Diffraction-grating neutron interferometers

Physica B 151 (1988) 50-56 North-Holland, Amsterdam

DIFFRACTION-GRATING N E U T R O N I N T E R F E R O M E T E R S A.I. IOFFE B.P. Konstantinov Leningrad Nuclear Physics Institute, Academy of Sciences of the USSR, Gatchina, Leningrad District, 188350 USSR Aberration distortions of wavefronts in a very cold neutron interferometer using diffraction gratings are analyzed. Aberrations that considerably reduce the efficiency of a two-grating interferometer are shown to be fully compensable by adding a third diffraction grating, which also permits the interferometer to operate with a non-collimated and nonmonochromatized illuminating beam thereby raising its efficiency. A fourth diffraction grating additionally permits compensation of effects of the terrestrial rotation that affect performance of a large interferometer in which the spatial separation of beams can be of the order of a few meters. It is demonstrated to be practically possible to implement an interferometer for neutrons having a wavelength A = 20 ,~ and to use it in experiments aimed at finding the electric charge of the neutron at the level of 10 ~3 to 10 22 of the electronic charge.

1. Introduction A c h i e v e m e n t s of the n e u t r o n i n t e r f e r o m e t r y in the thermal region of the spectrum ( A ~ 2 A ) [1, 2] m a k e it feasible to d e v e l o p i n t e r f e r o m e t e r s for longer wavelengths, including ultracold neutron ( U C N ) i n t e r f e r o m e t e r s that are expected to permit b r e a k t h r o u g h s in p r o b l e m s of f u n d a m e n tal physics [3-6]. T h e r e f o r e an i n t e r f e r o m e t e r for very low e n e r g y n e u t r o n s must be based on a different m e t h o d of c o h e r e n t splitting and rec o m b i n a t i o n of n e u t r o n beams. T h e amplitude splitting of wavefronts assuring a g o o d spatial separation of interfering b e a m s of very cold n e u t r o n s ( V C N ) can be i m p l e m e n t e d by using n e u t r o n diffraction gratings [7].

part of the profile), and the structure b e c o m e s a reflection difraction grating. T h e diffraction grating effiencies are 7% and 13% for diffraction orders +1 and 0, respectively (for selected angle of incidence). T h e optical diagram of the n e u t r o n interf e r o m e t e r is shown in fig. 2. T h e incident b e a m is diffracted by the c o h e r e n t splitter BS 1 to the 0 and +1 orders of diffraction ( b e a m s I and II, respectively). T h e b e a m s are r e c o m b i n e d by the mirrors M 1 and M 2 on the diffraction grating BS 2 and are aligned by diffraction of b e a m I to the 0 o r d e r and by b e a m II to the - 1 order. Thus interference is p r o d u c e d by superposition of twice mirror-reflected and twice diffracted beams to the +1 and - 1 orders.

03

2. Diffraction-grating interferometer for thermal neutrons T h e n e u t r o n diffraction gratings used in o u r experiments [8, 9] are p h o t o l i t o g r a p h e d diffraction gratings on glass with a rectangular surface relief, on which a 58Ni film = 1500 A thick is deposited (fig. 1). For a n e u t r o n b e a m incident at an angle smaller than the critical angle for the coating material, the reflection coefficient becomes m o d u l a t e d (i.e. it vanishes for the vertical

~g

~/¢

l/

V2/ez//tcz//z/izz,q/]

)£

"

ra:-0 Fig. 1. (a) Neutron diffraction grating; 1: photolithographed diffraction grating on glass; 2:5~Ni film. (b) Experimental arrangement.

0378-4363 / 88 / $03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

A.I. loffe / Diffraction-grating neutron interferometers a.)

51

250\

/

t

~

xx

g ~oo. L

',,t / t,

o.os

~',_

&~

d~s

o:z g,mm

Fig. 2. Beam path in diffraction grating interferometer for thermal neutrons. •~

The incident beam is monochromatized by being reflected from a F e - C o mirror and shaped by two narrow slits (not shown in fig. 2). The wavelength in the spectrum maximum is Amax = 3.15 A, AA/A -- 32%, the dimension of the beam is 0.3 x 25 mm, the beam divergence -+10-4. The gratings measure 7 0 m m 2 and have a period of 21 Ixm and a profile depth of 1000 A. The reflecting surfaces of the quartz mirrors M~ and M E w e r e polished flat to 0.025 Ixm, i.e. one twentieth of the green band all over the mirror surface. The total length of the interferometer (fig. 2) is L = 55.5 cm assuring a spatial separation of the beams of about 0.8 mm. To minimize vibration effects, the interferometer was mounted on a 1.5ton solid granite base separated from the reactor hall floor by a 15 cm layer of sea sand. The interferometer was assembled and the first measurements made at a horizontal channel of the 3 MW power reactor in Riga, USSR. The performance of the interferometer was checked both by shifting the beam splitter BS 2 along its working surface in steps of 2.5 ixm and by changing the thickness of A1 foil placed in one of the interferometer's arm. Modulation of the recorded beam intensity is clearly seen in fig. 3. The measurement results were processed using the least squares method with a sine approximating function yielding a curve (shown with a dashed line) whose period d = (22.7 _+ 2.3) i~m (fig. 3b) is in a good agreement with the 21 lxm diffraction grating period. The visibilities of recorded interference patterns are 23% (fig. 3a) and 26% (fig. 3b) and also agree acceptably with the estimates made with the help of the aberration analysis technique

~oo. ~.00.

2'0

6b

8b

Fig. 3. The intensity of recorded interference patterns vs. the thickness of AL foil placed in one of the interferometer's arm (a) and the shift of recombination grating (b). Dashed line shows the result of data processing by least squares method with sine approximating function.

developed [8] for interferometer wayefront propagation studies.

3. Interferometers for very low energy neutrons

It was suggested [7] that the challenge could be met by using phase diffraction gratings as coherent splitters of neutron beams. However, in spite of a symmetric design of the interferometer (fig. 4a), there occur reciprocally uncompensating aberration distortions of waveffonts that propagate in the instrument, even when highspeed thermal neutrons are used [10]. This aberration results in a poorer visibility of the interference pattern recorded, so that it becomes imperative to modify the instrument with a view to reducing and ideally fully compensating all the wave aberrations. The aberration analysis performed in ref. [10] shows that the fronts which propagate over different arms of a three-grating interferometer (fig. 4b) are distorted identically and their phase difference, after they were brought together by the grating BS2, is constant over the crosssection of the recorded beam. Consecutively, no

A.I. loffe / Diffraction-gratingneutron interferometers

52

I

B5 a

55 z

Fig. 4. (a) Two- and (b) three-grating interferometers. BS1, BS2, G: diffraction gratings; M1, M2: mirrors. amplitude modulation that caused a poorer visibility of the interference pattern occurs. Moreover, because this result holds true for any wavelength the design under discussion is also achromatic. At the same time, the use of very cold neutrons results in considerable aberration distortions due to the interaction between the neutrons and the gravitational field. The phase shift associated with the propagation of neutrons over parabolic trajectories is [10]

mov yy(i +

~b --- - ~ -

,

(1)

here Vy and Vu are projections of the initial velocity vector V onto the coordinate axes Oy and Ou, respectively (fig. 5), m n is the neutron mass, g is the free fall acceleration and h is the Planck constant. Because of the substantial vertical displacement of the VCN due to the action of the gravitational field of the Earth during their flight through the interferometer, the instrument has to be fitted to the horizontal diffraction gratings; however, the period of diffraction gratings G z and G 3 is twice as small as that of the gratings G 1 and G 4. The lines of all gratings are parallel. Here we assume the aberration-compensating diffraction gratings G : (fig. 4b) to consist of two gratings G 2 and G 3. This design may be quite

practical with a substantional beam separation in the interferometer. By calculations of the initial velocity vector components at the opposite sections of trajectories O1H~O2-O3H204 and O1H'1Oa-OEH304 we obtain from eq. (1) that the phase shifts of neutron waves that propagate over different interferometer's arms coincide. This result is obtained for the vector of initial velocity of neutrons which is arbitrarily oriented in space, in general, without specifying the magnitude of this velocity. Consequently, the phase difference of the neutron beams propagating in the interferometer is identically zero for a non-collimated and non-monochromatized illuminating beam. Thus the incorporation of a third diffraction grating likewise fully compensates the aberration distortions of the wavefronts caused by the interaction of the neutrons with the gravitational field of the earth, and the three-grating design of the neutron interferometer under discussion is completely aberration-free. A number of modifications to this design are possible. Of highest practical interest is a threegrating arrangement with the diffraction gratings of an identical period (fig. 6) which uses beams diffracted to the 0 and 1 orders. This design is topologically similar to the very common perfect crystal neutron interferometer [1] and also permits the use of two detectors. The introduction of a third diffraction grating reduces somewhat the output intensity because

A.I. loffe / Diffraction-grating neutron interferometers

53

Fig. 5. Aberration-free VCN interferometer using + 1 and -1 diffraction orders.

'

~"

|

,

IG~

G2

Fig. 6. Beam path in aberration-free VCN interferometer using O and -1 diffraction orders. G1, G2, G3: diffraction gratings, D 1, D 2 neutron detectors.

its diffraction efficiency is other than unity. With the phase diffraction gratings [7] used, the recorded intensity is 60% lower; however, this drawback is more than compensated by the advantages offered by using the non-collimated and non-monochromatized illuminating beam. In particular, the spatial separation of the beams in the inteferometer can attain a few meters in an instrument of a considerable size.

4. Compensation of Earth's rotation effects Development of large neutron interferometers can be supported by using the Sagnac effect [12] which is the introduction of an additional phase

shift between the interfering beams because of the interferometer being on the surface of the rotating Earth. The value of this effect is proportional to the scalar product of the vectors of the instrument's angular rotational velocity to and of the area A normal to the instrument plan, 2m, 2m, ~s = T to" A = - - ~ tooA sin 01,

(2)

where too is the angular velocity of the Earth's rotation and 01 is the latitude angle of the position of the instrument. Scattering in the area covered by various trajectories because of the divergence of the incident beam results in scattering of the phase difference (eq. 2) and in a poorer visibility of the interference pattern. This can be avoided if the interferometer comprises two symmetrical parts [13] so that the phase shifts which take rise in each part compensate each other. The arrangement of such an instrument is shown in fig. 7. Unlike the above design, in this arrangement use is made of two additional gratings 6 4 and G 5 and a flat mirror M. As shown in ref. [10] the neutron paths O102OMO506 and O103OMO406 over the different arms of the interferometer are fully identical, and there are still no aberration distortions

A.I. loffe / Diffraction-grating neutron interferometers

54

,G~

G~!%-- ~ , / 0,1J"

k

,

~

'G,

,0~

o~Lj

G6

%'[ 0 2

Fig. 7. Beam path in Sagnac effect-compensating VCN interferometer.

of the wavefronts in the instrument. Now, however, the Sagnac effect is compensated to an accuracy within the equality of the areas A 1 and A 2 covered by the trajectories in the symmetrical parts of the instrument, but because A 1 equals A 2 for symmetry reasons, this compensation is complete.

5. Cold neutron interferometers and neutrons charge quest It was shown [14] that large size interferometers that feature an extremely high interferometric sensitivity coupled to a long interaction of VCN with the external field make it possible to lower considerably the present-day experimental limit for the neutron charge qn. At the same time, as will be shown below, the use of cold neutrons with a wavelength of a few tens of angstroms likewise permits an important reduction of the experimental limit of qn" Let us first consider the feasibility of developing an interferometer for neutrons with h = 2 0 ~ . This wavelength is chosen because it still permits reasonable intensities of the neutron beams. It was precisely such a beam that was used in the quest for q~ at H F R of ILL (Grenoble, France) by the narrow-slit image procedure with the help of the focussing optical facilities, when the best result was attained for qn = (1.5 --- 1.4) × 10 -20 qe, qe being the electron charge, at a confidence level of 68% [15]. The vertical displacement of such neutrons, as they fly through a 10 m long experimental setup, is about 1 cm, and it is possible to apply the procedure described in ref. [9], which made use

of neutron diffraction gratings with vertical lines (fig. 8). However, unlike that procedure [9], here we implement the three-grating interferometers that have, as shown in section 3, a higher luminosity because of operating with noncollimated and non-monochromatized beams. Consider an interferometer with the diffraction gratings having a period d of 4 I~m and a spacing at L = 5 m (fig. 8). Then the angular divergence of the beams at the interferometer exit is 0 -- A/d = 5 × 10-4. Their reliable separation by the detector is made possible by the collimation of the illuminating beam 0c ~< 0, which sets the intensity of the illuminating beam. The neutron diffraction gratings to be used in the experiment are phase diffraction gratings formed by equally spaced strips of a material with a refractive index larger than that of the substrate. Similar structures were produced as Fresnel zone plates with a minimum zone width of 2 I~m by depositing electrolitically a 2.4 Ixm layer of copper onto a metallized mask [16]. The resulting efficiencies were close to the theoretical limit and amounted to 40%. The estimates of the exit intensity of such an interferometer [10] are based on the intensity (--200n/s) of the neutron beam of A= (20--0.15)A with a divergence 0c= 10 -4 from the prismatic monochromator at ILL [17]. The resulting intensity is about 9 n/s. Now the procedure of ref. [14] permits estimation of the sensitivity of the instrument to the interference pattern displacement about the recombination grating G 3 (fig. 8); this displacement is equivalent to the introduction of a phase shift ~(A) = 2,rrA/d into one of the beams. By applying a direct current electric field of intensity E between the gratings (fig. 9) we can obtain this effect if the neutron has a weak

I

I •

L,

Fig. 8. Cold neutron three-grating interferometer with identical periods of all the gratings.

55

A.I. loffe / Diffraction-grating neutron interferometers

-f

V ~LD°

I

-

I

0.5G~

g

Fig. 9. Diagram of the neutron interferometer experimental search for the neutron electric charge.

,,X,~

Fig. 10. Visibility V of the interference pattern vs. monochromaticity AA of the illuminating beam (01 = 45°). electric charge qn" A magnitude of qn as measured during a 40-day experiment by the neutron beam under discussion is q/> 2 × 10 -22 q~. It was assumed that E = 60 kV/cm, L = 10m and the interference pattern visibility, as mentioned in section 3, is unity. Because of the large size of such interferometers and a sizeable area covered by neutron trajectories therein, the luminosity can be lowered substantially by the Sagnac effect and the difference of the areas AA covered by trajectories of neutrons with wavelengths over the range [A0 +_ AA], leads to a phase scattering (see eq. 2), Aq~s =

2m n

~

to0 A A s i n 0 1 .

(3)

For the intensity of the recorded interference pattern [10] we obtain I(q0 - [1 + sinc(c AA) cos(q~ + c AA)],

(4)

where sinc(t) = s i n ( t ) / t

clear, among other things, that at AA = 0.15 A, V = 0.99 and that no compensation is needed here. At the same time, because, as shown above, no requirements are placed on monochromacity of the illuminating beam and on the size of the shaping slits and, consequently, the intensity can be increased considerably. In this case a considerable non-monochromacity of illuminating beam leads to a lower visibility of the interference pattern because of the Sagnac effect (fig. 10). By mean compensation of this effect (see section 4) it is possible to attain a substantional increase in the intensity of the recorded beam and in the statistical accuracy of the experimental search for the neutron charge lowering the experimental limit to qn i>5 x 10-23qe.

N o t e a d d e d in p r o o f

A new experimental limit of a neutron electric charge was announced at this workshop: q, = (-0.6___ 1 . 1 ) x 10-2~qe (see J. Baumann et al. these Proceedings).

and References

c = mnO)o L 2 sin 0 1 / h d .

The visibility of the interference pattern is •

[mntOo L 2 sin

V = slncl

01 AA) ¢

(5)

The chart of the interferometer schemes under discussion is given in fig. 10, which makes it

[1] U. Bonse and H. Rauch, eds., Neutron Interferometry (Oxford, 1979). [2] H. Rauch, in: The Investigationsof Fundamental Interactions with Cold Neutrons, NBS Special Publication 711 (NBS, Washington, DC, 1986) p. 106. [3] A. Zeilinger, ibid., p. 112. [4] R.D. Deslattes, ibid., p. 118. [5] J. Anandan, Phys. Rev. Lett. 48 (1982) 1660. [6] I.S. Shapiro, Pis'ma v Zh Eksp Teor. Fiz. 35 (1982) 39.

56

A.I. loffe / Diffraction-grating neutron interferometers

[7] A.I. Ioffe, Nucl. Instrum and Methods 204 (1983) 565. [8] A.I. Ioffe, G.M. Drabkin, Yu.G. Turkevich, JETP Lett. 33 (1981) 374. A.I. Ioffe et al., Preprint LIYaF-643 (Leningrad, 1981). [9] A.I. Ioffe, V.S. Zabiyakin, G.M. Drabkin, Phys. Lett. A 111 (1985) 373. [10] A.I. Ioffe, Preprint LIYaF-1150 (Leningrad, 1986). [11] A.I. Ioffe, Preprint LIYaF-742 (Leningrad, 1982). [12] Sagnac M.G., C. R. Acad. Sci. Paris 51 (1913) 43. L.A. Page, Phys. Rev. Lett. 35 (1975) 543.

[13] A.I. Frank, Zh. Tekh. Fiz. 53 (1983) 935. [14] A.I. Ioffe, Nucl. Instrum. and Methods 228 (1984) 141. [15] R. G~hler, J. Kalus and W. Mampe, Phys. Rev. D 25 (1982) 2887. [16] P.D. Kearney, A.G. Klein, G.I. Opat and R. G~ihler, Nature 287 (1980) 313. [17] R. G~ihler, J. Kalus, W. Mampe, J. Phys. E 13 (1980) 546.