The n2EDM experiment at the Paul Scherrer Institute
C. Abel, N. J. Ayres, G. Ban, G. Bison, K. Bodek, V. Bondar, E. Chanel, P.-J. Chiu, B. Clement, C. Crawford, M. Daum, S. Emmenegger, P. Flaux, L. Ferraris-Bouchez, W. C. Griffith, Z. D. Grujić, P. G. Harris, W. Heil, N. Hild, K. Kirch, P. A. Koss, A. Kozela, J. Krempel, B. Lauss, T. Lefort, Y. Lemière, A. Leredde, P. Mohanmurthy, O. Naviliat-Cuncic, D. Pais, F. M. Piegsa, G. Pignol, M. Rawlik, D. Rebreyend, D. Ries, S. Roccia, K. Ross, D. Rozpedzik, P. Schmidt-Wellenburg, A. Schnabel, N. Severijns, J. Thorne, R. Virot, J. Voigt, A. Weis, E. Wursten, J. Zejma, G. Zsigmond
TThe n2EDM experiment at the Paul Scherrer Institute C. Abel , N. J.
Ayres , G. Ban , G. Bison , K. Bodek , V. Bondar , E. Chanel , P.-J.
Chiu , B. Clement , C. Crawford , M. Daum , S. Emmenegger , P. Flaux , L. Ferraris-Bouchez , W. C.
Gri ffi th , Z. D.
Gruji´c , P. G.
Harris , W. Heil , N. Hild , K. Kirch , , P. A.
Koss , ∗ , A. Kozela , J. Krempel , B. Lauss , ∗∗ , T. Lefort , Y. Lemière , A. Leredde , P. Mohanmurthy , , O. Naviliat-Cuncic , ∗∗∗ , D. Pais , F. M.
Piegsa , G. Pignol , M. Rawlik , D. Rebreyend , D. Ries , S. Roccia , K. Ross , D. Rozpedzik , P. Schmidt-Wellenburg , A. Schnabel , N. Severijns , J. Thorne , , R. Virot , J. Voigt , A. Weis , E. Wursten , J. Zejma , and G. Zsigmond University of Sussex, Brighton, United Kingdom Normandie Univ, ENSICAEN, UNICAEN, CNRS / IN2P3, LPC Caen, Caen France Paul Scherrer Institute, 5232 Villigen, Switzerland Jagiellonian University, Cracow, Poland Instituut voor Kern- en Stralingsfysica, KU Leuven, 3001 Heverlee, Belgium Laboratory for High Energy Physics and Albert Einstein Center for Fundamental Physics, University of Bern, Bern, Switzerland Laboratoire de Physique Subatomique et de Cosmologie, Grenoble, France University of Kentucky, Lexington, United States of America Institute for Particle Physics and Astrophysics, ETH Zürich, 8093 Zürich, Switzerland Physics Department, University of Fribourg, 1700 Fribourg, Switzerland Institut für Physik, Johannes-Gutenberg-Universität, Mainz, Germany Henryk Niedwodnicza´nski Institute for Nuclear Physics, Cracow, Poland Institut für Kernchemie, Johannes-Gutenberg-Universität, Mainz, Germany CSNSM, Université Paris Sud, CNRS / IN2P3, Université Paris Saclay, Orsay-Campus, France Physikalisch Technische Bundesanstalt, Berlin, Germany
Abstract.
We present the new spectrometer for the neutron electric dipole moment (nEDM) search at the PaulScherrer Institute (PSI), called n2EDM. The setup is at room temperature in vacuum using ultracold neutrons.n2EDM features a large UCN double storage chamber design with neutron transport adapted to the PSI UCNsource. The design builds on experience gained from the previous apparatus operated at PSI until 2017. Anorder of magnitude increase in sensitivity is calculated for the new baseline setup based on scalable results fromthe previous apparatus, and the UCN source performance achieved in 2016.
A static neutron electric dipole moment (nEDM) wouldviolate parity P and time reversal T symmetries. Afterthe observations of both P and CP violation in weak de-cays [1, 2], one expects a non-zero contribution to thenEDM from the weak sector; here we neglect the possibil-ity of CP violation in the strong sector. The contributionfrom the weak sector yields the Standard Model estimateof the size of the nEDM on the order of 10 − e cm [3],well below the present best experimental limit of 3 × − e cm (90% C.L.) [4].Thus, nEDM searches integrate well in investigations intonew sources of CP-violation in nature [5], which pointtowards beyond Standard Model (BSM) physics [6]. Along standing problem only solvable with BSM physics isbaryogenesis, namely the production of an imbalance ofmatter over anti-matter in the early Universe. The three ∗ [email protected] / ORCiD: 0000-0001-5094-3056 ∗∗ [email protected] / ORCiD: 0000-0002-1986-391X ∗∗∗
Present address: Michigan State University, East-Lansing, MI, USA basic criteria necessary for baryogenesis were formulatedby Sakharov [7]. One of them is a new source of CP vi-olation, orders of magnitude larger than in the StandardModel. Several BSM models incorporate stronger CP vio-lation [8] and at the same time predict much larger EDMsfor fundamental particles. Thus, finding a non-zero nEDMwould contribute to the understanding of baryogenesis.The possible existence of static electric dipole moments offundamental particles was formulated as a question to ex-perimental physics almost 70 years ago [9], followed bythe first upper limit of the nEDM in 1957 [10]. Since then,a long line of experiments have pushed the limit downby six orders of magnitude [11]. These investigations arecomplementary to many other experimental and theoreti-cal e ff orts in low- and high-energy physics [6, 12–14].Our collaboration has a staged experimental program [15].In the initial phase, we made use of an upgraded versionof the RAL / Sussex / ILL spectrometer [16]. The acquireddata [17] will allow us to improve on the present best up-per limit [4]. Additionally, during the commissioning anddata taking of the initial experimental phase, our collabo- a r X i v : . [ phy s i c s . i n s - d e t ] F e b ation has been developing a completely new spectrometercalled n2EDM. It is a room temperature in vacuum exper-iment using ultracold neutrons (UCN). The spectrometerdesign combines the pioneering PNPI double chamber de-sign [18] and a Hg co-magnetometry system [19]. It drawsfrom the expertise in technical development and systemat-ics control of our collaboration [4]. All nEDM experiments look for a coupling of the neutronspin to an applied electric field on top of a known mag-netic coupling. This is illustrated by the Hamiltonian of aneutron in a magnetic and electric field H = − (cid:126)µ n · (cid:126) B − (cid:126) d n · (cid:126) E , (1)where (cid:126)µ n is the magnetic dipole moment, (cid:126) d n the electricdipole moment, (cid:126) B and (cid:126) E are the magnetic and electricfields.Since the first nEDM result in 1957, almost all experi-ments have been using the Ramsey method of time sep-arated oscillating fields [20]. With this method measure-ments of the Larmor precession frequency of polarizedneutrons in a magnetic field are performed. In our appara-tus, the Larmor frequency is measured in the two cases ofparallel / anti-parallel (cid:126) B and (cid:126) E fields. The Larmor frequen-cies are given following Eq. (1) h ν ↑↑ = − µ n B ↑↑ + d n E ↑↑ ) (2) h ν ↑↓ = − µ n B ↑↓ − d n E ↑↓ ) , (3)where ↑↑ stands for parallel (cid:126) B / (cid:126) E -fields and ↑↓ stands foranti-parallel (cid:126) B / (cid:126) E -fields.The nEDM, d n , can be extracted from a di ff erential mea-surement between the frequencies ν ↑↑ and ν ↑↓ with d n = h ( ν ↑↓ − ν ↑↑ ) − µ n ( B ↑↑ − B ↑↓ )2( E ↑↑ + E ↑↓ ) . (4)The statistical sensitivity of a single measurement with thismethod is given by σ ( d n ) = (cid:126) α | E | T √ N , (5)where | E | is the electric field strength, T is the free preces-sion time of the neutrons, N is the number of counted neu-trons and α is a measure of the neutron polarization. Theanalysis of a single chamber experiment, as with our pre-vious apparatus, uses corrected neutron Larmor frequen-cies [17]. These frequencies are corrected using R -values,which are given by R = ν n ν Hg = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) γ n γ Hg (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:18) + (cid:104) z (cid:105) GB (cid:19) + E π h ν Hg d n , (6)where γ n , γ Hg are the gyromagnetic ratios of the neutron(resp. mercury), G is the vertical linear magnetic gradientover the UCN chamber, E is the electric field and (cid:104) z (cid:105) is thecenter-of-mass di ff erence between the Hg atoms and the UCN.In the case of a double chamber design one can use the R -values for both chambers in the analysis. The di ff er-ence between the top ( R T ) and the bottom ( R B ) chamber R -values yields R T − R B = E π h ν Hg d n + (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) γ n γ Hg (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) ( (cid:104) z (cid:105) T − (cid:104) z (cid:105) B ) GB , (7)where (cid:104) z (cid:105) T , (cid:104) z (cid:105) B are the di ff erences in center-of-mass be-tween the Hg atoms and the UCN in the top (resp. bottom)chamber. From eq. (7) we immediately see that the gradi-ent induced systematic is strongly suppressed in a doublechamber setup to a contribution proportional only to thedi ff erence in center-of-mass, i.e., (cid:104) z (cid:105) T − (cid:104) z (cid:105) B . Figure 1:
Experimental apparatus.
The UCN comingfrom the source are polarized after passing a 5 T supercon-ducting polarizer magnet (1). Two switches (2), containingeach 2 UCN guides are used to fill and empty the UCNchambers (3). After a typical precession time of 180 s,the UCN are counted in the detectors (4). The storagechambers and the vacuum vessel (6) are in a magneticallyshielded room (5), which rests on an Aluminum framesupported by four granite pillars (7). The magnetic fieldis monitored in situ with a Hg system (8) and a Cs magne-tometer array (9). The high voltage is provided via a cable(10) and the vacuum vessel is pumped with turbo molec-ular pumps situated outside of the magnetically shieldedroom (11). The entire setup is inside an insulation shell,thermally stabilized by air-conditioning (12). A surround-ing field compensation (SFC) system will actively reducethe magnetic perturbations of the environment (13).The n2EDM apparatus will significantly improve theneutron counting statistics and lower systematics with re-spect to its predecessor. A factor of 10 improvement insensitivity compared to the present best limit [4, 21] iscalculated, based on the known performance of the pre-vious apparatus, the average UCN source performancein 2016 and a full simulation of the n2EDM apparatusbenchmarked with several measurements. The experimentill profit from the high UCN intensity provided by thePSI UCN source [22, 23]. The experimental apparatus isshown in Fig. 1.The experimental setup is based on our experience withthe previous nEDM apparatus, the main di ff erence being adouble chamber design as pioneered in [18]. This dou-ble chamber design, as shown in Fig. 2, has a numberof advantages including a direct increase of the statisticsthrough a larger total UCN volume with a diameter of 80cm. The high voltage electrode is at the center of the stackwith the two ground electrodes connected to the rest of thesetup. This way, E-fields up to 15 kV / cm are expected.Most importantly, we will be able to measure in both fieldconfigurations of eqs. 2 and 3 simultaneously. This willstrongly reduce any time dependent systematic e ff ects.The following sections will describe the subsystems ofn2EDM as they are planned for the baseline setup.Figure 2: Double chamber design.
The center elec-trode is at high voltage while the two outer electrodes aregrounded. Both UCN chambers will also contain polar-ized Hg atoms used as a co-magnetometer. An array ofCs magnetometers will surround the top and bottom elec-trodes. This entire setup will be placed in a uniform mag-netic field of 1 µ T. The new magnetically shielded room (MSR) for n2EDMwill comprise of 6 cubic layers of mu-metal and one addi-tional layer of aluminum for RF-shielding, see Fig. 1. TheMSR consists of an outer and inner cabin where enoughspace is left between the cabins for an intermediate room.This room will contain the equipment sensitive to electro-magnetic noise (e.g., pre-amplifiers, current sources, etc.).The innermost shielding layer is a cube of approx. 3 m sidelength. The innermost room with its 2 m × × × VAC GmbH, Hanau, Germany (https: // one side and more than 70 openings in the walls to operatethe experiment. The largest have a diameter of 220 mm,adapted to the planned UCN guide diameter. Similarlysized openings are placed on the opposite side of the shieldfor field symmetry and uniformity reasons. These will beused for the main pumping tubes of the vacuum vessel.In order to achieve the planned statistical and systematicsensitivity, the MSR needs to provide a magnetically sta-ble and uniform environment. For the magnetic shield, aquasistatic shielding factor better than 80’000 at 0.01 Hzis expected. The residual magnetic field is expected to beless than 0.5 nT over the volume covering the two pre-cession chambers. The gradient at that location should besmaller than 3 pT / cm. Each layer of the MSR is equippedwith a separate set of degaussing coils. The ability to de-gauss each layer in this manner helps to obtain uniformresidual magnetic fields [24]. The n2EDM experiment is located in the vicinity of otherfacilities generating strong magnetic fields (e.g., SULTAN,COMET) [25, 26]. They induce changes in the magneticfield at the experiment location of up to tens of µ T ontime scales from minutes to hours [27]. Even though then2EDM measurement volume will be shielded from theseperturbations by the MSR, we might be left with measur-able changes in the magnetic field of the experiment. Anactive surrounding field compensation (SFC) system is be-ing developed as an additional shielding layer and mightbe installed after initial characterization measurements.A new method for designing coils of arbitrary field shapes,to compensate specific gradients and fields was devel-oped [28]. In our case, the coils will be mounted on a gridwhich will surround the MSR. This grid will be able tosupport a large number of sensors and coils which generatecomplex fields and gradients. Additionally, coils tailoredfor specific magnetic field disturbances are considered asan option. This way, specific magnetic field changes pro-duced by experiments could be compensated. n2EDM requires a very stable and uniform magnetic field, B . The main reasons are to precisely control gradientswhich induce motional false EDMs and to ensure that themean field is the same in both UCN chambers [29, 30]. Aset of dedicated coils inside the innermost shielding layerwill generate the B field. The coils need to be suppliedwith a very low noise and stable current to yield the bestpossible performance.The target for n2EDM is a magnetic field uniformitybetter than 10 − in the UCN chambers. The B coil isa single layer cubic solenoid mounted inside the MSR,around 10 cm from the innermost mu-metal layer. Thecalculated field uniformity for this coil is shown in Fig. 3for a 1 µ T field in absolute terms, as we are interested inthe absolute accuracy.Even though the field uniformity in the simulation alreadyreaches our target value, perturbations in the magnetic [m]1 − − − − − y [ m ] − − − − − − (a) B uniformity in the XY plane in pT. x [m]1 − − − − − z [ m ] − − − − − − (b) B uniformity in the XZ plane in pT. Figure 3: B field uniformity. Calculated magnetic fielddeviation in pT from the nominal 1 µ T for the B coil. The B field is aligned with the z-axis on the graphs. The reddisc (3a) and the boxes (3b) represent the UCN chamberswith a diameter of 80 cm and a height of 12 cm. The UCNchambers are within the 10 − field uniformity region, i.e.,100 pT on a 1 µ T field.environment will worsen this performance. The targetmagnetic field uniformity will be achieved with a B coilaccompanied by a set of correcting trim coils, which willbe installed on the same frame as the B coil. An arrayof 56 rectangular trim coils will be used to produce allgeneric field gradients up to the 6th order [28].Additionally, we require a long term stability of the 1 µ T B field on the order of 30 fT for a period of about 300s, i.e., one measurement cycle. This field stability isnecessary in order to reduce the error contribution dueto the Hg co-magnetometer below 2% of the neutron statistical error [32]. The longterm stability depends onthe stability and the noise level of the current sourcesupplying the B coil. Therefore, we are developing anatomic magnetic resonance based current controller whichcan actively stabilize the current in the B coil [31]. With the MSR, the SFC and the set of coils in the inner-most shielding layer, we expect to achieve the requiredmagnetic environment in the UCN chambers. However,experience from previous nEDM experiments has shownthat it is important to accurately monitor the magnetic fieldin the experimental volume [19]. For this purpose we willuse several di ff erent types of magnetometers inside of thevacuum vessel.First, a mercury ( Hg) co-magnetometer occupying thesame volume as the UCN. Second, an array of cesium(
Cs) magnetometers which surrounds the UCN volumesand measures the distribution of the magnetic field in thevacuum vessel.
Optically polarized Hg atoms occupying the same vol-ume as the UCN will measure the magnetic field in theUCN chambers. With the magnetic field readings of theco-magnetometer, one can correct shifts in the neutronLarmor frequency ν n due to B-field changes as given ineq. 6. The first phase of the experiment used such a Hg co-magnetometer [16]. There, microwave-excited Hg lampswere used for the optical pumping and probing of the Hgmedium. Meanwhile, we have developed a laser-based Hgco-magnetometer. The light for the optical pumping andprobing of the Hg medium will be delivered by a singlelaser. This new laser-based system system has a 5.5 timeshigher signal-to-noise ratio than its lamp-based predeces-sor with a sensitivity of 5 fT [32]. The primary goal of the Cs magnetometer array is to pro-vide the necessary information about the magnetic fielduniformity in the experiment. The field uniformity is char-acterized by a set of gradient multipoles which will beestimated using magnetic field readings from many inde-pendent magnetometer modules [30, 33]. We developed amethod to make the B -field more uniform using the read-out of all Cs magnetometers and the correcting trim coilsof the experiment [34].The new Cs magnetometer array envisioned for then2EDM experiment is shown in Fig. 2. The sensors willbe of the Bell-Bloom type [35], where the Cs mediumis polarized by modulating the pumping rate at the Lar-mor frequency. More specifically, we intend to use AM-modulated pumping of the medium followed by a free spinprecession (FSP) period. The FSP operation mode yields asensitivity <
100 fT / √ Hz [36]. Additional advantages ofhis mode are the all-optical nature of the sensor, i.e., be-ing magnetically silent, with low systematics on the Lar-mor frequency readout. Recent design studies suggest thata particular sensor arrangement in the array will enhanceits performance.
Figure 4:
UCN system.
The UCN are supplied from theUCN source (1). The UCN are polarized after passing a5 T superconducting polarizer magnet (2). The polarizedUCN are guided into the UCN chambers through a UCNswitch (3). After the measurement cycle, spin analyzers(4) select separate spin states of the UCN and guide themto separate neutron detectors for each spin state. Only thedetector mount points are shown at (5).UCN statistics are the main limiting factor for allnEDM experiments. Therefore, the design of the n2EDMexperiment was based on optimizing the UCN statistics forour UCN source. The position of the UCN chambers andthe guiding of the UCN from the UCN source to the UCNchambers were optimized using the MCUCN code [37].We have developed guides which will be made fromDURAN glass tubes with sub-nanometer surface rough-ness [38]. Some bent parts will be machined from alu-minum. Non-magnetic nickel-molybdenum coating willbe sputter-coated on the inside of the tubes and bends us-ing the PSI coating facility.The so-called “switch” is located between the supercon-ducting polarizer magnet and the UCN chambers. Its func-tion is to allow the selection of di ff erent guiding paths forthe UCN. First, the UCN are guided from the source to theUCN chambers during an initial filling period. Then, aftera precession time of typically 180 s, the UCN are guided tothe UCN detectors. The switch must work very preciselysince all UCN guiding parts must be carefully aligned inorder to minimize gaps and UCN losses.Each UCN chamber will be emptied into a simultaneousspin analyzer, which is able to count neutrons for both spin components at the same time. A similar system wasalready employed in the previous apparatus [39]. Eacharm of the spin analyzers will be equipped with a high-rate neutron detector. While the previous spectrometerused Li-doped glass scintillators [40], we are investigat-ing a gaseous scintillator operating at atmospheric pres-sure with a gas mixture of CF and He for n2EDM. Thisdetector has the advantage of a faster response and lowerbackground compared to the Li scintillator.
The apparatus as described above represents the base-line setup for n2EDM. We have performed a simulationof the full apparatus connected to the UCN source usingMCUCN to determine the statistical sensitivity of n2EDM,see Table 1. This simulation was based on the averageUCN source performance in 2016 and on absolute ratecalibration measurements on the PSI West-1 beamline.The improvement in UCN statistics mostly comes fromthe two much larger UCN chambers and from the UCNguides with improved coating and larger diameter whichare adapted to the PSI UCN source. The vertical posi-tioning of the chamber was optimized with respect to theUCN energy spectrum and the material optical potentialof the precession chamber coating material. It is clear thatany improvement of the UCN source will immediately im-prove the statistical sensitivity of the n2EDM experiment.The UCN storage time is limited by the quality of thecoating and the gaps of the UCN chambers. For the es-timate of the expected sensitivity we keep the previouslyaccomplished performance with a free precession period T =
180 s.The electric field E was limited to 11kV / cm in the prede-cessor experiment by the presence of many optical fibersleading to the HV electrode, used to operate the Cs magne-tometer array [33]. Without these fibers, stable operationup to 15 kV / cm was achieved. The double chamber designof n2EDM will remove these di ffi culties since all Cs mag-netometers will be grounded. Thus, operation at 15 kV / cmis expected.The visibility, α , is a measure of the UCN polarizationafter storage in the UCN chambers. The best initial polar-ization achieved in the previous apparatus was α = . α = .
75 [34]. Three di ff erent de-polarization mechanisms will decrease the UCN polariza-tion. First, the depolarization of UCN induced by wallcollisions. Second, the intrinsic depolarization where allUCN are a ff ected by a magnetic gradient. Last, the grav-itationally enhanced depolarization where UCN of di ff er-ent energy classes acquire phases at di ff erent rates [41, 42].We expect the uniformity of the B field to be su ffi cient toobtain an average polarization of α = . In reference [4] we have laid out a large set of system-atic e ff ects which have to be dealt with during the analysisof our acquired nEDM data. The systematic e ff ects canEDM 2016 n2EDM baselinediameter (cm) 47 80 α E (kV / cm) 11 15 T (s) 180 180 N (per cycle) 15’000 121’000 σ ( d n ) (per day) 11 × − e cm 2 . × − e cm σ ( d n ) (total) 9 . × − e cm 1 . × − e cmTable 1: Statistical sensitivity at 68% C.L.
Comparisonbetween the achieved performance of the previous appara-tus and the estimate for n2EDM as described in the text.The total sensitivity estimate for nEDM 2016 is based onthe total data acquired with the predecessor experimentuntil the end of 2016. The total sensitivity estimate forn2EDM is based on projected 500 days of measurementwith about 280 cycles per day. PSI usually operates theproton beam and the UCN source on about 200 days percalendar year.be classified in two di ff erent categories: direct and indi-rect. A direct systematic e ff ect means that a variation ofa measurement parameter immediately a ff ects the value ofthe extracted nEDM. An indirect systematic e ff ect is intro-duced through data analysis [43].Here we shall describe two important systematic e ff ectsof the previous apparatus and how they are intended to becontrolled in n2EDM. The application of the electric field might itself generate achange in the magnetic field which is correlated with theelectric polarity. This is a major concern in any EDM ex-periment as it can produce a direct systematic e ff ect. Suchan e ff ect might be due to the leakage current from the highvoltage electrode to the ground electrodes. It could also bedue to magnetization of a part of the apparatus by chargingcurrents during voltage ramps.In principle, the correction using the mercury co-magnetometers cancels any magnetic field fluctuations,including those correlated with the electric field. How-ever, the cancellation is not perfect due to the gravitationalshift [41]. This shift arises due to the di ff erence in center-of-mass between the Hg atoms and the UCN, i.e., (cid:104) z (cid:105) . Thefalse EDM due to a correlated part of the gradient δ G ( E )for a double chamber design reads d falsen = (cid:126) | γ n | E ( (cid:104) z (cid:105) B − (cid:104) z (cid:105) T ) δ G ( E ) . (8)In the double chamber design only the di ff erence in thecenter-of-mass o ff sets contributes. Therefore the e ff ectwill be strongly reduced. The goal for n2EDM is to havethis systematic e ff ect under control at the level of 5 × − e cm . Assuming E =
15 kV / cm, and (cid:104) z (cid:105) B − (cid:104) z (cid:105) T = ≤ / cm. The Cs magne-tometer array is intended to control this e ff ect. When a particle moves with a velocity, (cid:126)v , with respectto a static electric field, (cid:126) E , it is a ff ected by a motionalmagnetic field (cid:126) B m = (cid:126) E × (cid:126)v/ c . In our case, we considerthe motion of the UCN and Hg atoms in the UCN cham-bers. For the trapped particles the velocity averages tozero and therefore one is naively led to conclude that thee ff ect vanishes. However, (cid:126) B m does induce a Larmor fre-quency shift linear to the electric field when the particlesevolve in a non-uniform magnetic field [43, 44]. In theseconditions, a given particle with the trajectory (cid:126) r ( τ ) is sub-jected to a time dependent transverse magnetic field givenby B x ( τ ) = B x ( (cid:126) r ( τ )) + B m , x and B y ( τ ) = B y ( (cid:126) r ( τ )) + B m ,y ,where B x and B y are the transverse components of the B field.Redfield’s theory provides a general approach to calculatefrequency shifts and relaxation rates on a quantum systemcaused by a randomly fluctuating perturbation [44, 45].Specifying this theory to the problem of spins in a bot-tle, one finds that the fluctuating transverse magnetic fieldseen by the individual particles induces a frequency shifton the ensemble proportional to E . This leads to a falseEDM e ff ect which is given by d false = (cid:126) γ c (cid:90) ∞ d τ cos( ωτ ) (cid:104) B x (0) v x ( τ ) + B y (0) v y ( τ ) (cid:105) , (9)where ω = γ Hg B and (cid:104)·(cid:105) is the field-velocity correlationfunction of the particles in the UCN chamber. The gyro-magnetic ratio in eq. (9) depends on the species consid-ered, and can be both γ n or γ Hg .Because the mercury co-magnetometers will be used tocorrect the neutron frequency in each chamber for the fluc-tuations of the magnetic field, the false EDM on the mer-cury atoms will appear as a false neutron EDM, with amagnitude of d falseHg → n = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) γ n γ Hg (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) d falseHg = × − e cm × G (pT / cm) , (10)where G (pT / cm) is the linear gradient over the volume ofthe chambers. This induced false EDM is two orders ofmagnitude larger than the direct false EDM d falsen .The general strategy to cancel this e ff ect is to split the data-production into many runs with di ff erent vertical gradientconfigurations. Then, the measured EDM is plotted as afunction of the gradient and extrapolated to zero gradients.If managing the e ff ect through applying di ff erent gradientsproves too di ffi cult, we have devised a way to operate then2EDM spectrometer at higher B field strengths. For cer-tain UCN chamber diameters at higher B field strengths,the integral in eq. (9) vanishes and the false EDM e ff ectbecomes zero [46]. We have presented the new n2EDM spectrometer for thenEDM search at PSI. The design of the apparatus is basedon the technical expertise which our collaboration hasgained during the first phase of the experiment. Its designs guided by optimizing neutron statistics under adequatecontrol of corresponding systematics. The large volumedouble chamber setup will allow us to increase the sta-tistical precision of the measurement as well as to bettercontrol some systematic e ff ects. Its large size howevermakes the requirement on magnetic field control muchmore stringent. The large size of the magnetically shieldedroom and of the magnetic field coils array will provide thenecessary magnetic field stability and uniformity. The twoHg co-magnetometers and the large array of high precisionCs magnetometers will provide the necessary field moni-toring and control. With this new setup and conservativeperformance estimates based on the previous apparatus,we expect to reach a sensitivity of 1 × − e cm in 500days of data taking using the described baseline setup. Up-grades and changes to this apparatus are currently subjectof intense research and could further expand the n2EDMsensitivity into the 10 − e cm range. Acknowledgments
The experiment could not be realized without themany excellent ideas and continuous dedicated work ofD. Goupillière (LPC), M. Meier (PSI), J. Menu (LPSC),Y. Merrer (LPC) and T. Stapf (PSI). We acknowledge thecontinuous outstanding support at LPC by B. Bougard,B. Carniol, P. Desrues, D. Etasse, J.M. Fontbonne,C. Fontbonne, J. Hommet, J. Lory, C. Pain, J. Perronnel,J. Poincheval, H. de Préaumont, C. Van Damme;at LPSC by M. Chala, R. Faure, C. Fourel, J. Fu-lachier, C. Geraci, J. Marpaud, C. Martin, M. Marton,J. Odier, S. Roni, S. Roudier, J.P. Scordilis, C. Thomassé,C. Vescovi;at PSI by B. Blau, K. Boutellier, F. Burri, P. Eris-man, A. Ersin, A. Gnädinger, U. Greuter, J. Hadobas,L. Holitzner, M. Horisberger, B. Jehle, R. Käch, G. Käslin,C. Kramer, M. Mähr, M. Müller, O. Morath, W. Pfister,D. Reggiani, R. Schwarz, V. Talanov, V. Teufel, A. van-Loon, X. Wang, J. Welte, M. Wohlmuther;and at Sussex by D. Shires.We are grateful to many PSI support groups.P. Mohanmurthy acknowledges grant SERI-FCS2015.0594. STFC, via grants ST / M003426 / / N504452 / / N000307 /
1; the School of Mathe-matical and Physical Sciences at the University of Sussexfor a studentship and other financial support. Support bythe Swiss National Science Foundation Projects 200020-137664 (PSI), 200021-117696 (PSI), 200020-144473(PSI), 200021-126562 (PSI), 200021-181996 (Bern),200020-172639 (ETH) and 200020-140421 (Fribourg) isgratefully acknowledged. The LPC Caen and the LPSCGrenoble acknowledge the support of the French AgenceNationale de la Recherche (ANR) under reference ANR-14-CE33-0007 and the ERC project 716651-NEDM. ThePolish collaborators wish to acknowledge support fromthe National Science Center, Poland, under grant no.2015 / / M / ST2 / / /
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