A precision measurement of the electron's electric dipole moment using trapped molecular ions

TL;DR

This paper reports a highly sensitive measurement of the electron's electric dipole moment using trapped molecular ions, achieving a new upper bound and demonstrating the technique's potential for future improvements.

Contribution

First precision measurement of the eEDM with trapped molecular ions using long spin interrogation times, enhancing sensitivity and systematic error rejection.

Findings

Set an upper bound of |d_e| < 1.3 x 10^{-28} e·cm

Confirmed previous upper bounds with an independent method

Demonstrated long coherence times over 700 ms

Abstract

We describe the first precision measurement of the electron's electric dipole moment (eEDM, $d_e$) using trapped molecular ions, demonstrating the application of spin interrogation times over 700 ms to achieve high sensitivity and stringent rejection of systematic errors. Through electron spin resonance spectroscopy on $^{180}{\rm Hf}^{19}{\rm F}^{+}$ in its metastable $^{3}\Delta_{1}$ electronic state, we obtain $d_e = (0.9 \pm 7.7_{\rm stat} \pm 1.7_{\rm syst}) \times 10^{-29}\,e\,{\rm cm}$, resulting in an upper bound of $|d_e| < 1.3 \times 10^{-28}\,e\,{\rm cm}$ (90% confidence). Our result provides independent confirmation of the current upper bound of $|d_e| < 9.3 \times 10^{-29}\,e\,{\rm cm}$ [J. Baron $\textit{et al.}$, Science $\textbf{343}$, 269 (2014)], and offers the potential to improve on this limit in the near future.

Tables

Table 1. Table 1: Selected frequency channels, their leading expression in terms of experimental parameters, and their interpretations. Here δ ​ g eff 𝛿 subscript 𝑔 eff {\delta g}_{\rm eff} is half the effective magnetic g-factor difference between Stark doublets, α 𝛼 \alpha is the tilt angle of 𝓔 rot subscript 𝓔 rot \bm{\mathcal{E}}_{\rm rot} above the radial plane of the ion trap, and f rot subscript 𝑓 rot f_{\rm rot} is the rotation frequency of ℰ rot subscript ℰ rot {\mathcal{E}}_{\rm rot} .

Channel	Leading term	Interpretation
$f^0$	$3\left|g_F\right|{\mu }_B{ℬ}_{\mathrm{rot}}/h$	Avg. precession frequency
$f^B$	$3\left|g_F\right|{\mu }_B{ℬ}_{\mathrm{rot}}^{\mathrm{nr}}/h$	Non-reversing ${ℬ}_{\mathrm{rot}}$
$f^D$	$3\delta g_{\mathrm{eff}}{\mu }_B{ℬ}_{\mathrm{rot}}\mathrm{sgn}\left(g_F\right)/h$	Level-dependent g-factor
$f^{BR}$	$-3⟨\alpha ⟩f_{\mathrm{rot}}\mathrm{sgn}\left(g_F\right)$	Geometric phase
$f^{BD}$	$-2d_e\left|{ℰ}_{\mathrm{eff}}\right|\mathrm{sgn}\left(g_F\right)/h$	eEDM shift

Table 2. Table 2: Systematic effects and corrections applied to the eEDM channel f B ​ D superscript 𝑓 𝐵 𝐷 f^{BD} , in units of μ ​ Hz 𝜇 Hz \mu{\rm Hz} (with 1 ​ μ ​ Hz 1 𝜇 Hz 1\,\mu{\rm Hz} corresponding to ∼ 10 − 31 ​ e ​ cm similar-to absent superscript 10 31 𝑒 cm \sim 10^{-31}\,e\,{\rm cm} ) sup .

Effect	Correction	Uncertainty
Non-reversing ${ℬ}_{\mathrm{rot}}$	$-1$	$5$
Geometric phases		$4$
Axial secular motion		$2$
Rotation-odd ${ℰ}_{\mathrm{rot}}$		$14$
Doublet population background		$195$
Total systematic	$-1$	$195$
Statistical		$868$
Total uncertainty		$890$

Equations

$$\mathcal{A}(t)\simeq -\mathcal{C}{e}^{-\gamma t}\cos (2\pi ft+\varphi )+\mathcal{O},$$

$$\begin{array}{rl}hf(\tilde{S})& \approx \left|-3g_F{\mu }_B\tilde{B}{\mathcal{B}}_{\mathrm{rot}}+2\tilde{D}{d}_e|{\mathcal{E}}_{\mathrm{eff}}|\right|\\ & =3|g_F|{\mu }_B{\mathcal{B}}_{\mathrm{rot}}-2\tilde{B}\tilde{D}\mathrm{sgn}(g_F)d_e|{\mathcal{E}}_{\mathrm{eff}}|.\end{array}$$

$$f^{BD}=0.10\pm 0.87_{\mathrm{stat}}\pm 0.20_{\mathrm{syst}}\mathrm{mHz}.$$

$$d_e=(0.9\pm 7.7_{\mathrm{stat}}\pm 1.7_{\mathrm{syst}})\times 10^{-29}e\mathrm{cm},$$

$$|d_e|<1.3\times 10^{-28}e\mathrm{cm}\text{(90\% confidence)}.$$

Full text

A search for a nonzero permanent electric dipole moment of the electron (eEDM, $d_{e}$) constitutes a nearly background-free test for physics beyond the Standard Model (SM), since the SM predicts $|d_{e}|\lesssim 10^{-38}\,e\,{\rm cm}$ Pospelov and Khriplovich (1991), while the natural scale of $d_{e}$ in many proposed SM extensions is typically $10^{-27}$ to $10^{-30}\,e\,{\rm cm}$ Pospelov and Ritz (2005). Present experimental techniques now constrain these theories Baron et al. (2014); hence, there have been many recent experimental efforts to measure an eEDM Baron et al. (2014); Hudson et al. (2011); Regan et al. (2002); Eckel et al. (2013); Zhu et al. (2013); Heidenreich et al. (2005); Lee et al. (2013).

The most precise eEDM measurements to date were performed using thermal beams of neutral atoms or molecules Regan et al. (2002); Hudson et al. (2011); Baron et al. (2014). These experiments benefited from excellent statistical sensitivity provided by a high flux of neutral atoms or molecules, and decades of past work have produced a thorough understanding of their common sources of systematic error. Nonetheless, a crucial systematics check can be provided by independent measurements conducted using different physical systems and experimental techniques. Moreover, techniques that allow longer interrogation times offer significant potential for sensitivity improvements in eEDM searches and other tests of fundamental physics Skripnikov et al. (2017).

In this Letter, we report on a precision measurement of the eEDM using molecular ions confined in a radio frequency (RF) trap, applying the methods proposed in Ref. Leanhardt et al. (2011) and demonstrated in Ref. Loh et al. (2013). We perform an electron spin precession experiment on ${}^{180}{\rm Hf}^{19}{\rm F}^{+}$ molecules in their metastable ${{}^{3}\Delta_{1}}$ electronic state, and extract the relativistically enhanced eEDM-induced energy shift $\sim 2d_{e}{\mathcal{E}}_{\rm eff}$ between stretched Zeeman sublevels, where ${\mathcal{E}}_{\rm eff}\approx 23$ GV/cm in HfF+ Eef ; Meyer et al. (2006); Petrov et al. (2007); Fleig and Nayak (2013); skr . In addition to leveraging the high eEDM sensitivity and systematic error rejection intrinsic to an $|\Omega|=1$ electronic state in a heavy polar molecule Eckel et al. (2013), including in particular the small magnetic moment of a ${{}^{3}\Delta_{1}}$ state Meyer et al. (2006), we use a unique experimental approach that is robust against sources of systematic error common to other methods. The 2.1(1) s lifetime of the ${{}^{3}\Delta_{1}}$ state in HfF+ Ni et al. (2014) and our use of an RF trap allow us to attain spin precession times in excess of 700 ms – nearly three orders of magnitude longer than in contemporary neutral beam experiments. This exceptionally long interrogation time allows us to obtain high eEDM sensitivity despite our lower count rate. In addition, performing an experiment on trapped particles permits the measurement of spin precession fringes at arbitrary free-evolution times, making our experiment relatively immune to systematic errors due to initial phase shifts associated with imperfectly characterized state preparation.

Our apparatus and experimental sequence, shown schematically in Fig. 1, have been described in detail previously Leanhardt et al. (2011); Loh et al. (2011, 2012, 2013); Ni et al. (2014); Cossel et al. (2012). We produce HfF by ablation of Hf metal into a pulsed supersonic expansion of Ar and SF6. The reaction of Hf with SF6 produces HfF, which is entrained in the supersonic expansion and rovibrationally cooled through collisions with Ar. The resulting beam enters the RF trap, where HfF is ionized with pulsed UV lasers at 309.4 nm and 367.7 nm to form HfF+ in its ${}^{1}\Sigma^{+}$, $v=0$ ground vibronic state Loh et al. (2011, 2012). The ions are stopped at the center of the RF trap by a pulsed voltage on the radial trap electrodes, then confined by a DC axial electric quadrupole field and an RF radial electric quadrupole field with frequency $f_{\rm rf}=50$ kHz. We next adiabatically turn on a spatially uniform electric bias field ${\mathcal{E}}_{\rm rot}\approx 24$ V/cm that rotates in the radial plane of the ion trap with typical frequency $f_{\rm rot}\approx 250\,{\rm kHz}$, causing the ions to undergo circular motion with radius $r_{\rm rot}\approx 0.5\,{\rm mm}$. A pair of magnet coils aligned with the $Z$ axis produce an axial magnetic gradient $\bm{\mathcal{B}}={\mathcal{B}}^{\prime}_{\rm axgrad}(2\bm{Z}-\bm{X}-\bm{Y})$ where $|{\mathcal{B}}^{\prime}_{\rm axgrad}|\approx 40\,{\rm mG/cm}$, which in the rotating, translating frame of the ions creates a magnetic bias field ${\mathcal{B}}_{\rm rot}\equiv|\langle\bm{\mathcal{B}}\cdot\bm{\mathcal{E}}_{\rm rot}/{\mathcal{E}}_{\rm rot}\rangle|\simeq|{\mathcal{B}}^{\prime}_{\rm axgrad}r_{\rm rot}|$ that is parallel (antiparallel) to ${\mathcal{E}}_{\rm rot}$ if ${\mathcal{B}}^{\prime}_{\rm axgrad}>0$ ($<0$) Leanhardt et al. (2011); Loh et al. (2013).

Our state preparation consists of population transfer to the eEDM-sensitive ${{}^{3}\Delta_{1}}$ state and selective depletion of magnetic sublevels to produce a pure spin state [Fig. 1(b-c)]. Two cw lasers at $899.7\,{\rm nm}$ and $986.4\,{\rm nm}$ co-propagating along the $-\hat{Z}$ axis drive a stimulated Raman transition through a ${}^{3}\Pi_{0^{+}}$, $v=1$, $J=1$ intermediate state, transferring approximately $40\%$ of the ground rovibronic state population to the ${{}^{3}\Delta_{1}}$, $J=1$, $F=3/2$ state. Figure 2(a) shows the structure of this state in a frame defined by the instantaneous direction of $\bm{\mathcal{E}}_{\rm rot}\equiv{\mathcal{E}}_{\rm rot}\hat{z}$. It consists of four Stark doublets (pairs of magnetic sublevels) separated by $d_{{\rm mf}}{\mathcal{E}}_{\rm rot}/3h\approx 14~{}{\rm MHz}$, where $d_{{\rm mf}}$ is the ${{}^{3}\Delta_{1}}$ molecule-frame dipole moment and $h$ is Planck’s constant. The population transfer process resolves Stark doublets, but produces an incoherent mixture of $m_{F}=\pm 3/2$ states in either the upper or lower doublet, depending on the detuning of the second transfer laser. Selective depletion is then performed by a circularly polarized 814.5 nm Ti:sapphire laser resonant with the $P(1)$ line of a ${}^{3}\Sigma^{-}_{0^{+}}\leftarrow{{}^{3}\Delta_{1}}$ transition. The depletion laser is strobed synchronously with the rotating electric field so that its wavevector is either parallel or antiparallel to $\bm{\mathcal{E}}_{\rm rot}$, thus driving a $\sigma^{\pm}$ transition to an $F^{\prime}=1/2$ manifold and leaving a single $m_{F}=\pm 3/2$ level populated in the ${{}^{3}\Delta_{1}}$ state.

Following the production of a pure spin state by strobed depletion, we perform a $\pi/2$ pulse to prepare an equal superposition of $m_{F}=\pm 3/2$ states. This is accomplished by reducing ${\mathcal{E}}_{\rm rot}$ for a brief interval, which increases a rotation-induced fourth-order coupling $\Delta^{u/l}$ between $m_{F}=\pm 3/2$ states [Fig. 2(b)] and causes a pure spin state to evolve into an equal superposition in $\sim 1\,{\rm ms}$ Leanhardt et al. (2011); Loh et al. (2013); sup . We return ${\mathcal{E}}_{\rm rot}$ to its nominal value and allow the phase of the superposition state to evolve for a variable precession time up to $\sim 700$ ms, then apply a second $\pi/2$ pulse to map the relative phase of the superposition onto a population difference between $m_{F}=\pm 3/2$ states. A second set of strobed laser pulses again depletes all but a single $m_{F}=\pm 3/2$ level. Finally, to selectively detect the remaining population in the ${{}^{3}\Delta_{1}}$, $J=1$ state, we resonantly photodissociate HfF+ using pulsed UV lasers at 285.7 nm and 266 nm. We eject all ions from the trap with a pulsed voltage on the radial trap electrodes, and count both Hf+ and the temporally resolved background HfF+ using a microchannel plate (MCP) detector Ni et al. (2014).

We interleave experimental trials where the two sets of strobed depletion pulses have the same or opposite phase with respect to ${\mathcal{E}}_{\rm rot}$ in order to alternately prepare and detect population in the $m_{F}=\pm 3/2$ states. Denoting by $N_{A}$ ($N_{B}$) the measured population when the depletion phases are the same (opposite), we form the asymmetry ${\mathcal{A}}=(N_{A}-N_{B})/(N_{A}+N_{B})$, which normalizes drifts in the absolute ${{}^{3}\Delta_{1}}$ population. The asymmetry forms an interference fringe that is well-approximated by a sinusoidal function of precession time $t$,

[TABLE]

with frequency $f$ proportional to the energy difference between the $m_{F}=\pm 3/2$ states, as shown in Fig. 2(c). The initial contrast $\mathcal{C}$, initial phase $\phi$, offset $\mathcal{O}$, and decoherence rate $\gamma$ parametrize imperfect state preparation and the loss of coherence, which is primarily due to ion-ion collisions. We perform nonlinear least squares fitting of the asymmetry with the functional form of Eq. (1) with $\mathcal{C}$, $\gamma$, $f$, $\phi$, and $\mathcal{O}$ as fit parameters. Standard errors $\delta\mathcal{C}$, $\delta\gamma$, $\delta f$, $\delta\phi$, and $\delta\mathcal{O}$ are estimated from the Jacobian of the fit function at the optimum parameter values. The precession frequency contains the eEDM signal, while the other fit parameters are used to diagnose experimental imperfections and sources of systematic error.

To isolate an eEDM-dependent frequency shift and diagnose systematic errors, we form data “channels”: components of a measurement that have a particular parity under a set of chosen “switches” – experimental parameters that are modulated between opposite values on a short timescale 111Our notation for data channels closely follows that used by the authors of Refs. Baron et al. (2014, ).. Our switches are the sign of the magnetic bias field ${\tilde{B}}={\rm sgn}(\langle\bm{\mathcal{B}}\cdot\bm{\mathcal{E}}_{\rm rot}\rangle)$, the populated Stark doublet ${\tilde{D}}=-{\rm sgn}(m_{F}\Omega)$, and the sense of the electric bias field rotation ${\tilde{R}}=-{\rm sgn}(\bm{\omega}_{\rm rot}\cdot\hat{Z})$. We repeat our spin precession measurement in each of the eight unique “switch states” ${\tilde{S}}=({\tilde{B}},{\tilde{D}},{\tilde{R}})$ to form a “block,” and form channels $X^{s}$ with parities $s\subset\{B,D,R\}$ from linear combinations of the eight measurements $X({\tilde{S}})$, where $X\in\{{\mathcal{C}},\gamma,f,\phi,{\mathcal{O}}\}$ (See Eq. (S1) in Ref. sup ). For example, for a given block of data, $f^{B}$ is given by half the difference between the average value of $f$ for the ${\tilde{B}}=+1$ fringes and that for the ${\tilde{B}}=-1$ fringes. We estimate the standard error $\delta X$, which is the same for all parities $s$, by propagating the error estimates $\delta X({\tilde{S}})$ resulting from the nonlinear least squares fit of Eq. (1).

If higher order effects are neglected, the measured spin precession frequency is dominated by the Zeeman shift between populated magnetic sublevels, and includes a $BD$-odd contribution from an eEDM:

[TABLE]

An eEDM signal thus appears as the lowest-order contribution to the $f^{BD}$ frequency channel, while any non-ideal contributions to $f^{BD}$ constitute potential sources of systematic error. The seven non-eEDM frequency channels contain information about experimental conditions such as non-reversing magnetic fields, and we use these channels to construct and confirm models of non-ideal experimental behavior and to correct for systematic shifts in $f^{BD}$. Some examples of frequency channels, their leading-order expressions in terms of experimental parameters, and their physical interpretations are shown in Table 1.

Prior to eEDM data collection, we tuned a wide variety of experimental parameters over an exaggerated dynamic range and observed the response of the data channels in order to create models of non-ideal frequency shifts in our system. Two illustrative examples of these observations are shown in Fig. 3, and the contributions of these shifts to the eEDM channel are discussed in Ref. sup . The result of this study was the validation of a unified numerical model of our spin precession sequence. In this model, we integrate the classical motion of ions in simulated time-varying electric and magnetic fields, then propagate the internal quantum state of the molecules using an effective Hamiltonian that explicitly includes all sublevels of the two lowest rotational levels of ${{}^{3}\Delta_{1}}$. Using known experimental parameters and realistic estimates of construction imperfections, this model was able to reproduce all observed frequency shifts.

In total, we collected 1024 blocks (360.3 hours) of eEDM-sensitive data, with each block resulting in one value of $f^{BD}$ and thus one eEDM measurement. Throughout the collection and analysis of this eEDM data, we added to the $f^{BD}$ channel an unknown, computer-generated pseudo-random value drawn from a normal distribution with a standard deviation of $5\times 10^{-28}\,e\,{\rm cm}$. This “blind” allowed us to investigate systematic frequency shifts and perform statistical analysis while mitigating the effects of operator bias. We applied cuts to the blinded data based on non-eEDM channels indicating signal quality: blocks with ${\mathcal{C}}<0.1$ or ${\mathcal{C}}e^{-\gamma T}<0.1$ were cut due to low signal to noise (where $T$ is the largest value of $t$ sampled in a block). In addition, we cut data where shifts in the “co-magnetometer” channel $f^{B}$ exceeded $0.4~{}{\rm Hz}$ due to its contribution to systematic errors. After these cuts, our eEDM dataset consists of 903 blocks or 313.8 hours of data. The unblinded dataset is shown in Fig. 4(a-b). Visual inspection of a normal probability plot, as well as Kolmogorov-Smirnov and Shapiro-Wilk normality tests indicate that the distribution of normalized and centered eEDM measurements $(f^{BD}-\langle f^{BD}\rangle)/\delta f$ is consistent with a normal distribution. The reduced chi-squared statistic for fitting a weighted mean to the eEDM dataset is $\chi^{2}_{r}=1.22(5)$. This over-scatter is attributable to magnetic field drifts sup , and to correct for it we scale our final statistical error bar by $\sqrt{\chi^{2}_{r}}\approx 1.1$.

During eEDM data collection, we suppressed sources of systematic error that appeared in our earlier model-building investigation by applying active feedback to relevant experimental parameters between the collection of data blocks. The only one of these that produced an observable shift in the $f^{BD}$ channel was the combined effect of a non-reversing magnetic bias field ${\mathcal{B}}_{\rm rot}^{\rm nr}$ and the difference in effective magnetic g-factor between Stark doublets, which in our system arises from Stark mixing with ${{}^{3}\Delta_{1}}$, $J=2$ and from our rotating quantization axis sup ; Leanhardt et al. (2011). The $f^{B}$ and $f^{D}$ frequency channels, which are acquired concurrently with $f^{BD}$, provide direct measurements of these contributions. Since the value of $f^{D}\approx 10^{-3}f^{0}$ is fixed by the values of ${\mathcal{E}}_{\rm rot}$, ${\mathcal{B}}_{\rm rot}$, and $f_{\rm rot}$, we suppress the systematic shift in the eEDM channel by applying a compensating ${\mathcal{B}}^{\prime}_{\rm axgrad}$ to minimize $|f^{B}|$. We also apply a block-by-block correction to $f^{BD}$ based on the measured values of $f^{B}$ and $f^{D}$, the validity of which was verified in our earlier model-building study sup .

Though they were too small to be observed at our level of sensitivity, we predicted systematic shifts in the eEDM channel due to the non-ideal frequency shifts in the $f^{B}$ and $f^{BR}$ channels shown in Fig. 3. We suppressed the first of these by adding a feedforward signal to ${\mathcal{E}}_{\rm rot}$ to cancel the harmonic distortion component at $2f_{\rm rot}$, reducing it from $-48$ dBc to $-70$ dBc, and by using magnet coils to null the ambient uniform magnetic field at the RF trap center to within $\sim\pm 30$ mG. To suppress the shift in $f^{BR}$ caused by ${\mathcal{E}}_{\rm rot}$ inhomogeneity shown in Fig. 3(b), we measured the ion cloud position once per data block on a pair of MCPs, and applied DC potentials on the trap electrodes to position the ion cloud within $\sim 2\,{\rm mm}$ of the minimum of the quadratic shift. The residual offset of $f^{BR}\approx-100~{}{\rm mHz}$ and gradient of $\partial f^{BR}/\partial Y_{0}\approx 20\,{\rm mHz/mm}$ shown in Fig. 3 are consistent with ${\mathcal{E}}_{\rm rot}$ inhomogeneity resulting from realistic machining, welding, and assembly imperfections in the construction of our RF trap.

While collecting eEDM data, we also searched for new systematic errors correlated with parameters that could not be tuned over a significantly exaggerated dynamic range, including ${\mathcal{E}}_{\rm rot}$, $f_{\rm rot}$, and the number of HfF+ ions trapped per experimental trial [Fig. 4(c)]. We did not observe significant variation of $f^{BD}$ (or five of seven other non-eEDM frequency channels) with these parameters at our current level of precision. The variations of the non-eEDM frequency channels $f^{0}$ and $f^{D}$, in which we did anticipate variation with ${\mathcal{E}}_{\rm rot}$ and $f_{\rm rot}$, were consistent with model predictions. Finally, we modified our data collection by randomizing the order of switch states in each block to search for and suppress systematic errors caused by parameter drifts correlated with our switches, and observed no significant variation of data channels sup . The final results of our systematic error searches and corrections are summarized in Table 2.

We removed our blind on 31 March 2017, and obtained a final value for the eEDM-sensitive frequency channel

[TABLE]

Dividing by $-2|{\mathcal{E}}_{\rm eff}|{\rm sgn}(g_{F})/h\approx 1.13\times 10^{28}~{}{\rm mHz}/e\,{\rm cm}$ Petrov et al. (2007); Fleig and Nayak (2013), we obtain a value for the eEDM

[TABLE]

which is consistent with zero within one standard error. The resulting upper bound is

[TABLE]

Our result is consistent with the limit of $|d_{e}|<9.3\times 10^{-29}~{}e\,{\rm cm}$ set by the ACME Collaboration Baron et al. (2014, ), and we have confirmed their result using a radically different experimental approach. Our measurement is limited by statistics, and our dominant source of systematic error can be further suppressed to the $10^{-30}\,e\,{\rm cm}$ level sup . Here we have assumed that parity and time-reversal violating effects arise purely from $d_{e}$. An additional contribution $\sim W_{S}C_{S}$ can arise from a pseudoscalar-scalar electron-nucleon coupling $C_{S}$ Chupp and Ramsey-Musolf (2015); Skripnikov (2016); Denis et al. (2015), however to our knowledge a published value of $W_{S}$ is not yet available for HfF+.

Since the completion of this first generation eEDM measurement, we have designed and constructed a second generation ion trap, which we will use to confine up to an order of magnitude more ions, cool them via adiabatic expansion to a volume up to one hundred times larger, and polarize them using a rotating electric bias field that is more uniform due to an improved electrode design. We estimate that these and other improvements should provide an order of magnitude higher eEDM sensitivity. In the further future, we plan to pursue a third generation eEDM measurement using 232Th19F+, in which the ${{}^{3}\Delta_{1}}$ ground electronic state with ${\mathcal{E}}_{\rm eff}\approx 36\,{\rm GV/cm}$ may allow a high-sensitivity eEDM experiment with a coherence time up to tens of seconds Gresh et al. (2016); Skripnikov and Titov (2015); Denis et al. (2015).