GENERAL ARTICLE Quantum Interference of Moleculesgovind/teaching/qm1-s11/molecular... · 2011-02-15 · inant and accepted theory of the nature of light in the 19th century. In 1864,

16 RESONANCE January 2010

GENERAL ARTICLE

Quantum Interference of Molecules

Probing the Wave Nature of Matter

Anu Venugopalan

Keywords

Matter waves, wave-particle du-

ality, electron interference,

decoherence.

Anu Venugopalan is on the

faculty of the School of

Basic and Applied

Sciences, GGS

Indraprastha University,

Delhi. Her primary

research interests are in

the areas of Foundations of

Quantum mechanics,

Quantum Optics and

Quantum Information.

The double-slit interference experiment has beenfamously described by Richard Feynman as con-taining the \only mystery of quantum mechan-ics". While the double-slit experiment for lightis easily understood in terms of its wave nature,the very same experiment for particles like theelectron is somewhat more di±cult to compre-hend. It has taken almost six decades after theestablishment of its wave nature to carry outa `double-slit interference' experiment for elec-trons. This has set the stage for interferenceexperiments with atoms and molecules. In thelast decade there has been a spectacular progressin matter{wave intereference experiments. To-day, molecules with over a hundred atoms canbe made to interfere. In this article we discusssome of these exciting developments which probenew regimes of Nature, bringing us closer to theheart of quantum mechanics and its hidden mys-teries.

1. Introduction: The Dual Nature of Radiationand Matter and the Birth of Quantum Mechanics

At the turn of the last century, there were several ex-perimental observations which could not be explainedin terms of the established laws of classical physics andcalled for a radically di®erent way of thinking. Thisled to the development of quantum mechanics, whichis today regarded as the fundamental theory of Natureand the most elegant tool for describing the physicsof the microworld. Some key events and developmentsthat set the stage for the coming of quantum mechan-

17RESONANCE January 2010

GENERAL ARTICLE

The birth of

quantum

mechanics is

intimately linked

with discoveries

relating to the

nature of light.

The wave theory

became the

dominant and

accepted theory of

the nature of light

in the 19th century.

ics were associated with the black-body radiation spec-trum (Planck, 1901), the photoelectric e®ect (Einstein,1905), the model of the atom (Rutherford, 1911), atomicspectra (Bohr, 1913), scattering of photons o® electrons(Compton, 1922), the exclusion principle (Pauli, 1922),the hypothesis of matter waves (de Broglie, 1925) andthe experimental con¯rmation of the existence of matterwaves (Davisson and Germer, 1927).

The birth of quantum mechanics is intimately linkedwith discoveries relating to the nature of light. Theoriesrelating to the nature of light have a long and chequeredhistory. Is light a wave or is it made up of particles? Theearliest theory on the nature of light goes back to thecorpuscular theory of Newton in 1704. Though Chris-tian Huygens had proposed the wave theory of light in1690, Newton's corpuscular theory, according to whichlight is composed of tiny particles or corpuscles, was thefavoured one for over a hundred years { a consequence ofNewton's towering presence and authority in the scien-ti¯c community at that time. In 1801, Thomas Youngperformed an experiment with light where a beam oflight was passed through two parallel slits in an opaquescreen and formed a pattern of alternating light and darkbands on a screen beyond { this we know as interference{ a phenomenon which is associated with waves. Later,other important experiments on di®raction and interfer-ence of light were also done, notably by Fresnel (1814)and others that could only be interpreted in terms of thewave theory for light. In the face of such irrefutable ex-perimental evidence, the wave theory became the dom-inant and accepted theory of the nature of light in the19th century. In 1864, James Clerk Maxwell showedthat electric and magnetic ¯elds propagated togetherand that the speed of these electromagnetic waves wasidentical to the speed of light. It became clear at thatpoint that light is a form of electromagnetic radiation.Maxwell's theory was con¯rmed experimentally with the


GENERAL ARTICLE

The discovery of the

photoelectric effect

and its explanation

by Einstein firmly

established that light

(radiation) has a dual

nature.

In 1927, Clinton

Davisson and Lester

Germer observed the

diffraction of electron

beams from a nickel

crystal –

demonstrating the

wave-like properties

of particles for the

first time

discovery of radio waves by Heinrich Hertz in 1886. Anexperiment performed by Taylor in 1909 showed thateven the weakest light source { equivalent to \a candleburning at a distance slightly exceeding a mile" { couldlead to interference fringes. This led to Dirac's famousstatement that \each photon then interferes only withitself ". However, the wave nature of light was not the¯nal word in this debate; there was experimental evi-dence, the photoelectric e®ect, which clearly needed analternate interpretation. The discovery of the photoelec-tric e®ect and its explanation by Einstein ¯rmly estab-lished that light (radiation) has a dual nature. In 1924,Louis de Broglie put forth the hypothesis that matterhas a wave nature and the now famous de Broglie re-lation connects the wavelength ¸ of a particle with itsmomentum p:

¸ =h

p; (1)

h being Planck's constant. While this wavelength wouldbe extremely small for large objects, particles like elec-trons have a wavelength which could be large enough togive observable e®ects. In 1927, Clinton Davisson andLester Germer observed the di®raction of electron beamsfrom a nickel crystal { demonstrating the wave-like prop-erties of particles for the ¯rst time { and George (G P)Thompson did the same with thin ¯lms of celluloid andother materials shortly afterwards. Davisson and Thom-son shared the 1937 Nobel Prize for \discovery of the in-terference phenomena arising when crystals are exposedto electronic beams". Their work was a landmark resultin the development of quantum theory as it providedthe critical con¯rmation of Louis de Broglie's hypothe-sis. Now that the wave nature of electrons was estab-lished, it remained to be seen if they indeed showed theclassic signature of the quantum world { the double-slitinterference e®ect, which would be the most satisfyingcon¯rmation of the dual nature of electrons as predictedby quantum theory.


GENERAL ARTICLE

Figure 1. The double-slit

interference experiment.

In the quantum

mechanical

description the

wave and particle

aspects are

inseparable.

Most students of physics are familar with Richard Feyn-man's famous description of the double-slit experiment(Figure 1) which captures the dual nature of matteras described by quantum mechanics. Feynman goes togreat lengths to explain the apparently paradoxical phe-nomenon by using the example of `bullets' and `singleelectrons'. The most ba²ing conclusion of this exper-iment is that even when there is only one electron (orphoton) ¯red at the double slit, there will be an interfer-ence pattern on the screen { something that can only beunderstood by the quantum mechanical description interms of wavefunctions, linear superposition and proba-bility amplitudes. In the quantum mechanical descrip-tion the wave and particle aspects are inseparable andit is as though the electron went through both slits si-multaneously and the amplitudes for these combined atthe screen to give the interference pattern. Here lies thegreat 'mystery' of quantum mechanics, its predictionsbeing completely in contrast to our cherished classical'common-sense' perceptions.

While most people have heard about Young's double-slit experiment for light, not many know about the ex-periments for electrons. Who actually performed thedouble-slit interference experiment for single electronsand when? The earliest experiment can be attributedto Ladislaus Laszlo Marton of the US National Bureau ofStandards (now NIST) in Washington, DC, who demon-strated electron interference in the early 1950s. How-ever, his experiment was in a Mach{Zehnder rather thana double-slit geometry. A few years later Gottfried MÄolle-nstedt and Heinrich DÄukertheory of the University ofTÄubingen in Germany used an electron biprism to splitan electron beam into two components and observe in-terference between them. In 1961 Claus JÄonsson per-formed an actual double-slit experiment with electronsfor the ¯rst time. Finally, in 1989, the now famousexperiment involving single electrons was performed by


GENERAL ARTICLE

Davisson and Germer

showed that the

electron beam was

scattered by the

surface atoms on the

nickel crystal at the

exact angles that had

been predicted for the

diffraction of X-rays by

Bragg’s formula.

These are stunning

experiments with the

largest objects ever

to show quantum

interference —

probing a hitherto

inaccesible regime

which lies in the

twilight zone

between the

classical and

quantum worlds.

Akira Tonomura and co-workers at Hitachi, Japan, wherethey observed the build-up of the fringe pattern with avery weak electron source and an electron biprism. Fordetails on the history of these interference experimentswith electrons the interested reader is referred to an in-formative article in Physics World listed at the end ofthis article. In the following we will brie°y review theDavisson and Germer experiment and discuss the clas-sic double-slit experiment for a single electron performedby Tonomura et al. We will then discuss recent exper-iments which carry interference experiments to a com-pletely new level { molecules with as many as 100 atomsshowing quantum interference! These are stunning ex-periments with the largest objects ever to show quan-tum interference { probing a hitherto inaccesible regimewhich lies in the twilight zone between the classical andquantum worlds. This is an an area of fundamental sci-enti¯c curiosity and perhaps holds the key to a myriadpossibilities of practical importance.

2. The Davisson and Germer Experiment

Clinton Davisson and Lester Germer performed the con-clusive experimental test of Louis de Broglie's hypoth-esis in 1927 at Bell Labs. For this work they sharedthe Nobel Prize in 1937 with G P Thomson. Their re-sults were published in a paper entitled `The scatterringof electrons by a single crystal of nickel' in the jour-nal Nature in 1927. In their paper, Davisson and Ger-mer reported their analysis of the angular distribution ofelectrons scattered from nickel. They showed that theelectron beam was scattered by the surface atoms onthe nickel crystal at the exact angles that had been pre-dicted for the di®raction of X-rays by Bragg's formula,with a wavelength given by the de Broglie equation (1).This was the ¯rst time that Bragg's law was applied toelectrons. In the same year, Thomson reported his ex-periments in which a beam of electrons was di®ractedby a thin foil. Thomson found patterns that resembled


GENERAL ARTICLE

Figure 2. TheDavisson and

Germer experiment.

the X-ray patterns.

The Davisson and Germer experiment is very simple tounderstand. Electrons strike a nickel crystal which iscut parallel to a set of its 111 planes (see Figure 2).The kinetic energy of these electrons is controlled bythe accelerating voltage V . Electrons are scattered in alldirections at all speeds of bombardment. The intensityof the electrons scatterred o® the target at various angleswas analyzed. It was seen that this intensity peaked forcertain critical energies at a given scatterring angle. TheBragg condition for maximum constructive interferenceis

2d sinA = m¸; m = 1; 2; :::; (2)

where d is the spacing between the planes as shown inFigure 2, ¸ is the wavelength and A is the angle betweenthe incident beam and the plane from which scatterringis taking place (see Figure 2). From this ¯gure it is clearthat this can be re-written in terms of the angle B as:

2d cosB

2= m¸; m = 1; 2; ::: (3)

and

d = a sinB

2; (4)

where a is the lattice spacing in the nickel crystal. Thisgives us

¸ =a sinB

m: (5)

scatteredbeam


GENERAL ARTICLE

These two

experiments were

stunning validations

of the de Broglie

hypothesis – particles

can also propagate

like waves.

For nickel, a = 0:215 nm. A peak in the electron in-tensity at an angle Á = 50± for m = 1 gives the elec-tron wavelength as 0:165 nm. Davisson and Germerfound that at this angle the peak corresponds to a volt-age V = 54 volts. Corresponding to this voltage, themomentum of the electron is given by

p =q

2meeV ; (6)

where me is the mass of the electron and e is its charge.The de Broglie wavelength corresponding to this mo-mentum is

¸ =h

p= 0:167 nm: (7)

This was undoubtedly in excellent agreement with theexperimental results. Shortly after this experiment,Thomson demonstrated a similar interference phenom-enon with electrons. These two experiments were stun-ning validations of the de Broglie hypothesis and theunderstanding of the physical world took a whole newmeaning { particles can also propagate like waves.

3. The Hitachi Group's Double-Slit InterferenceExperiment for Electrons

While the Davisson and Germer experiment left no doubtabout the wave nature of electrons, the most appeal-ing and satisfying testimonial of the electron's wave-likeproperties would de¯nitely be the classic paradigm ofquantum mechanics { the double-slit interference exper-iment. As already mentioned in the introduction, the¯rst attempts to do this go back to the late 1950s whenGottfried MÄollenstedt and Heinrich DÄuker of the Univer-sity of TÄubingen in Germany used an electron biprismto split an electron beam into two components and ob-serve interference between them. Following this, ClausJÄonsson of the University of TÄubingen did the exper-iment. In 1974 researchers led by Pier Giorgio Merli


GENERAL ARTICLE

Figure3.Set- up for double-

slit interference with single

electrons.

Akira Tonomura and

colleagues at the

Hitachi Advanced

Research Laboratory

in Japan reported

the double-slit

interference

experiment with

single electrons.

did the electron interference experiment at the Univer-sity of Milan. The experiment was repeated in 1989 byTonomura et al at Hitachi in Japan. By 1989, stunningadvances in technology, particularly in electronics, madethe Hitachi group's equipment far more sophisticated,precise and elegant. In a paper entitled `Demonstrationof Single-Electron Buildup of an Interference Pattern'published in the American Journal of Physics in 1989,Akira Tonomura and colleagues at the Hitachi AdvancedResearch Laboratory in Japan reported the double-slitinterference experiment with single electrons. In theirexperiment they used an electron microscope equippedwith an electron biprism and a position sensitive elec-tron counting system. In the following, we describe thisexperiment brie°y.

Electrons are emitted one by one from the source in theelectron microscope and they encounter the biprism (seeFigure 3). These electrons were accelerated to 50,000volts. Electrons having passed through on both sides ofthe ¯lament were then detected one by one as particlesat the detector. The detectors used were so good thateven a single electron would be detected with a hundredpercent e±ciency. At the beginning of the experimentbright spots began to appear { these were signatures ofelectrons detected one by one as particles. These bright


GENERAL ARTICLE

The Hitachi group’s

experiment clearly

demonstrated that

electrons behave like

waves as described

by quantum

mechanics.

The electron biprism

invented in 1953 by

Gottfried Möllenstedt

has proven to be an

important tool in the

study of electron

waves.

spots in the beginning appear to be randomly positionedon the detector screen. It may be noted that only oneelectron is emitted at a time. When a large numberof electrons is accumulated over time, a pattern thatlooks like regular fringes begins to appear on the de-tector screen. After about twenty minutes very clearinterference fringes can be seen { these fringes are madeup of accumulated bright spots, each of which recordsthe detection of an electron! Each time a bright spotis seen, we understand it as an electron detected as a`particle" and yet, the build-up over time of an unmis-takable inteference pattern is undoubtedly a signatureof waves! Keeping in mind that that there was onlyone electron entering the set-up at a time, the Hitachigroup's experiment clearly demonstrated that electronsbehave like waves as described by quantum mechanics.The interference pattern is a consequence of the possi-bilities of two di®erent paths (amplitudes) for the singleelectron to pass through as it encounters the biprism{ a situation exactly equivalent to a single electron en-countering a double-slit. The out of the way chancethat the pattern is due to two electrons being together(electron{electron interaction) is completely ruled outin the experiment as the seond electron is not even pro-duced from the cathode of the electron microscope tilllong after the ¯rst electron is detected.

It is easy to see how the experiment implements thedouble-slit situation. At the heart of the Hitachi group'sexperiment was the electron biprism. The electron bipr-ism was invented in 1953 by Gottfried MÄollenstedt. Forthe past ¯ve decades it has proven to be an importanttool in the study of electron waves and applications insolid state physics and holds tremendous potential forapplications in modern nanotechnology. Together withhis PhD student, Heinrich DÄuker, MÄollenstedt developedthe electron biprism. This initially consisted of a 1¹mthin wire which was chargeable through a voltage source.


GENERAL ARTICLE

The biprism of the kind that was used by the Hitachigroup consists of two grounded plates with a ¯ne ¯la-ment between them. The ¯lament has a positive poten-tial with respect to the plates. The ¯lament used bythe group was thinner than 1 micron in diameter. If theincoming electron wave is given by

Ã = eikzz; (8)

the action of the biprism is to de°ect the beam. If theelectrostatic potential in the xz-plane is V (x; z), thenthe de°ected wave is:

Ã(x; z) = exp³ikzz ¡

me

¹h2kz

Z z

¡1V (x; z0)dz0

´: (9)

In the experiment, the kinetic energy of the electrons,¹h2k2

z

2m>> ejV (x; z)j. There are two possible ways this

wave can be de°ected by the biprism, depending onwhich side it passes by. In each case, the de°ected wavecan be approximated as eikzz§e

ikxxupto a constant fac-

tor, where

kx = ¡me

¹h2kz

Z 1

¡1

³@V (x; z0)

@x

´

x=adz0; (10)

taking into account the fact that V (x; z) = V (¡x; x),i.e., the potential is symmetrical. After de°ection, thewaves propagate towards the centre as kx > 0. This de-°ection can be viewed as some sort of an impulse thateach wave would experience { having the same ampli-tude but di®erent signs depending on which side of the¯lament they pass. The overlapping of these two ampli-tudes in the observation plane would then give rise tothe wave:

Ã(x; z) = ekzz(e¡ikxx + eikxx): (11)

The probability distribution corresponding to this wouldcontain an interference term, 4 cos2(kxx), and this is


GENERAL ARTICLE

Figure 4. Single electron

events build up to from an

interference pattern in the

double-slit experiments:

The number of electrons

accumulatedonthescreen.

(a) 8 electrons; (b)270 elec-

trons; (c) 2000 electrons;

(d) is 20 min.

Reproduced from

http://www.hqrd.hitachi.co.jp/em/doublislit.cfm, with permissionfrom the authors.

The double-slit

experiment with

electrons is

transformative, being

able to convince even

the most die-hard

sceptics of the truth of

quantum mechanics.

what is observed. In the Hitachi group experiment, pa-rameters were chosen to give a fringe spacing of thepattern of the order of 900 ºA. The electrons were de-tected using a two-dimensional position sensitive elec-tron counting system. This system comprised of a °oures-cent ¯lm and a photon counting image acquisition sys-tem. (For more details on this stunning experiment, theinterested reader is referred to the literature listed at theend of the article.) Some readers might be aware thatin September 2002, the double-slit experiment of ClausJÄonsson was voted \the most beautiful experiment" byreaders of Physics World. To quote Robert Crease in anarticle dicussing this poll, \The double-slit experimentwith electrons possesses all of the aspects of beauty.... Itis transformative, being able to convince even the mostdie-hard sceptics of the truth of quantum mechanics".Interestingly, unlike Young's double-slit experiment forlight, the double-slit interference experiment for elec-trons has nobody's name attached to it.

The experiment by Tonomura and colleagues at Hitachiunambiguosly demonstrated the single electron interfer-ence phenomenon in all its glory, brilliantly capturingthe image of the interference patterns in the now famouspicture (Figure 4).


GENERAL ARTICLE

Figure 5. The C-60 fulle-

rene molecule.Picture downloaded from http://commons.wikimedia.org/wiki/Image:Fullerene-C60.png.

What is the limit

for observing this

quantum feature in

terms of size,

mass, complexity?

4. Interference Experiments with Atoms, Mole-cules, Bucky Balls and More

Clearly, the wave nature of matter has been demon-strated beyond doubt with the experiments mentionedand discussed in the previous sections. It is often arguedthat this uniquely quantum mechanical feature escapesour everyday perception because of the `smallness' ofPlanck's constant, h being as small as 6:6 x 10¡34 Js.For a macroscopic object this would make the de Brogliewavelength so small that its quantum nature (wave-particle duality) would not be observable. However, thishas been no deterrent for a large number of brave exper-imentalists who have veri¯ed the wave nature of mat-ter not only for electrons but also for atoms, dimers,neutrons, molecules, noble gas clusters and even Bose{Einstein condensates. Quantum leaps in technology andsophisticated instrumentation have made dreams of thesegedanken experiments a reality. An interesting questionthat arises is, how far can we go with larger objects?What is the limit for observing this quantum featurein terms of size, mass, complexity? In the followingwe describe a recent set of experiments which demon-strate quantum interference in some of the most massivemolecules { C60 and C70 fullerenes and tetraphenylpor-phyrin molecules which are biological molecules presentin chlorophyll and haemoglobin and are twice the size offullerenes. These experiments could hold the key to an-swering fundamental questions about quantum mechan-ics and the nature of the quantum{classical transitionand more.

C60, the third allotropic form of carbon was discoveredin 1985 by Kroto and colleagues. These carbon mole-cules have a structure of a truncated icosahedron (seeFigure 5). The truncated icosahedron has 12 pentagonand 20 hexagon rings and has 60 vertices { the shape ofa soccer ball. These molecules have been called `buck-minsterfullerenes' or just 'fullerenes' because of their


GENERAL ARTICLE

This is a fascinating

result – intuitively

one would expect a

60 atom molecule

like the fullerene to

behave more like a

classical particle

than like a quantum

mechanical particle!

striking resemblance to geodesic structures ¯rst discussedby Leanardo da Vinci and then implemented in archi-tecture by the architect Buckminster Fuller. In a paperpublished in Nature in 1999, the group led by AntonZeilinger in Vienna observed de Broglie wave interfer-ence of the buckminsterfullerene C60 { the most stablefullerene with a mass of 720 atomic units, composed of60 tightly bound carbon atoms. This is a fascinating re-sult { intuitively one would expect a 60 atom moleculelike the fullerene to behave more like a classical particlethan like a quantum mechanical particle! In the follow-ing we brie°y describe this experiment.

Fullerene molecules were brought into the gas phase bysublimating the powder form in an oven at a tempera-ture of approximately 900 K. Molecules are ejected oneby one through a small slit in the oven. The de Brogliewavelength of these molecules (uniquely determined bythe momentum of the molecule) is ¸ = 2:8 pm. It turnsout that the de Broglie wave length is approximately 400times smaller than the size of the particle! The inter-ference pattern expected would therefore be very smalland very sophisticated machinery will be needed to seeit. The di®racting element used by the group was ananofabricated free standing silicon nitride grating witha grating constant d = 100 nm and a slit opening ofapproximately 50 nm. After free evolution over 1 me-ter, the fullerene molecules are detected via thermionicionization by a tightly focused Argon ion laser beamoperating at 24 W. The positive ions are counted bya secondary electron counting system. The counts, as afunction of position clearly showed a di®raction pattern.Note that just as in the case of the Hitachi experiment,the pattern is built up atom by atom. The experimentensures that there is no interference between two or moreparticles during their evolution in the apparatus { so thisis indeed a single particle quantum phenomenon.


GENERAL ARTICLE

C60

F48

(a fluorofullerene )

is the largest and

most complex

molecule till date

to show quantum

interference.

These spectacular

experiments offer the

tantalizing possibility

of probing the twilight

zone between

quantum and

classical worlds by

performing

interference

experiments with

increasingly heavier

and complex objects.

From C60, the group has gone on to repeat the experi-ment for larger, more complex molecules. Starting ¯rstwith the C70 fullerene, the group demonstrated this re-markable phenomenon in C60F48 { a °uorofullerene {which at 1632 atomic units is the largest and most com-plex molecule till date to show quantum interference.The group also demonstrated quantum interference fortetraphenylporphyrin, a derivative of a biodye which isfound in chlorophyll. This is the ¯rst biomolecule ex-hibiting wave nature and has a spatial extent of 2nm {almost twice as much as C60. There is hardly any needto emphasize that these large molecules are, in many re-spects, like classical objects. They can store a lot of in-ternal energy in many degrees of freedom. When heatedto about 3000 K, fullerenes can emit electrons, photonsand even diatomic carbon molecules. This is similar toa hot object glowing and emitting black-body radiation.This makes these experiments even more remarkable asthey achieve nothing less than capturing the underlyingquantum footprints (the wave-particle duality) of largeand complex classical-like objects. This begs the ques-tion: Is there a limit to the size and complexity of theobject that can show quantum interference? This ques-tion leads us to the age-old debate about the classical{quantum transition and the connection between thesetwo complelety di®erent descriptions of reality. It is of-ten argued that quantum mechanics is the descriptionfor an abstract micro world far removed from realitywhile classical mechanics describes the physics of themacro world of our everyday experience. But the macrois ¯nally composed of the micro! Where then, is theboundary, if any? These spectacular experiments o®erthe tantalizing possibility of probing the twilight zonebetween quantum and classical worlds by performinginterference experiments with increasingly heavier andcomplex objects.


GENERAL ARTICLE

Apart from confirming

the qualitative and

quantitative

predictions of the

decoherence theory,

these experiments

allow one to estimate

the vacuum conditions

that are required for

the successful

observation of

quantum interference

of much larger

objects.

4.1 The Quantum-Classical Boundary and De-coherence

A widely accepted explanation for the appearance ofclassical like features from an underlying quantum worldis the environment induced decoherence approach. Ac-cording to this theory, coupling to a large number ofdegrees of freedom (the environment) results in a loss ofquantum coherence which leads to emergent classical-ity. In the context of the experiments described abovefor fullerenes and other large molecules, an importantdecoherence mechanism comes from its interaction withparticles from the background gas. By °ooding the in-terferometer with various gases at low pressure AntonZeilinger's group studied the e®ect of decoherence onthe inteference phenomenon. In fact, in keeping withthe theoretical predictions, they saw an exponential de-crease of the observed fringe visibility. It is interestingto note that such decoherence which is caused by colli-sions is almost impossible to test in the usual matter{wave interferometry with smaller particles (like electronsand neutrons) as the particles are themselves so lightthat they would be kicked out of the interferometer aftercolliding with a gas particle. In the case of fullerenes andlarger molecules, the molecules themselves are heavyenough to remain in the interferometer after a typicalcollision. Apart from con¯rming the qualitative andquantitative predictions of the decoherence theory, theseexperiments allow one to estimate the vacuum condi-tions that are required for the successful observationof quantum interference of much larger objects. Thesurprising observation by the group was that collisionswould not limit quantum interference even for an objectas large as a virus provided the background pressure ofthe gas is reduced to below 3 x 10¡10 mbar.

5. Conclusions

The matter{wave interference experiments of massive


GENERAL ARTICLE

Suggested Reading

The topics touched upon in this article cover several references. The interested reader may look at some of the

following:

[1] R P Feynman et al, The Feynman Lectures, Vol.3, Addison-Wesley, 2006.

[2] The Double-Slit Experiment, Physics World, p.15, September 2002. An extended version of this article

including three letters about the history of the double-slit experiment with single electrons is available at http:/

/physicsworld.com/cws/article/print/9745.

[3] A Tonomura et al., Demonstration of single electron build up of an interference pattern, American Journal

of Physics, Vol.57, No.2, February 1989. A nice description of this experiment can also be found at the Hitachi

web site: http://www.hqrd.hitachi.co.jp/global/doubleslit.cfm.

[4] A non-technical description of the Fullerene diffraction experiments can be found at the web site of Anton

Zeilinger’s Research group at the Universitit Wien, Austria: http://www.quantum.univie.ac.at/research/

matterwave/c60/index.html.

[5] Anu Venugopalan, The Coming of a Classical World, Resonance: Journal of Science Education,Vol.9, No.10,

2004. The birth of quantum mechanics is intimately linked with discoveries relating to the nature of light.

Address for Correspondence

Anu Venugopalan

University School of Basic

and Applied Sciences

GGS Indraprastha University

Kashmere Gate

Delhi 11 0 453, India.

Email:

[email protected]

These stunning

studies have

demonstrated beyond

doubt that the

quantum nature of

large objects can

indeed be captured

experimentally in the

classic paradigm of

the double-slit

interference and

diffraction set-ups.

molecules described above have allowed us to probe andexplore a new regime of Nature and opened up the pos-siblity of experimentally studying the elusive quantum{classical boundary. These stunning studies have demon-strated beyond doubt that the quantum nature of largeobjects can indeed be captured experimentally in theclassic paradigm of the double-slit interference and dif-fraction set-ups. Important decoherence mechanismshave been studied and identi¯ed and the good news isthat it is possible to carry these experiments further forheavier and more complex molecules. Infact, there istalk of doing these interference experiemnts for proteinslike insulin and then on to larger proteins, clusters andnanocrystals. In the last two decades matter{wave in-terferrometry have demonstrated e®ects that were previ-ously unthinkable. More importantly, they have openedup exciting possibilities of exploring questions of funda-mental interest in the foundations of quantum mechan-ics { like the quantum{classical boundary. Imaginativeand novel ideas continue to fuel the ¯eld and it can besafely said that in our pursuit of the \only mystery ofquantum mechanics" the best and the most interestingexperiments are yet to come.

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GENERAL ARTICLE Quantum Interference of Moleculesgovind/teaching/qm1-s11/molecular... · 2011-02-15 · inant and accepted theory of the nature of light in the 19th century. In 1864,