Spin clocks: Probing fundamental symmetries in nature


Corresponding author E-mail: wheil@uni-mainz.de


The detection of the free precession of co-located 3He/129Xe nuclear spins (clock comparison) is used as ultra-sensitive probe for non-magnetic spin interactions, since the magnetic dipole interaction (Zeeman-term) drops out in the weighted frequency difference, i.e., Δω = ωHe- γHeXe·ωXe of the respective Larmor frequencies. Recent results are reported on searches for (i) short-range P- and T-violating interactions between nucleons, and (ii) Lorentz violating signatures by monitoring the Larmor frequencies as the laboratory reference frame rotates with respect to distant stars (sidereal modulation). Finally, a new experimental initiative to search for an electric dipole moment of 129Xe (CP-violation) is discussed, which strongly benefits from the long spin-coherence times obtained, reaching math formula> 100 h and math formula> 8 h in case of 3He and 129Xe, respectively.

1 Features of frequency standards and clocks

Since Galileo Galilei and Christiaan Huygens invented the pendulum clock, time and frequency have been the quantities that we can measure with the highest precision. Since 1967 the Cs atomic clock defines our unit of time, the second, as the period during which a cesium-133 atom oscillates 9,192,631,770 number of cycles on the hyperfine clock transition math formula in the 62S1/2 atomic ground state. Cesium atomic clocks have been gradually improved to the point where modern cesium-fountain clocks realize the definition of the second with a relative uncertainty of about 4 × 10−16 [1]. In the near future, the cesium clock defining the fundamental timing reference will be replaced with an optical clock, since suppression of systematic effects shifting the frequency of a standard is greatly facilitated by the use of higher frequencies. Thanks to the incredible high relative accuracy of frequency determination, atomic clocks may touch the μHz range on an absolute scale, but will essentially not go far below.

To address fundamental questions in physics often associated with the experimental search for violation of fundamental symmetries in nature, much smaller frequencies or frequency shifts as a result of tiny changes in the clock transition must be tracked. From that point of view it is more appropriate to develop a “clock” that oscillates at low frequencies (∼10 Hz), but shows the same relative accuracy as a Cs atomic clock. Thus, frequency shifts in the pHz range caused by hypothetical interaction potentials might be accessible.

“Spin clocks” which are based on nuclear spin precession are the most promising approach to reach such sensitivity limits. The „spin clock“ described here is based on the detection of free spin-precession of gaseous, nuclear spin-polarized 3He or 129Xe samples [2]. Like in a free induction decay (FID) measurement, the decay of the transverse magnetization is monitored and the Larmor frequency ω of the precessing sample magnetization is related to the magnetic field B0 through math formula, where γ is the gyromagnetic ratio of the corresponding nucleus. Since this type of clock will preferably operate at low magnetic fields and thus at low frequencies, using a SQUID as magnetic field detector is appropriate due to its high sensitivity in that spectral range. The 3He/129Xe nuclear spins are polarized by means of optical pumping. Thus, the nuclear polarization obtained exceeds the Boltzmann polarization as used in typical NMR experiments by four to five orders of magnitude.

2 Co-located 3He/129Xe spin samples

Precision measurement of the Zeeman splitting in a two state system is important for magnetometry, as well as the search for physics beyond the standard model [3-11]. The most precise tests of new physics are often realized in differential experiments that compare the transition frequencies of two co-located clocks, typically radiating on their Zeeman or hyperfine transitions. The advantage of differential measurements is that they render the experiment insensitive to common systematic effects, such as uniform magnetic field fluctuations [8, 11]. That's why clock comparison experiments are often used to study fundamental symmetries of nature. In clock-comparison experiments, the Zeeman-term and thus any dependence on magnetic field fluctuations should drop out for the given combination of Larmor frequencies, i.e.,

display math(1)

For the 3He/129Xe gyromagnetic ratios we take the literature values [12, 13] given by math formula 2.75408159(20). The weighted frequency difference Δω or its equivalent, the weighted phase difference math formula is sensitive to anomalous frequency shifts due to non-magnetic spin interactions of type

display math(2)

where the interaction can formally be written like the magnetic potential energy −μ·B. Examples of non-magnetic spin interactions that can be addressed by clock-comparison experiments are:

  • Search for spin-dependent short-range interactions [14]: math formula
  • Search for a Lorentz violating (LV) sidereal modulation of the Larmor frequency [15]: math formula
  • Search for electric dipole moment (EDM) of Xenon [8]: math formula
  • Search for a gravitoelectric dipole moment [16]: math formula

On a closer look, the effect of Earth's rotation is not compensated by co-magnetometry as well as frequency shifts due to the Ramsey-Bloch-Siegert shift [2]. The latter ones include “self shift”, i.e., coupling of the precessing magnetic moments of the same spin species, as well as “cross talk”, i.e., coupling of the 3He and 129Xe magnetic moments among each other. The time dependences of these frequency drifts, however, are well known. For example, the “self shift” induced frequency shift is directly proportional to the particular net magnetization, i.e., the signal amplitude given bymath formula, and will show up in the weighted frequency and/or phase difference.

Thus, non-magnetic spin interactions can be extracted reasonably well from the measured weighted frequency difference Δω(t) if their preset time dependences (if possible) are almost orthogonal, such that the correlated error approaches the uncorrelated one.

According to the Cramer-Rao Lower Bound (CRLB) [2, 17], the accuracy by which the frequency of a damped sinusoidal signal can be determined is given by

display math(3)

SNR0 denotes the initial signal-to-noise ratio, fBW the bandwidth, and C(T,T2*) describes the effect of exponential damping of the signal amplitude with the transverse relaxation time math formula. For observation times Tmath formula, C(T, math formula) is of order one. Thus, the sensitivity of a co-located 3He/129Xe spin clock strongly depends on the observation time T. Deviations from the CRLB power-law (∼T−3/2), due to noise sources inherent in the co-magnetometer have to be tested in Allan standard deviation plots [18] used to identify the power-law model for the phase noise spectrum. We could show, that the phase noise of our 3He/129Xe spin clock is Gaussian distributed (after subtraction of the frequency- or phase drifts, mentioned above) at least up to observation times of T≈50000s (see Fig. 1) – one essential requirement the derivation of CRLB is based on. Long spin coherence times math formula of macroscopic samples are therefore essential to reach the pHz sensitivity range. As an example: Let the initial signal-to-noise ratio be SNR0 = 10000:1 in a bandwidth of 1 Hz, we obtain by use of Eq. (3) a measurement sensitivity of math formula for an observation time of T = 1 day (math formula). These values can easily be achieved for helium. However, practical constraints in sensitivity of our co-located 3He/129Xe spin sample are presently set by the spin-polarized xenon, where we measure a signal-to-noise ratio of SNR0 ≈ 2500:1 and a math formula of math formula, typically. According to Eq. (3), that results in a reduced sensitivity of math formula. The measurement sensitivity can be further reduced if correlated errors dominate the statistical one (see section 'Constraints on spin-dependent short-range interaction between nucleons' and 'Limit on Lorentz and CPT violation of the bound neutron using a free precession 3He/129Xe co-magnetometer').

Figure 1.

Allan standard deviations (ASD) of the residual phase noise measured in runs called C92 and C02 using nuclear spin precession of co-located 3He and 129Xe gas. In both runs the total observation time was T = 52 000 s. For integration times τ beyond 4 s (fBW = 0.125 Hz) the observed fluctuations decrease as ∝ τ−1/2 indicating the presence of white phase noise. To fulfill the ASD statistics criteria (N − 1) >> 1, only data for integration times τ ≤ 7000 s are shown, where we have N−1 ≥ 6 with N = T/τ.

3 Basic layout of experimental setup and principle of measurement

The instrumental setup is sketched in Figure 2 and discussed in detail in ref. [2]. Thus, only a rough description is given here: In our measurements, we use a SQUID vector magnetometer system, which was originally designed for biomagnetic applications inside the strongly magnetically shielded room BMSR-2 at PTB [19]. In all experiments reported below, the glass vessels containing the spin samples are placed directly below the dewar as close as possible to a SQUID sensor, which detects a sinusoidal B field change due to the spin precession of the gas atoms. Inside the μ-metal shielded room, a homogeneous magnetic field of about 400 nT was provided by two square coil pairs (Bx-coil and By-coil) which were arranged perpendicular to each other (see Fig. 2). The use of two coil pairs was chosen in order to manipulate the sample spins, e.g., π/2 spin-flip. The longitudinal relaxation times of helium and xenon in cells made from low-relaxation GE180 glass [20-22] have been measured before in a conventional NMR setup. For our uncoated glass cells, T1-values were found reaching T1,He 160 h and T1,Xe 11 h, respectively.

Figure 2.

(Left) Horizontal cut view through building, shielded room and annex with data acquisition chamber and sample cell preparation area. The passive shielding factor of the BMSR-2 exceeds 108 above 6 Hz. With additional active shielding the room has a shielding factor of more than 7 × 106 down to 0.01 Hz. (Right): side view of inner room (2.9 × 2.9 × 2.9 m3) seen from the door opening. The pneumatically driven sliding door is indicated by a rectangle with thin dashed lines. The black rectangle is the Dewar housing the SQUIDs. The big open rectangles are the Bx- and By-coil pairs. The small circle below the Dewar represents the sample cell (fixation not shown). The (−x)-axis of the chosen coordinate system points at an angle of ρ = 280 to the north-south direction.

Figure 3 shows the measured signal amplitude of the precessing co-located 3He/129Xe spins. The transverse relaxation times are extracted from the envelope of the decaying signal amplitudes for 3He and 129Xe with math formula h andmath formula h at gas mixtures with pressures of 3He : 129Xe : N2 ≈ (2 : 8 : 35 ) mbar, typically. Nitrogen had to be added to suppress 129Xe relaxation due to the formation of long lived Xe-Xe van der Waals molecules [23]. At present, the relatively short T1,Xe wall relaxation time of 129Xe limits the total observation time T of free spin-precession in our 3He/129Xe clock comparison experiments. Efforts to decrease considerably the 129Xe wall-relaxation times are therefore essential.

Figure 3.

Typical sub-data set of 3.2 s length showing the recorded SQUID gradiometer signal of the precessing 3He/129Xe sample spins (sampling rate: rs = 250 Hz). The uncertainty at each data point is ± 34 fT and therefore less than the symbol size. The signal amplitudes at the beginning of each run were typically AHe ≈ 13 pT and AXe ≈ 4 pT.

4 Constraints on spin-dependent short-range interaction between nucleons

Axions are light, pseudoscalar particles that arise in theories in which the Peccei-Quinn U(1) symmetry has been introduced to solve the strong CP problem [24]. They could have been produced in early stages of the Universe being attractive candidates to the cold dark matter that could compose up to ∼1/3 of the ingredients of the Universe [25]. Several constraints from astrophysics, cosmology, and laboratory experiments have been applied in order to prove or rule out the existence of the axion, i.e., constrain the axions mass ma and/or its couplings. The mass range, in which axions are still likely to exist, could thus be narrowed down to a window reaching from μeV [26] up to some meV [27] (axion window). Most axion searches look for the conversion of a galactic [28], solar [29], or laboratory [30] origin axion into a photon in the presence of a static magnetic field. However, any axion or axion-like particle that couples with both scalar and pseudoscalar vertices to fundamental fermions would also mediate a parity and time-reversal symmetry violating force between a fermion f and the spin of another fermion fσ, which is parameterized by a Yukawa-type potential with range λ and a monopole-dipole coupling given by [31]:

display math(4)

math formula is the spin vector and λ is the range of the Yukawa-force with math formula. Thus the entire axion window can be probed by searching for spin-dependent short-range forces in the range between 20μm and 0.1 m. math formula and math formula are dimensionless scalar and pseudoscalar coupling constants which in our case correspond to the scalar coupling of an axion-like particle to a nucleon (math formula ) and its pseudoscalar coupling to a polarized bound neutron (math formula). math formula is the unit distance vector from the bound neutron to the nucleon. The potential given by Eq. 4 effectively acts near the surface of a massive unpolarized sample („close“ position) as a pseudomagnetic field and gives rise to a shift math formula in the precession frequency of nuclear spin-polarized gases (3He and 129Xe), which according to the Schmidt model [32] can be regarded as an effective probe of spin-polarized bound neutrons. The potentialmath formulais obtained by integration of math formula from Eq. (4) over the volume of the massive unpolarized sample averaged over the volume of the polarized spin-sample. Based on the analytical derivation of math formula for disc-shaped spin- and matter samples with respective thicknesses D and d [33], we can derive the following expression for math formula given by

display math(5)

math formula takes account for the finite size in transverse direction of our cylindrical samples and Δx represents the finite gap between them. math formula is determined numerically for our cylindrically shaped spin- and matter samples (D = 60 mm, øD = 58 mm; d = 70 mm, ød = 60 mm) at "close"-position (Δx = 2.2 mm). As unpolarized matter sample, a cylindrical BGO crystal (Bi4Ge3O12, ρBGO = 7.13 g/cm3) was used, which has a high nucleon number density, is a non-conductive material that shows low Johnson-Nyquist noise and is said to have an unusual magnetism-related behaviour in weak constant magnetic fields (math formula) [34]. In case of a non-zero spin-dependent axion fermion interaction, a shift math formula in the weighted frequency difference (Eq. 1) can be extracted from respective frequency measurements with the BGO in "close" and "distant" position given by

display math(6)

Our result gives math formula nHz (95% C.L.) for the measured pseudoscalar frequency shift. More details on data analysis and estimation of systematic errors can be found in ref. [35]. From the total error δ(Δνsp) = ±7.3 nHz we can derive exclusion bounds for math formulausing Eq. 2 and math formula which are shown in Fig. 4. We have substantially improved the bounds on a spin-dependent short-range interaction between polarized (bound) neutrons and unpolarized nucleons over most of the axion window, tightening existing constrains on axion-like particles heavier than 20 μeV by up to four orders of magnitudes. And there are clear strategies on how to improve our experimental sensitivity: For Δx ≈ 0 mm, i.e., direct contact of the 3He/129Xe spin sample with the unpolarized mass (BGO), our present measurement sensitivity will significantly increase for λ ≤ 10−3 m (see Fig. 4). This can be accomplished by rotating the whole arrangement with respect to the applied magnetic field or vice versa. Since math formula, the effect changes its sign (rotation by π) for the different orientations. Possible changes of magnetic field gradients which may mimic a pseudoscalar frequency shift or even compensate the effect we are looking for drop out to first order due to co-magnetometry. The same is true for field-gradient induced changes of themath formula-times , provided the effect one is looking for leads to an additional linear phase drift, such asmath formula[35] or math formula as it is the case with the search for a gravitoelectric dipole moment (see section 'Search for a coupling of the Earth's gravitational field to nuclear spins').

Figure 4.

The experimental 95% confidence upper limit on math formulaplotted versus λ, the range of the Yukawa-force with math formula. The axion window is indicated by the light grey area. (1): result of [36], (2): result of [37], (3): result of [38], (4): result of [39], (5): result of [40], (6): result of [41], (7): this experiment [35]. The expected results for Δx≈ 0 mm (8) using the same data set demonstrates the gain in measurement sensitivity for λ≤ 10−3 m by reducing the minimal gap between the polarized and unpolarized matter sample (see Eq. (5)). See [14] for bounds on the pseudoscalar short-range force between polarized electrons and unpolarized nucleons. In (4), the relative precession frequency of Hg and Cs magnetometers were measured as a function of the position of two lead masses with respect to an applied magnetic field. Similar to our experiment, a magnetically shielded co-magnetometer cell containing spin-polarized 129Xe and 131Xe was used in (5), measuring the frequency ratio of the two species by recording their FID. (2) uses polarized ultracold neutrons and could improve the limits at the λ length scale of λ≈ 20 μm.

5 Limit on Lorentz and CPT violation of the bound neutron using a free precession 3He/129Xe co-magnetometer

A great number of laboratory experiments have been designed to detect diminutive violations of Lorentz invariance. Among others, the Hughes-Drever-like experiments [42, 43], have been performed to search for anomalous spin coupling to an anisotropy in space using electron and nuclear spins with steadily increasing sensitivity [44, 45]. Lorentz violating theories should generally predict the existence of privileged reference systems. In contrast with the situation at the end of the 19th century, we have a rather unique choice nowadays for such a ”preferred inertial frame”, i.e., the frame where the dipole anisotropy of the Cosmic Microwave Background (CMB) vanishes. Trying to measure an anomalous coupling of spins to a relic background field which permeates the Universe and points in a preferred direction in space as a sort of New Aether wind is a modern analogue of the original Michelson-Morley experiment. The theoretical framework presented by A. Kostelecky and colleagues parameterizes the general treatment of CPT- and Lorentz violating effects in a Standard-Model extension (SME) [46].

To determine the leading-order effects of a Lorentz violating potential V, it suffices to use a non-relativistic description for the particles involved given by [47]

display math(7)

Like in [15, 45], we search for sidereal variations of the frequency of co-located spin species while the Earth and hence the laboratory reference-frame rotates with respect to a relic background field. The observable to trace possible tiny sidereal frequency modulations is the combination of measured Larmor frequencies (see Eq. 1) and the weighted phase differences, respectively. In March 2009, we performed a measurement consisting of 7 runs in series, each with duration of 13 hours at least.

LV spin interactions – if they exist – would result in a temporal change of the phase residuals after subtraction of the general phase drifts (math formula). For that, a piecewise fit function was defined, which is a combined fit to all seven runs, now including the parameterization of the hypothetic sidereal phase modulation

display math(8)

ΩSD is the angular frequency of the sidereal day and ϕSD represents the phase offset of the sidereal modulation at the local sidereal time tSD = 0.4053 (units of sidereal day) at the beginning t0,1 of the first run with ϕSD = 2π·tSD. From that, the RMS magnitude of the sidereal phase amplitude math formula, yielding ΦSD = (2.25 ± 2.29) mrad (95% CL) could be extracted [48] (see Fig. 5). This result is consistent with no Lorentz- and CPT-violating effects. In terms of the SME [47] we can express ΦSD according to

display math(9)
Figure 5.

Sequence of phase residuals (j = 1,.,7) with fit results for the sidereal phase modulation (see Eq. 8). The RMS magnitude of the extracted sidereal phase amplitude math formula is ΦSD = (2.25 ± 2.29) mrad (95% CL).

χ is the angle between the Earth's rotation axis and the quantization axis of the spins (χ = 570). Within the Schmidt model, the valence neutron of 3He and 129Xe determines the spin and the magnetic moment of the nucleus. Thus, 3He/129Xe co-magnetometer is sensitive to the bound neutron parameter math formula. With math formula GeV (95% CL) we deduced an upper limit on neutron spin coupling to possible Lorentz and CPT violating background tensor fields. Together with the recent result from [45] using a K-3He co-magnetometer, where one could further increase the sensitivity by a factor of 5 (95% CL), the tightest constrains on the SME parameters are presently set on the neutron sector.

The present sensitivity of our 3He/129Xe co-magnetometer is limited by the correlated error, which is about a factor of 50 bigger than the uncorrelated error on as and ac. This is caused by a piecewise similar time structure of math formula and the sidereal phase modulation in the fit function of Eq. 8. In order to overcome this obvious limitation, the relatively short transversal relaxation time of 129Xe has to be increased. In March 2012 a new LV-run was performed (data analysis ongoing). This time the measurement periods of coherent spin precession could be extended up to 26 h, i.e., covering the full period of a possible sidereal phase modulation. In addition, the SNR0 of xenon could be improved thanks to the higher degrees of polarization (PXe ≈ 40%).

6 Search for an electric dipole moment of 129Xe

The existence of electric dipole moments (EDMs) of atoms or the neutron would imply a breakdown of both parity P and time-reversal symmetry T and, through the CPT theorem, a breakdown in CP, the combined symmetries of charge conjugation C and parity P. P violation is a well-known feature of the weak interaction. The only known example of CP (and hence T) violation, discovered more than 30 years ago [49], has been found in the decay of the neutral Ko meson and, recently, in heavier neutral B-meson decay channels [50]. The Standard Model (SM) of weak interactions gives the basis for describing the observed CP violation [51], in which CP violation occurs as a phase factor δKM, being one of the free parameters of the weak quark-mixing matrix (CKM-matrix). In the leading order, δKM only causes CP violation in flavor changing processes. Since this complex phase factor only enters in matrix elements where heavier quarks are involved, SM contributions to particle EDMs in particular the neutron EDM are of second order in the weak interaction coupling constants and hence are very small being of order 10−31 to 10−33 e cm. SM contributions to the electron EDM occur at the three loop level and are de ≈ 10−37 − 10−40 e cm [52]. Thus, the predicted EDMs are at least four orders of magnitude below the present experimentally established limits and a search for a permanent EDM is still hailed as an unambiguous test of CP violation beyond the SM. Extensions to the SM, such as additional Higgs fields, right handed currents, or super symmetric partners, give rise to dipole contributions which are of first order. These are necessarily much larger and for the neutron EDM typically of the order 10−27 to 10−26 e cm [53].

EDMs are also connected with another fundamental puzzle: the Baryon Asymmetry of the universe. The asymmetry is generally described by the ratio rB, between the number of baryons and the number of photons in the universe today. This ratio can be related to the number of baryons and antibaryons at the time of baryon freeze-out in baryogenesis models [54]. The observations indicate that rB ∼ 6 × 10−10, which is about 9 orders of magnitude larger than expected in baryogenesis models based on the SM. A possible explanation for this huge discrepancy was suggested by Sakharov [55]. As a consequence, it is expected that observations and theory could be reconciled if additional sources of CP violation are at work.

Historically, the non-observation of particle EDM has ruled out more speculative models than any other single experimental approach in particle physics. At present, and in future, EDM precision measurements will continue to constrain severely proposed models of new physics. In principal there is no preferred system to search for an EDM. Investigation of different systems is required to discriminate between various EDM sources: intrinsic leptonic, intrinsic hadronic, those resulting from interactions in composite particles, or, possible CP-odd forces between constituents in, e.g., atoms. In composite systems, such as molecules and atoms, the coupling to, and hence the visibility of, constituent EDMs may be significantly enhanced due to internal fields. The highest sensitivity to fundamental CP-violation today comes from measurements on the neutron [56], the diamagnetic 199Hg atom [57] (predominantly sensitive to the nuclear EDM (η)) and the paramagnetic 205Tl atom [58] or YbF-molecule [59] (predominantly sensitive to the electron EDM (de)). All of the effects mentioned above become much more prominent for heavy atoms, and so an atomic EDM tends to scale as Z2 or Z3. For this reason atomic EDM measurements can set much more stringent limits on certain CP violating processes than neutron EDM measurements can. The most precise EDM limit was measured in the diamagnetic atom 199Hg (dHg < 3.1 × 10−29 ecm ).

Several different theorists [60, 61] have gone beyond this order of magnitude estimate and predicted quantitative values for these CP-violating coefficients (de, CT,CS,CPS, and η). From these, an expression for dXe can be found

display math(10)

Such coefficients are generally determined to perhaps 30%, given the complicated theory involved. With our initiative to search for a Xe-EDM using co-located 3He/129Xe spin clocks, we want to get more stringent limits than the 199Hg experiment. The key issue for a high-sensitivity EDM detection are the long spin-coherence times: Let Tm be the measurement time. A repetition (n) of short measurements of free spin precession (T) with Tm = n·T results in a final accuracy of frequency determination of (see Eq. 3)

display math(11)

whereas a measurement of uninterrupted precession gives math formula. Hence, the gain in sensitivity is g = Tm/T. In the 199Hg-Experiment [57], the possible EDM frequency shift was extracted from the decay of free spin precession of the Hg-atoms using an optical detection method with math formula being the characteristic time constant for the exponential damping of the signal amplitude, there. Since the limiting time constant for coherent spin-precession of our 3He/129Xe co-magnetometer is presently set by math formulaof xenon with math formula, our gain in EDM sensitivity is g ≈ 160 over a measurement period of Tm ≈ 8h. Then, like in the 199Hg-Experiment, the measurement sensitivity will only scale with 1/math formula.

Fig. 6 shows the sketch of the experimental setup. Again, the weighted frequency difference (Eq. 1) is measured both for electric field parallel and antiparallel to the applied B0-field, i.e., math formulaand math formulawith

display math(12)
Figure 6.

Sketch of experimental setup to measure the EDM of 129Xe. (1) cylindrical container made out of conducting plastic which is at ground potential, (2) 3He/129Xe gas container made out of a cylindrical glass tube (ø = 10 cm, l = 5 cm) with silicon discs used as lids. Not shown, stem with glass valve to fill in the polarized gases together with SF6 which is used as buffer gas (3He:129Xe:SF6 ≈ (2:8:50) mbar), (3) HV-feedthrough and electrodes (conducting plastic), (4) SF6 gas at ∼ 1 bar to minimize leakage currents, (5) dewar housing low-temperature SQUIDs; gradiometric sensor combinations (6 in total) are used in order to suppress environmental disturbance fields like vibrational modes.

Using math formula, the sensitivity limit on dXe can be extracted to be

display math(13)

A first analysis of our March 2012 run shows, that we can measure the spin precession frequencies with an accuracy of Δν ≈ 0.1 nHz per day. Even for a moderate electrical field of E = 2kV/cm applied between the lids (silicon semiconductors) of a cylindrical glass vessel containing the 3He/129Xe spin sample, we will reach a xenon EDM sensitivity of math formula. Thus, an overall sensitivity of math formula ecm is envisaged, after accumulation of sufficient statistics corresponding to ∼100 days of data acquisition, typical for EDM-type experiments.

Because the intrinsic sensitivity of 129Xe to underlying physics of CP-violation is less than for 199Hg, this experiment must in fact have much better rejection of systematics than the 199Hg experiment has now, in order to get a better ultimate sensitivity. A worrisome source of magnetic fields correlated with the high voltage are steady state leakage currents flowing between the electrodes of the cell. Using a co-magnetometer (absent in the 199Hg experiment) leakage currents can be suppressed much more efficient than in spatially separated cell geometries, in particular if higher magnetic multipoles are involved. Nonetheless, we have independent measures to monitor the leakage currents. Our SQUID gradiometers (6 in total) are very sensitive devices and only react on magnetic field changes. Thus, we will use them to monitor the leakage currents, too. The 199Hg-experiment has some potential systematic effects which are absent in our experiment. For example light induced false EDM effects: DC and AC stark shift, gradient in light intensity coupled to a magnetic field gradient [57]. Furthermore, possible problems with geometric phases due to motional magnetic fields and applied field gradients [62] have to be considered. 3He is most sensitive to false EDM effects due to geometric phases, but these effects can be kept low (math formula ecm ), since SF6 (∼50 mbar) is used as buffer gas. We even have the flexibility to vary the buffer-gas pressure, the cell radius, and the magnetic field B0. To summarize: We do see much less potential systematic effects with our 3He/129Xe-comagnetometer arrangement.

7 Search for a coupling of the Earth's gravitational field to nuclear spins

The equivalence between the gravitational and inertial masses of unpolarized matter has been verified to high precision. Very little is known, however, about the microscopic properties of gravity, and there remains the possibility that sensitive experiments will uncover evidence for symmetry violations or other new phenomena associated with this interaction. In particular, the notion that polarized objects may violate the equivalence principle through a coupling of intrinsic spin to gravity has been considered by a number of authors [63-68]. An interaction of type math formula, where math formula is the spin operator of the nucleus, math formula is the unit vector pointing towards the center of the Earth, and math formula is the spin-dependent component of the gravitational energy , violates both parity and time-reversal symmetry and could result, for example, from a breakdown of the equivalence principle for spin-polarized matter. In [16], an upper limit on A′ with math formula eV corresponding to math formula was obtained by measuring the ratio of nuclear spin-precession frequencies of 199Hg and 201Hg atoms for two orientations of magnetic field relative to the Earth's gravitational field. The same measuring principle is applicable to the co-located 3He/129Xe spin-sample, where we expect a considerably higher measurement sensitivity of ∼0.1 nHz/day (see section 'Search for an electric dipole moment of 129Xe'). The essential requirement is that the change of magnetic field doesn't induce false effects. That mainly concerns field gradient dependent correlated changes of the math formula-times of 3He and 129Xe, discussed already in section 'Basic layout of experimental setup and principle of measurement'. Although the linear phase drift math formula is insensitive to possible changes of math formula, the impact of themath formula-dependence of higher order terms on math formula has to be taken into account above a certain sensitivity level.

In order to collect first experiences, feasibility studies were performed by adjusting the currents in the twin coil set shown in Fig. 1. The direction of the static field could be oriented in any direction within the horizontal plane, while its strength was left unchanged. With this set-up, the precession decay of hyperpolarized 3He gas was measured for various field orientations α. Fig. 7 shows the variation of the math formula-relaxation times that were obtained from these measurements when the field orientation was varied in steps of 45°. The data show a clear and reproducible periodicity with that is emphasized by fitting a function with a circular periodicity to the data. At α = 70°, both 3He and 129Xe exhibit the longest T2*, indicating that with this orientation of the instrumental field, the gradient of the applied field compensates best the gradient of the residual field inside BMSR-2. There are several strategies on how to reduce the “strong” math formulavariation: a) use field orientations, even if they are not exactly opposed, where the math formula-values are equal (see Fig. 7) and/or b) use additional field-gradient coils to match the field gradients across the sample cell for the selected field orientations.

Figure 7.

Dependence of the measured transversal relaxation time T2* of 3He and 129Xe on the orientation of the applied field. The solid line is a fit-function with circular periodicity to guide the eyes. The field was slowly rotated (math formula) in steps of 450 that took about 1 min. Then T2* was measured by monitoring the exponential decay of the precessing spins. During the T2* measurements (∼15 min), the direction of the field has not changed. The drawn bar indicates field orientations which differ by Δα = 1450 and provide the same T2* values.

8 Conclusion

Nuclear spin clocks, based on the detection of free spin precession of gaseous, nuclear polarized 3He or 129Xe samples with a SQUID as magnetic flux detector can be used as ultra-sensitive probe for non-magnetic spin interactions, since the magnetic dipole interaction (Zeeman-term) drops out in case of co-located spin samples. With the long spin-coherence times, measurements of uninterrupted precession of T ∼ 1 day can be achieved at the present stage of investigation. Together with a signal-to-noise ratio which by far exceeds 1000:1 in a bandwidth of 1 Hz, thanks to an exceptional low system noise inside BMSR-2, the sensitivity to trace tiny frequency changes reaches ∼ 0.1 nHz/day.

We reported on recent results on the search for a new spin-dependent P- and T-violating interaction between nucleons mediated by light, pseudoscalar bosons (exclusion plot) and the search for a LV sidereal modulation of the Larmor precession (upper limit) that sets the tightest constrains on the SME parameters of the bound neutron. Finally, our challenging project to measure the EDM of 129Xe down to a sensitivity limit of math formula ecm was presented. All experimental investigations will benefit considerably by the increase of the still moderate longitudinal wall relaxation time T1 of xenon (∼ 11h), which is the bottleneck to reach math formula-times > 100 h as it is the case for 3He, already.