The Neutron Electric Dipole Moment - Essay Example

The Neutron Electric Dipole Moment (Neutron EDM) 2 August Table of Contents Tile Page Acknowledgment Table of Contents List of Figures CHAPTER I Introduction CHAPTER II Background CP and T Violation The Neutron EDM Ultra-Cold Neutrons Modelling of Neutron Spin Summary CHAPTER III Experimental Techniques Room Temperature Experiment: Apparatus Ramsey’s Technique of Separated Oscillatory Fields Mercury Magnetometer Sensitivity Summary CHAPTER IV Systematic Uncertainties Systematic Uncertainties Overview Geometric Phase Effect Magnetic Dipoles Summary CHAPTER V Modelling of Systematic Effects Modelling of Magnetic Dipoles Depolarization Studies Effects of Gravity Summary CHAPTER VI Conclusions BIBLIOGRAPHY CHAPTER III Experimental Techniques A neutron EDM is indicated by a change in the Larmor frequency (also known as the neutron’s resonant frequency) with respect to the electric field E.1 Provided that parallel and anti-parallel magnetic (B) and electric fields are present; the precession frequency v is given by , Thus the ‘frequency difference between the parallel and anti-parallel cases’2, where it must be ensured that the magnetic field does not change, is Furthermore, the measure of the neutron EDM is obtained as This chapter will provide an in-depth review of the different experimental techniques employed in the study of neutron electric dipole moment which includes the ILL room-temperature experiment, Ramsey’s technique of separated oscillatory fields and mercury magnetometer. It will also include data and analysis of the present progress and development in the discovery of neutron EDM. Room – Temperature Experiment: Apparatus The room – temperature experiment was carried out in Institut Laue-Langevin (ILL) and the final results from this research were published in 2006.3 4 A thorough discussion of the experiment’s apparatus and flow process are included in this review. The figure below depicts the schematic diagram of the room-temperature experiment at the ILL. Figure 1 Neutron EDM Room-temperature Experiment Apparatus in ILL.5 6 7 Ultra-cold neutrons are utilized in the room-temperature experiment; these are generated by the UCN turbine. To begin the process, UCNs ‘entered the apparatus from the lower right (as indicated by the red arrow in Figure 1) and flowed upwards to the polarizer foil’.8 Harris described the UCNs behaviour as similar to ‘a diffuse gas’.9 He further explained, Those of the correct spin passed through the foil and continued to rise until they reached the storage bottle at the heart of the apparatus. The bottle was located in a 10 mG (1 μT) vertical magnetic field; four layers of mu-metal were used to shield out external fields, including that of the Earth. After a filling period of about 20 seconds, the neutron door was closed, and the Ramsey sequence was applied to the trapped neutrons. The door was then opened, and the neutrons fell back down to the polarizer, which then acted as an analyser. Those in the original spin state could pass through and down to a gaseous 3He neutron detector (the curved guide tube from the source having been moved aside in favour of a vertical guide leading to the detector). Neutrons of the “wrong” spin state, which bounced off the polarizer, were counted in their turn by employing a fast-passage adiabatic spin flipper to reverse the direction of the spins of the neutrons in the guide tube just above the polarizer: this spin flipper consisted simply of a solenoid wrapped around the guide tube, situated in a region of magnetic field gradient, to which a high-frequency (20 kHz) alternating current was applied.10 The time needed to process each batch of neutrons takes about four (4) minutes. In Figure 2, the Ramsey curve is shown marking four points which represents the applied frequency used successively in between neutron batches. The electric field was regularly, usually every hour, reversed by applying a 10kV (or more) to the closure of the neutron storage container. The system’s resonant frequency was determined by ‘fitting successive neutron counts to a sinusoid; this is clearly exemplified by the ‘central valley of the Ramsey curve’ in Figure 2.11 Figure 2 The number of neutrons remaining with their spins unflipped after application of Ramsey separated oscillatory fields, as a function of the frequency.12 13 In Figure 3, the behavior of the measured resonant frequency over 24 hours was shown by the points marked raw neutron frequency; it was noted that there is no observable correlation with the hourly electric field reversal. Moreover, the figure below reveals apparently ‘the necessity to measure and to control the magnetic environment precisely’.14 Figure 3 Neutron resonant frequency measured over a 26 hour period, before and after magnetic field drifts corrections.15 16 Ramsey’s Technique of Separated Oscillatory Fields Neutron EDM measurement attempts were based primarily upon the application of Ramsey’s technique of separated oscillatory fields to free neutrons.17 18 This technique involves the magnetic moment or ‘spin’ of neutrons. The simplified illustration and basic explanation of Ramsey’s measurement principle used in Ramsey’s technique of separate oscillatory fields is shown in Figure 4 and 5. Figure 4 Ramsey’s technique of separated oscillatory fields19 20 Figure 5 Ramsey’s Neutron EDM Measurement Principle.21 22 The number of spin-up neutrons left behind as a function of the frequency of the applied RF (Radio Frequency) pulses is shown in Figure 2. The highest number of neutrons have their spins flipped downwards (the fraction being limited by depolarization) is exactly at resonance; ‘1/2T away from resonance, the acquired phase difference is 180◦, and the spins are not flipped’.23 Harris24 further explained: Absolute frequency measurements are not necessary; the EDM depends upon measuring a frequency difference when the electric field direction is reversed. In order to achieve the maximum sensitivity to such frequency shifts, the experiment operates halfway up the central valley in the regions marked by “×” on the curve. Here, the slope is steepest, so a small frequency shift produces a large change in the number of spin-up neutrons counted. Mercury Magnetometer An inventive atomic mercury magnetometer was used to monitor the magnetic field within the neutron storage container of the ILL room-temperature experiment (as discussed earlier on).25 26 Its design is comparable to the cell used in the 199Hg EDM measurement.27 A comprehensive illustration of the construction, operational standard and output from the mercury magnetometer is shown in Figure 6. ‘The effect of correcting the neutron frequency for the magnetic field drift’ can be seen in Figure 3: ‘the variation is reduced to a small scatter about the mean, dominated entirely by neutron counting statistics’.28 Figure 6 The structure and operational principle of the mercury magnetometer. A typical output signal is also shown; the fitted frequency yields the strength of the ambient magnetic field.29 Sensitivity The value for the EDM can be extracted simply: ‘A straight-line fit to the corrected frequency as a function of the applied electric field E yields a gradient that is directly proportional to the EDM’.30 “The statistical ambiguity acquired is Wherein N is the total number of neutrons counted, the Ramsey period T >> t, and α is the visibility (averaged over the two spin states) of the central resonance fringe: With a similar expression for α↓. The visibility is effectively a measure of the polarization that can be achieved and maintained throughout the measurement period.”31 Summary This chapter provided an in-depth review of the different experimental techniques employed in the study of neutron electric dipole moment. Experiments conducted in search of a neutron EDM was the room – temperature experiment which was carried out in Institut Laue-Langevin (ILL). This experiment made use of the mercury magnetometer to monitor the magnetic field within the neutron storage container, an essential component of the experiment used to hoard ultra cold neutrons. Furthermore, it discussed about the statistical ambiguity acquired the acquisition of the value for the EDM. BIBLIOGRAPHY 1. K. Green, P. G. Harris, P. Iayldjiev, et al., Nucl. Instr. Meth. A:404:381 (1998). 2. Philip Harris, The Neutron EDM Experiment, Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, UK. 3. C. A. Baker, D. D. Doyle, P. Geltenbort, K. Green, M. G. D. van der Grinten, P. G. Harris, P. S. Iaydjiev, S. N. Ivanov, D. J. R May, J. M. Pendlebury, J. D. Richardson, D. Shiers, and K. F. Smith, Improved Experimental Limit on the Electric Dipole Moment of the Neutron, Physical Review Letters 97, 131801 (2006). 4. Oscar Naviliat – Cuncic, The Neutron Electric Dipole Moment, International Workshop on Fundamental Symmetries: from nuclei and neutrinos to the Universe ECT Trento (June 25-29 2007). 5. M.V. Romalis, W.C. Griffith, and E.N. Fortson. Phys. Rev. Lett., 86:2505–2508, 2001. Read More