Low-frequency 129Xe nuclear spin oscillator with optical spin detection

Physics Letters A 376 (2012) 1924–1929

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Physics Letters A www.elsevier.com/locate/pla

Low-frequency

129

Xe nuclear spin oscillator with optical spin detection

A. Yoshimi a,∗,1 , T. Inoue b , T. Furukawa c , T. Nanao b , K. Suzuki b , M. Chikamori b , M. Tsuchiya b , H. Hayashi b , M. Uchida b , N. Hatakeyama b , S. Kagami b , Y. Ichikawa b , H. Miyatake b , K. Asahi b a b c

RIKEN Nishina Center, 2-1 Hirosawa, Saitama 351-0198, Japan Department of Physics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro, Tokyo 152-8551, Japan Department of Physics, Tokyo Metropolitan University, Hino-shi, Tokyo 191-0065, Japan

a r t i c l e

i n f o

Article history: Received 28 June 2011 Received in revised form 29 March 2012 Accepted 20 April 2012 Available online 26 April 2012 Communicated by P.R. Holland Keywords: Nuclear spin oscillator Frequency precision Spin polarization Electric dipole moment

a b s t r a c t We have constructed a 129 Xe nuclear spin oscillator which executes a self-sustained oscillation through an external feedback loop with optical detection of nuclear spin. The oscillator is capable of operating at frequencies much lower than the conventional nuclear spin maser. A method for efficient optical detection of spin has been developed and applied to the nuclear spin oscillator, and the frequency characteristics of the oscillator at low frequencies has been investigated. The spin oscillator was operated at frequencies 2.5–36 Hz. The frequency performance of the oscillator is discussed in relation to a planned search for an atomic electric dipole moment taking advantage of the present oscillator scheme. © 2012 Elsevier B.V. All rights reserved.

1. Introduction

Since the process of spin exchange between an optically polarized alkali atom and the nucleus of a noble gas atom was first recognized [1,2], noble gas atom with a highly polarized nuclear spin has been a useful tool in various research fields, such as fundamental physics [3–5], hadron physics [6], and other applications including material and medical sciences [7–9]. In particular, 3 He and 129 Xe, whose nuclear spin is 1/2 and is therefore free from the quadrupole interaction, are often adopted because of their extraordinarily long spin relaxation times. This feature is advantageous in an experiment searching for a permanent electric dipole moment (EDM) in atoms where precise measurement of the spin precession frequency is required. Non-zero EDM of an atom or a particle violates the time reversal symmetry, and the EDM search has been an important objective in particle physics [10,11]. In pursuing a high precision measurement of spin precession frequency for the EDM search, one of the most desirable features is a long observation time for a continued precession.

*

Corresponding author. E-mail address: [email protected] (A. Yoshimi). 1 Present address: Research Core for Extreme Quantum World, Okayama University, Tsushima-Naka 3-1-1, Okayama 700-8530, Japan. 0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.04.043

Previously, we demonstrated the realization of a 129 Xe nuclear spin oscillator in which the coherent precession of spin is maintained beyond its transverse relaxation time T 2 , by incorporating an external feedback loop based on optical detection of the nuclear spin [12]. This mechanism of oscillation is quite parallel to that of a conventional spin maser in which case the feedback occurs naturally through coupling of the magnetization vector of spins to a resonating coil surrounding them [13,14]. In fact a conventional spin maser of 129 Xe was used in the experiment which obtained the most stringent upper limit of the atomic EDM of 129 Xe [3]. By virtue of a superior sensitivity provided by the optical spin detection, the present spin oscillator is capable of operating at much lower frequencies than that of conventional nuclear spin masers. The concept of the artificial masing mechanism for atomic spin has been mentioned by Dehmelt [15], and its application to the search for an atomic EDM in Rb has been examined [16]. The aim of the present Letter is to report the result of study to achieve high precision and stability in frequency of the 129 Xe nuclear spin oscillator with external feedback by optical spin detection. Efforts have been made to suppress the fluctuation of the applied static magnetic field B 0 , which has been one of the main sources of frequency fluctuations in spin masers, by adopting lower B 0 fields for operating the oscillator. The frequency characteristics of a low-frequency oscillator have been investigated. Also, the frequency stability of the spin oscillator has been improved by suppressing fluctuations in the current in the magnet for the B 0 field. At present, the

A. Yoshimi et al. / Physics Letters A 376 (2012) 1924–1929

Fig. 1. (a) A schematic representation of the experimental setup for the optical detection of the spin precession of 129 Xe nuclei.

129

1925

Xe nuclear spin precession. (b) A block diagram of the detection system for

measured frequency precision is 9.3 nHz for a measurement time of 3 × 104 s. 2. 129 Xe-based low-frequency nuclear spin oscillator with optically coupled feedback As discussed in [12,13,17], a self-sustained mode of spin oscillation (spin maser) occurs as a special steady-state solution to the set of Bloch equations which include the pumping effect and the effect of the feedback field B fb : The precession of the polarization vector P of spins in a static field will be maintained beyond their intrinsic transverse relaxation time T 2 , when the transverse field B fb oscillates in synchronism with the spin precession under the condition that (i) the amplitude of B fb (t ) is proportional to the transverse polarization P T (t ), (ii) the phase of B fb (t ) is always by π /2 in advance from the spin precession, and (iii) B fb (t ) points to the direction such that the spin polarization tends to be more tilted off the pumping direction by the torque. The B fb field, synchronized with the spin precession, thus should come as a feedback field from the spin precession. The frequency precision and stability of the maser oscillation can be improved if the maser operates with lower static fields B 0 because the fluctuation in frequency is governed by the absolute value of fluctuation amplitudes δ B 0 . In order to realize the maser oscillation in static fields as low as 1 μT, we adopt a masing scheme with an artificially produced feedback field from observed phase and amplitude of the spin precession. Fig. 1 shows the experimental setup for a spin-polarized 129 Xe maser with the artificial feedback system. The magnetic shielding and stability of the B 0 field have been improved from those of the previous setup [12,18]. The nuclear spin of 129 Xe was polarized through spin exchange with optically pumped Rb atoms [2]. A spherical glass cell (18 mm in diameter) containing Xe gas, buffer gas (nitrogen) and a small amount of Rb vapor was prepared from Pyrex glass whose inner wall was coated with a siliconebased coating agent (SurfaSil). The cell typically contained a gas of 79%-enriched 129 Xe at a partial pressure of 230 torr at the room temperature. The cell was mounted inside a cylindrical 4-layer magnetic shield to reduce the effects of environmental magnetic field noise. The shielding factor of about 104 was obtained: an improvement of almost one order of magnitude from the previous setup. The cell was irradiated with a circularly polarized pumping light in order to polarize the Rb atoms. The cell temperature was kept at 71.8 ± 0.3 ◦ C so that the Rb vapor atomic density of about 7.3 × 1011 atom/cm3 was estimated. The phase and amplitude of the precession of 129 Xe spins were monitored with a probe laser light traversing the cell perpendicularly to the pumping light. The probe light was obtained from a 15 mW tunable

Fig. 2. The current stabilities with the new and the previous current source measured by a precise ammeter.

DFB diode laser (DL-DFB, Toptica Photonics Co., Ltd.), whose wavelength was tuned to the D1 absorption line of Rb within frequency widths 0.5–4 MHz. A photoelastic modulator (PEM) was inserted before the cell, which modulated the circular polarization of the probe light at 50 kHz. The transverse polarization of the 129 Xe nuclear spins was transferred to the Rb atoms through spin exchange (re-polarization). The re-polarization is efficient when the precession frequency of the 129 Xe is smaller than the spin exchange rate of the re-polarization. With this condition satisfied, the intensity of the transmitted probe light is modulated by the precession frequency of the 129 Xe due to the dichroism of Rb atoms with transverse polarization. The intensity of the transmitted probe light was phase-sensitively detected with two lock-in amplifiers, one at the PEM driving frequency (50 kHz) and the other at the precession frequency of 129 Xe, as shown in Fig. 1(b). A static field B 0 = 3.04 μT was produced with a solenoid magnet installed inside the innermost layer of the magnetic shield. At this field the Larmor frequency for the 129 Xe spin is 36.0 Hz, sufficiently low as compared to the repolarization time scale of 0.1 ms as required for the optical detection scheme described above. For the current for the solenoid magnet, a new current source (PSE-11, Emac Co., Ltd.) equipped with low-noise integrated circuits (ICs) was specially designed for the present experiment. Two

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A. Yoshimi et al. / Physics Letters A 376 (2012) 1924–1929

Fig. 3. (a) Spin maser oscillation signal observed in a time span of 24 hours. (b) Transient pattern in the initial spin maser oscillation. (c) Steady state oscillation after the transient settled. The signals shown in the ordinates represent the beat between the spin detection signal and a 36.12 Hz fixed frequency reference signal for a lock-in amplifier.

important issues were considered in the fabrication of this new current source: the suppression of the current fluctuation coming from (i) fluctuations in the power line and (ii) the variation in temperature. For the issue (i), a precision voltage reference IC was introduced while the reference voltage had been taken from a three-terminal regulator in the previous current source. To improve the stability concerning the issue (ii), low-noise, high-stability ICs (OP-27; the equivalent input noise voltage V noise = 80 nV, the temperature coefficient 0.2 μV/◦ C) are adopted for all the operational amplifiers in the new current source instead of the previous ones (OP-07; V noise = 600 nV, 1.3 μV/◦ C). Additionally, resistors made of manganese were employed because of the small temperature coefficient of resistivity (∼10 ppm/◦ C) instead of the fixed metal oxide film resistors which had been used in the previous current source. This new current source was encapsulated in a three-layer case for insulation and noise shielding. The stabilities of the solenoid currents with the new and the previous current sources during 2 × 104 s were compared in Fig. 2. These currents were measured with a precision ammeter (DMM 2002, Keithley Inst. Inc.). The measured current fluctuation was typically 5 nA (δ I / I ∼ 10−6 ) for the new current source in this time scale, which is an improvement of 2 orders of magnitude from that measured with the previous current source. In the present experiment with B 0 = 3.04 μT, a current of 7.35 mA was supplied from this current source. In order to bring the present spin oscillator into operation, the optically detected precession signal should be converted into a feedback field. Generation of B fb is accomplished by employing an operational amplifier in which the required feedback signal is

Fig. 4. Steady state oscillations observed at three low frequencies: (a) ν0 = 17.7 Hz, (b) ν0 = 8.9 Hz, (c) ν0 = 2.5 Hz. The strength of the static field adopted in the individual operations are indicated in the respective panels.

produced by combining the phase-sensitively detected precession signal and the reference signal used for the lock-in detection [12, 18]. Fig. 3(a) shows a typical signal of the spin oscillation, carried out for a 24 hours duration. After the 129 Xe nuclei were polarized in the absence of B fb , the output of the analogue operational circuit was connected to the feedback coil at t = 0 to switch on the B fb field. The precession signal appeared with a time constant of 100 s after the B fb field was applied. The signal then approached a steady-state oscillation which eventually settled after the transient on a time scale of several thousand seconds, as shown in Fig. 3(b) and (c). The present maser scheme with optical spin detection may be operated at lower frequencies (hence lower magnetic fields). In fact, we confirmed that the present oscillator operates with stable amplitudes at frequencies down to 2.5 Hz as shown in Fig. 4(a)–(c). Here the oscillator signals with three B 0 settings, B 0 = 1.50 μT, 0.76 μT and 0.21 μT, are shown. The stabilities in the observed oscillator amplitudes A in these operations remain at almost the same level, δ A / A = 1–3%. 3. Frequency precision and stability Fig. 5(a) shows the Fourier transform of an oscillator signal obtained with the new current source for the B 0 field. For comparison, a similar plot is presented in Fig. 5(b) for the oscillator signal obtained with the previous current source. The magnetic field and the order of the operation time were similar for the two plots

A. Yoshimi et al. / Physics Letters A 376 (2012) 1924–1929

Fig. 5. (a) Fourier spectrum obtained when the newly introduced current source was used for the oscillator operation. The measurement time was 3 × 104 seconds. (b) Fourier spectrum obtained when the previous current source was used for the oscillator operation. The measurement time was 1 × 104 seconds.

[B 0 = 3.04 μT and T m = 3 × 104 s for (a), and B 0 = 2.87 μT and T m = 1 × 104 s for (b)]. The relatively large width of 2.5 mHz and the two-peak structure observed for the previous setup in Fig. 5(b) would indicate that some temporal drifts rather than simple random fluctuations of the B 0 field might dominate the width of the frequency spectrum. With the new current source, as shown in Fig. 5(a), the frequency width is reduced to 50 μHz, an improvement by a factor 50. The remaining width of frequency, 50 μHz, may come from various sources of drifts and fluctuations such as environmental magnetic fields and cell temperature. The major part of it still seems to originate from the fluctuation in the current in the solenoid magnet since the standard deviation of the measured current with a high precision ammeter during this measurement was 7.7 nA, which corresponded to fluctuations of 3.0 pT in the applied B 0 field and frequency width of 30 μHz. The maser beat signal from the lock-in amplifier and its quadrature signal were recorded at a sampling rate of 20 Hz. The phase of oscillation

φ(t ) = tan−1 ( V y / V x )

(1)

was extracted from the two signals V x (t ) and V y (t ). Fig. 6(a) shows the phase evolution extracted from the 3 × 104 s-long measurement. The average frequency over the measurement interval was obtained by performing a least-χ 2 fitting of a linear function

φ(t ) = ωt + φ0

(2)

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Fig. 6. (a) Precession phase as calculated from the observed V x and V y . (b) Phase deviation from the fitted linear function in (a).

to the obtained phases. The phase residual from the fitted linear function is shown in Fig. 6(b). The estimated frequency precision, or the minimal variance of the oscillator, for the data presented in Fig. 6(a) is found to be 9.3 nHz. The frequency precision thus estimated coincides with the error σω assigned to the slope parameter ω of the function φ(t ) = ωt + φ0 fitted to the data, and is given by σω2 = σφ2 N /Δ. Here, N denotes the number of sampling points for phase σφ the error of the   data, individual values of phase, and Δ = N tn2 − ( tn )2 . By inserting an expression

Δ=

1 12

N 2 ( N + 1)( N − 1)( t )2 ≈

1 12

N 4 ( t )2

(3)

for N equally spaced sampling points with an interval time t, the frequency precision σν is written as



σω σν = = 2π

12σφ2 t 2π

−3/2

Tm

,

(4)

where T m = N t denotes the total measurement time. This equa−3/2 tion indicates that σν changes as σν ∝ T m , provided the noise in the maser operation is governed by a white phase noise σφ . Empirical errors assigned to the oscillation frequencies determined from the measured phases are plotted as a function of the measurement time T m in Fig. 7. The solid, dotted and dashed lines −3/2 −1 and represent, respectively, the hypothetical σν ∝ T m , σν ∝ T m

−1/2 σν ∝ T m dependences on T m . The empirical σν seem to follow −3/2 line up to around 103 s, while for T m > 103 s they the σν ∝ T m

tend to lie off this line indicating that noise components other

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A. Yoshimi et al. / Physics Letters A 376 (2012) 1924–1929

Fig. 7. Frequency precision of the spin oscillation. The abscissa represents the standard deviation of the frequency ν determined by fitting a function φ(t ) = 2π ν t + φ0 to the observed precession phases φ from t = 0 to t = T m . Solid, dotted and dashed lines are the presentation of three cases with power laws and

−1/2 σν ∝ T m respectively.

−3/2 −1 , σν ∝ T m , σν ∝ T m

than the white phase noise affect the frequency precision in long−1/2 term measurements. It should be noted that the trend σν ∝ T m , observed locally for T m = 103 –104 s, is considered to arise from the contribution of white f requenc y noise: If the oscillation signal is governed by the white frequency noise, the phase noise σφ in Eq. (4) is no longer a T m -independent parameter but should show √ a random walk-type dependence, σφ ∝ t, resulting in σφ (t =

√

−1/2

T m ) ∝ T m so that σν (t = T m ) ∝ σφ (t = T m )/2π T m ∝ T m . Thus, the observed trend of σν for T m > 103 s is quite indicative of that white frequency noises partially affect the frequency precision. The frequency noise may arise from several types of fluctuation, such as fluctuations in the applied B 0 field and in the local magnetic field produced by the coexisting polarized Rb atoms. The whole time behavior of σν for T m < 3 × 104 s, being neither σν −3/2 −1/2 of ∝ T m nor of σν ∝ T m , is likely to be due to mixing of different kinds of noise. Finally, for even longer measurement times (T m > 3 × 104 s), σν appears to rise again, indicating the presence of other low-frequency noises, such as the linear frequency drift or the random walk frequency noise. This type of frequency drift arises from long-term drifts in magnetic fields (the applied field and the environmental field) and temperature, the investigation of which will be described elsewhere. 4. Application to an EDM experiment One important application of the present low-frequency spin oscillator with optical spin detection would be that to an experimental search for EDM, as stated in Section 1. Recently, a number of experiments have been performed, proposed, or are in the preparation stage which aim to search for EDM in neutron [19], diamagnetic and paramagnetic atoms, molecules [20], and even charged particles such as muon and ions [21]. Among them the search for EDM thus far carried out in diamagnetic atoms

are for atoms of 199 Hg and 129 Xe. The most stringent upper limits at present are d = (0.7 ± 3.3) × 10−27 e cm [3] for 129 Xe and d < 3.1 × 10−29 e cm for 199 Hg [22]. The frequency precision obtained with the present 129 Xe nuclear spin oscillator in a 3 × 104 s measurement time reached 9.3 nHz, as observed in Fig. 7. The above precision in frequency has been achieved without any attempt to compensate drifts in the magnetic field. The investigation of the correlation between the frequency fluctuations and environmental drifts (those in the magnet current, cell temperature, environmental magnetic field, etc.) for the present setup will be reported elsewhere. The presently obtained value of frequency precision of 9.3 nHz, if one simply put in a scale for EDM, would amount to an EDM equivalent precision of 9.6 × 10−28 e cm for a case that an electric field of 10 kV/cm is applied. In order to achieve an actual EDM sensitivity of this order, however, one has to bear two points in mind which are crucial to the frequency stability: the interaction between the Xe nuclei and Rb atoms, and the maser amplitude fluctuation. The Xe–Rb coupling, which induces a frequency shift because of the relatively high density of the polarized Rb atoms in the present setup, will be largely suppressed by employing a split cell configuration in the EDM experiments in which a heated pumping cell and a cooled masing cell are connected with a transfer tube [13]. The maser amplitude fluctuations observed (∼ 1%) in the present setup would produce a frequency fluctuations of

ν = 0.01 × γXe B T,Xe / tan θ , where B T,Xe indicates the transverse magnetic field produced by the masing Xe nuclei, and θ is the angle between the masing spin and the longitudinal axis. In order to suppress the frequency shift or fluctuation from this phenomenon, temperature stabilization in the cell box, introduction of a stable pumping laser etc. would be needed. The introduction of a high sensitivity magnetometer and a feedback control of the current source for the B 0 field are currently under way [23]. We expect that such efforts would allow the σν ∝ T −3/2 trend to hold beyond 103 s, and would thus enable the frequency precision of 1 nHz in a few-days measurement. 5. Summary A low-frequency nuclear spin oscillator has been developed for use as a new means to perform a high-precision measurement of the nuclear spin precession. This oscillator at frequencies as low as 2.5–36.0 Hz have proven to run through an artificial feedback of optically detected nuclear precession. In this regard, the optical detection of the nuclear spin precession of 129 Xe and the frequency performance of the oscillator were investigated in the present study. The frequency width of the present oscillator was greatly improved from the conventional masers. Until present, a frequency precision of 9.3 nHz has been achieved in a measurement time of 3 × 104 s. The application of the present oscillation to a search for EDM is currently under progress. Acknowledgements This work was supported by the Grant-in-Aid for Scientific Research (No. 20340067, No. 21104004 and No. 21244029) of the Ministry of Education, Culture, Sports, Science, and Technology, Japan. We also acknowledge the financial support from the Global Center of Excellence Program by MEXT, Japan, through the “Nanoscience and Quantum Physics” Project of Tokyo Institute of Technology. References [1] B.C. Grover, Phys. Rev. Lett. 40 (1978) 391. [2] W. Happer, E. Miron, S. Schaefer, D. Schreiber, W.A. van Wijngaarden, X. Zeng, Phys. Rev. A 29 (1984) 3092.

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