FRIB Topical Program: Hadronic EDM August 23, 2019 Simulations of neutron spin manipulation and transport for the LANL neutron EDM experiment Doug Wong

nEDM searches and Baryon Asymmetry FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 nEDM searches and Baryon Asymmetry A probe of CP violation Baryon asymmetry (Sakharov requirements) - Baryon number violation - Departure from thermodynamic equilibrium - C and CP violation If CP is conserved, any process producing a particle must have a counterpart reaction producing the charge-conjugate particle at the same rate  no net baryon number Also good at killing off theories Good probe of BSM physics Small SM background Current limit is at 10-26 e cm, the Lanl nEDM search is aiming for 10-27 e cm CP Violation and Strangeness

nEDM search at LANL Room temperature nEDM apparatus FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 nEDM search at LANL Room temperature nEDM apparatus Double precession chamber, Ramsey’s oscillatory fields method, with 199Hg co-magnetometer. LANL UCN source capable of providing 200 UCN/cc at exit of the biological shield Preliminary test: Cell densities were measured via fill/dump storage experiments to be < 5 UCN/cc Crude Ramsey fringes created successfully using a test setup in 2017 Magnetically shielded room had 2 layers and a shielding factor of ~150 Projected data collection start: 2021 Ramsey fringes (T1 = 30 sec) Plaster 2018 R.W.P Jr. 2018

nEDM search at Lanl Indicates the B field direction FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 nEDM search at Lanl Indicates the B field direction Guiding field coils UCN gate-valve AFP spin flipper (short solenoid) Spin analyzer (magnetized Fe foil) UCN detector (B-ZnS foil + PMT) Frequency (RF) reference Lanl nEDM TPR 2018

FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey’s method: Neutron spin manipulation using an oscillatory field (i.e., RF field)

Ramsey’s method: Rabi π flip FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey’s method: Rabi π flip Circular: Linear: ω = 20 [rad/s] ω0 = 20 [rad/s] ωC = 1.57 [rad/s] ωL = 3.14 [rad/s] t = 2 [sec] a0 = 1 b0 = 0

Ramsey’s method: On resonance sequence FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey’s method: On resonance sequence Neutron starts spin up at t = 0 Above: Plot of the “tip” of the semiclassical neutron spin vector. Origin of the vector is at P(x),P(y), P(z) = (0.5, 0.5, 0.5) Note: this is just for demonstration purposes, the animation skips lots of precession time

Ramsey’s method: Making a fringe FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey’s method: Making a fringe Off resonance On resonance Also off resonance In experiment it is unnecessary to make the whole fringe. Pick 4 points along the central peak along which the slope is fastest changing, and extrapolate resonant frequency from that Each point on the fringe comes from one ramsey sequence. Experimentally, to make this fringe, all you need to do is to apply a ramsey sequence (for various RF frequencies) on a population of neutrons, and count the number of spin up neutrons at the end. Note: this is just for demonstration purposes, the animation skips lots of precession time, and the ramsey fringe was made with different parameters

Statistical requirements FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Statistical requirements Takayesu Ito 2018

Spin transport into the precession cell FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 What determines α? Initial polarization Spin transport into the precession cell Spin decoherence/depolarization in the precession cell Spin transport out of the precession cell into the spin analyzer Spin analyzer efficiency

Improving and characterizing α FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Improving and characterizing α 1s free precession 10s free precession T1 as a function of holding time

FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 T1 and T2 spin relaxation Longitudinal spin depolarization time T1 (no polarization left = no signal) Transverse spin depolarization time T2 Transverse depolarization time T2 (Spin of precessing neutrons fall out of alignment) Leung 2018

Computational tools PENTrack FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Computational tools PENTrack Monte Carlo spin tracking and particle trajectory simulation Time dependent / static B and E fields (both numerical and analytical) Supports complicated experimental geometries (e.g. storage chambers, pipes in and out of the chamber, valves) COMSOL Finite element physics simulator Indiana University Carbonate Computing Cluster 72 general-purpose compute nodes, each with 256 GB of RAM, and eight large-memory compute nodes, each with 512 GB of RAM Each node equipped with 12 two 12-core Intel Xeon E5-2680 v3 CPUs and four 480 GB solid-state drives

https://github.com/wschreyer/PENTrack FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Features: Spin tracking of neutrons, Hg, neutron decay products via the BMT equations (relativistic) RK5 integrator w/ adaptive step size Local tricubic interpolation for non analytic magnetic fields Allows importing of STL files Supports time dependent magnetic fields Diffuse/specular reflection for different materials based on fermi potential https://github.com/wschreyer/PENTrack

Ramsey method: PENTrack vs numerical SE solution FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey method: PENTrack vs numerical SE solution B0 = 1 uT (w0 = 183.247 rad/s) BL = 4 nT (wL = 0.732989) Precession = 180s π/2 pulse time = 4.286 sec (for an optimized ramsey fringe, wL = π/tpulse) gyromagnetic ratio of the neutron 1.832 471 72 x 10^8 rad s^-1 T^-1 Result from integrating Schrodinger equation

Ramsey method (For varying B0 gradients, PENTrack) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Ramsey method (For varying B0 gradients, PENTrack) dB0/dz = 1e-9 [T/m] (1000 neutrons, bin size = 0.1) dB0/dz = 0 [T/m] (1000 neutrons, bin size = 0.1) B0 = 1 uT (w0 = 183.247 rad/s) BL = 4 nT (wL = 0.732989) Precession = 180s π/2 pulse time = 4.286 sec Height of precession chamber = 0.1 m dB0/dz = 1e-7 [T/m] (1000 neutrons, bin size = 0.1)

T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Basic method: Plot <Sx> vs t, which should tend towards 0 as spins decouple B0 = 1 uT. Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m Neutron energy: Uniform distribution 0 - 200 nEv Number of neutrons simulated: 5000 dB/dZ = 1e-7 [T/m] dB/dZ = 1e-8 [T/m]

T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Fit with exp(-(t - c) / T2 ) * sin(w*t + phi) B0 = 1 uT. Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m Neutron energy: Uniform distribution 0 - 200 nEv Number of neutrons simulated: 5000 dB/dZ = 1e-7 [T/m] dB/dZ = 1e-8 [T/m] dB/dZ = 1e-8 [T/m]

T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Can also get out of the rotating frame by using <Sx>^2 + <Sy>^2 Fit exp(-(t - c) / T2 ) B0 = 1 uT. Specularity = 0.05. Cylindrical chamber of h = 0.1 m, r = 0.5 m Neutron energy: Uniform distribution 0 - 200 nEv Number of neutrons simulated: 5000 dB/dZ = 1e-7 [T/m] dB/dZ = 1e-8 [T/m]

T2 FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 T2 as a function of gradient: non-specularity = 30%

FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Spin transport Before we can validate our T1/T2 models with experimental data, we must first understand the polarization of the neutrons entering the precession chamber Rough field map taken in Dec. 2019, not enough to characterize transport into the chamber Planned neutron transport through the magnetically shielded room in Fall 2019 New magnetic field mapper recently built will also provide a better field profile

December 2019 field mapping FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 December 2019 field mapping Non-adiabaticity parameter k Wall B0 coil Center of MSR transport coils (3 solenoids) We want k << 1 for good spin transport vn = 4m/s Fluxgate inserted into the MSR starting at z=0 B0 generates a field along the y axis

Comsol simulation FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Comsol simulation ~100 uT (1 gauss) external uniform field along +y B0 generates field along -z MSR walls modeled as a fixed magnetic boundary w/ 2mm thickness, which is a little thin z y transport coils Center of MSR B0 coil transport coils Wall Center of MSR Wall B0 coil transport coils

Comsol simulation FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Comsol simulation ~100 uT (1 gauss) external uniform field along +y B0 generates field along -z MSR walls modeled as a fixed magnetic boundary w/ 2mm thickness, which is a little thin z y transport coils B0 coil transport coils Center of MSR Wall B0 coil transport coils

PENTrack simulation Spin tracking output (single pass) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 PENTrack simulation Neutrons are propagated along y in a pipe of ID 3 inches Starting from outside the MSR at y=-2m, absorbed at center of the MSR at y=0 Specular reflection, magnetic vector field imported from Comsol and interpolated Ending polarization calculated using the relation 1000 neutrons Storage time = 5s Av = 0.92 Spin tracking output (single pass) 1000 neutrons Storage time = 20s Av = 0.73

B0 coil design and new MSR FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 B0 coil design and new MSR We also need to model spin transport for the recently-ordered magnetically shielded room (MSR) This includes transport past B0 coils

B0 coil design and new MSR FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 B0 coil design and new MSR

B0 coil design and new MSR FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 B0 coil design and new MSR Polarization after transport (single pass):  B field along guide Spin polarization in transport (single pass):  Non adiabaticity along pipe Note: the shield walls are at 1.2[m], 1.3[m], 1.5[m], 1.75[m]

Approaching a full simulation of the nEDM experiment FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Approaching a full simulation of the nEDM experiment Complete fill and dump, with Ramsey sequence in the chamber Spin analyzer simulation (AFP spin flipper with polarized iron foil. Examine drop height effect) AFP spin flipper (short solenoid) Spin analyzer (magnetized Fe foil) UCN detector (B-ZnS foil + PMT) Lanl nEDM TPR 2018

FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Window study at LANL (2018) Pre-polarizing magnet (PPM) is ramped up from 0 to 5 T We measure neutron count as a function of B field strength, both with and without a ‘window’

UCN Transmission: No window FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 UCN Transmission: No window PPM Field Neutron transmission B = 0 T N- + N+ B = 5 T N+ Energy spectrum can be guessed from ramping curve

UCN Transmission: With window FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 UCN Transmission: With window PPM Field Neutron transmission B = 0 T (N- + N+) f B = 5 T N+ Takeyasu Ito 

PPM ramping simulation (a work in progress) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 PPM ramping simulation (a work in progress) High field seekers No PPM window (B = 0 T) Low field seekers Mixed spin states

PPM ramping simulation (a work in progress) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 PPM ramping simulation (a work in progress) High field seekers No PPM window (B = 2 T) Low field seekers Mixed spin states

PPM ramping simulation (a work in progress) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 PPM ramping simulation (a work in progress) High field seekers No PPM window (B = 5 T) Low field seekers Mixed spin states

PPM ramping simulation (a work in progress) FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 PPM ramping simulation (a work in progress) An easy way to validate these results: in the upcoming run cycle, perform a ramp with the spin flipper on, in order to count low field seekers Low field seekers Mixed spin states

False nEDM sources FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 False nEDM sources

Geometric Phase: Bloch Siegert shift FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Geometric Phase: Bloch Siegert shift A linear RF = two circular RFs with equal frequency but opposite directions of rotation (sin is odd, cos is even)  N. F. Ramsey, Phys. Rev. 100, 1191–1194 (1955)

Geometric Phase FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Geometric Phase False EDM from gradient in chamber and the v x E effect Say there is some gradient along both xy and z Bloch siegert shift Maxwell eq. and by cylindrical symmetry Assume constant B0z gradient, integrating gives Now plug B0xy and into bloch siegert shift formula up top Frequency shift correlates to false EDM linear E term gives false EDM if you reverse the E field! Plugging in values gives something on the order of 10^-27 e cm!

Comagnetometer and neutron COM difference FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Comagnetometer and neutron COM difference

FRIB Topical Program: Hadronic EDMs – Doug Wong August 23, 2019 Summary To better characterize the value of α in the figure of merit, we must understand Initial polarization Spin transport into the precession cell Spin decoherence/depolarization in the precession cell Spin transport out of the precession cell into the spin analyzer Spin analyzer efficiency To improve the accuracy of our simulations, we have planned B field mappings and transport/storage tests in the upcoming run cycle Understanding of the 1/√ N factor requires simulation and measurement of the neutron energy spectrum As simulations approach a full transport/Ramsey/dump sequence, false nEDM signals such as geometric phase must also be considered