The search for the neutron electric dipole moment at PSI

The existence of a nonzero permanent electric dipole moment (EDM) of the neutron would reveal a new source of CP violation and shed light on the origin of the matter--antimatter asymmetry of the Universe. The sensitivity of current experiments using stored ultracold neutrons (UCN) probes new physics beyond the TeV scale. Using the UCN source at the Paul Scherrer Institut, the nEDM collaboration has performed the most sensitive measurement of the neutron EDM to date, still compatible with zero ($|d_n|<1.8\times 10^{-26} \, e {\rm cm}$, C.L.90%). A new experiment designed to improve the sensitivity by an order of magnitude, n2EDM, is currently in construction.


Introduction
The permanent electric dipole moment (EDM) d of a simple quantum system of spin 1/2 represents the coupling between the particle spin and an externally applied electric field E, in the same way that the magnetic dipole moment µ quantifies the coupling between the spin and an applied magnetic field B. The spin dynamics is entirely described by the Hamiltonian where σ are the Pauli matrices. Becauseˆ σ · E is odd with respect to time reversal, the CPT theorem implies that a non-zero EDM would result in a violation of CP symmetry. The search for a nonzero EDM was initiated in the 1950's [1], applying the newly invented resonance method with separated oscillating fields [2] on a thermal neutron beam. The quest for an EDM was then extended to many other systems, as shown in Figure 27.1, (see [3] for a review on EDM searches). All experiments to date have reported results compatible with zero, despite the million-fold improvement of the sensitivity of modern experiments. As discussed in the theory chapter of this volume, the present limits on EDMs provide stringent constraints on theories beyond the Standard Model of particle physics, which generally predict new sources of CP violation and therefore non-zero EDMs. The next generation of experiments with improved sensitivity are motivated by the exciting possibility of discovering a non-zero EDM induced by new physics at the multi-TeV scale.  [4].
An international collaboration of 15 laboratories (the nEDM collaboration) is conducting a longterm program at PSI to search for the neutron EDM. In 2009, the RAL/Sussex/ ILL instrument [5], which was previously used at the Institut Laue Langevin in Grenoble for a long series of nEDM measurements [6][7][8][9], was connected to the newly built high-intensity source of ultracold neutrons [10,11]. After a phase of hardware upgrades and commissioning of the instrument, data was collected during 2015 and 2016. This resulted in the currently most precise measurement of the neutron EDM, d n = (0.0 ± 1.1 stat ± 0.2 sys ) × 10 −26 e · cm [12]. This measurement, with the single chamber instrument, will be described in Section 27.3. The construction of the new double chamber instrument (called n2EDM: the new neutron EDM apparatus) started in 2018. It will be described in Section 27.4. In the next section we elaborate on the main challenges to neutron EDM searches.

The three challenges for searches for the neutron EDM
The coupling in (27.1) leads to a precession of the neutron spin around the fields at an angular frequency given by ω = 2 (µB + d E) /ħ h in parallel electric and magnetic fields. In principle the EDM term can be separated from the magnetic term by taking the difference of the frequency measured in parallel and anti-parallel field configurations. However, the electric term that is to be measured is extremely small. For d = 10 −26 ecm and E = 15 kV/cm, the spin would complete just about two full turns per year, due to the electric term. For the detection of such a minuscule coupling, one needs (i) a long interaction time with a large electric field, (ii) a high flux of neutrons, and (iii) precise control of the magnetic field. These requirements constitute the three main challenges for the measurement.
In many experiments, the neutron precession frequency is measured using Ramsey's resonance method: neutrons with spins parallel to the magnetic field are selected, then a first oscillating 30  transverse magnetic-field pulse is applied with a strength and duration adjusted to tilt the spin into the plane transverse to the magnetic field. The spins then precess freely during a precession time T , after which a second pulse, identical to and in phase with the first one, is applied. At the end of the process the neutron spins are analyzed in order to extract the asymmetry A of neutrons counted with spin up and down. The asymmetry is a function of the applied pulse frequency and of the precession frequency to be measured, as shown in Figure 27.2. By measuring the asymmetry, the neutron precession frequency f n is extracted. After combining several measurements, aka cycles, of f n with different polarities of the electric field the neutron EDM is measured with a statistical sensitivity per cycle of (27.2) where N is the total number of neutron counts and α is the visibility of the resonance, corresponding to the product of the neutron polarization at the end of the precession period and the analyzing power of the spin analyzer. It is apparent from (27.2) that the combination E T enters linearly in the statistical sensitivity and must be maximized (first challenge) along with the statistical factor N (second challenge). The first neutron EDM experiments used beams of neutrons interacting with the fields for only a few milliseconds. The turning point for higher sensitivities was the advent of ultracold neutron (UCN) sources which permitted neutrons to be stored in a precession chamber for a duration approaching the neutron half-life of 10 minutes. Care must be taken in the choice of materials constituting the precession chamber in order to minimize neutron losses.
In the single chamber apparatus at PSI, the precession chamber was a cylinder of radius 23.5 cm and height 12 cm, assembled from two aluminum electrodes coated with diamond-likecarbon [13][14][15][16] and a polystyrene ring coated with deuterated polystyrene [17]. In average N = 15000 neutrons per cycle were exposed to an electric field of 11 kV/cm during T = 180 s.
Based on experience and demonstrated developments, a double chamber apparatus was designed. Two vertically stacked chambers, with larger radii of 40 cm will sustain a larger electric field of opposite polarity and store more neutrons.  The high statistical sensitivity must be combined with precise control of the magnetic field: the third challenge. This is accomplished with a combination of magnetic shielding, the generation of a stable and uniform magnetic field inside the shield, and measurements of the magnetic field with atomic magnetometry. In the single chamber experiment, the change of the magnetic field between reversals of the electric polarity (typically every 4 hours), needed to be controlled at a level better than 10 fT. This was established by making sure that the Allan deviation for a field average over 4 hours was below 10 fT.
For this purpose, the co-magnetometer technique [18,19] was used. Polarized 199 Hg atoms were injected in the chamber and the precession frequency of the atoms was measured optically, providing the magnetic-field average over the same time and almost the same volume as the neutrons.
The mercury co-magnetometer is essential to control the residual time variations of the magnetic field (both correlated and uncorrelated with the electric polarity). However, this comes at the price of inducing a false EDM due to the combined effect of the relativistic motional field v × E/c 2 seen by the mercury atoms and the magnetic field non-uniformities [20][21][22][23]. Due to this important systematic effect, the control of the uniformity of the magnetic field is of utmost importance. In particular, ferromagnetic impurities close to the precession chamber(s) must be avoided, and the residual large-scale magnetic gradients must be minimized and measured with a combination of online and offline methods.

Measurement and result
The principal characteristic of the instrument operated between 2009 to 2017 at PSI was a singlechamber precession volume for UCN, which at the same time contained spin-polarized 199 Hg atoms as reference or cohabiting magnetometer [18,19]. Figure 27.3 shows a technical sketch of the instrument. Ultracold neutrons from the PSI UCN source [11,24] were polarized upon the passage through the 5 T solenoid and entered the precession chamber from the bottom. The spin-manipulation and free precession of UCN and 199 Hg took part here, 125 cm above the horizontal beam line, inside a 4-layer mu-metal shield. The top electrode made contact to the tip of a high voltage (HV) feed-through tested in operation up to 200 kV. An electric field of E = ±11 kV/cm was used for data-taking. The magnetic field, B ≈ 1 µT, was generated by a current of about 17 mA in a cos θ -coil wound directly onto the cylindrical vacuum tank. In addition to the cos θ -coil there were a total of 35 saddle and cylindrical coils, aka trim coils, wound on the tank to adjust magnetic-field gradients. Two of these saddle coils, on the top and bottom of the vacuum tank, were used to set a small vertical magnetic-field gradient ∂ B z /∂ z, for each sequence. The 199 Hg-comagnetometer measured the time and volume averaged magnetic field within the precession chamber and was subject to the above-described motional systematic effect. At the same time an array of 15 optically-pumped Cs vapor magnetometers (CsM) [25], mounted above and below the chamber, was used to monitor the magneticfield uniformity with a sampling rate of 1 Hz. Another three coils, two of them in a Helmholtz-like geometry and one a saddle coil, wound onto the outside of the vacuum tank were used to generate the spin-manipulation pulses, once the UCN and 199 Hg-atoms were inside the chamber, with frequencies close to the resonance Larmor frequency of 199 Hg (∼ 7.8 Hz) and neutron (∼ 30.2 Hz). After the second t = 2 s long spin-flip pulse of the Ramsey sequence the neutrons were counted in a spin-sensitive detection system [26,27]. For each cycle, from the recorded number of neutrons with spin up N u and down N d the asymmetry During data taking, the files containing the detector data were blinded by injection of an artificial unknown EDM signal [28], different for two distinct analysis groups.
During the nEDM data acquisition period from July 2015 until December 2016 a total of 54 068 cycles each with an average of about 11400 neutrons were recorded. The data were taken with different magnetic-field configurations, e.g. B up or downwards pointing with −25 pT/cm ≥ ∂ B z /∂ z ≤ 25 pT/cm. Each of these sequences contained several hundred cycles and multiple electric-field changes as can be seen in Figure 27.4. A total of 99 sequences were analyzed. In a first step, each sequence was divided into sub-sequences including at least two changes of the electric field polarity. The data of a sub-sequence, typically 114 cycles, was fit to  f Hg and ν = 1/(T + 4t/π) is the width (FWHM) of the central fringe (see Figure 27.2). To extract the neutron resonance frequency, f n,i , the fit parameters A off , α were fixed for each cycle and (27.3) was solved for φ = π f n,i /ν. Figure 27.4 bottom shows the ratio R i = f n,i / f Hg,i for a full measurement sequence. An optimized analysis strategy was implemented, accounting for all known effects [12] which affect the R ratio: in particular the EDM term δ EDM = 2E/(ħ hγ n B)d n . In fact, the dominating effect is the gravitational shift δ grav = G grav 〈z〉/B, which is due to the relative center-of-mass offset 〈z〉 = −0.39(3) cm between UCN and 199 Hg. This is both a source of drifts (a nuisance) and also an excellent measure of the effective vertical magnetic-field gradient G grav . In each sub-sequence, the EDM signal d meas n and 〈R〉 are determined by fitting the R i values, compensated for the relative gradient drift, as a function of time and electric field by allowing, also, for a linear time drift, as shown in Figure 27.5. The measured d meas n for a given field configuration is shifted by the term δ false EDM = 2E/(ħ hγ n B)d false corresponding to the motional false effect of 199 Hg mentioned previous section. This effect depends on the magnetic field gradients and can be expressed as [25]: whereĜ is the contribution from higher-order gradients and does not produce a gravitational shift. After correction of 〈R〉 and d meas n for δ T and δ Earth , the contribution fromĜ, and minor systematic shifts, the remaining shift is linear in G grav and was removed by a crossing point fit as shown in Figure 4 of [12].

n2EDM: The double chamber apparatus
The concept and design of the new double chamber instrument, n2EDM [29], was based on maximizing the statistical sensitivity of a single measurement, see Table 27.1, while at the same time further reducing systematic effects.
As can be seen in Figure 27.6, the new apparatus has two cylindrical storage chambers of diameter ∅80 cm, made from proven materials, stacked one above the other, separated only by a common high voltage electrode in the center. The UCN transport and storage layout was optimized for a maximum number of neutrons per cycle using the established and bench marked Monte Carlo code of the collaboration [30]. This resulted in ultracold-neutron guides with constant effective cross section and sub-nanometer roughness along the path up to the two precession chambers which in turn are placed at the optimal height relative to the beam line.
Both chambers are centered inside the same uniform magnetic field generated by a main magnetic-field coil and an advanced trim-coil system within a 6-layer magnetic and one-layer Eddy current shield. First measurements of the quasi-static shielding factor in 2020 exceeded the specified value of 80 000 in all directions. This is supplemented by an active magnetic shield (AMS), similar to the active coil system used previously [31], with eight degrees of freedom devised to further improve the shielding factors at very low frequencies. Dedicated coils were designed [32] and mounted onto the inner wall surfaces of the wooden thermal enclosure to compensate gradient magnetic fields up to first order. Hence, neutrons and mercury inside the two precession chambers are exposed to the same extremely low noise, highly uniform magnetic field while the electric field points in opposite directions. We expect that an application of electric fields up to |E| ≥ 15 kV/cm can be achieved without difficulties, as the HV electrode is entirely enclosed in a grounded Faraday cage.
All CsM are placed at ground potential and the previous limitation on the electric-field strength due to flashovers along optical fibers of the CsM can be ruled out. The sensors were designed for an operation in Bell-Bloom mode [33], recording free spin-precession waveforms for highest accuracy and with a sensitivity of better than 200 fT/ Hz. This is an essential improvement for the accurate determination of higher order magnetic-field terms relevant for the correction of systematic effects.
Each precession chamber is connected via a UCN switch to a simultaneous spin detection device featuring each two UCN detectors. A gas mixture of CF4 and 3 He is used for neutron detection. The short scintillation pulse is registered by large surface photo-multipliers and enables high count rate with very low background counts from gamma rays or cosmic radiation.
In summary the new double chamber spectrometer, n2EDM, at PSI combines the newest concepts and technologies while relying on proven techniques and methods to improve the sensitivity frontier.
An attractive future option, which is described in great detail in [34], eliminates the motional false EDM by adjusting the magnetic-field strength so that the integral in equation (9) in [29] vanishes. This magic field configuration indicates a possible path to ultimate sensitivity using the n2EDM spectrometer at PSI.

Outlook and world-wide competition
With the publication of the latest, most stringent limit of d n < 1.8 × 10 −26 e·cm, PSI became the fourth member of the exclusive club of institutes that have hosted a successful nEDM search. It is now competing with a group of fierce and passionate competitors from all around the world [35][36][37][38][39] to break into the range of 1 × 10 −27 e·cm within the next decade. A discovery of an nEDM or a further improved limit would markedly and indelibly shape future models of particle physics beyond the current Standard Model.
We wish to thank all the members of the nEDM collaboration for their dedication to the experimental effort, and the Paul Scherrer Institute for the fantastic hosting conditions.