumpphoton
sufficientlybelowtheswitchingcurrent. Thiscouldresult is correlated with the central frequency of the spectra of
in less than optimal performances such as, in the worst the signal and idler photons, which are determined by
case,adetectionefficiencyof60%withadarkcountrate the filters. Secondly, the residual 532 nm light present
of a few kHz. in the unused output ports of the two polarizing beam
splitters that are just before the cavity and the etalon is
used to continuously lock the phase ϕ of the entangled
Broadband source of polarization-entangled photons state. Forthis,anerrorsignalisderivedfromthe532nm
light, and a feedback is applied on two piezo mounted
mirrors (one for the signal photon and one for the idler
Thesourceisusingtwoperiodically-poled(PP)nonlin-
photon) that are placed right after the dichroic mirrors.
ear waveguides (see Fig. 1). One is a 1.3 cm-long waveg-
Fast fluctuations are compensated for, but ϕ could nev-
uide embedded in potassium titanyl phosphate (PP-
ertheless slowly drift by a few degrees per hour, at most.
KTP), and the other is a 6 cm-long titanium-indiffused
Thirdly,acharacterizationofthepropertiesofthesource
waveguide based in lithium niobate (PPLN). The fab-
is performed every 30 minutes with a completely autom-
rication of the PPLN waveguide required improvements
atized procedure. For this, the teleportation is stopped
of the poling technologies to realize periods as short as
6.5 µm, which was required for this experiment. It com- momentarily for a few minutes by switching off the weak
coherentstate. Then, bymeasuringtwofoldcoincidences
prises an input taper to facilitate the coupling of the
betweentheidlerphotonandthetransmittedsignalpho-
pump light at 532 nm into the fundamental mode of
ton,thevisibilityofthesourceismeasured,andthevalue
the waveguide, and is coated with anti-reflection coat-
of the phase ϕ is extracted (see SI). The measured av-
ings. A pair of photons at 883 and 1338 nm is created
erage visibility was 93%. From these measurements, the
from spontaneous parametric downconversion (SPDC).
For this, pump light at 532 nm with 45° polarization is second-order cross-correlation function between the idler
and the signal photons is estimated and used to moni-
first split on a polarizing beam splitter (PBS). Waveg-
tor the probability p to emit a pair of photons in a time
uides are inserted in the two output modes of the PBS
window of about 500 ps. We measured p ∼ 10−2. The
and are pumped coherently. Hence a pair is in a super-
monitoring and stabilization yield stability for periods
position of being created in the PPLN waveguide (with
7
as long as 24 hours. We note that the 532-nm light is 120MHzlimitimposedbytheeffectivebandwidthofthe
pulsedin25ns-longgaussianpulseswith100nsbetween double-passAOM,thelightattheoutputoftheAOMis
successive pulses, which is twice the storage time. This sentintoaphasemodulatorthatcreatesfirstandsecond-
removes most of the detrimental optical noise stemming order sidebands, all separated by 120 MHz. In this way,
from the superposition of a signal photon retrieved from thecombatthecarrierfrequencyiscopiedtwiceoneach
thememorywithanotherphotoncreated50nslaterand side, yielding an overall comb width of 600 MHz. The
thatistransmittedthroughthememoryinsteadofbeing overall efficiency of the polarization preserving memory
stored[18]. Thisimprovesthesignal-to-noiseratioofthe is 5% with a 50 ns storage time. This is slightly lower
teleportation by a factor ≥ 10 with respect to previous thanwhatweachievedinourpreviousdevice(about8%,
experiments [6, 18]. see [20]). WeattributethisreductiontotheshorterZee-
manrelaxationtime,whichreducestheopticaldepthand
contrastoftheatomicfrequencycomb. Therelaxationof
the comb structure, during the 10 ms of the experimen-
Polarization-preserving quantum memory
tal cycle during which teleportation is performed, also
causes a decay of the efficiency. Finally, the bandwidth
The compact, broadband and polarization-preserving
extension using the sideband caused a comb structure
quantum memory was obtained by placing two 5.8 mm-
with reduced contrast at the edges, due to insufficient
long Nd3+:Y SiO crystals around a 2 mm-thick half-
2 5 optical power in the outer sidebands.
wave plate, resulting in a total device length of 14 mm.
The light beam was focused in the centre of the crys-
tals using a 250 mm lens. The compact device made it
possible to achieve a sufficiently tight focus over the en-
tirelength, whichiscrucialforefficientopticalpumping.
Our previous memory device [20] required two separate
passesthroughthecryostat,oneforeachcrystal,thereby
causingexcessivelossesduetothemanyopticalsurfaces.
Herewealsoaddedanti-reflectivecoatingsonallsurfaces
(cryostat windows, crystals and half-wave plate), further
reducinglosses. Theresultingoff-resonancetransmission
coefficient was 95%, much higher than our previous de-
vices. Using shorter crystals would, however, reduce the
optical depth of the memory, which in turn would lower
the intrinsic memory efficiency [12]. To overcome this
losswegrewcustomizedNd3+:Y SiO crystalsusingthe
2 5
Czochralski process, with higher neodymium concentra-
tion (estimated to be 75 ppm). These crystals have an
optical inhomogeneous broadening of about 6 GHz, sim-
ilar to our previous crystal (with 30 ppm doping level),
but with a higher absorption coefficient of α=3.7 cm−1
(with an applied magnetic field of 300 mT). The result-
ing optical depth of the polarization-preserving memory
device is d = 2.3±0.1. The optical pumping necessary
for preparing the atomic frequency comb requires two
ground-statelevels,whereoneisusedforpopulationstor-
age, which can be obtained by splitting the ground-state
4I Zeeman doublet with a magnetic field. We used
9/2
the same field strength and orientation as in previous
memory demonstrations [16]. We measured a Zeeman
population relaxation lifetime T = 43 ms in our new
Z
crystals, smaller than in the lower doped crystals (about
100 ms, see Ref. [16]). The atomic frequency comb is
preparedusinganacousto-opticmodulator(AOM),used
in double-pass configuration, that modulates the inten-
sity and frequency of the light from a external cavity
diode laser at 883 nm (centred on the absorption line of
the 4I -4F transition) in order to pump some of the
9/2 3/2
atoms to the other Zeeman level. This is used to create
a 120 MHz comb with a spacing of 20 MHz between the
peaks. To increase the memory bandwidth beyond the
8
SUPPLEMENTARY INFORMATION common horizontal offset of the four curves. The phase
slowly drifted with time, typically by a few degrees per
several hours. For the teleportation measurements, this
I. INTRODUCTION
phase was effectively cancelled by rotating the quarter
wave plate of the analyzer to set the offset of the visibil-
In this Supplementary Information, we provide addi-
ity curves to zero. By monitoring the overall variations
tional details on our experiment. Section II describes
of the amplitudes of the visibility curves, we could also
how the monitoring of the properties of the source of
monitor the balance between two waveguides, as well as
entangled photons and of the source of weak coherent
the coincidence rate of the source. The visibility, aver-
state is done. Section III presents a detailed description
aged over all measurements, was 93%.
of the features of the two-dimensional histograms of the
threefold coincidences from which the quantum state to-
a
mography results are derived. We also model the noise
Chs. 13
stemming from multiple photon pairs and multiple pho- Chs. 14
tons in the weak coherent. Section IV provides details
onthehowthequantumstatetomographyisperformed.
Theeffectoftheaforementionednoiseonthefidelityand
purity is discussed.
b
II. MONITORING OF THE SOURCE OF Chs. 23
ENTANGLED PHOTONS AND SOURCE OF Chs. 24
WEAK COHERENT STATE
A. Characterization of the source of entangled
photon pairs
The source of entangled photons was continuously
monitored during the experiment. Here we provide de-
FIG. S3. Visibility curves for, a, detector pairs D -D and
tails on how we monitored the relative phase ϕ of the 1 3
D -D ,andb,pairsD -D andD -D ,whereD andD are
entangledstate √1 (|HH(cid:105)+eiϕ|VV(cid:105))thatwasproduced, 1 4 2 3 2 4 1 2
2 the detectors for the idler photons, and D3 and D4 are the
as well as the fluctuations of the number of photon pairs detectors of the analyzer of the signal photon.
created in a given time window.
1. Entanglement visibility and phase drift compensation
2. Cross-correlation of idler and signal modes
Automatizedmonitoringofthesourcewasperformeda
leastonceperhourbyproducingavisibilitycurve,which Tomonitorthemagnitudeandstabilityofthenumber
was accomplished as follows. First, the weak coherent of photon pairs created in a given time window, we mea-
state (WCS) was switched off (see Fig. 1), which is the sured the zero-time second-order cross-correlation func-
sameasFig.1ofthemaintext). Then,ahalfwaveplate tionbetweenthedetectedidlerphotonandthetransmit-
wasinsertedbeforethe50/50beamsplitter(BS)usedfor ted signal photon, g , defined as
si
Bell state measurement, and its angle was set such that,
when combined with the polarizers placed just after the g = (cid:104)d†idid†sds(cid:105) ,
beam splitter, a detection on D1 would project on |+(cid:105), si (cid:104)d†idi(cid:105)(cid:104)d†sds(cid:105)
and D would project on |−(cid:105). The state of the corre-
2
sponding signal photon, e.g. √1 |H(cid:105)+eiϕ|V(cid:105) when the where d (or d ) is the annihilation operator for the idler
2 i s
detection occurred at D , was then analyzed by rotating mode (or signal mode), and d† (or d†) is the associated
1 i s
thehalfwaveplate(HWP)oftheanalyzer,projectingon creation operator [32]. With negligible dark counts and
states on the equator of the Bloch sphere. For this mea- single-photon detectors having a timing resolution that
surement we use only coincidences stemming from the is much smaller than the coherence time of the photons,
transmitted photons, i.e. the signal photons that passed one can show that g = 1+1/p ≈ p−1, where p (cid:28) 1 is
si
through the quantum memory without being absorbed. theprobabilitytocreateapairofphotonsinagiventime
The resulting visibility curves (see Fig. S3 for an ex- window [33]. It is also equal to the ratio of the probabil-
ample)showthenumberofcoincidencesoneachdetector itytodetectacoincidencestemmingfromtwophotonsof
of the analyzer (i.e. D and D ), as a function of the an- thesamepair,overtheprobabilitytodetecttwophotons
3 4
gle of the HWP. The phase ϕ is determined from the from different pairs. Measuring a value g > 2 implies
si
9
that the signal and idler fields are non-classically corre-
lated [33]. Moreover, measuring a value g (cid:29) 1 (which
si
implies that p (cid:28) 1) is a necessary condition to create
close-to-maximally entangled states [32] and to show the
non-classical nature of the heralded signal photon [20].
In practice, g was estimated using all the data accu-
si
mulated for the visibility curves during one day. Using
thesedata,weproducedahistogramofthenumberofco-
incidences between the idler and signal modes as a func-
tionofthedelaybetweenthem. Fig.S4-ashowsonesuch
histogram, on which we can see two main peaks over an
oscillating background level. The peak at 0 ns is due to
coincidences involving a transmitted signal photon, and FIG. S4. Histogram of the number of coincidences as a func-
theoneat50nsisduetoastoredsignalphoton,i.e.asig- tion of the delay between the detection of a signal and an
nal photon that was stored and retrieved from the quan- idlerphoton. Eachbinis162pswide. Weseethepeakcorre-
tum memory. Note that the transmitted peak is clipped sponding to the detection of a transmitted signal photon (at
0ns)andthepeakofthestoredandretrievedphoton(50ns).
because we expanded the vertical scale so that we could
The transmitted peak is vertically clipped.
seetheeffectofthepulsedpumplaser,whichgivesriseto
thewideandsmallbumpscentredon-100,0and100ns,
etc (we recall that the pump light at 25 ns was shaped
into 25 ns-wide gaussian pulses separated by 100 ns).
able spectral properties to be indistinguishable from the
We see the reduction of the number of accidental coinci-
idler photons, and therefore to encode the input state of
dences between the bumps, which was the desired effect.
the teleportation. The intensity of the WCS was moni-
Thecross-correlationofthetransmittedpeakg(t) isesti- toredandstabilizedbydivertingasmallportiontowards
si
matedbydividingthenumberofcoincidencesinanarrow a single-photon detector creating a feedback signal con-
window centred on 0 ns by the number of coincidences trolling a variable attenuator. We estimated that the
inanotherwindowcentredonaneighbouringbumpthat meannumberofphotonscontainedina486ps-widewin-
is 100 ns away. The average value of g(t) was 100, and dow at the centre of one WCS was µ≈0.011±0.002 for
si
varied from 80 to 150 for all the measurements. The the teleportation of |−(cid:105), and 0.016 for the teleportation
cross-correlation of the stored photon g(s) is estimated of |+(cid:105), |R(cid:105) and |H(cid:105).
si
bycenteringthefirstwindowonthestoredphotonpeak,
andthesecondone100nsaway, whichisfallsonamini-
mum of the oscillating background. The measured value C. Indistinguishability of the idler and the WCS
ofg(s)variedfrom6to20. Allvaluesweremeasuredwith
si
486 ps-wide coincidence windows. The measured values Projecting the input state and the idler photon on a
of g(s) fluctuate strongly, but they are nevertheless well Bell state (see Fig. 1) requires the ability to post-select
si
above the classical upper bound of 2, which highlights events where the two photons temporally overlapped on
the single-photon nature of the polarization state that is the 50/50 beam splitter (see Fig. 1). This is possible
retrieved from the quantum memory [18, 20, 33]. only if the temporal resolution (i.e. the jitter) of the de-
tectors is smaller than the coherence time of the idler
photon (because the WCS is generated from DFG be-
tween two narrowband lasers, its coherence time is much
B. Weak coherent state (WCS)
longer than the 1.4 ns coherence time of the idler). The
temporal resolution effectively defines temporal modes
As explained in the main text, the source of entangled on which the photons are projected onto when they are
photons was designed such that central frequency of sig- detected. Therefore, we need to consider the indistin-
nal photons corresponds to the centre of the atomic fre- guishability in these modes, which was verified through
quencycombthatiscreatedusingthe883nmdiodelaser, the observation of a Hong-Ou-Mandel dip in an exper-
andsuchthatthefrequencyofthepumplightat532nm iment performed before the quantum teleportation [34].
create photon pairs that satisfy the energy-conservation Forthis,continuous-wave(CW)lightat532nmwasused
imposed by the transmission wavelength of the Fabry- topumpthePPLNwaveguideofthesourcewhilethePP-
Perot cavity of the idler photon. Hence, mixing part of KTPwaveguidewasblocked(seeFig.1),andthefiltered
the 532 nm light and part of the 883 nm diode laser into idlerphotonsweremixedonthe50/50beamsplitterwith
a separate PPKTP waveguide automatically creates co- the WCS. The signal photon was bypassing the quan-
herent pulses of light (through difference-frequency gen- tum memory and used to herald an idler photon with an
eration, DFG) having a frequency that matches the cen- horizontal polarization, the same as the WCS. The idler
tral frequency of the Fabry-Perot cavity, and thus of the photonwasdetectedwithaniobiumnitrideSNSPDs(7%
idler photons (see Fig 1). This light therefore has suit- efficiency) that had jitter of about 100 ps. The photon-
10
We first describe what we would expect in the vicinity
of the central bin of the histogram, at δt = δt = 0,
j1 j2
assuming ideal conditions (i.e perfect optical alignment;
negligible contribution from multi-photons in the WCS,
multi-pairs and dark counts; negligible detection jitter
and dark counts). This centre region corresponds to
the threefold coincidences where the idler photon and
a photon from the WCS were temporally overlapping
at the 50/50 beam splitter (which heralds a successful
Bell state measurement), and the detected signal photon
is the entangled companion of the detected idler pho-
ton. The area of the region is of the order of τ2, where
i
τ ≈ 1.4 ns coherence time of the idler photon. In this
i
region, the probability to have a photon from the WCS
just before the BS and to have an idler photon just be-
fore the BS, is given by pµ (we do not need to take into
account the losses and detector efficiencies in the system
FIG. S5. Coincidence histogram showing a Hong-Ou-Mandel becausetheyallfactoroutinthefinalstepofthecalcula-
dipbetweenanheraldedsignalphotonandtheweakcoherent tion when we compare the probabilities for the different
light. The visibility of the dip is 81%. The horizontal axis is events). Given this, the probability that they split at
thedelaybetweenthedetectionofthesignalphotonandone
the BS can be shown to be equal to 1/4, which corre-
of the detectors behind the 50/50 beam splitter.
sponds to the probability of a successful projection on
the|Ψ−(cid:105)=2−1/2(|HV(cid:105)−|VH(cid:105))Bellstate[23]. Because
the two photons are indistinguishable, they must have
orthogonal polarizations behind the BS (otherwise they
pair creation probability p ≈ 1/g was ≈ 0.0025 in a
si would bunch), but there are two possibilities happening
486-ps window, and the mean number of photon for the
with equal probabilities, namely V in one mode and H
WCS was µ ≈ 0.0035. Fig. S5 shows the observed dip,
in the other, or the opposite. Hence, the presence of the
with avisibility of 81%. From this, we conclude thatthe
orthogonally oriented polarizers after the BS further re-
idler photons and the WCS are close to be completely
duces by a factor of 2 the probability to find one photon
indistinguishable. The visibility is partly reduced by the
in each output arm after the polarizers. In practice, the
noisestemmingfromtheaccidentaldetectionoftwopho-
polarizers were introduced to minimize the probability
tonfromtheWCSortwoidlerphotonscomingfromtwo
to detect two photons with the same polarization after
pairs created simultaneously.
theBS,whichcanhappenifthephotonarenotperfectly
indistinguishable.
When a successful teleportation occurs, the polariza-
III. THREEFOLD DETECTION HISTOGRAMS tionstateofthesignalphotonisequaltothepolarization
state of the photon from the WCS, up to a constant uni-
tary transformation that we include in the analyzer. We
A. Teleportation of |−(cid:105), |R(cid:105) and |+(cid:105)
assume the analyzer is oriented such that a detection at
D corresponds to a projection on the input state. The
Let us consider the conceptual setup of Fig. S6 rep- 3
total threefold coincidence probability is given by
resenting the teleportation of the |−(cid:105) state. We will
use it to explain the main features of the two 2D his- 1 1 1
P (δt =0,δt =0)=pµ· · = pµ. (S1)
tograms corresponding to teleportation of the |−(cid:105) state 123 31 32 4 2 8
towards the signal, when the analyzer is set to measure
Since D projects on |+(cid:105), the probability to register a
inthe{|+(cid:105),|−(cid:105)}basis; see Fig.S7-aandFig.S7-b(they 4
threefold coincidence at D , D and D should be zero:
are identical to Fig. 2-a and 2-b on the main text). For 1 2 4
comparison, the histograms corresponding to the events
P (δt =0,δt =0)=0. (S2)
124 41 42
wherethedetectedsignalphotonwasnotabsorbedbythe
memory (the transmitted photon) are shown on Fig. S8- Let us now consider the case where the WCS photon
a and S8-b. Each histogram shows either the number is arriving later (by a time greater than τ ) compared to
i
of threefold coincidences at D , D and D , or at D , the two entangled photons. A possible realization of this
1 2 3 1
D and D . Each bin (i.e. each pixel) corresponds to would be a threefold with δt = 0 and δt > τ . In
2 4 31 32 i
a window of fixed width and height, which is (486 ps)2 this specific case, the detection at D must stem from
2
here. For a histogram with a detection at D (j = 3 or the WCS, because its detection time is not correlated to
j
4), the y-axis corresponds to the delay δt between the the detection of the signal photon, contrary to the idler
j1
detectionsatD andD ,andthex-axistothedelayδt photon (this is true only if µ (cid:29) p, which is shown in
j 1 j2
between the detections at D and D . section IIIC to be a necessary condition to get a good
j 2