Entanglement, Decoherence and the Quantum∕Classical BoundarySerge Haroche Citation: Phys. Today 51(7), 36 (1998); doi: 10.1063/1.882326 View online: http://dx.doi.org/10.1063/1.882326 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v51/i7 Published by the American Institute of Physics. Additional resources for Physics TodayHomepage: http://www.physicstoday.org/ Information: http://www.physicstoday.org/about_us Daily Edition: http://www.physicstoday.org/daily_edition

Downloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

ENTANGLEMENT,DECOHERENCE AND THE

QUANTUM/CLASSICALBOUNDARY

mechanics is^very puzzling. A parti-

cle can be delocalized, it canbe simultaneously in severalenergy states and it can evenhave several different iden-tities at once. This schizo-phrenic behavior is encodedin its wavefunction, whichcan always be written as asuperposition of quantumstates, each characterized bya complex probability ampli-tude. Interferences betweenthese amplitudes occur whenthe particle can follow several indistinguishable paths.Any attempt to determine which trajectory it "actually takes"destroys these interferences. This is a manifestation ofwave—particle complementarity, which has recently beenillustrated in textbook fashion by several beautiful experi-ments.1

Nonlocality in quantum systems consisting of spa-tially separated parts is even more puzzling, as AlbertEinstein and collaborators Boris Podolsky and NathanRosen pointed out in the famous "EPR" paper of 1935.2

Recent decades have witnessed a rash of EPR experi-ments, designed to test whether nature really does exhibitthis implausible nonlocality.3 In such experiments, thewavefunction of a pair of particles flying apart from eachother is entangled into a non-separable superposition ofstates. The quantum formalism asserts that detectingone of the particles has an immediate effect on the other,even if they are very far apart. The experimenter caneven delay deciding on the kind of measurement to beperformed on the particles until after they are out ofinteraction range. Nonetheless, these experiments clearlydemonstrate that the state of one particle is always cor-related to the result of the measurement performed onthe other, in just the strange way predicted by quantummechanics.

The results of all these experiments are counterintui-tive. Such things are never observed in our macroscopicworld. Nobody has ever seen a billard ball going throughtwo holes at once, or two of them spinning away fromeach other after a collision in a quantum superposition ofanticorrelated states!

Schrodinger's catNonetheless, macroscopic objects are made of atoms that

SERGE HAROCHE is a professor of physics at the Ecole NormaleSuperieure in Paris and at the Pierre and Marie CurieUniversity (University of Paris VI).

Schrodinger intended his gedankenexperiment of a hapless cat mortally

entangled with a quantum trigger as areductio ad absurdum. But nowadays such

experiments are being realized inlaboratories—without offending the

antivivisectionists

Serge Haroche

individually obey quantummechanics. There's theparadox. Erwin Schrodingerfamously illustrated this co-nundrum with his provoca-tive cat gedanken experi-ment.4 He described adiabolical contraption inwhich a feline would becomeentangled with a singleatom. The system would bedescribed by a wavefunctionrepresenting at the sametime the cat alive with theatom excited and the cat

dead with the atom back in its ground state after its decayemission has triggered a lethal device. Quantum expertswill object that a cat is a complex and open system whichcannot, even at the initial time of this cruel experiment,be described by a wavefunction. The metaphor, neverthe-less raises an important question: Why and how doesquantum weirdness disappear in large systems?

Explanations for this "decoherence" phenomenon canbe traced back to discussions by the founding fathers ofquantum mechanics, and to 50-year-old developments inthe theory of relaxation phenomena. But only in the last15 years have entirely solvable models of decoherence inlarge systems been discussed, notably by Anthony Leggett,Eric Joos, Roland Omnes, Dieter Zeh and Wojciech Zurek.5

(See also the article by Zurek in PHYSICS TODAY, October1991, page 36.) These models are based on the distinctionin large objects between a few relevant macroscopic ob-servables like the position or momentum of the object,and an "environment" described by a huge number ofvariables, such as positions and velocities of air molecules,number of blackbody-radiation photons and the like.

When the system is brought into a superposition ofdifferent macroscopic states, information about this super-position is unavoidably and irreversibly leaking into theenvironment at a rate that increases with the separationbetween the parts, thus efficiently randomizing theirquantum coherence. The link with complementarity isstriking. As Zurek put it, the environment is watchingthe path followed by the system, and thus suppressinginterference effects and quantum weirdness. The strongdependence of the decoherence rate on the system's sizeand the separation of its parts is the trademark of thisphenomenon, which makes it different from other mani-festations of relaxation.

In macroscopic systems, this process is so efficientthat we see only its final result: the classical world aroundus. Could one prepare wiesoscopic systems—somewherebetween the macro- and microscopic—in which decoher-ence would occur, but slowly enough to be observed? Until

36 JULY 1998 PHYSICS TODAY CD 1998,Xmtrican Institute of Phj-sics. S-003I-922S-95C7-030-6Downloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

; s the^lingerthis co-irovofa-esperi-ibed a;ion inbecome

singlerould beb e t ae samevith the

enment.levertie-

;non canitheis ofments mi the to•rente inLegptiiZrfOctote

diner*

ie object.unbtr i

,;,tlijD tl

i s sop*'into ll«

tbeiiitaritj" n

recently, such a thing could be imagined only as agedanken experiment. But technological advances havenow made such experiments real, and they have openedthis field to practical investigation.

Various condensed matter systems have been consid-ered as possible candidates for such studies. The pos-sibility of using Josephson junctions and SQUID tech-nology to prepare and study quantum coherences in-volving mesoscopic superconducting currents has beendiscussed by Leggett,5 and interesting quantum tunnel-ing experiments have been realized in this context. Butthey have not yet directly addressed the decoherence issuequantitatively.

Entangling experimentsIn the last two years, great progress has been made increating entangled quantum states of ions in traps oratoms in high-Q cavities. These two kinds of quantum

FIGURE 1. ION TRAP electrode structureused by the NIST group in Boulder,Colorado.9 Single beryllium ions areconfined along the vertical axis in themiddle of the tiny 0.2-mm-wide notch atthe center by potentials on the gold-platedelectrodes. Through this notch, laserpulses can be directed at the oscillating ion.(Photo courtesy of C. Myatt, NIST.)

optics experiments, very disparate intheir techniques, have a striking simi-larity. They both realize a simple situ-ation in which a two-level atom iscoupled to a quantized harmonic oscil-lator. The Hamiltonian of this system,first studied by Edwin Jaynes andFrederick Cummings in 1963, hasbeen a favorite of the theorists eversince. In spite of its simplicity, thesystem describes a great variety ofinteresting situations.7

There have been many proposalsover the last 15 years to realize em-bodiments of Schrodinger's cat withsuch a system.8 The feline role wouldbe played by an excited harmonic os-cillator. These experiments have nowcome of age. By taming small labora-tory versions of Schrodinger's cat ex-periment in which the number ofquanta can be progressively increased,we are learning more about decoher-ence and the elusive quantum/classicalboundary.

In the ion trap experiment doneby David Wineland, Chistopher Mon-roe and coworkers at the National In-stitute of Standards and Technology(NIST) laboratory in Boulder, Colo-rado, a single beryllium ion is moni-tored.9 The trap is created in ultra-high vacuum by a combination of staticand oscillating electric fields appliedto tiny metallic electrodes (See fig-ure 1.) The ion is manipulated anddetected in an exquisitely refined wayby sequences of carefully tailored laser

pulses. The ion oscillates in the trap along one directionat a frequency of 11.2 MHz. It has two relevant internalenergy levels, which we call, for simplicity, | +> and | ->.They are two hyperfine sublevels of the ion's ground state.The transition frequency between them is 12 GHz. The| +> state can be selectively detected by applying a polar-ized detection laser (Ld) beam tuned to a transition thatcouples this state to an excited level. As the ion sub-sequently decays back to its ground state, it emits fluo-rescence photons. Many photons are scattered when theion is cycling under laser excitation. The | -> state, whichdoes not interact with the tuned Ld beam, announces itselfby the absence of light scattering—a null measurement.

At the beginning of the NIST experiment, cooling laserbeams bring the ion down to its vibrational ground state.Its motional wavefunction is then a Gaussian wave packetlocalized at the trap's center. The packet's width, a fewnanometers, is due to the zero-point quantum fluctuations

JULY 1998 PHYSICS TODAY 37Downloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

FIGURE 2. SCHRODINGER'S CAT in the Boulder ion trap, a: An ion in its lower hyperfine state | -> sits motionless at the bottomof the potential well, b: The internal state \- .•> is transformed into a still motionless superposition of | + / and | -y by a TT/2 laserpulse L,L,'. c: A kicking laser pulse L,L,' starts only the | + ? component oscillating macroscopically. d: The ion's internal statesare swapped by a 77 pulse from L,L,'. e: A second LiL/ pulse launches the motionless | +/ and recombines the two hyperfinecomponents. The resulting wave-packet overlap depends on the relative phase of kicks c and e. After a final mixing of thehyperfine states by an L,L,' pulse, the detecting laser Lj reveals the hyperfine state by fluorescence. (Adapted from ref. 9.)

of the ion oscillator. The cold ion is initially in thehyperfine state | ->. A pair of laser pulses, Lj and L/,whose frequencies differ by the 12 Ghz hyperfine fre-quency, are then used to coherently mix the states | +,>and I -X without affecting the ion's motion. These lasersexchange pairs of photons whose energy difference is fedinto the ion's internal energy. In the language of classicaloptics, we would say that the ion is responding to the beatfrequency. By adjusting the pulse duration, one can obtainany desired superposition of the two internal ion states.In this first stage of the experiment, the pulse is adjustedto prepare the two hyperfine states with equal weights—aso-called W2 pulse.

A second pair of excitation kicking laser pulses, L2and L./, is then applied to set the ion in motion. Theirfrequency difference is now the 11.2 MHz vibration fre-quency of the trapped ion. The coherent interaction ofthe ion with this second pair of pulsed laser beams feedsenergy into the ion's vibrational state, without affectingits internal hyperfine state. The second pair of beams ispolarized in a direction such that the ion interacts withthem only when it's in the | +> state; they have no effecton the I ~y state. As a result, the ion wavefunction splitsinto two wave packets: One, correlated to the | + > hyper-fine state, swings back and forth in the potential well.The other, correlated to | --)>, remains at rest at the centerof the trap. The situation is obviously reminiscent ofSchrodinger's cat.

The ion's state is analyzed by recombining the twowave packets and looking for interferences. The twointernal states of the ion are switched by an L]L/ pulselasting twice as long as the first (a TT pulse). Then a finalL2L2' kick launches the motionless part of the wavefunc-tion (now correlated with the hyperfine state | + >) intooscillation with an adjustable phase <p relative to the firstoscillating state.

1.0-

90°

PHASE DIFFERENCE v

One gets maximum overlap if ip = 0. The two over-lapping wave packets can still be distinguished by theirdifferent internal states. To observe interferences, onemixes these two states again by applying another TT/2pulse with LjL/. Each of the two recombining wavepackets then contains both hyperfine states. Finally theexperimenters apply an Ld pulse from the detecting laserand collect the fluorescence for a small time interval. (Seefigure 2.)

Wineland and company repeat the experiment fordifferent values of </> and observe interference fringes inthe I +,- fluorescence signal as <p is swept around zero(figure 3). The interference pattern clearly demonstratesthe coherent superposition of the ion's two states of motion.

Before recombination, the separation of the two wavepackets can reach a few tens of nanometers, several timesthe size of each individual packet. The ion's quantumstate in each packet is a superposition of vibration stateswith relatively large quantum numbers, up to n = 10.In that sense, one may say that the system is mesoscopic.

Merely splitting a wave packet into two coherent partsis, of course, not new. All interferometry experiments dothat routinely. The novel point here is that these packetsremain Gaussian and do not disperse in time. Thesestable shapes provide a simple visualization of the systemas a particle rolling in a bowl while it is simultaneouslyin two different states of motion. The ability to observethe oscillating ion for many periods, without dispersion,is potentially useful for decoherence studies. The deco-herence one observes in these experiments, however, re-sults from several sources of technical noise rather thanfrom fundamental decay processes.

Feline decoherenceThe study of Schrodinger cats and their decoherence hasbeen pushed one step further in an experiment performed

FIGURE 3. INTERFERENCE between the two ion wave packetsin the Boulder experiment is seen in this plot of thephase-angle {if) dependence of the probability of finding theion in the internal hyperfine state | + .> after recombining thetwo separated wave packets packets and mixing the twointernal states. (Adapted from ref. 9.)

38 IULY 1998 PHYSICS TODAYDownloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

FIGURE 4. IN THE PARIS EXPERIMENT,10 Schrodinger's cat isembodied by a few photons stored in the cavity C, whose

mirrors are shown in the photo at right. A rubidium atomfrom oven O is prepared in box B in the Rydberg state | +>. In

the auxiliary cavity R|, a microwave pulse turns it into asuperposition of | + > and | —>. Traversing C, the atom imparts

to the cavity field two different phases at once. A second pulse inR2 remixes the Rydberg states. The atomic state is measured indetectors D+ and D_ by applying state-selective ionizing electric-

fields. A second atom, the "quantum mouse," tests the "cat" stateprepared by the first atom. Statistical analysis of atomic energy

correlations in many runs determines the quantum coherence ofthe cavity field. By varying the delay between the two atoms,

one observes the cat's rapid decoherence.

at the Ecole Normale Superieure in Paris by a group thatincludes Jean-Michel Raimond, Michel Brune and my-self.10 The role of the cat in our experiment is playedby a field oscillator consisting of a few photons stored ina high-Q cavity. After interacting with a single atom, thefield oscillates with two different phases at once—againa Schrodinger cat situation. The box in which the photoniccat is trapped is a cavity 3 cm long, consisting of twocarefully polished niobium mirrors facing each other. (Seethe photo in figure 4.)

The photons are produced by a coherent millimeter-wave source coupled to the cavity by a waveguide. Assoon as a few photons are stored, the source is switchedoff and the photons are left free to bounce back and forthbetween the mirrors. Coupling to the environment isminimized by cooling the setup to very low temperature(0.6 K), because blackbody radiation can cause unwanted,trivial relaxation effects. Furthermore, at this tempera-ture the niobium is superconducting. The photons sur-vive on average 160 microseconds before being scatteredoutside by mirror surface defects. One can tune thefrequency of the field near 51 GHz by slightly moving themirrors.

Once the radiation field is prepared, a single atom issent across the cavity with an adjustable velocity (typically400 m/s). This atom has a resonant frequency differentfrom the field. Therefore it cannot absorb photons. Theatom behaves like a small piece of transparent dielectricmaterial with a refractive index slightly different fromunity. It thus induces a small dispersive effect on the

field, momentarily changing its fre-quency by a few kHz. The frequencyresumes its initial value when theatom exits the cavity, after about 20/J.S. But in the process the phase of theradiation field has been shifted.

Such an effect requires a specialkind of atom. The refractive indexcorresponding to an ordinary atom ina volume of about 1 cm3 differs fromunity by only a few parts in 1O22. Toget a much larger refractive index ef-fect, we excited rubidium atoms froman atomic beam by laser and rf irra-diation to a very high Rydberg state—with principal quantum numbern = 51. By adjusting the laser inten-sity, we can reduce the flux of Rydbergatoms to the point where they crossthe cavity one at a time.

A Rydberg level has a large de-generacy, corresponding to all possiblevalues of the atomic angular momen-tum. The sublevel we prepare is the

highest angular momentum state, with the excited elec-tron moving around the nucleus in a very circular orbit.Although the radius of an ordinary atomic state is halfan angstrom (0.05 nm), this state has a enormous orbitalradius of 125 nm. The atom then behaves like a hugeantenna strongly coupled to the radiation. It also has avery long radiative damping time, so that the loss ofcoherence due to spontaneous emission is negligible.

A single Rydberg atom in the 1 cm3 cavity volumechanges the refractive index by as much as a part in 107.That's 15 orders of magnitude more than one gets withan ordinary atom! The dephasing produced by such anatom on the field is on the order of a radian. Its valuecan be adjusted by controlling the atom's velocity andhence its transit time through the cavity, or by changingthe frequency of the radiation field. (The refractive indexis strongly frequency dependent.)

Introducing weirdnessWe introduce quantum weirdness into these proceedingsby subjecting the atom to an auxiliary microwave pulsebefore it enters the cavity. The pulse leaves the atom ina linear superposition of the two circular Rydberg stateswith principal quantum numbers 51 and 50. To stressthe similarity with the ion experiment, we again labelthese states, respectively, The cavity field+> andis detuned slightly from the transition between these twostates, which induces opposite refractive index changes inthe cavity.

After the atom's traversal, the field thus acquires two

TTTT v 1QQS TnnavDownloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

FIGURE 5. ELECTROMAGNETIC CAVITY FIELD in the Paris

experiment.10 a: The initial coherent field can be described bya vector whose length gives its amplitude (square root of the

mean photon population) and whose direction defines itsphase. The uncertainty circle at the tip represents field

quantum fluctuation, b: After interacting with a single atomprepared in a superposition of two Rydberg states

corresponding to different refractive indices, the field becomesa superposition of two states with different phases. The field

vector points in two different directions at once.

distinct phases, each entangled with a different atomicstate. One can think of a classical field as a vector in aplane, whose length is proportional to the field's amplitudeand whose direction defines the field's phase. When thereare only a few photons, the amplitude and phase exhibitrelatively large quantum fluctuations. The field's state,called a coherent or Glauber state, is the analog of aGaussian wave packet for a mechanical oscillator. Thecorresponding vector has a length equal to the square rootof the average photon number, with a small uncertaintycircle of radius unity at its tip.

The interaction with a single atom in the superposi-tion state transforms the field into two vectors orientedalong two different directions at once, symmetrical withrespect to the initial field. (See figure 5.) The state ofthe atom-plus-field system can be written as:

(1)

where the field of each Dirac ket is represented by itsvector .

NonlocalityHere, as distinguished from the NIST ion experiment, theentanglement becomes nonlocal when the atom leaves thecavity. That imparts a distinctive EPR twist to our ex-periment. There is indeed no easy way to detect the fielditself. The only practical way to get information is todetect the atom's energy and infer the field's state fromit. The energy state is measured by selectively ionizingthe atom in one of two detectors (D+ or D j and collectingthe resulting electrons. One gets the necessary energyselectivity by taking advantage of the fact that the thresh-old ionizing field is slightly different for the two Rydberglevels.

We must, however, take a final precaution if we wantto preserve quantum weirdness. If we were to detect theatom directly after it leaves the cavity, we would find itin one or the other Rydberg state, and the field, inaccordance with equation 1, would be projected into awell-defined Glauber state. The quantum ambiguitywould be lost. To avoid this loss, we subject the atom,just before detection, to a second microwave pulse thatremixes the two Rydberg states again. If the phase ofthis pulse is properly adjusted, | + > becomes( I +> + !-> )/V2" and | -> becomes ( | -. - |+>)/V2". Thecavity field is not affected.

The combined atom-plus-field system thus evolvesinto a new state:

i '> = (i +> (K> - h » +1 - x k> + ch»)/V2". (2)Each atomic state is now correlated to a superposition ofcoherent field states. We have the freedom to decide whatkind of field state we will finally produce by choosingwhether or not to apply the second microwave field pulseafter the atom and the cavity have ceased to interact. Atypical EPR paradox!

A quantum mouseHow can we detect the oscillator's quantum coherence?As in the ion trap experiment, we recombine the two statecomponents and look for interference effects. The idea,first suggested in a paper we published in 1996 with LuisDavidovich from the University of Rio de Janeiro,11 is tosend a second atom across the same apparatus after adelay. This second atom, identical to the first, plays therole of a quantum mouse probing the coherence of the catstate produced by the first atom. The probing atom issubjected to the same sequence of pulses. So, once again,it splits the phase of each field component in two. In thisprocess, two parts of the system's wavefunction recombinewith a unique final phase. When the first and secondatoms traverse the cavity in different states, the secondatom undoes the phase shift produced by the first.

This recombination leads to an interference term inthe joint probability for finding the pair of atoms in anyparticular combination of the two Rydberg states. Byrepeating the experiment many times, we have recon-structed these joint probabilities and combined them toproduce a two-atom correlation signal proportional to theinterference term.

Repeating the experiment with increasing delays be-tween the atoms, we found that the correlation, large atshort times, vanishes as the delay increases. (See fig-ure 6.) The loss of correlation is always faster than thedamping of the field energy. It speeds up as the numberof photons increases, becoming too fast to be observedwhen there are about 10. For a given field intensity, thedecorrelation becomes faster when the angle between thefield components increases.

These features are a direct demonstration of decoher-ence at work in a well-controlled situation. Because thepart of the field scattered away by mirror defects is asmaller, entangled copy of the cavity field, it carries awaycrucial information about the field's phase. In principle,a leaking field with the intensity of only a single photonis large enough to yield information about its phase,provided that the two components are split by an angleon the order of one radian or more. At such an angle,the uncertainty disks of the two leaking field componentsare disjoint. If the splitting angle is small, extracting thisphase information requires a somewhat larger leakingfield. The mere fact that this information is available,even if it is not in fact read out, is enough to destroy, ata distance, the quantum coherence of the cavity field.Here, once again, complementarity manifests itself!

The time it takes for the first photon to escape is theaverage photon damping time divided by the mean photonnumber. This first-photon-escape time becomes shorterand shorter as the field energy stored in the cavity isincreased. If the probe atom arrives after this first escapetime, the cavity field has become an incoherent statisticalmixture and all interference effects in the two-atom cor-

40 IULY 1998 PHYSICS TODAYDownloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

oEn

o<• 1

22Ouso<

160DELAY TIME

320

relation are lost. This argument agrees well with ourobservations, as shown in figure 6 together with predic-tions calculated from decoherence theory.

The fragility of coherenceThe two-atom experiment gives us a visceral feeling forthe extreme fragility of quantum coherences betweenmacroscopically distinct states. The coherence vanishesas soon as a single quantum is lost to the environment.So we understand why real cats, or even much smallerobjects made of enormous numbers of molecules, losecoherence immediately.

The experiment's connection with quantum measure-ment theory12 is also striking. Consider, for the sake ofargument, that it is the cavity field that's observing theatom, and not the other way around. The field can indeedbe seen as a meter pointing in different directions accord-ing to the state of the atom, thus realizing a first step inan ideal atomic energy measurement. To complete theprocess, one would have to detect the field by amplifyingit and then coupling it to a phase-sensitive radiationdetector.

We recognize here the chain of operations, first de-scribed by John von Neumann, that connects by successivesteps a microscopic object to the observer.12 If all theinstruments along this chain simply obeyed the linearevolution equations of quantum mechanics, they wouldget entangled into state superpositions of the kind de-scribed by equation 1, all the way up to the macroscopiclevel.

Collapsing the wavefunctionSuch superpositions are, of course, never observed. Onefinds instead that the meter points randomly here or there.That's the state of affairs postulated by the orthodoxCopenhagen interpretation of quantum mechanics, whichenjoins us to disregard superpositions of apparatus statesand to "collapse" them instantaneously to one of thepossible meter states, the probability for any one of thosemeter readings being given by the absolute square of thecorresponding wavefunction amplitude.

By contrast, the proponents of the modern decoher-ence theories prefer to view this wavefunction collapse asa real physical process caused by the coupling of themeasuring apparatus to its environment. For all practicalpurposes, of course, the orthodox and decoherence points

FIGURE 6. TWO-ATOM CORRELATION signal, which measuresthe coherence of the Schrodinger-cat cavity field produced bythe first atom in the Paris experiment,10 decreases withincreasing time delay before sending the second atom. Thetwo data sets correspond to two different dephasing anglesbetween the cavity field "cat state" components. The fieldcontains, on average, 3.3 photons. Decoherence is faster whenthe phase separation between cavity field components is larger.Then the decoherence time is about three times faster than the160-/XS field-energy decay time. The curves show decoherencetheory predictions.

of view are equivalent, because the decoherence time isinfinitessimal for any measurement that ultimately in-volves a macroscopic apparatus.

Our atom—cavity experiment, however, by isolating afirst stage involving a mesoscopic meter in the measure-ment chain, has allowed us to catch the elusive momentwhen the meter loses its coherence. The choice of basisstates in which decoherence occurs is also an importantissue. Before decoherence, the entanglement between themicroscopic system and the measuring apparatus de-scribes possible correlations in all possible basis-staterepresentations. (Compare equations 1 and 2.) The cou-pling to the environment, however, favors one basis of"robust" coherent states over other, very fragile superpo-sitions. In that representation, all the weird EPR-likecorrelations that would otherwise introduce a fundamentalambiguity into the measurement process are destroyed.

In both the atom-cavity and ion trap experiments,quantum mechanics predicts a statistical distribution ofoutcomes over many repetitions of the experiments. Noth-ing more specific can be said a priori about the outcomeof any one trial. Even when quantum coherence hasvanished, we still have, in each run, two possible outcomes.The agency of choice remains mysterious. Attempts havebeen made to modify the quantum theory by adding subtlemechanisms that would "explain" quantum choice in sys-tems with macroscopic components.13 Whether such theo-ries will be successful and lead to testable experimentalpredictions remains dubious.

Unless these unorthodox approaches are eventuallyvindicated, it seems, to paraphrase the disapproving Ein-stein, that God does indeed play dice. The atom-cavitySchrodinger's cat experiment does not address this ulti-mate mystery, but at least it offers us a glimpse at theprocess by which this dice game proceeds from the quan-tum mechanical (with the cat both dead and alive I to theclassical realm (where the cat is either dead or alive).

These experiments are first steps along a challengingroad. Entangling atoms and photons together in a con-trolled manner will open the way to fascinating applica-tions. Two-level atoms and two-state vibration modes ofquantum oscillators can be regarded as binary "quantumbits" in which information could be stored and manipu-lated in quantum computers by the promisingly permissiverules of quantum logic.11 Following an idea of IgnazioCirac and Peter Zoller at Innsbruck University, Wineland'sgroup has already demonstrated with a single ion in atrap the elementary operation of a quantum gate.15 Ourgroup and Jeffrey Kimble and coworkers at Caltech havealso shown that atom-cavity experiments can be turnedinto elementary quantum information processing ma-chines.16 (See PHYSICS TODAY, March 1996, page 21.) Wehave also recently achieved controlled entanglement ofatoms crossing a cavity one at a time.17 In a relatedarea, quantum teleportation based on entanglement, pro-posed by Charles Bennett and coworkers 1992, has re-

TULY 1998 PHYSICS TODAY 41Downloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

extensiverange of

cryogenicaccessories,electronics,sensors and

consumablesavailable

ex-stock forfast delivery

I I I I I I !

Phone, fax, e-mail now for the latest comprehensive catalogor view the catalog on-line at

//www.oxford-instruments.com/ri/cryospares/

I I I I I I I :

130A Baker Avenue ExtensionConcord MA 01742-2121, USAe-mail cs.n@oxinst co I A

re' 1978) 369-9933

fax 19781 369-6616Oxford Instruments

Research Instruments

Circle number 20 on Reader Service Card

liiianil

ComputersIn Physics

The computer magazine for scientists and engineers

Six times a year this full-color publica-tion brings you news and comment,product and book reviews, peer-reviewed journal articles, and more:

• Computers in Education

• Practical NumericalAlgorithms

• Scientific Programming

• Computer Simulation

• Guide to the Internet

• Laboratory Applications

S PHYSICS..

TUB Scholarly WebulildisciDilnarv Visualization

AMERICANINSTITUTESEPHY5IC5

Send for yourFREE issue today

e-mail: mktg@aip.org

500 Sunnyside Blvd., Woodbury. NY 11797

cently been demonstrated,18 (See PHYSICSTODAY, February1998, page 18, and the article by Bennett in the October1995 issue, page 24.)

How big will Schrodinger cats eventually become, andhow far can the quantum/classical boundary be pushed?These remain open questions. Decoherence becomes moreand more efficient as the size of a system increases. Itprotects with a vengeance the classical character of ourmacroscopic world. That makes large-scale practicalquantum computing a very distant dream, to say the least.(See the article by Haroche and Raimond in PHYSICS TODAY,August 1996, page 51.) In the meanwhile, experimenterswill go on breeding all kinds of Schrodinger kittens made ofa few particles, in the hope of learning more about thefascinating mysteries of quantum mechanics.

References.1. T. Pfau, S. Spalter, C. Kurtsiefer, C. Ekstrom, J. Mlynek, Phys,

Rev. Lett. 73, 122.3 U994). M. Chapman, T. Hammond, A.Lenef, J. Schiedmeyer, R. Rubinstein, E. Smith, D. Pritchard,Phys. Rev. Lett. 75, 3783 (1995).

2. A. Einstein, B. Podolsky, N. Rosen, Phys.Rev. 47, 477 (1935).3. J. Clauser, Phys. Rev. Lett, 36, 1223 (1976). S. Fry, R.

Thompson, Phys. Rev. Lett, 37, 465 (1976). A. Aspect, P.Grangier, G. Roger, Phys. Rev. Lett. 49, 91 (1982). A. Aspect,J. Dalibard, G. Roger, Phys. Rev. Lett. 49, 1804 (1982). Z. Ou,L. Mandel, Phys. Rev. Lett. 61, 50 (1988). P. Kwiat, K. Mattle,H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 75, 4337 (1995).W. Tittel et al., Phys. Rev. A57, 3229 (1998).

4. E. Schrodinger, Naturwissenschaften 23, 807, 823 and 844(1935), reprinted in English in ref. 12.

5. See D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I. Stamatescu, H.D. Zeh, Decoherence and the Appearance of a Classical Worldin Quantum Theory, Springer, New York (1996).

6. A. Leggett, in Chance and Matter, Proc. Les Houches SummerSchool XLVI, J. Souletie, J. Vannimenus, R. Stora, eds., NorthHolland, Amsterdam (1987).

7. E. Jaynes, F. Cummings, Proc. IEEE 51, 89(1963). L.Allen,J. Eberly, Optical. Resonance and Two-Level Atoms, Wiley, NewYork (1975).

8. B. Yurke, D. Stoler, Phys. Rev. Lett,, 57, 13 (1986). J. Gea-Ba-nacloche, Phys. Rev. A, 44, 5913 (1991). V. Buzek. H. Moya-Cessa, P. Knight, Phys. Rev. A45, 8190 (1992). C. Savage, S.Braunstein, D. Walls, Opt. Lett. 15, 628 (1990).

9. C. Monroe, D. Meekhof, B. King, D. Wineland, Science, 272,1131 (19961.

10. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wun-derlich, J. Raimond, S. Haroche, Phys. Rev. Lett. 77, 4887(1996).

11. L. Davidovich, M. Brune, J. Raimond, S. Haroche, Phys. Rev.A 53, 1295 11996).

12. J. A. Wheeler, W. Zurek, Quantum Theory of Measurement,Princeton U. P., Princeton, N.J. (1983).

13. See, for example, G. Ghirardi, A. Rimini, T. Weber, Phys. Rev.D 34, 470(1986).

14. A. Ekert, R. Josza, Rev. Mod. Phys. 68, 733 (1996).15. J.Cirac, P. Zoller, Phys. Rev. Lett. 74, 4091(1995). C.Monroe,

D. Meekhof, B. King, W. Itano, D. Wineland, Phys. Rev. Lett.75,4714(1995).

16. P. Domokos, J. Raimond, M. Brune, S. Haroche, Phys. Rev. A52, 3554 (1995). X. Maitre, E. Hagley, G. Nogues, C. Wunder-lich, P. Goy, M. Brune, J. Raimond, S. Haroche, Phys. Rev. Lett.79, 769 (1997). Q. Turchette, C. Hood, W. Lange, H. Mabuchi,H. Kimble, Phys. Rev. Lett. 75, 4710 (1995).

17. E. Hagley, X. Maitre, G. Nogues, C. Wunderlich, M. Brune, J.Raimond, S. Haroche, Phys. Rev. Lett. 79. 1 (1997).

18. D. Bouwmeester, J. W Pan, K. Mattle, M. Eibl, H. Weinfurter,A. Zeilinger, Nature 390, 575 (1997). D. Boschi, S. Branca, F.De Martini, L. Hardy, S. Popescu, Phys. Rev. L«tt. 80, 1121(1998). •

Circle number 21 on Reader Service Card 42 JULY 1998Downloaded 09 Oct 2012 to 152.3.102.242. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms