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gamma rays of 14.4 keY emitted by the excited 57mFestate (r= 141 ns,I=312), the coherencelength is about 40 m. Forthe 6.2 Quantumoptics with keV gammaradiation from 181~a,having alifetime of8.73 flS,the coherence length is 4 km. The appreciable coherence length of these gamma allows us to observe the interference gamma radiation between the transition amplitudes from two paths of the single , , passing through two different samples. In one path the Romain Coussement'·2,Rustem Shahkmoumtov ,3, GerdaNeyens' photon interacts with nuclei ofa reference sample and in the other and JosOdeurs1 path it interacts with the nuclei of a sample under investigation. lInstituut voorKern- en Stmlingsfysica, Katholieke Universiteit The distance between the samples canbeas large as the coherence Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium length of the photon. Interference of these two transition ampli­ 2Optique Nonlineaire Theorique, UniversiteLibre de Bruxelles, tudes provides spectroscopic CP231, Bid du Triomphe,B-lOS0 Bruxelles, Belgium information about the hyper- 3Kazan Physico-TechnicalInstitute ofRussian Academy of fine interaction of the nuclei in Sciences,10/7 Sibirsky tmkt, Kazan 420029, Russia the investigated sample, pro­ vided the hyperfine spectrum Since the discovery of the nuclei in the reference AN one slow down a gamma photon to a group velocity of a sample is known. Such interfer­ of optical ,the Cfew m/s, or can one stop it in a piece of material only a few ence phenomena have been micron thick and release it? Can one, on command, induce trans­ explored using synchrotron scientificcommunity parency of a nuclear resonant absorber for gamma radiation and radiation [5) and are nowadays make a gate? Can one change the index of refraction for gamma used as a tool for solid state hasbeenchallenged rays in such a way that one could think of optical devices for physics studies. gamma radiation such as mirrors, cavities etc? Because of their very high to realise a gamma Such questions would all soundlike science fiction if we did not energy, the gamma photons knowthat such effects were first predictedbytheoretical quantum have very shortwavelengths: of optics and are observed experimentally with optical photons the order of an Angstrom or a raylaser. interacting with atoms [1-4). Since gamma radiation and optical fraction of it. Consequently, it radiation are of the same electromagnetic , we can ask becomes possible to investi- seriouslywhywe couldnot observe the same effects when gamma gate crystalline structures radiation interacts with . These are the questions using nuclear Bragg scattering. Methods based on this feature, that one tries to answer in the field of "quantum nucleonics", such as nuclear emission (6) and absorption holography [7), sometimes also called"gamma optics". have been explored recently. There are obviously some important differences between Having photons with a verylong coherence length and a very quantum optics (interaction of photons with atomic ) small wavelength allows us to conceive an interferometer that is and gamma optics (interaction of gamma photons with atomic very sensitive to small changes in optical length. The idea has not nuclei). In particular for the investigation ofthe former the basic yet been explored and one ofthe possible applications maybe the ingredient is the use of (called the'driving'laser) for detection ofthe gravityred shift with a muchhigher precision [8). inducing coherence and interference effects in atomic systems Because nuclear cross sections are many orders-of-magnitude with three or more levels (Box 1: the basic principles of coher­ smaller than the atomic ones, nuclear gamma optics experiments ence and interference). require the use of high density targets, which means the use of The exploration of coherence with gamma radiation has been hindered by the fact that one does not have a driving a-----,~- laser. Furthermore, gamma radiation is emitted by a radioactive source and there is no phase coherence between photons as is the case for photons emitted by a laser in the optical domain. But this restriction can be circumvented to a large extent by the use of mixed level doublets in the nucleus (Box 2). We will show that the study of coherence and interference with gamma radiation has interference some unique features compared with the optical case. First one should note that the gamma photons are emitted and detected as single photons. This is a restriction, but it also pro­ vides a unique opportunity to see interference effects using a A single photon. Optical single photon experiments require sophis­ 2 ticated equipment (which is available but needs special care and Preparati n of oherent excitation skills), while with gamma radiation each experiment is a single photon experiment. It allows us to address some fundamental 1 questions about the quantum mechanical,dual nature ofthe sin­ glephoton. .. fig. 1:Thelevelsaand bcan be coherentlyexcitedbythe Another interesting feature is that one can easily choose fieldsA1and A2proVidedthat both fieldsare lockedin phase.Ina gamma rays emitted from a nuclear . Because of the long subsequent process,in whichthese states makeatransition to lifetime ofthe isomeric state, its linewidth is extremelysmall and the same final level,interference can be observed. the coherence length of the emitted photon is verylong. For the

190 europhysics news SEPTEMBER/OCTOBER 2003 Article available at http://www.europhysicsnews.org or http://dx.doi.org/10.1051/epn:2003505 F~ATURES solid materials. As the nuclear recoil energy induced by the an adequate pump mechanism does not exist. Because the pump gamma decay is verylarge (because ofthe large gamma ray ener­ efficiency is veryweak, while the losses due to electronic absorp­ gy) and because the recoil energy depends on the spectrum of tion processes are important, one needs a tremendous energy phonons created in the lattice, the gamma ray emitted from a input. Under extreme pump irradiation, the non-resonant power nucleus embedded in a solid has a large statistical energy distrib­ input would be so large that the sample would be destroyed by ution. To allow experiments with narrow gamma lines it is melting or evaporation before lasing could occur. As a result we necessary to use solids in which this large statistical energyvaria­ are faced by the so called gamma laser dilemma [13) in that one tion is reduced. This is a major restriction on the gamma needs a solidwith a high recoilless fraction and thatthe condition transitions available for gamma optics research, as only Moss­ for recoilless fraction will be destroyed by the required pump bauer fulfill this condition. For such isotopes the recoil power. To try to circumvent this dilemma, one follows two momentum is transferred to the lattice as a whole and the gamma avenues. They have in common that one will store energy in decay is registered as a 'recoilless' decay, giving rise to narrow long-lived and find a mechanism to release it on com­ gamma ray lines. One could lift this restriction by using dilute mand. Storing large amounts of energyin nuclear isomers is not gases or mono-energeticbeams ofnuclear isomers [9). The recoil the real challenge. One can produce these long-lived isomers in energies would then be the same for all events, and averaging all nuclear reactors or with accelerator beams and separate them transition amplitudes over a large ensemble of events would not from other types of material bychemical and!or physical means. lead to the cancellation of the interference term. However the The technologyis available in principle or atleastthere is enough smallness of the densities together with the small cross sections knowledge available for it to be developed. The problem is the put such experiments out of reach with the present means of release of the stored energy 'on command' and in a very short producing nuclear isomers. time. It is on this point that the two approaches diverge concep­ tually. The gamma ray laser Since the discovery ofoptical lasers, the scientific communityhas Energy conversion been interested and challenged to realise a gamma ray laser (see One ofthe roads followed is to pump a long-lived for example [12)). A gamma ray laser would offer many applica­ into an excited nuclear statevialow energyX-rayirradiation. Sub­ tions because of the short wavelength and because of the high sequently this decays via the emission of gamma power density. Despite the considerable efforts of many groups, rays, representing a multiple of the input energy (see figure 3). In there still exists no idea of how to build such a device using pre­ this scenario the long-lived isomeric state could act as a nuclear sent and our available knowledge of laser, nuclear battery; in which energyis stored. and atomic physics. A proof of principle for releasing the stored energy has been The main problem is the realisation of population inversion. demonstratedusinga K-isomeras the storagelevel [14). Fromthe Because ofthe small cross sections for nuclear photo-absorption, point of view of nuclear models the result is surprising. Indeed,

Coherenceand Interference B2) the interference is observed. The arbitrary phase ofthe inter­ A quantum transition from state i to statef can be describedby mediate state does not affect the result because this state occurs an amplitudeA = A'ifeXP(iq»,where q>standsfor thephase ofthe with its complex conjugate in the transition amplitude from field inducing this transition and A'if is the complex transition state i to statef, i.e., (A'J)ib(B'db!. When calculating the transition matrixelement,which depends on the relative phases ofthe ini­ probability of two quantum paths, each following a two-step tial and final states. Inmostprocesses allthephases are cancelled process (Fig. I),thephasefactors ofthe initial andthefinal states since the observ~bleis just a transition probability P =IAI2. cancel, provided that both paths start and end at the same ini­ However, if the experiment is designed in order to observe a tial and final states. Coherent preparation is mostly called process with two quantum paths,one must first sum the ampli­ coherent excitation and the interferences are observed in the tudes and then square the norm. This procedure will produce subsequent step. However the role of the preparation and interference terms in which the phase factors play an important observation step maybe reversed. In that case the interferences role: can be observed in the first step, provided that the experiment is constructed such that the ob erved transition in the first step is conditionedby the second step. In short, the rule for observing interference in quantum transi­ In an experimenta large number of events is observed. Ifall the tions is that the observed transition can pass via two phases are different from eventto event then the experimentally indistinguishable quantum paths, which have a common initial observable is an average of all possible phase differences. The and a common final state, and that the radiation fields in the interference term cancels and the probability is just the sum of preparation step are phaselocked. the partial probabilities Pi = IAi\2. While in quantum optics the phase locking of the laser fields However one can design an experiment in which the inter­ became a routine,in case ofgamma radiation, where single pho­ ference term is not zero. Thenthe interference is constructive or ton processes are to be considered, this problem needs special destructive, depending onthesignofthe phase difference ((>J-IpJ., care. To be coherent the first step of excitation must go to close­ if thelatter is fixed for the ensemble or chain of events. This can lyspaced nuclear levels. These levels are to be close enough in be doneif the transition is splitin two paths due to the two-step energythat a single photon can induce thetransition to the two processes, as shown in Fig. 1. In one step (AI andA2) the coher­ states, despite its sharp frequency distribution. In box 2 we encebetweena andb states is prepared,if thephase difference of explain how to produce such closely-spaced nuclear levels and theAI andA2fields is fixed (which is the case ofthephaselocked later in this article we demonstrate that theyfulfill all the condi­ fields or mutually correlated fields). In the secondstep (BI and tions to be coherentlyexcited by a single gammaphoton.

europhysics news SEPTEMBER/OCTOBER 2003 191 FEATURES the K-isomeric state has a long lifetime because the K-selection rule hinders its decay into nuclear states at lower energy as this involves a large change in the projection ofthe angular momen­ tum [15].1t comes as a surprise that the transitions to higher energy states in this band are then less affected by this hindrance. It is certainly an interesting phenomenon for m=+312 nuclear spectroscopists. However because ofthe weak coupling of the X-ray pump with the possible lasing level, this is not yet an efficient mechanism for producing a gamma raylaser.

Lasingwithout inversion m==+ll2 A prime condition for gain with is popula­ tion inversion, or explicitly, the number of excited state nuclei from which lasing has to occur, exceeds the number of ground m:::o:-1I2 state nuclei. This condition requires that one must be able to per­ Quadrupole ZeemsD m=-312 form a nuclear isomeric separation in order to obtain nearly pure spIll1lng spUlllng isomeric material. Such a technology could be developed in the future, for example using the laser ionisation method for produc­ ing isomeric enrichment, the separation being based on the .. Fig. 2: Nuclear hyperfine levelsas afunction ofthe magnetic difference in the hyperfine structure [16]. field,for the 1=3/2 isomericstate in 57Fesubjected to an electric Even if a solid material could be prepared with most of the field gradient and a static magnetic field.Ifthe symmetryaxes of nuclei in the ground state as well as a large number in some long­ both interactions are parallel,crossing of hyperfinelevels occurs lived isomeric state, without having an inverted system, lasing at particular values of the magnetic field (smallcircles).Ifthe might still be realised. To obtain lasing from such a system, the axialsymmetry is broken by slightly misaligningthe magnetic concept of"lasingwithout inversion" as introduced in quantum field with respect to the electric field gradient symmetryaxis, optics, could be translated to gamma radiation. In the optical then the hyperfine levelsare mixed (enlarged part around the crossing). range the effect of"lasing without inversion" has been demon­ strated experimentally [4] and it was pointed out that the main new application will be the realization oflasers at very high fre­ tion can for example be induced bya radio frequency (rf) mag­ quency, for example UV; X-ray or even a gamma ray laser. The netic field (also called a Nuclear Magnetic Resonance, NMR,field) main point here is that one can create coherence in a three level [18]. In that case the fourth level must be a member ofthe same system in such a way that absorption of the lasing frequency is hyperfine manifold. It can also be induced by the coupling cancelled by destructive interference while the emission, and in between the atomic and nuclear spins, via the excitation ofthe particular the stimulated emission, is not [18]. atomic state. In that case the radiation canbe optical [19). In optics one can coherently excite two atomic levels by irradi­ Another problem that remains is related to the weak coupling ating the atoms with two lasers of different frequency (color) but of the nuclei with the gamma radiation. When choosing nuclei coupled in phase. Such phase-locked, two-frequency laser light is with a verylong lifetime, there is enough time to produce large called 'bichromatic light' and can easily be obtained from one quantities of the , to make isomeric enrichment and to laser using frequency doubling or dividing crystals. store it before triggering the release of all stored energybyturn­ One does not have an equivalent toolin gammaoptics. There­ ing on the driving radiation. However, there is a price to pay. As fore one is restricted to excitations of two 'nuclear hyperfine the isomeric state has a long lifetime, the coupling ofthe gamma levels' which can be excited with a single gamma photon despite radiation to the nuclei is weak. Thus the cross sectionfor stimu­ its small naturalline width. Two conditions need to be fulfilled for lated emission is small and the losses from electronic absorption this. One, the energy difference between these two levels mustbe can not be compensatedbythe gain from stimulated emission. less than the natural line width ofthe photon. This condition can There could be a way out of this problem if the gamma radia­ easily be fulfilled by the method of nuclear level mixing, also tion couldbe coupledto a collective ensemble ofexcited nuclei to sometimes called nuclearlevel anticrossing (see box2). Secondly, form a state similar to a Base Einstein condensate of atoms. In the selection rules, which apply to transitions between nuclear such a condensate,the probabilityfor stimulated emissionis mul­ hyperfine levels, need to be allowed in both paths. This condition tiplied bythe number ofexcited nuclei in the collective ensemble. is automatically fulfilled by the nature of the mixedlevels pro­ Now thatBase Einstein condensates have beenproduced inatom­ duced via nuclear level mixing: the doublet consists of an ic systems, one might in the future think of ways to create a in-phase and an anti-phase superposition ofm-quantum states. nuclear collective coherent state and thus pave the way for a The selection rules, also taking into account the polarization of gamma raylaser. the photon, allow for example the transition to the angular momentum component m (which occurs in both mixed levels). Nuclear level mixing induced transparency Excitation of both levels of the doublet can then be achieved Consider an ensemble ofnuclei in their nuclear groundstate, and with a single photon. thatthese nucleihave an excited statethatis isomeric.Suppose the In order to observe interference effects in this absorption ensemble is submitted to the necessary conditions for creating a process, another condition needs to be fulfilled, namely the two level mixed doublet in the isomeric state. As explained in box 1, interfering quantum paths need to be fully coherent (see box 1). interference in such a system can occur in the decay from such The coherence is created bythe connection ofthe two states ofthe coherently excited, level mixed states, provided decay to a partic­ doubletwith a single fourth quantum statewith someresonant or ular final state is observed. This final state could be a particular quasi-resonant radiation (called the driving field). Such radia- member ofthe ground state manifold, even the same state from

192 europhysics news SEPTEMBER/OCTOBER 2003 FEATURES which the mixed states were populated. Indeed in such a scheme decay modes. The enhancement in the forward direction strong­ there are two paths which start and end on the same state so that ly depends on the thickness of the absorber. In such conditions we the quantum phase factors cancel. However, one must notice that can expect that interferences can be observed because,in the case once the doublet states are excited, spontaneous decaywill hap­ of a strong enhancement, the process of excitation and subse­ pen not only to one but to all members of the ground state quent deexcitation is reduced to the two dominant paths. These hyperfine manifold. One can demonstrate that in the case of a two paths are coherent because they both start and end on the spontaneous decay in a 41t geometry the sum of the interference samelevel. These interferences can,in principle,leadto more or to terms will cancel. In order to observe interference in the decay less absorption. Interferences will be observed for gamma pho­ process, decay to a particular final state needs to be observed tons which can excite both levels of the hyperfine doublet. The which means that the 41t symmetry must be broken. requirement is that the bandwidth of the incoming gamma pho­ For a large ensemble ofnuclei, the 41tsymmetry ofthe re-emis­ ton must be about the same as the energysplitting of the doublet sion can be broken to some extent because of collective decay in states. With the technique of nuclear level mixing (box 2), the some directions. It is well known from theories and experiments energy splitting oftwo nuclear hyperfine levels canbe fine tuned. on elastic dynamical diffraction that the re-emission in the for­ An experiment was performed using the Mossbauer absorption ward direction is enhanced. of the 14.4 keV radiation by the 57Fe nuclei in a single crystal The enhancement of the radiative decay in the forward direc­ absorber of FeC0 3• This material has a hexagonal close packed tion can be understood as a collective effect. When a photon hits lattice structure, thus inducing a quadrupole splitting of the the sample, it hits all the resonant nuclei in their ground state. In the quantum mechanical picture of a photon being a particle, we Box 2 would say that one of these nuclei may be excited with a certain probability. In the quantum mechanical picture of the photon as Crossing and mixing of nuclear hyperfine levels a wave, each resonant nucleus can be considered as a superposi­ Consider nuclei subjected to static electromagnetic fields. The tion of the "ground state plus a photon" and the "excited state interaction of the nuclear magnetic moment with a magnetic without a photon". In this way the photon is not absorbed by one field induces a Zeeman splitting of the nuclear m-quantwn of the nuclei but by the 'collective ensemble' of nuclei. The re­ states. Theinteraction of the nuclear quadrupole momentwith emission occurs then from this collective excitation, which is an electricfield gradient gives rise to a quadrupole splitting. If called an 'exciton'. The radiative decay from such an exciton is both interactions are applied simultaneously and with their very special because each nucleus will give an amplitude for the symmetryaxisparallel,one obtainsnuclearhyperfinelevels as emitted photon. The phases at a point of the detector will depend shown in figure 2. Because the quadrupole splitting is propor­ 2 on the difference in optical length between two quantum paths tional to m , while the Zeeman splitting is proportional to rn, (originating from the decay of two different nuclei). In the for­ the crossing of two quantum levels occurs at particular mag­ ward direction these lengths are equal, while in a single crystal neticfields, called crossingfields, He.The ratio ofthe magnetic and quadrupole interaction frequencies determines the mag­ they are proportional to an integer number ofwavelengths if scat­ netic field atwhichthe crossing will occur [10]. tering in the Bragg directions is observed. In these directions all When the axial symmetry is broken slightly, because of a the individual amplitudes add up coherently and consequently small misalignment of the magnetic field with respect to the the emission probabilityis enhancedby a factor equal to the num­ symmetry axis of the electric field gradient, one can show ber of nuclei involved. that its effect on the quantum levels and their wave functions We can thus conclude that for a thick absorber the radiative is negligible, except near the magnetic fields Hewhere level deexcitation in the forward direction toward the initial state is crossing occurs. At these fields, the degeneracy of m-quan­ favoured over the other decay modes,including the non radiative tum states is lifted due to the small degree of symmetry breaking,which can be demonstrated by quasi-degenerate intermediate Slale ... Fig. 3; The pump perturbation theory [10]. Anti-crossing of nuclear hyperfine scheme, using a"nuclear levels occurs and the wave functions are mixed in coherent I I energy battery"as a way superpositions of the wave functions belonging to the cross­ towards a gamma-ray laser. ing states.At the crossing field, the mixed wave functions x-raYPu~ The initial state is a loog- form exactly an in-phase and an anti-phase superpositionof y lived state at high and rnand rn' (inset of figure 2): excitation energy (in which initial state all nuclei are produced by 11)z I-V2{ Irn) + Im')} (2) some means).The state is 12)= 1~2{Im')-Im)} (3) isomeric because decay to the lower levels is forbidden The minimum energy difference between the levels occurs y by K-selection ru.les.The at the crossing field and is dependent on the strength of the energy from this 'battery'is symmetry breaking term, which is determined by the mis­ released by pumping it into alignment angle between the applied interactions. Thus we 1 an intermediate 'K-mixed' can adjust the energy difference between the two levels. state, which subsequently Such mixing nuclear hyperfine states have been used in decays via a cascade of several fields of physics. For example as a tool to investigate y gamma transitions. K- the structure of solids using synchrotron radiation [5) or as mixing is here the crucial a tool to study the strudure of exotic nuclear states using ingredient to open the their anisotropic (11]. They may also pro­ decay channel. vide a step towards a gamma ray laser, as discussed later in I final slate this article. i 1-.- .._J

europhysics news SEPTEMBER/OCTOBER 2003 193 FEATURES nuclear levels in 57Fe.Below 40 K, the material becomes magnetic the determination of spins, magnetic and quadrupole moments as well, thus allowing the fulfilment of the level mixing condi­ of exotic nuclei that are produced at a few accelerators in the tions (figure 2). In a Mossbauer absorption measurement, the world. intensity in the Mossbauer line corresponding to the absorption Finally, lasing and gain withoutinversion cannotbe achieved in into the level mixed doublet, does not correspond to the sum of nuclear transtions so far, because an adequate pump mechanism the intensities ofthe individualtransitions [20]. This is a clear sig­ is still missing. On the contrary, nuclear level mixing induced nature for the presence of interference effects in nuclear gamma transparency has been observed experimentally and can be con­ ray absorption towards level mixed nuclear hyperfine levels. sidered as the nuclear equivalent of optical, electromagnetically Moreover the effect of coherence is demonstrated for single pho­ induced transparancy. Future investigations in this rich field of ton events. research, at the border of , quantum optics, solid state physics and laser physics, will certainlyreveal interestingnew Slowgroup velocity for gamma radiation? phenomena and applications for the future. From classical electromagnetism it is well known that an electro­ magnetic pulse can propagate through a resonant medium with Acknowledgements a group velocity that can be much slower than the phase velocity The authors are very grateful to P. Mandel (U.L.B.,Belgium), O. or the velocity of light [21]. The effect derives from the fact that Kocharovskaya and Y.Rostovtsev (Texas A&M, USA) for fruitful near a resonance the index of refraction changes drastically. exchange ofideas on this subject. Therefore, each frequency component of the pulse will have ·•·••••·••·•••••••·••••••••••••••• ••••• u u . another velocity, resulting in a slower propagation of the pulse References shape through the medium. In a two level system it is difficult to [1J For recent achievements inthis domain ofquantum optics, see, for observe the effect because, at resonance, there is strong resonant example, S. E. Harris, Physics Today 50, No 7,36 (1997); M. Xiao, H. absorption and, consequently, the pulse will bejust absorbed and Wang, and D. Goorskey; Optics & Photonics News, p.44, September not transmitted to the detector. 2002. In a three level system, however, the absorption is cancelled in [2] O. Kocharovskaya, Phys. Rep. 219, 175 (1992). the energy (or frequency) region about halfway between the [3] M. O. Scully, Phys. Rep. 219, 191 (1992). doublet levels. Exactly in that region, the index of refraction changes enormously [4] and consequentlythe group velocitycan [4) C. Liu et al., Nature 409, 490 (2001); D.F.Phillips et al., Phys. Rev. be much slower than the velocity of light. From the transparency Lett. 86, 783 (2001); A. B.Matsko et al.,Advances in Atomic, Molec­ thatwas observed in the Mossbauer experiment [20] one can esti­ ular and Optical Physics 46, 191 (2001). mate that the propagation velocity of the gamma photon is [5J R. Coussement et al., Phys. Rev.B54, 16003 (1996); R. Coussement reduced to about 1 kmIs. et al., Hyp. Int. 125, 113 (2000), R. Callens et al.,Phys. Rev.B65, 180404 (2002)

Conclusions [6] J.Odeurs et al., Phys. Rev.B60,7140 (1999). Coherence and interference effects in the interaction oflightwith [7J P.Korecki et al., Phys. Rev.Lett. 79, 3518 (1997); Phys. Rev.B59, matterled to veryinteresting and somewhat unexpectedresults in 6139 (1999). the field of quantum optics, such as gain without inversion, elec­ tromagnetically induced transparency, changes in index of [8] H. Frauenfelder,"The Mossbauer effect", Ed. Benjarnin 1963, New refraction etc. [4]. In the challenging quest for a laser with gamma York radiation these phenomena have been suggested as possible solu­ [9] L.A.Rivlin, Hyp. Int.107,57 (1997). tions to the gamma-ray laser dilemma. For that, a translation of [lOJ R. Coussement et al., Hyp. Int. 23, 273 (1985) the optical phenomena into the field of gamma optics, the inter­ [11] G.Neyens et al.,Phys.Lett. B 1-2,36 (1997) action of gamma radiation with nuclei, has to be performed. A rich field of research related to coherence and interference in [12J Proc. ofthe Int. Gamma Ray Laser conference (GARALAS'97), Hyp. gamma radiation has evolved out of this. Int. 107 (1997). Because of the single photon character of nuclear events, the [13] G. C. Baldwin, J. C. Solem, and V.I. Goldanskii, Rev.Mod. Phys. 51, 4 conditions for coherence and interference need to be realized in a (1981); G. C. Baldwin and J.C. Solem. Laser Phys. 5,231,326 very different way. For example the bichromatic driving field that (1995). is used in optics, is replaced by a single photon and in the nuclear [14] C. B.Collins et al., Phys. Rev.Lett. 82, 695 (1999); J.J.Carroll et al., three level system a particular hyperfine doublet, as obtained Hyp. Int.135, 3 (2001); C. B.Collins et al., Hyp. Int. 135,51 (2001). from anticrossing oftwo nuclear hyperfine levels (Box 2) needs to be used to allow coherent excitation (box 1). [ISJ P.Walkerand G.Dracoulis,Nature 399,35 (1999) The concepts of coherence and interference were applied to [16J U. Koster et al., Nud. Instr. and Meth. in Phys. Res. B 160,528 (2000) nuclear resonant scattering of synchrotron radiation and a new [17J E.S. Fry et al, Phys. Rev.Lett. 70,3235 (1993); W.E. van derVeer et nuclear interferometer was designed in which one observes the al, Phys. Rev.Lett. 70, 3243 (1993); J.Vanier et al, Phys. Rev.A 58, interference between two nuclear resonant scattering amplitudes, 2345 (1998); KYamamoto et al, Phys. Rev.A 58, 2460 (1998); one from a reference sample and one from a sample under inves­ [18J R. Coussement et al., Phys. Rev.Lett. 71,1824 (1993). tigation. From these experiments the hyperfine splitting of the investigated sample can be deduced. Thistechniquehas opened a [19) R. N.Shakhmuratov et al., Opt. Comm. 179,525 (2000); G. Kozyreff, newfield ofapplication in the investigation ofmaterialproperties et al., Phys. Rev.A 64, 013810 (2001). using nuclear radiation. [20J R. Coussement et al., Phys. Rev.Lett. 89,107601 (2002). The studyof coherence phenomena in nuclear radiation led to [21J J.D.Jackson,"Classical Electrodynamics". 2nd ed. John Wiley and useful applications also in other fields. For example in nuclear Sons, NewYork,1975 physics the principle oflevelmixing resonances (LMR) is used for

194 europhysics news SEPTEMBER/OCTOBER 2003