99 Hg g co-magn magnet etometr ometry y stu tudy dy in in th the nE e nEDM DM 199 ex exper periment iment at at th the P e Pau aul l Sc Scher errer er In Insti titu tute e (Swit itzerlan zerland) d) Yoann nn Kerm ermaïd ïdic ic Sém Séminaire inaire de des do doctorants ctorants 16 Avril 2015
MOTIVATION 2
Sci cient entific ific mot otiv ivati ations ons • The neutron states are only defined relatively to its spin 𝝉 • Any spin 𝝉 couples to: to 𝐶 via 𝝂 ← magnetic moment to 𝐹 via 𝒆 ← electric dipole moment Τ | ⟩ 𝜈 = −| ⟩ Τ | ⟩ 𝑒 = +| ⟩ 𝜈 𝑒 • • If 𝒆 𝐨 is not zero, T (CP) symmetry is violated � 3
Sci cient entific ific mot otiv ivati ations ons 𝒆 𝐨 𝒇𝒚𝒒 < 𝟒. 𝟐𝟏 �𝟑𝟕 𝒇. 𝐝𝐧 Experimental upper bound: [Ral al-Su Sussex ssex-ILL, ILL, 2006] 006] 1. SM predicts 𝒆 𝐨 ∼ 𝟐𝟏 �𝟒𝟑 𝒇. 𝐝𝐧 weak CPV ( 𝜀 CKM @ 2 loops) weak [Khriplovitch, 1981] 2. Additional CPV sources from BSM models constrained by 𝑒 � ��� 3. How sensitive to new physics we are to 1 loop process? � 1 𝑈𝑓𝑊 𝑒 � ≈ 10 ��� 𝑓.cm × sin(𝝌 𝑫𝑸 ) × 𝑁 �� [Pospelov & Ritz, 2005] 4
Internationa ernational l co context ext • PS PSI nEDM collaboration at the Paul Scherrer Institute (Switzerland) 8 countries (Switzerland, Germany, France, UK, Poland, Belgium, USA, Russia) 48 members / 11 PhD students • SNS SNS nEDM collaboration Oak Ridge (USA) • PNPI PI-ILL ILL nEDM experiment Grenoble (France) • TRI RIUMF MF nEDM collaboration Vancouver (Canada) • LA LANL nEDM collaboration Los Alamos (USA) • And others… 5
The nEDM experiment 6
The Th e measu asurement ement pri rinciple nciple • Hamiltonian of the problem: 𝐼 = −𝜈 ⃗ 𝜏 � 𝐶 − 𝑒 ⃗ 𝜏 � 𝐹 • Energy level splitting: 𝚬𝑭 𝐅 𝚬𝑭 𝐂 < 𝟒. 𝟐𝟏 �𝟑𝟑 eV = 𝟕. 𝟐𝟏 �𝟐𝟓 eV ⁄ 𝐅 = 𝟐𝟏 𝐥𝐖 𝐝𝐧 𝑪 = 𝟐 𝛎𝐔 2𝑒𝐹 GS 2𝜈𝐶 2𝑒𝐹 7
Th The e measu asurement ement pri rinciple nciple • Hamiltonian of the problem: 𝜈 � 𝐶 − ⃗ 𝐼 = − ⃗ 𝑒 � 𝐹 • Measure a neutron spin precession frequency shift proportional to an applied electric field! �� ↑↑ = −𝜈𝐶 ↑ − 𝑒𝐹 ↑ 𝒊 (𝝃 ↑↑ �𝝃 ↑↓ ) � y if 𝑪 ↑ = 𝑪 ↑ ! � 𝒆 = True rue only �� ↑↓ 𝟓𝑭 = −𝜈𝐶 ↑ + 𝑒𝐹 ↓ � 8
Expe xperim riment ental al setup up ~2 m B 0 0 ≈ 1 � T E E ≈ ¡10 ¡kV/cm ~2 m ~50 cm NB: Upgraded RAL-Sussex spectrometer 9
Expe xperim riment ental al setup up 1. 1. Production duction of Ultr tra a Cold ld Neutr utron ons s (UCN) N) in the new PSI UCN source ce 𝑭 𝐕𝐃𝐎 ∼ 𝟐𝟏𝟏 𝐨𝐟𝐖 2. 2. UCN are spin in-polari polarize zed d ↑ wit ith a 5T 5T magnetic etic field ld 3. 3. Fi Fill l the prec eces essio sion chamber mber B 0 0 ≈ 1 � T E ≈ ¡10 ¡kV/cm E 4. 4. Stor tore e UCN for 20 200 0 s with th (E, B) paral allel lel or antip iparallel arallel 𝝆 1. 1. Ap Apply 𝟑 pul pulse (2 (2s) 2. 2. Spin freely precess s (2 (200s) 𝝆 3. 3. Ap Apply 𝟑 pul pulse e (2s 2s) [Ramsey, 1956] 5. Measu 5. sure e neutron counts nts with th spin in Up & D Down own 10 10
The Th e Ramsey msey meth ethod od Fit to to the e centra ntral Rams msey y fring nge e (201 013 3 data) ta) 𝝆 𝟑 pulse se = oscil cillating lating magnet netic ic field ld 𝐶 � 𝑢 = 𝐶 � cos 𝜕 �� 𝑢 ⃗ 𝑦 + sin 𝜕 �� 𝑢 ⃗ 𝑧 → N spin ↓ 𝑸(↑→↓) ∝ cos 𝑔 �� − 𝒈 𝐌 N spin ↑ Δ𝜉 𝜹 𝐨 𝑸(↑→↓ ) maximiz imized ed if 𝒈 𝐒𝐆 = 𝒈 𝐌 = 𝟑𝝆 𝑪 𝟏 Larmor mor 11 11 frequen quency cy
Expe xperim riment ental al ch chall llenges enges Reminder: Earth magnetic field ≈ 50 50 � T = = 5 50.10 6 6 pT pT Neutron frequency (run 7650) ORDER RDER OF MAGNITUDE DE OF MAGNET NETIC IC FIELD LD FLUCT UCTUATION IONS: S: 𝝉 𝒆 𝒐 ~ 𝟑. 𝟐𝟏 �𝟑𝟒 𝒇 .cm • E + + to to E - : : ∆𝑪 ~ 𝟖 pT (1970) 𝝉 𝒆 𝒐 ~ 𝟐. 𝟐𝟏 �𝟑𝟓 𝒇 .cm • Cyc ycle le: ∆𝑪 ~ 𝟏. 𝟔 pT (1980) 𝝉 𝒆 𝒐 ~ 𝟐. 𝟐𝟏 �𝟑𝟕 𝒇 .cm • nEDM: M: ∆𝑪 ~ 𝟔 f T E ↑ No E-field E ↓ How w can we we achieve ieve a 5 5 fT magnetic etic field ld sensitiv itivity ity? 12 12 3 days
199 Hg co-magnetometry 13 13
Fu Functioni ctioning ng pri rinciple nciple Need to correct for magnetic field drift every cycle with a 100 fT precision [Ral-Sussex-ILL, 1997] 199 Hg Hg atomi tomic c magnet etomet etry 19 = Same sampled led vo volu lume durin ring g the same integrat tegrated ed ti time as as UCN [Bison, 2006] 133 Cs Cs ato tomic mic magnet etomet ometry 13 = Spatia tial l magnet etic ic field ld distributi tribution on 14 14
Fu Functioni ctioning ng pri rinciple nciple • 199 Hg atoms are spin polarized by z optical pumping (40s) B 0 x 𝝆 • Apply a 𝟑 puls lse (2s) y • Free precession in (x, y) plane (200s) 𝐽 𝑢 = 𝐵𝑓 �� 𝝊 sin 𝝏 𝐌 𝒖 + 𝝌 Relaxation time Oscillating phase constant due to @ Larmor frequency wall collision ≈ 100 s 𝑔 � = 𝛿 �� 𝐶 � ≈ 8 Hz I(t) 15 15 T (s)
Corr orrecti ection on of ma magnetic netic fie ield ld drif rift 𝝉 𝒈 𝐨 𝟐 = ≈ 𝟏. 𝟔 𝐪𝐪𝐧 x 7 𝒈 𝐨 𝟑𝝆 𝑼 𝐪 𝜷 𝑶 𝐕𝐃𝐎 𝝉 𝒈 𝐈𝐡 = 𝟒 𝟐 𝑼 𝐪 𝝊 ≈ 𝟏. 𝟏𝟖 𝐪𝐪𝐧 ⁄ 𝟐 + 𝒇 𝟑 𝒈 𝐈𝐡 𝟑 𝐓𝐎𝐒 𝑼 𝐪 𝑶 𝐠𝐣𝐮 • The co-magnetometry allows to be only statist atistica ically lly limit ited ed by UCN → ¡ ¡ ¡ ¡ 𝝉 𝒆 /𝐝𝐳𝐝𝐦𝐟 = 𝟐. 𝟐𝟏 �𝟑𝟓 𝒇. 𝐝𝐧 • Need to repeat X cycles to reach the 𝟐𝟏 �𝟑𝟕 𝒇. 𝐝𝐧 level, with 𝑌 → ∞ !! (Actually ~ 10 000 = months hs) 16 16
Curr urrent ent stati atistica stical l sensitivity nsitivity 𝒆 𝐨 < 𝟐𝟑. 𝟒 × 𝟐𝟏 �𝟑𝟕 𝒇. 𝐝𝐧 (2 months full time) • nEDM data analysis software → ¡ ¡ ¡ ¡ EDM EDMA • Expected sensitivity in 2-3 years → ¡ ¡ ¡ ¡ 𝝉 𝒆 = 𝟐 − 𝟑. 𝟐𝟏 �𝟑𝟕 𝒇. 𝐝𝐧 • Control of systematics? 17 17
Curr urrent ent co contr trol ol of s f syst stematics ematics Moti tional al 19 199 Hg g false se EDM 𝟓𝟏 ± 𝟓𝟏 ← corr rrec ection tion of this is effect ct 18 18
Mot otional ional 19 199 Hg Hg in induced uced fa fals lse e EDM DM 𝑒 = ℏ (𝜕 ↑↑ − 𝜕 ↑↓ ) • Reminder : 4𝐹 • The motional 199 Hg induced false EDM arises from transverse magnetic field : Vertica cal magnetic c 𝐶 � ⃗ 𝑨 Position n in the 𝑪 field field gr gradie dient trans nsverse plane ≈ 𝜖𝐶 � � 𝐶 �� 𝑢 𝜖𝑨 𝑠 𝑢 � 𝐶 �� 𝑢 + � � 𝜀𝜕 ∝ 𝐶 �×� 𝑢 + ⋯ 𝐶 �×� 𝑢 ≈ 𝐹 � � 𝑑 𝑤 �� (𝑢) Longitud udinal nal Spee Speed d in in the e 𝐶 � ⃗ 𝑠 electri ric field trans nsverse plane • Different 199 Hg frequency shift source arise: 𝜀𝜕 = 𝜀𝜕 � � + 𝜀𝜕 �� + 𝜀𝜕 � � + ⋯ 19 19
Mot otional ional 19 199 Hg Hg in induced uced fa fals lse e EDM DM 𝑒 = ℏ (𝜕 ↑↑ − 𝜕 ↑↓ ) • Reminder : 4𝐹 • Different 199 Hg frequency shift source arise: 𝜀𝜕 = 𝜀𝜕 � � + 𝜀𝜕 �� + 𝜀𝜕 � � + ⋯ • Hypothesis: Unifo form rm vertical magnetic field gradients in a cylind lindric rical al cell [Pendelbury, 2006] [Pignol, 2012] � � � � �� � • Theoretical expression: which leads to: 𝜀𝜕 �� = ± � � � 𝐹 �� ℏ𝜹 𝟑 𝑬 𝟑 𝐠𝐛𝐦𝐭𝐟 = ± 𝝐𝑪 𝒜 𝒆 𝐈𝐡 𝟒𝟑 𝒅 𝟑 𝝐𝒜 20 20
Mot otional ional 19 199 Hg Hg in induced uced fa fals lse e EDM DM Data B 0 down Data B 0 up Best fit to the data: 𝑒 �� ����� ( � ) = 𝑏 . � Theoretical slope sult: 𝒃 𝐟𝐲𝐪 = 𝟐. 𝟐𝟑𝟑 𝟒𝟔 × 𝟐𝟏 �𝟑𝟖 𝒇. 𝐝𝐧/ 𝐪𝐔 Result: 𝐝𝐧 × 𝟐𝟏 �𝟑𝟖 𝒇. 𝐝𝐧/ 𝐪𝐔 𝒃 𝐮𝐢 = 𝟐. 𝟐𝟓𝟗 𝐝𝐧 Available: arxiv:1410.8259 “Measurement of a false electric dipole moment signal from 199 Hg atoms exposed to an inhomogeneous magnetic field” 19 21 21
Ne Neut utron on to o 19 199 Hg Hg mag agnetic netic moment oment ra ratio io 𝜹 Larmor frequency definition: 𝒈 𝐌 = 𝟑𝝆 𝑪 𝟏 The gyromagnetic ratio of the two species reads: 𝑺 = 𝒈 𝐨 = 𝜹 𝐨 𝟐 + 𝜺 𝐟𝐛𝐬𝐮𝐢 + 𝜺 𝐡𝐬𝐛𝐰 + ⋯ 𝒈 𝐈𝐡 𝜹 𝐈𝐡 𝜹 𝐨 = 𝟒. 𝟗𝟓𝟑𝟓𝟔𝟖𝟓 𝟒𝟏 [𝟏. 𝟖𝟗 𝐪𝐪𝐧] 𝜹 𝐈𝐡 Interpretation as a new measurement of whether 𝛿 � or 𝛿 �� at the ppm level Results in agreement with previous measurement Available: Physics Letters B 739, 128-132 (2014) 22 22
Toward n2EDM 23 23
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