文档库 最新最全的文档下载
当前位置:文档库 › 2012 Realization of reliable solid-state quantum memory for photonic polarization-qubit 1201.4441

2012 Realization of reliable solid-state quantum memory for photonic polarization-qubit 1201.4441

a r

X

i

v

:12

1

.

4

4

4

1

v

2

[

q

u

a n

t

-

p

h

]

2

4

J

a n

2

1

2

Realization of reliable solid-state quantum memory for photonic polarization-qubit Zong-Quan Zhou,1Wei-Bin Lin,1Ming Yang,1Chuan-Feng Li ?,1and Guang-Can Guo 11Key Laboratory of Quantum Information,University of Science and Technology of China,CAS,Hefei,230026,China (Dated:January 25,2012)Abstract We demonstrate a solid-state quantum memory for photonic polarization-qubit.We measure the memory ?delity up to 0.999at 200ns storage time by performing quantum process tomography on the system.This high performance of ?delity should make the memory be suitable for applications in fault-tolerant quantum computation.

Faithfully storing an unknown quantum light state is essential to advanced quantum com-munication and distributed quantum computation applications[1,2].The required quantum memory must have high?delity to improve the performance of a quantum network,which is especially important in fault-tolerant quantum computation[3].For most of the quan-tum error correction schemes,the error rate is restricted below0.01and previous quantum memory based on various physical systems cannot reach this threshold error rate[4–12]. Here we report,for the?rst time,the reversible transfer of photonic polarization states into collective atomic excitation in a solid-state device.The quantum memory is based on an atomic frequency comb(AFC)[13,14]in two pieces of Nd3+:YVO4crystal.The memory performance is tested with single-photon-level coherent pulse.By performing full quantum process tomography on the system,we obtain up to0.999process?delity for the storage and retrieval process.The memory?delity shows little dependence on decoherence for longer storage time.This reliable quantum memory is a crucial step toward quantum networks based on solid-state devices.

Quantum communication channels are naturally carried by photons.To realize a quan-tum network,we must coherently transfer quantum information between the stationary qubits and the?ying photon qubits.Despite some remarkable e?orts in quantum networks based on cold atoms[4–7],trapped ions[2,12],atomic vapors[10,11]and Bose-Einstein condensate[9],there are strong motivations for using more practical systems,e.g.solid-state devices.Rare-earth(RE)ion-doped solids provide a particular electronic structure that can be seen as a frozen gas of atoms,they have excellent coherence properties for op-tical and spin transitions.Moreover,they have already shown excellent capability to store light for extended periods[15]with high e?ciency[16]and a large bandwidth[17–19].Re-cent achievements include the storage of photonic time-bin entanglement generated through spontaneous parametric down conversion(SPDC)[19,20].

Logical qubits with photons can be encoded in several ways,for example via polariza-tion,time-bin,path,phase or photon-number encodings.The polarization degree of freedom is particularly useful because it allows a single-photon qubit to be transmitted in a single spatial and temporal mode.Polarized photons are more easily transportable qubits and are more robust against decoherence.Note that many quantum light sources generate entangled photons with information encoded in their polarization degree,such as the eight-photon en-tangled state generated by SPDC[21]and the on-demand entangled photon pairs generated

by biexciton decay in quantum dots[22].Realizing the quantum interface between quantum memory and other quantum light source will also require the capability of the quantum memory to store the polarization information for light.Therefore,the ability to store polar-ization information with high?delity is of particular interests.One approach to realizing a polarization-qubit memory is to?rst transform the polarization encoding into path encod-ing and then store it into two distant ensembles.This approach has been implemented in both atomic ensembles[4,5,7]and atomic vapors[23].The abovementioned realizations su?er from several practical drawbacks due to the extra step of spatially splitting the input state.Phase locking of the two optical paths[7]may be required,and imperfect spatial mode matching may limit the memory?delity.Another approach is using uniformly ab-sorbed samples for two orthogonal polarizations,which requires no spatially splitting of the input photon.This approach has been implemented with two spatially overlapped atomic ensembles[6],BEC[9]and with a single-atom in a cavity[8].Up to now,the best?delity performance achieved with single-photon-level input is0.95[9].All of these experiments are based on the Raman process or electromagnetically induced transparency(EIT).These processes require a strong control or read light pulse during the memory sequence,which introduces unavoidable noise into the retrieval signal.

AFC is an alternative protocol for realizing quantum memory without a strong control light during the memory sequence.AFC quantum memory with RE doped solids has shown an excellent capability to store quantum light[13,17–20,24,25].Because of the strongly polarization-dependent absorption of ions in crystal,however,all previous experiments have been conducted with a single pre-de?ned polarization.Here,we use an alternative approach to realize AFC quantum memory for polarization-encoded single photons.Two pieces of crystals are used to absorb the orthogonal polarized components that are in the same optical path but at di?erent sites.

The hardware of our quantum memory,which is shown in Fig.1(a),is composed of two pieces of Nd3+:YVO4crystals(doping level10ppm)sandwiching a half-wave plate(HWP). The sizes of the two crystals are nearly equal with1.4mm length along the a-axis.The 4I9/2→4F3/2transition of Nd3+at about879.705nm in the Nd3+:YVO4crystal shows strong absorption of H polarized photons and little absorption of V polarized photons[26]. Here,H(V)denotes horizontal(vertical),which is de?ned to be parallel(perpendicular)to the crystal’s c-axis.This prevents a single piece of Nd3+:YVO4crystal from functioning

>

I n t e n s i t y G Nd 3+(a)

(b)(c)

FIG.1:(a).Illustration of the sample used as the memory hardware for arbitrary polarizations.The arrows represent the c-axis of the crystals.(b).The near 880nm input photons are absorbed at the 4I 9/2→4F 3/2transition of Nd 3+.This transition is strongly H polarized.After a pro-grammable time,the photon will be collectively emitted in a desirable spatial mode.(c).The preparation and storage sequence used in the experiment.

as a polarization-qubit memory because most of the V polarized photons will pass through the crystal without being absorbed.By using a 45?HWP,sandwiched between two parallel Nd 3+:YVO 4crystals,the sample shows near equal absorption depth for H ,V and arbitrary polarized photons.

The AFC protocol requires a pumping procedure to tailor the absorption pro?le of an inhomogeneously broadened solid state atomic medium with a series of periodic and narrow absorbing peaks separated by ?(see Fig.1).The single input photon is then collectively absorbed by all of the atoms in the comb.The atomic state can be represented by,[14],

|1 A =

j c j e iδj t e ikz j |g 1···e j ···g N .(1)

Here N is the total number of atoms in the comb;|g j and |e j represent the ground and

excited states,respectively,of atom j ;z j is the position of atom j ;k is the wavenumber of the input ?eld;δj is the detuning of the atom frequency and the amplitudes c j depend on

FIG.2:The experimental setup for quantum storage of a photonic polarization-qubit in solids. The upper acousto-optic modulators(AOM)produces pump light for the AFC preparation.The lower AOM produces a weak probe light for the storage sequence.The light’s polarizations are initialized by the polarization beam splitters(PBS).The probe light’s polarizations are controlled by the half-wave plate(HWP1)and quarter-wave plate(QWP1).The samples are placed in a cryostat at a temperature of1.5K.Beyond the sample,a phase plate(θ)and HWP4corrects any polarization rotation caused by the sample.The probe light’s polarizations are then analyzed with QWP2,HWP5and a Wollaston prism.The two MCs are used to protect the single-photon detector(SPD)from classical pump pulses.

the frequency and on the position of atom j.The atoms at di?erent frequencies will dephase after absorption,but because of the periodic structure of AFC,a rephasing occurs after a timeτs=2π/?.The photon is re-emitted in the forward direction as a result of a collective interference between all of the atoms that are in phase.The collective optical excitation can be transferred into a long-lived ground state to achieve a longer storage time and an on-demand readout[25].The AFC preparation pulse sequence are shown in Fig.1c,in which pulses with temporal spacing ofτs are sent into the sample every16us.The pumping sequences are repeated300times to achieve an optimal AFC structure.During the storage cycle,N g trials of single-photon-level coherent pulses are sent into the sample,and the AFC echoes are emitted at a time2π/?that is programmed in the pumping procedure.To avoid the?uorescence noise caused by the classical pumping light,the memory cycle begins after waiting for time T w=10T1=1000us after the preparation cycle is completed,where T1is the lifetime of the excited state|e .The complete pump and probe cycles are repeated at a frequency of40Hz.

The experimental setup is shown in Fig.2.The laser source is a CW Ti:Sappier laser(M Squared,Solstis),and the laser’s wavelength is monitored with a wavelength meter(Bristol 621A).The pump light is generated with a260MHz AOM(Brimrose)in a double-pass

con?guration.To protect the single-photon detectors during the preparation procedure,a mechanical chopper(MC)is placed in the pumping optical path.To achieve a uniform memory e?ciency for arbitrary polarized photons,the pumping light should be polarized close to H+V.The H polarized light will be mostly absorbed by the?rst crystal,and the V polarized light will be mostly absorbed by the second crystal,after the polarization rotation by the HWP3.Carefully adjusting the HWP2angle and the pump power can optimize the storage e?ciency and balance the e?ciency of the H and V components.The photons to be stored are generated by another260MHz AOM in double-pass con?guration.The AOMs are controlled by an arbitrary function generator(Tektronix,AFG3252).The HWP1and QWP1 prepares input photons with arbitrary polarizations.The input photons are decreased to single-photon level by the neutral density(ND)?lters.The storage sequence is repeated 1600times at a frequency of1MHz.

Note that the beam splitters and single mode?ber may degrade the?delity of the input photons.To achieve a optimum polarization storage performance,we use a setup that di?ers from those of previous experiments,in which the pump light and probe light have been in counterpropagation or copropagation con?gurations.The pump light is only overlapped with the probe light at the sample.The pump light and probe light are focused with the same lens(focal length:250mm).This setup achieves a small angle(~15mrad)between pump and probe lights.The probe light focuses to a diameter of about100um,while the pump light is collimated to produces a much larger diameter on the sample.The sample is placed in a cryostat(Oxford Instruments,SpectromagPT)at a temperature of1.5K and with a magnetic?eld of0.3T in the horizontal direction.The two parallel Nd3+:YVO4 crystals’c axes are placed in the horizontal direction.The HWP3at45?can exchange H and V polarizations.Because each crystal only strongly absorbs H polarized light,the H polarized input photon is stored in the?rst crystal,and the V polarized light is stored in the second crystal.To rotate the polarization back to the input state,another HWP(HWP4) is placed at45?outside of the cryostat.Because of the small di?erence in the lengths of the two crystals,a phase plate is inserted in the optical path to compensate for the small phase shift between H and V polarized photons.The QWP2,HWP5and Wollaston Prism together choose the polarization of the single photon detections.Another MC is used to protect the single-photon detector(SPD)from the classical pump light.The signal from the SPD is sent to the time-interval analyzed(TIA)and time-correlated single photon counting

FIG.3:(a).With an AFC prepared with a periodicity of5MHz,the H+V polarized single-photon pulses are collectively re-emitted after a200ns storage time in the sample.(b).The real part numbers in the process matrixχas obtained from a quantum process tomography.All of the imaginary numbers are close to zero,with the largest amplitude being0.017.

(TCSPC)system(Picoquant,Hydraharp400).

Fig.3(a)shows an example of weak coherent pulses(the average photon number is0.8 photons per pulse)with a duration of60ns and a polarization of H+V that are collectively mapped onto the sample.A strong echo is emitted after a preprogrammed storage time of 200ns.The measured storage and retrieval e?ciency is about3%.

To characterize the polarization storage performance of the memory,we perform complete quantum process tomography(QPT)[28]on the system(see methods).The tomography result of the process matrixχwith a memory time of200ns are shown in Fig.3(b). The results give a process?delity of0.999±0.002for an average input photon number of0.8photons per pulse.The?delities of the four input states are0.995,0.997,1and 0.999for H,V,R,and D,respectively.Note that no dark counts of SPD are corrected through our experiment.Our results are far beyond the2/3bound,which is the maximum average?delity that can be achieved with a classical memory[27].Controlled reversible inhomogeneous broadening(CRIB)[10,11,16]is a protocol that is similar to AFC.CRIB uses an external?eld to rephase the atoms and thus eliminates any classical light during the storage cycle;therefor,it should achieve a similar?delity performance.Our scheme is applicable to the CRIB protocol.

By carefully designing the optical setup,we have eliminated most of the noise from the

0.00.5 1.0 1.5 2.0

E f f i c i e n c y (%)Storage tim e (us)

FIG.4:The storage e?ciency as a function of storage time.The storage sequence is repeated 400times at a frequency of 400KHz.

setup or the environment.The remaining imperfections are mostly introduced by the statis-tical photon drift and detector noise.We have also characterized our memory by measuring the read-write ?delity as a function of the storage time.The process ?delity shows little dependence on the storage time.For a longer storage time (500ns),the ?delity decreases to 0.981±0.003.Because the storage e?ciency decreases quickly (as shown in Fig.4),the sig-nal to noise ratio decreases.This factor account for most of the degradation.In general,the echo-type memory based on collective interference is not sensitive to decoherence,although the e?ciency degrades signi?cantly.This phenomenon is elucidated by results showing that most of the atoms that are decohered do not contribute to the collective interference,as has been observed in classical photon-echo memory [29].Our low-noise scheme should enable accurate experimental investigations into the in?uence of decoherence on memory ?delity.

We have demonstrated an ultra-reliable quantum memory for photonic polarization-qubit

in solids.By performing quantum process tomography,we measure the process ?delity for a 200ns storage tim ewith single photon level input pulses at 0.999±0.002.This excellent ?delity performance should make the quantum memory suitable for quantum error-correction applications in large-scale quantum computation [30].Moreover,the absence of ions’motion in the solid state means that even complex spatial structures can be generated by light and stored.Our results should produce solid-state devices that are capable of functioning as a hyper-quantum memory for light’s polarization,temporal,and spatial information.

We note that related results have been obtained by two other groups[31,32].Compared with their results,our quantum memory is compact and has ultra-high?delity.

Methods

Sample.The sample is composed of two pieces of Nd3+:YVO4crystals(doping level 10ppm),sandwiching a half-wave plate(HWP).The sizes of the two crystals are nearly equal,with10*10mm apertures and1.4mm lengths along the a-axis.The absorption of a single piece of Nd3+:YVO4crystal shows strong polarization dependence,with absorption coe?cients ofαof4.6/mm for H polarized light andαof0.7/mm for V polarized light.To improve the accuracy of the crystal alignment and the HWP,the HWP is designed as a10*10 mm square with an optical axis at the45?diagonal line of the square.This con?guration can exchange the H and V polarizations with an extinction ratio of better than2000:1. The complete experimental setup gives an extinction ratio of about900:1for the H+V and H?V polarizations.

Quantum process tomography.The quantum process can be represented by the process matrixχ.Theχmatrix can be expressed on the basis ofσm and maps an input density matrixρin onto the corresponding output stateρout via

ρout=

3

m,n=0

χmnσmρinσ?n.(2)

We chose is[I,X,Y,Z]as the basis forσi,where I represents the identity operation and X,Y and Z represent the three Pauli operators.Here,?denotes the adjoint operator. Theχmatrix completely and uniquely describes the process and can be reconstructed by experimental tomographic measurements.We prepare and measure four polarization states (H,V,R=H+iV,and D=H+V)and perform quantum state tomography for the output state generated by each input pulse.In the experiment,the physical matrixχis estimated by the maximum-likelihood procedure[33],which is shown in Fig.3(b).The?delity of the experimental result is about0.999,as calculated by(T r√χ)2withχideal=1.

This work was supported by the National Basic Research Program(2011CB921200),

National Natural Science Foundation of China(Grant Nos.60921091and10874162).

[1]Lvovsky,A.I.,Sanders,B.C.,and Tittel,W.Optical quantum memory.Nature Photonics3,

706(2009).

[2]Duan,L.-M.and Monroe,C.Quantum networks with trapped ions.Rev.Mod.Phys.82,1209

(2010).

[3]Ladd,T.D.,Jelezko,F.,La?amme,R.,Nakamura,Y.,Monroe,C.and O’Brien,J.L.Quan-

tum computers.Nature464,45(2010).

[4]Matsukevich D.N.and Kuzmich A.Quantum state transfer between matter and light.Science

306,663(2004).

[5]Choi,K.S.,Deng,H.,Laurat,J.and Kimble,H.J.Mapping photonic entanglement into and

out of a quantum memory.Nature452,67(2008).

[6]Tanji,H.,Ghosh,S.,Simon,J.,Bloom,B.and Vuleti′c,V.Heralded Single-Magnon Quantum

Memory for Photon Polarization States.Phys.Rev.Lett.103,043601(2009).

[7]Zhang,H.,Jin,X.M.,Yang,J.,Dai,H.N.,Yang,S.J.,Zhao,T.M.,Rui,J.,He,Y.,Jiang,

X.,Yang,F.,Pan,G.S.,Yuan,Z.S.,Deng,Y.,Chen,Z.B.,Bao,X.H.,Chen,S.,Zhao,

B.and Pan J.W.Preparation and storage of frequency-uncorrelated entangled photons from

cavity-enhanced spontaneous parametric downconversion.Nature Photonics5,628(2011).

[8]Specht,H.P.,N¨o lleke,C.,Reiserer,A.,Upho?,M.,Figueroa,E.,Ritter,S.and Rempe,G.

A single atom quantum memory.Nature473,190(2011).

[9]Lettner,M.,M¨u cke,M.,Riedl,S.,Vo,C.,Hahn,C.,Baur,S.,Bochmann,J.,Ritter,S.,

D¨u rr,S.and Rempe,G.Remote entanglement between a single atom and a Bose-Einstein condensate.Phys.Rev.Lett.106,210503(2011).

[10]Hosseini,M.,Sparkes,B.M.,H′e tet,G.,Longdell,J.J.,Lam,P.K.and Buchler,B.C.

Coherent optical pulse sequencer for quantum applications.Nature461,241(2009).

[11]Hosseini,M.,Campbell,G.,Sparkes,B.M.,Lam,P.K.and Buchler,B.C.Unconditional

room-temperature quantum memory.Nature Physics79,10(2011).

[12]Olmschenk,S.,Matsukevich,D.N.,Maunz,P.,Hayes,D.,Duan,L.-M.and Monroe,C.

Quantum Teleportation Between Distant Matter Qubits.Science323,486(2009).

[13]de Riedmatten,H.,Afzelius,M.,Staudt,M.U.,Simon,C.and Gisin,N.A solid-state light-

matter interface at the single-photon level.Nature456,773(2008).

[14]Afzelius,M.,Simon,C.,de Riedmatten,H.and Gisin,N.Multimode quantummemory based

on atomic frequency combs.Phys.Rev.A.79,052329(2009).

[15]Longdell,J.J.,Fraval,E.,Sellars,M.J.and Manson,N.B.Stopped light with storage times

greater than one second using electromagnetically induced transparency in a solid.Phys.Rev.

Lett.95,063601(2005).

[16]Hedges,M.P.,Longdell,J.J.,Li,Y.and Sellars,M.J.E?cient quantum memory for light.

Nature465,1052(2010).

[17]Usmani,I.,Afzelius,M.,de Riedmatten,H.and Gisin,N.Mapping multiple photonic qubits

into and out of one solid-state atomic ensemble.Nature Communications1,12(2010). [18]Bonarota,M.,L.Gou¨e t,J.-L.and Chaneli`e re,T.Highly multimode storage in a crystal.New

Journal of Physics13,013013(2011)

[19]Saglamyurek,E.,Sinclair,N.,Jin,J.,Slater,J.A.,Oblak,D.,Bussi`e res,F.,George,M.,

Ricken,R.,Sohler,W.and Tittel,W.Broadband waveguide quantum memory for entangled photons.Nature469,512(2011).

[20]Clausen,C.,Usmani,I.,Bussi`e res,F.,Sangouard,N.,Afzelius,M.,de Riedmatten,H.,and

Gisin,N.Quantum storage of photonic entanglement in a crystal.Nature469,508(2011).

[21]Huang,Y.F.,Liu,B.H.,Peng,L.,Li,Y.H.,Li,L.,Li,C.F.and Guo G.C.Experimental

generation of an eight-photon Greenberger-Horne-Zeilinger state.Nature Communications2, 546(2011).

[22]Salter,C.L.,Stevenson,R.M.,Farrer,I.,Nicol,C.A.,Ritchie,D.A.,and Shields,A.J.An

entangled-light-emitting diode.Nature465,594(2010).

[23]England,D.G.,Michelberger,P.S.,Champion,T.F.M.,Reim,K.F.,Lee,K.C.,Sprague,M.

R.,Jin,X.-M.,Langford,N.K.,Kolthammer,W.S.,Nunn,J.and Walmsley,I.A.High-?delity polarization storage in a gigahertz bandwidth quantum memory.arXiv:1111.0900(2011) [24]Sabooni,M.et al.Storage and recall of weak coherent optical pulses with an e?ciency of25%.

Phys.Rev.Lett.105,060501(2010).(2010).

[25]Afzelius,M.et al.Demonstration of atomic frequency comb memory for light with spin-wave

storage.Phys.Rev.Lett.104,040503(2010).

[26]Hastings-Simon,S.R.,Afzelius,M.,Min′a?r,J.,Staudt,M.U.,Lauritzen,B.,de Riedmatten,

H.and Gisin,N.Spectral hole-burning spectroscopy in Nd3+:YVO4.Phys.Rev.B.77,125111

(2008).

[27]Grosshans,F.and Grangier,P.Quantum cloning and teleportation criteria for continuous

quantum variables.Phys.Rev.A.64,010301(R)(2001).

[28]Chuang,I.L.and Nielsen,M.A.Prescription for experimental determination of the dynamics

of a quantum black box.J.Mod.Opt.44,2455-2467(1997).

[29]Staudt,M.U.,Afzelius,M.,de Riedmatten,H.,Hastings-Simon,S.R.,Simon,C.,Ricken,

R.,Suche,H.,Sohler,W.and Gisin,N.Interference of Multimode Photon Echoes Generated in Spatially Separated Solid-State Atomic Ensembles.Phys.Rev.Lett.99,173602(2007). [30]Wang,D.S.,Fowler,A.G.and Hollenberg,L.C.L.Surface code quantum computing with

error rates over1%.Phys.Rev.A.83,020302(R)(2011).

[31]Clausen,C.,Bussieres,F.,Afzelius,M.,Gisin,N.Quantum storage of polarization qubits in

birefringent and anisotropically absorbing materials.arXiv:1201.4097v1(2011).

[32]G¨u ndo?g n,M.,Ledingham,P.M.,Almasi,A.,Cristiani,M.,de Riedmatten,H.Quantum

Storage of a Photonic Polarization Qubit in a Solid.arXiv:1201.4149v1(2011).

[33]O’Brien,J.L.et al.Quantum process tomography of a controlled-NOT gate.Phys.Rev.Lett.

93,080502(2004).

相关文档
相关文档 最新文档