Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more
demanding than just certifying entanglement. We theoretically and
experimentally analyze the low resource generation of bi-partite continuous
variable entanglement, as realized by mixing a squeezed mode with a vacuum mode
at a balanced beam splitter, i.e. the generation of so-called vacuum-class
entanglement. We find that in order to observe EPR entanglement the total
optical loss must be smaller than 33.3 %. However, arbitrary strong EPR
entanglement is generally possible with this scheme. We realize continuous wave
squeezed light at 1550 nm with up to 9.9 dB of non-classical noise reduction,
which is the highest value at a telecom wavelength so far. Using two phase
controlled balanced homodyne detectors we observe an EPR co-variance product of
0.502 \pm 0.006 < 1, where 1 is the critical value. We discuss the feasibility
of strong Gaussian entanglement and its application for quantum key
distribution in a short-distance fiber network.Comment: 4 pages, 4 figure

Duhme, Jörg

Eberle, Tobias

Franz, Torsten

Händchen, Vitus

Schnabel, Roman

Werner, Reinhard F.

English

arXiv

Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.3 %. However, arbitrarily strong EPR entanglement is generally possible with this scheme. We realize continuous-wave squeezed light at 1550 nm with up to 9.9 dB of nonclassical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balanced homodyne detectors we observe an EPR covariance product of 0.502±0.006<1, where 1 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network

Franz,Torsten

Institutionelles Repositorium der Leibniz Universität Hannover

PHYSICAL REVIEW A 83, 052329 (2011)Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light sourceTobias Eberle,1,2 Vitus Ha¨ndchen,1 Jo¨rg Duhme,2,3 Torsten Franz,3 Reinhard F. Werner,3 and Roman Schnabel1,*1Max-Planck-Institut fu¨r Gravitationsphysik (Albert-Einstein-Institut) and Institut fu¨r Gravitationsphysik der Leibniz Universita¨t Hannover,Callinstraße 38, D-30167 Hannover, Germany2Centre for Quantum Engineering and Space-Time Research - QUEST, Leibniz Universita¨t Hannover, Welfengarten 1,D-30167 Hannover, Germany3Institut fu¨r Theoretische Physik der Leibniz Universita¨t Hannover, Appelstraße 2, D-30167 Hannover, Germany(Received 9 March 2011; published 31 May 2011)Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifyingentanglement. We theoretically and experimentally analyze the low-resource generation of bipartite continuous-variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter,i.e., the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglementthe total optical loss must be smaller than 33.3 %. However, arbitrarily strong EPR entanglement is generallypossible with this scheme. We realize continuous-wave squeezed light at 1550 nm with up to 9.9 dB of nonclassicalnoise reduction, which is the highest value at a telecom wavelength so far. Using two phase-controlled balancedhomodyne detectors we observe an EPR covariance product of 0.502 ± 0.006 < 1, where 1 is the critical value.We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in ashort-distance fiber network.DOI: 10.1103/PhysRevA.83.052329 PACS number(s): 03.67.Bg, 03.65.Ud, 03.67.HkI. INTRODUCTIONIn this paper we explore entanglement in the quadraturemeasurements on a pair of laser beams. This is a concreterealization of the system considered in 1935 by Einstein,Podolsky, and Rosen (EPR) [1]: a two-mode system witha canonical pair of continuous variables measured on eachside, in an overall Gaussian state. It might appear that thissystem was ill chosen for the investigation of nonclassicalfeatures of quantum mechanics. After all, in this situation theWigner function immediately provides a classical probabilisticmodel for all measurements involved, and hence no Bellinequality can be violated in this setup. Nevertheless, EPRestablished some nonclassical features in such a state, forwhich a quantitative criterion was proposed by Reid [2]. Hercriterion,“EPR entanglement,” captures a distinction, whichis meaningful also in a broader context and has been called“steering” [3], after another term used by Schro¨dinger. For ourpaper it is important that this criterion is more demanding thanjust establishing entanglement [4]. Moreover, it is applicablewithout an assumption about the Gaussian nature of thestate.II. BACKGROUNDFollowing Reid, we call a state EPR entangled ifVarA|B( ˆXA, ˆXB) VarA|B( ˆPA, ˆPB) < 1, (1)where ˆX and ˆP are the amplitude quadrature (position)and phase quadrature (momentum) operators, respectively,and VarA|B denote conditional variances. These are de-fined as VarA|B( ˆXA, ˆXB) = ming Var( ˆXA − g ˆXB), where theparameter g is varied to minimize the variance of the*Corresponding author; roman.schnabel@aei.mpg.dediscrepancy of the measured and the inferred outcomes ofthe measurement.EPR entangled states were, e.g., generated in [5–9] bytype II parametric down-conversion, in [10,11] by type Iparametric down-conversion, and in [12] by the optical Kerreffect. In all these experiments the nonclassical resourceof the EPR entanglement generation could be described bythe interference of two squeezed modes. In the case oftype I parametric down-conversion, two squeezed modeswere generated in two independent nonlinear cavities andsubsequently overlapped on a balanced beam splitter.In [13,14] it was theoretically shown that an entangled stateis generated from a pure single squeezed mode for any nonzerosqueezing. EPR entanglement from a single squeezed modewas theoretically analyzed in [15]. However, experimentalimperfections such as optical loss were not considered in theseworks and so far EPR entanglement from a single squeezedmode has not been experimentally demonstrated.Here we report on the generation of EPR entanglement fromthe interference of a squeezed mode with a vacuum mode,which we call v-class entanglement [16]. For pure v-classentanglement the variance product (1) is given by42 + Varasqz + Varsqz < 1, (2)where Var(a)sqz describes the variance of the (anti)squeezedquadrature of the pure state normalized to the vacuum noisevariance. With sufficiently high squeezing this can becomearbitrarily small, while the entanglement, as measured by theentropy of a subsystem, diverges. Since just a single squeezedmode is required as the input beam of a balanced beam splitter,the experimental setup is less involved compared to previousexperiments. We observe a significant EPR entanglementyielding a value of 0.502 ± 0.006 according to Eq. (1) anddiscuss the influence of optical loss on our setting.052329-11050-2947/2011/83(5)/052329(4) ©2011 American Physical SocietyTOBIAS EBERLE et al. PHYSICAL REVIEW A 83, 052329 (2011)For the symmetric situation, i.e., with two equally squeezedstates as inputs to a balanced beam splitter (so-called s-classentanglement [16]), it is known that EPR entanglement canonly be observed if the total optical loss on the state is smallerthan 50%, as experimentally demonstrated in Ref. [10]. Inthe case of v-class entanglement and under the assumption ofsymmetric optical loss, EPR entanglement is observed if(1 − Varsqz)2(1 − µ)(13− µ)> 0. (3)Here µ describes the total optical loss of the initially purestate. This condition shows that the restriction on the opticalloss for v-class entanglement is more severe than for s-classentanglement. The loss on v-class entangled states has tobe smaller than 33.3% in order to be able to observe EPRentanglement. In contrast “inseparability” is present in thisscheme for any loss < 100%.III. DEMONSTRATION OF EPR ENTANGLEMENTFigure 1 shows a schematic of the experimental setup.The quadrature amplitudes of both output beams of the50 : 50 entanglement beam splitter were detected by meansof balanced homodyne detectors (Alice and Bob) consistingof two high quantum efficiency (>95%) InGaAs photodiodes(PDs) each. The phases of the local oscillators of the homodynedetectors were locked either to the amplitude or to thephase quadrature of the field. The outcomes were recordedsimultaneously by a data acquisition system at a sample rateof 500 kHz. For this purpose the signals were mixed downat a frequency of 5 MHz using a double balanced mixervacuumEPR SourceSecond HarmonicGenerationSqueezed LightSource50:5050:50Local OscillatorphaseBob1550nm LaserPDPDPPKTPPPKTPReference for Alice’s and Bob’s local oscillators50:50Local OscillatorphaseAlicePDPD(A)(B)FIG. 1. (Color online) Schematic of the experiment. Acontinuous-wave laser beam at 1550 nm (red) was frequency doubled(yellow) and used to produce squeezed light at the fundamentalwavelength via type I parametric down-conversion. A balanced beamsplitter subsequently mixed the squeezed light with a vacuum mode.Amplitude and phase quadrature amplitude measurements on theoutput beams by means of balanced homodyne detectors proved EPRentanglement among them. PD: photodiode.and a low-pass filter at 35 kHz which served also as anantialiasing filter for the 16 bit data acquisition system. Foreach measurement 5 × 106 data points were sampled.The squeezed light was produced by type I parametricdown-conversion in a periodically poled potassium titanylphosphate (PPKTP) crystal. One end face of the 9.3 mm longcrystal was curved with a radius of curvature of 12 mm forminga half-monolithic cavity together with an external couplingmirror with a radius of curvature of 25 mm. The curved endface of the crystal had a high-reflectivity coating for both thefundamental at 1550 nm and the pump at 775 nm, whereasthe other end face was coated antireflective. The couplingmirror had a reflectivity of R = 90% for the fundamental andR = 20% for the pump and could be actuated by means of apiezoelectric transducer (PZT) to keep the cavity on resonance.The crystal was temperature controlled to 35 ◦C to achievephase matching.The main laser source of the experiment was a 1 W fiberlaser at 1550 nm. Its beam served as pump for a secondharmonic generation, made of PPKTP as well, to generate the775 nm pump beam required for the squeezed-light source.A small fraction of the main laser beam was filtered by amode-cleaning ring cavity with a finesse of about 300 andserved as the homodyne detector local oscillators.Figure 2 presents a characterization of our squeezed-lightsource. For this measurement the entanglement beam splitterwas removed and the squeezed field directly characterized bybalanced homodyne detection. The graph shows the varianceof the squeezed and antisqueezed quadrature relative to thevacuum noise versus the pump power for the nonlinear process,given in decibels. For a pump power of 325 mW we observed9.9 dB of squeezing and 18.4 dB of antisqueezing. To thebest of our knowledge this is the highest squeezing value everobserved at a wavelength of 1550 nm [17,18]. Squeezing levelslarger than 10 dB were observed in Refs. [19–21] at 1064 nm.-12-10-8-6-4-2 0 2 4 6 8 10 12 14 16 18 20 0  50  100  150  200  250  300  350Normalized Quadrature Variance [dB]Pump Power [mW]squeezedanti-squeezedvacuum noiseFIG. 2. (Color online) Characterization of our squeezed-lightlaser at a sideband frequency of 5 MHz. Shown are the vacuum-noise-normalized squeezed and antisqueezed quadrature variancesfor several light powers of the pump field. The variances weremeasured by a balanced homodyne detector and averaged ten times.The detector’s dark noise was at −22 dB and therefore irrelevant, andnot subtracted from the data. The solid lines show a model for ourdata according to Eq. (4).052329-2STRONG EINSTEIN-PODOLSKY-ROSEN ENTANGLEMENT . . . PHYSICAL REVIEW A 83, 052329 (2011)-30-20-10 0 10 20 30Voltage [mV] Xa,XbXa-Xb-30-20-10 0 10 20 30Voltage [mV] Xa,XbXa-Xb-30-20-10 0 10 20 30 0  5  10  15  20Voltage [mV]Pa, Pb 0  5  10  15  20Sample NumberSample NumberVacuum State Quadrature DataEntangled State Amplitude Quadrature DataEntangled State Phase Quadrature DataPa+PbFIG. 3. (Color online) Typical time series of measured quadratureamplitude data. The first row shows the voltages measured by Alice’sand Bob’s homodyne detector for a vacuum-state input, whereas thelower two are for a v-class entangled state and its amplitude (X)and phase quadrature (P ), respectively. The gray areas indicate thestandard deviation of the vacuum noise for a single mode.The solid lines in the figure represent a theoretical model. Thesqueezed (sqz) and antisqueezed (asqz) quadrature variancesof the field can be described as a function of pump power Pby [22]Varsqz,asqz = 1 ± ηγ 4√P/Pth(1 ∓ √P/Pth)2 + 4K(f )2, (4)where η is the detection efficiency and γ the escape efficiencyof the nonlinear cavity. Pth is the threshold power and K(f ) =2πf/κ the ratio between Fourier frequency f = 5 MHz andthe cavity decay rate κ = (T + L)c/l with the output couplertransmission T , the intracavity loss L, the speed of light invacuum c, and the cavity round trip length l = 79.8 mm. Themodel fits best with a total optical loss of 1 − ηγ = 0.09, athreshold power of Pth = 445 mW, and T + L = 0.105.The EPR entanglement of the two light fields A and Bproduced by a single squeezed field overlapped with a vacuummode was characterized by two homodyne detectors, i.e.,the two observers Alice and Bob. They simultaneously tookeither amplitude quadrature or phase quadrature data. Typicaldata are shown in Fig. 3. For the measurement in the firstrow the output of the squeezed-light source was blocked andonly vacuum noise was present at both receivers. Hence thedifference (and the sum, not shown) shows a standard deviationthat is a factor of√2 above the vacuum noise. The lower tworows show the measurements on a v-class entangled state. Theamplitude quadrature data as well as the phase quadrature datataken at Alice’s and Bob’s sites show correlations. It is clearly 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 0  50  100  150  200  250Normalized Conditional VariancesConditional Variance Product (EPR)Pump Power [mW]VarA|B(PA,PB)VarA|B(XA,XB)EPRFIG. 4. (Color online) Conditional variances for amplitude andphase quadratures and the EPR criterion calculated from the measureddata. The dashed lines represent the theoretical model given byEq. (4); the solid lines represent the model with additional excessnoise. Both models coincide for the conditional variance of theamplitude quadrature.visible that the fluctuations in the right panels are less thanthose in the left panels.Figure 4 shows the conditional variances and their productfor the EPR criterion according to Eq. (1). In general, theroles of Alice and Bob are not interconvertible; i.e., EPRentanglement is not a symmetric quantity. Experimentallywe found only minor differences in the phase quadrature,which probably originated in asymmetric optical loss. Thedifferences for the EPR entanglement and the X quadraturemeasurements would not be visible in the figure, so only onedirection is plotted. Our best value for the EPR criterion is0.502 ± 0.006 and was achieved for a pump power of 225 mW.Here we found an entanglement of formation of 1.16 [23].Given the fact that we used just a single squeezed mode,our result is quite remarkable. To the best of our knowledgeonly one work reported a stronger EPR entanglement [8],however, based on type II parametric down-conversion andtherefore an equivalent of two squeezed input modes. Thedashed lines in Fig. 4 represent the predictions from Eq. (4). Weobserve a considerable difference in the experimental data athigher pump powers. Comparing the data with different noisesimulations we can identify excess noise in the (antisqueezed)phase quadrature as the main noise source, shown as a solid linein Fig. 4. This excess noise probably arose due to the nonlinearresponse of the detectors at high pump powers. Effects of phasenoise were only observed marginally and therefore omitted.IV. DISCUSSION AND OUTLOOKThe high strength of the entanglement generated from justa single squeezed field at 1550 nm is an encouraging result.By replacing the vacuum mode in our setup with a secondsqueezed mode the entanglement strength will further increaseconsiderably. Without additional loss, this would lead to anEPR value of around Var2A|B = (0.2)2 = 0.04.052329-3TOBIAS EBERLE et al. PHYSICAL REVIEW A 83, 052329 (2011)In the present work we have shown that balanced homodynedetectors can be locked to a certain quadrature phase preciselyenough to measure a conditional variance of just 0.2, seelower trace in Fig. 4. Furthermore, we have also shown thatthe spatial mode of our entangled field can be aligned tospatially filtered local oscillators in the fundamental GaussianTEM00 mode with a visibility of 99.5%. From this result weinfer that a similar high visibility will be achieved betweentwo squeezed modes as required to generate the envisagedextremely low conditional variance products. In a previousexperiment a continuous-wave squeezed field at 1550 nm wascoupled into an optical fiber, transmitted, and finally coupledout again in order to measure its nonclassical properties [18].This shows that one is able to overcome coupling losses and sofiber-based distribution of squeezing is feasible for distancesof several kilometers. Furthermore, the result can directlybe transferred to the distribution of Gaussian quadratureentanglement as analyzed here. A possible application is Gaus-sian quantum key distribution (see, e.g., [24] and referencestherein).Simulations show that by replacing the vacuum input witha second squeezed state, key rates around one bit per time binwill be possible. Since squeezed fields with bandwidths above100 MHz have already been demonstrated [20] quantum keydistribution with rates in the 100 Mbit/s regime should bepossible with two-mode squeezed states.ACKNOWLEDGMENTSThis research was supported by the FP 7 project Q-ESSENCE (Grant Agreement No. 248095). T.E. and V.H.thank the IMPRS on Gravitational Wave Astronomy forsupport. T.F. acknowledges support from DFG under GrantNo. WE-1240/12-1.[1] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777(1935).[2] M. D. Reid, Phys. Rev. A 40, 913 (1989).[3] H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett.98, 140402 (2007).[4] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid,Phys. Rev. A 80, 032112 (2009).[5] Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev.Lett. 68, 3663 (1992).[6] Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, Phys.Rev. A 62, 023813 (2000).[7] C. Schori, J. L. Sorensen, and E. S. Polzik, Phys. Rev. A 66,033802 (2002).[8] J. Laurat, T. Coudreau, G. Keller, N. Treps, and C. Fabre, Phys.Rev. A 71, 022313 (2005).[9] G. Keller, V. D’Auria, N. Treps, T. Coudreau, J. Laurat, andC. Fabre, Opt. Express 16, 9351 (2008).[10] W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, Phys.Rev. Lett. 90, 043601 (2003).[11] N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, andA. Furusawa, Phys. Rev. A 74, 060101(R) (2006).[12] C. Silberhorn, P. K. Lam, O. Weiß, F. Ko¨nig, N. Korolkova, andG. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).[13] Y. Aharonov, D. Falkoff, E. Lerner, and H. Pendleton, Ann.Phys. 39, 498 (1966).[14] P. van Loock and S. L. Braunstein, Phys. Rev. Lett. 84, 3482(2000).[15] W. P. Bowen, P. K. Lam, and T. C. Ralph, J. Mod. Opt. 50, 801(2003).[16] J. DiGuglielmo, B. Hage, A. Franzen, J. Fiura´sˇek, andR. Schnabel, Phys. Rev. A 76, 012323 (2007).[17] M. Mehmet, S. Steinlechner, T. Eberle, H. Vahlbruch,A. Thu¨ring, K. Danzmann, and R. Schnabel, Opt. Lett. 34, 1060(2009).[18] M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, andR. Schnabel, Opt. Lett. 35, 1665 (2010).[19] H. Vahlbruch, M. Mehmet, S. Chelkowski, B. Hage, A. Franzen,N. Lastzka, S. Goßler, K. Danzmann, and R. Schnabel, Phys.Rev. Lett. 100, 033602 (2008).[20] M. Mehmet, H. Vahlbruch, N. Lastzka, K. Danzmann, andR. Schnabel, Phys. Rev. A 81, 013814 (2010).[21] T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Ha¨ndchen,H. Vahlbruch, M. Mehmet, H. Mu¨ller-Ebhardt, and R. Schnabel,Phys. Rev. Lett. 104, 251102 (2010).[22] Y. Takeno, M. Yukawa, H. Yonezawa, and A. Furusawa, Opt.Express 15, 4321 (2007).[23] G. Rigolin and C. O. Escobar, Phys. Rev. A 69, 012307 (2004).[24] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dusek,N. Lu¨tkenhaus, and M. Peev, Rev. Mod. Phys. 81, 1301(2009).052329-4

Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source

Einstein-Podolsky-Rosen (EPR) entanglement is a criterion that is more demanding than just certifying entanglement. We theoretically and experimentally analyze the low resource generation of bi-partite continuous variable entanglement, as realized by mixing a squeezed mode with a vacuum mode at a balanced beam splitter, i.e. the generation of so-called vacuum-class entanglement. We find that in order to observe EPR entanglement the total optical loss must be smaller than 33.3 %. However, arbitrary strong EPR entanglement is generally possible with this scheme. We realize continuous wave squeezed light at 1550 nm with up to 9.9 dB of non-classical noise reduction, which is the highest value at a telecom wavelength so far. Using two phase controlled balanced homodyne detectors we observe an EPR co-variance product of 0.502 \pm 0.006 < 1, where 1 is the critical value. We discuss the feasibility of strong Gaussian entanglement and its application for quantum key distribution in a short-distance fiber network

Eberle, T.

Händchen, V.

Duhme, J.

Franz, T.

Werner, R.

Schnabel, R.

MPG.PuRe

Tobias Eberle

Vitus Händchen

Jörg Duhme

Torsten Franz

Reinhard F. Werner

Roman Schnabel

Crossref

Physical Review A

https://www.repo.uni-hannover.de/bitstream/123456789/8842/1/Strong%20Einstein-Podolsky-Rosen%20entanglement%20from%20a%20single%20squeezed%20light%20source.pdf

Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light
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Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source

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