VOLUMF 75, NUMBER 17 PHYSICAL REVIEW LETTERS 23 OcToaER 1995

Complementarity and the Quantum Eraser

Thomas J. Herzog, Paul G. Kwiat, ~ Harald Weinfurter, and Anton ZeilingerInstitut fur Experimentalphysik, Universitat Innsbruck, Technikerstrasse 25, A 60-20 Innsbruck, Austria

(Received 24 July 1995)

We present various experiments demonstrating the mutual exclusivity of observing interference andwhich-path information, as demanded by Bohr's complementarity principle. Using photon pairs createdin parametric down-conversion, no which-path measurements need to be performed on the interferingphoton itself. Instead the other photon can be used to introduce distinguishability, which consequentlydestroys interference. However, a suitable measurement erases this distinguishability and interferencecan be recovered.

PACS numbers: 03.65.Bz

Feynman described the phenomenon of interference ascontaining "the only mystery" of quantum mechanics [1]:Although a quantum system can display both wavelikebehavior (interference) and particlelike behavior (passagethrough only one of two slits), it is impossible to obtainboth interference and complete "Welcher Weg" -(which-

path) information in a single experiment. The classicexample is the recoiling-slit gedanken experiment intro-duced by Einstein and Bohr in their discussions leadingto the formulation of the complementarity principle [2].There a particle is first sent through a movable slit placedbefore a double slit. Any attempt to extract which-path in-formation from this interference experiment will degradethe contrast of the interference pattern —if one can fullydetermine the path, then there is no interference at all. In-deed, the interference will be lost even if one does notactually read out the which-path detector, as long as thereis the mere possibility of carrying out the measurement,i.e., as long as the contributing processes are distinguish-able in principle.

However, the loss of interference need not be irre-versible if the which-path detector is itself a quantumsystem. Scully and co-workers proposed experiments inwhich the distinguishability can be erased by a suitablemeasurement on the which-path detector [3]. By correlat-ing the results of this measurement with the detection ofthe initially interfering system, one once again observesinterference. Furthermore, if the path information is car-ried by a distinct which-path detector system, the decisionof whether to read out or to erase this information can bedelayed for an arbitrary time, even until after detectionof the interfering particle. This significantly extends theconcept of delayed-choice experiments as introduced byWheeler [4].

The basic elements of a "quantum eraser" are individ-ual interfering quantum systems, a method of introducingwhich-path information, and a method of subsequentlyerasing this information in order to restore interference.Several previous experiments, all using the photon pairsproduced in spontaneous parametric down-conversion,have been discussed within the context of quantum erasers

[5]. There are, however, other key ingredients desir-able for an optimal demonstration of the phenomena [6].In this Letter we report on several new which-path andquantum-eraser realizations [7], which avoid the deficien-cies of the earlier approaches. Employing different typesof which-path information —polarization and timing—along with the corresponding methods of erasure, we wereable to clearly demonstrate the complementary nature ofparticlelike and wavelike behaviors.

The basic experimental setup is shown in Fig. 1

[8]. The 351-nm light of a single-mode Ar+-ion laser(100 mW) was directed onto a nonlinear crystal (Lil03).There a pair of photons, historically called the "signal"and "idler, " can be created by spontaneous parametricdown-conversion of a UV photon. Because of type-Iphase matching, the photons share the same polarization,in our case vertical. For the following we consider onlysignal-idler pairs with wavelengths of about 633 and789 nm, respectively. Rejecting the pump beam backinto the crystal allowed a second possibility to createsuch a signal-idler pair. Using two more mirrors wealso redirected the signal and idler modes associated withthe first process back through the crystal, such that theyoverlapped with those of the second process. Finally,after irises and interference filters to define the modes,silicon-avalanche photodiodes were used as single-photon

[ coinc.)

FIG. 1. Basic setup of the interferometer: A nonlinear crystalis pumped by a laser to produce photon pairs via parametricdown-conversion. Directing the pump beam back through thecrystal gives a second possibility to create the photon pair.Rejecting the pairs created in the first process back into thecrystal makes them indistinguishable from pairs created in thesecond process, and interference occurs.

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VOLUME 75, NUMBER 17 PHYSICAL REVIEW LETTERS 23 OcToBER 1995

detectors, with an additional time-to-amplitude converterpermitting coincidence analysis (time window 5 ns) ofthe signal-idler pairs.

For convenience we will refer to down-conversion pho-tons created by a pump photon in its first (second) passthrough the crystal as being "reIIected" ("direct"). Be-cause of the overlap of the respective signal and idlermodes, after the down-conversion crystal the rejectedphotons are in principle indistinguishable from the directphotons. Therefore interference occurs, as observed ex-perimentally [8]. In particular, due to the symmetry ofthe experiment both the signal and idler detectors dis-play oscillating count rates as any of the three mirrorsis moved: I; = I, ~ 1 + cosh @, where we have defined6@ = P, + P, —P„, and @„P;,and P„denote thephases accumulated by the signal, idler, and pump beamsin propagating to their respective mirrors and back [9].

The experimental arrangement affords easy access tothe beam paths between the crystal and the mirrors (thesedistances were about 13 cm in our experiment). Thus onecan manipulate the rejected down-conversion photons insuch a way that they become distinguishable from thoseemitted directly towards the detectors. We call a devicewhich accomplishes this a "quantum marker. " In the firstexperiment our marker consisted of a quarter-wave platepolarization retarder in front of the mirror in the idlermode [Fig. 2(a)]. Correctly oriented, this plate rotatesthe polarization from vertical (U) to horizontal (H) upondouble passage.

One then has the possibility to obtain which-path in-formation for the idler photon just by measuring whetherits polarization is H (a refiected idler) or U (a directidler photon). The mere existence of this possibility de-mands that there cannot be any interference for the idler[Fig. 2(b)], because only processes that are indistinguish-able in principle can interfere. It also demands that therecannot be any interference for the signal photon either,since the two photons are always created in pairs, andwhich-path information for one photon necessarily implieswhich-path information for the other.

However, one may erase the which-path informationcarried by the idler photon by measuring its polarizationalong 45 [Fig. 2(a)]. It is then not possible, even in prin-ciple, to tell whether a registered idler was initially H orV polarized, and the idler count rate again shows interfer-ence as any of the mirrors is moved [Fig. 2(c)]. Note thatthe erasure of the idler photon's path information has noinfluence on the detection of the signal photon and doesnot suffice to restore interference in the signal count rate.Put loosely, the signal photon cannot "know" how the dis-tant idler polarizer will be oriented.

As indicated above, one should employ single particlesfor the interfering system in order for the which-pathnotion to be meaningful. Conditioned upon detectionof the signal photon, the idler photon is prepared ina single-photon state [10]. Therefore, the coincidence

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detection gives the result for which-path and quantum-eraser measurements for the single idler photon [Figs. 2(b)and 2(c)], and we have fulfilled the basic requirements fora TVelcher-Weg and quantum-eraser experiment.

Nevertheless, there are additional features that arehighly desirable for an optimal demonstration of theseideas [3,6]. In particular, the which-path detection processand the resulting nonseparability become much moreapparent when a system spatially distinct from the initialinterfering system carries the which-path information.

We now describe two experiments where this is thecase. As a starting point, consider the final configurationof the previous experiment —after the polarizer at 45 theidler photons display interference [Fig. 2(c)]. Next weintroduce a quantum marker, but in the signal path. Inthe first of the two realizations we used the polarization ofthe signal photon as a label for marking the path.

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VoLUMv 75, NUMBER 17 PH YS ICAL REVIEW LETTERS 23 OcTooER 1995

Specifically, we inserted a quarter-wave plate in front ofthe mirror in the signal mode [Fig. 3(a)], thereby rotatingthe polarization of the rejected signal photons from Vto H. Formally, this results in an entangled two-photonstate right after the crystal:

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The resulting possibility of using this arrangement fora test of Bell's inequality [11] demonstrates the closerelation between the idea of the quantum eraser and theissue of nonlocality in quantum mechanics.

Using a polarizing beam splitter for the analysis ofthe signal photon, there are four basic measurements (intwo complementary sets) on the which-path detection sys-tem. One can gain definite which-path information forthe idler photons by measuring the signal polarization:

an H-polarized signal photon means a reflected idler; aV-polarized signal means a direct idler photon. Conse-quently, the interference in the idler singles rate vanishes[Fig. 3(b)]. However, one may erase the which-path in-formation carried by the signal photons by means of apolarizer oriented at ~45 before the signal detector [12].This by itself does not suffice to restore the interferencefor the idler count rate; if it did, one could send superlumi-nal signals. Rather, the interference reappears only afterone correlates the measurement of the signal photon withthe detection of the idler photon, i.e., only in the coinci-dence rate [see Fig. 3(c)]. The probabilities for detectinga signal photon in coincidence with the idler photon (afterits 45' polarizer) show opposite interference oscillationsfor the two different signal polarizations [I(.s+45.) ~ 1 +cos(h@);1(s 4s ) ~ 1 —cos(AP)] [Fig. 3(c)]. Note thatthe sum of these fringes and antifringes does not displayinterference.

In our final experiment we started with the samequarter-wave plate and 45 -polarizer arrangement in theidler beam as before, so that interference was observablein the idler singles rate. However, we employed a dif-ferent degree of freedom for labeling the signal photon:By increasing the distance between the signal mirror andthe down-conversion crystal by more than the coherencelength of the detected photons (8, = 260 p, m correspond-ing to a spectral width of =1.7 nm), we introduced thepossibility to extract which-path information by measur-ing the relative arrival times of the photons [Fig. 4(a)].Figure 4(b) shows a coarse scan of the signal mirror.Away from the ideal alignment (5 = 0) the interferencein the idler, apparent in the large scatter of the intensity,rapidly fades away due to the in-principle temporal dis-tinguishability. The interference disappeared even thoughour detectors in practice could not resolve these short timedifferences.

In this experiment, the erasure was accomplished byplacing an interference filter with a smaller bandwidth(0.5 nm FWHM) in front of the signal detector, thusincreasing the coherence length of the detected signalphotons (8, ~ 800 p, m) [13]. Since the resulting coher-ence length was then greater than the relative delay (5 =425 p, m), interference was again observed after correlatingthe detection of the idler photons with the registered signalphotons, i.e. , in the coincidence intensity [Fig. 4(c)].

In the previous two experiments, because the which-path information was carried by a quantum system (thesignal photon) spatially distinct from the initially inter-fering system (idler photon), we can extend Wheeler'sdelayed-choice proposal [4]. Whereas in his proposal theinterference or which-path decision had to be made beforethe particle had left the interferometer, here we can delaythis decision (i.e., how to analyze the signal photon) untiafter the idler photon has been detected, clearly an irre-versible process. Again, the results of the measurementonly appear upon coincidence detection, however.

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VOLUME 75, NUMBER 17 PHYS ICAL REVIEW LETTERS 23 OcTo~ER 1995

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This work was supported by the Austrian Science Foun-dation (FWF), Project No. S065/02. One of us (P. G. K.)was supported by FWF Lise Meitner Postdoctoral Fellow-ship, M0077-PHY.

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It is straightforward to implement such a delayed-choice measurement in our experiments. For example,in our second experiment one could use an optical fiberto delay the signal photon's arrival at the Welcher-Wegor quantum-eraser analyzer. A fast polarization rotator(e.g. , Pockels cell) before the polarizing beam splittercould then be used to switch from which-path detection(analysis along H or V) to path-information erasure(analysis along ~45 ) at any arbitrary time.

In the experiments presented here, we used photon pairstogether with different types of quantum markers to per-form which-path and quantum-eraser operations. Note thatour markers and erasers allow continuous variation of thedegree of obtainable Welcher-Weg information, thus caus-ing a continuous loss of interference, in agreement withBohr's complementarity principle. The use of mutuallyexclusive settings of the experimental apparatus impliesthe complementarity between complete path informationand the occurrence of interference. In conclusion, our re-sults corroborate Bohr's view that the whole experimentalsetup determines the possible experimental predictions.

FIG. 4. (a) Experiment employing time delay as a quantummarker and a narrow-bandwidth interference filter in front ofthe signal detector as the quantum eraser. (b) Coarse scan ofthe signal mirror, showing the loss of interference for the idlerphotons at large A. The narrow-bandwidth filter in the signalbeam preserves interference in the coincidence rate. (c) Phasescan for 5 = 425 p, m.

*Present address: Physics Division, P-23, Los AlamosNational Laboratory, Los Alamos, NM 87545.

[1] R. P. Feynman, R. Leighton, and M. Sands, The FeynmanLectures on Physics (Addison-Wesley, Reading, MA,1965).

[2] N. Bohr, in Quantum Theory and Measurement, editedby J.A. Wheeler and W. H. Zurek (Princeton UniversityPress, Princeton, NJ, 1983), p. 9.

[3] M. O. Scully and K. Driihl, Phys. Rev. A 25, 2208 (1982);M. O. Scully, B.-G. Englert, and H. Walther, Nature(London) 351, 111 (1991).

[4] J.A. Wheeler, in Problems in the Formulation of Physics,edited by G. T. diFrancia (North-Holland, Amsterdam,1979).

[5] A. G. Zajonc, L. J. Wang, X.Y. Zou, and L. Mandel,Nature (London) 353, 507 (1991); Z. Y. Ou, L. J. Wang,X.Y. Zou, and L. Mandel, Phys. Rev. A 41, 566 (1990);P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev.A 45, 7729 (1992).

[6] P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, Phys. Rev.A 49, 61 (1994).

[7] A. Zeilinger, T. Herzog, M. A. Horne, P. G. Kwiat,K. Mattle, and H. Weinfurter, in Coherence and QuantumOptics UII, edited by J. Eberly, L. Mandel, and E. Wolf(Plenum Publishing Corp. , New York, 1995); a relatedexperiment is also reported there by C. H. Monken, D.Branning, and L. Mandel.

[8] T. J. Herzog, J. G. Rarity, H. Weinfurter, and A. Zeilinger,Phys. Rev. Lett. 72, 629 (1994).

[9] For a detailed multimode description, see P. W. Milonni,H. Fearn, and A. Zeilinger (to be published).

[10] P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1,173 (1986).

[11] L. Hardy, Phys. Lett. A 161, 326 (1992); H. Weinfurter,T. Herzog, P. G. Kwiat, J.G. Rarity, A. Zeilinger, and M.Zukowski, in Fundamental Problems on Quantum Theory,edited by D. M. Greenberger and A. Zeilinger, Annals ofthe New York Academy of Sciences Vol. 755 (New YorkAcademy of Sciences, New York, 1995).

[12] The passage through a polarizing beam splitter doesnot constitute a measurement of the polarization onecould always recombine the output beams in anotherbeam splitter to change the analysis basis. Similar issuesarise in other quantum erasers as well. Only after anirreversible registration of the photon should one speakof a measurement having been performed.

[13] Actually, the measurement of either photon through anarrow-bandwidth filter "collapses" the spectral bandwidthof the conjugate photon, thus increasing ils coherencelength as well.

[14] For this specific experiment the wavelengths of signal andidler photons were interchanged with respect to Fig. 2 forpractical reasons.

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