Closed-shell Atomic Electric Dipole Moments. K. V. P. Latha Angom Dilip Kumar Singh B. P. Das Rajat Chaudhuri

Transcription

1 Closed-shell Atomic Electric Dipole Moments K. V. P. Latha Angom Dilip Kumar Singh B. P. Das Rajat Chaudhuri

2 An observation of EDM of a non-degenerate physical system is a direct unambiguous evidence of violation of P and T symmetries. J D = d J J is the angular momentum of the physical system. Quantity Parity Time-reversal D D = D D = D J J = J J = J D 0 P and T violation Atoms can have a non-zero EDM

3 EDM of a diamagnetic atom arises predominantly from, Nuclear Schiff moment nucleon-nucleon interactions interactions and chromo EDMs. quark-quark Electron-nucleus interactions electron-quark interactions. EDMs are enhanced in atoms having, High nuclear charge ( Z ) P, T odd effects are dominant in heavy atoms. Close levels of opposite parity, D atom 1 E Theory D atom / C C = C T or Q Experiment D atom

4 The atomic EDM is H EDM is parameterized in terms of the P and T violating Coupling constants.

5 A new many-body theory to calculate Da / C Knowledge of the Hamiltonian of the system Accurate relativistic electronwavefunctions H a = Dirac Hamiltonian for a many-electron atom ( unperturbed Hamiltonian ) = i ( C i p i + m c 2 - Z e 2 / r i ) + i<j e 2 / r ij H a = t + g 0 h 0 (i) t = h 0 (i) + U DF Coulomb interaction (V N ) g 0 = V N - U DF = residual Coulomb interaction

6 Perturbed atomic Hamiltonian Hartree Fock equation, With H EDM as perturbation, H = H a + h EDM

7 Coupled-perturbed Hartree-Fock equations The perturbed Hartree-Fock equations are obtained by solving V ijkl = ij v kl - ij v lk

8 D atom = 2 ap a D p C pa (, 1) CPHF theory : Solving for the coefficients allows one to treat the residual Coulomb interaction to all orders with correlations of 2-paritcle and 2-hole type only. Perturbations which depend on the coordinate of a single particle.

9 Coupled-cluster method T 1 T 1 2, T2 T 1 2 T2, T 2 2, T4 Continuum Fermi level 0 = Hartree-Fock reference state = Exact atomic state = exp ( T0 ) = ( 1 + T0 + T0 2 / 2! +... ) 0 T 0 = T T 2 0 0

10 In Coupled-cluster theory, Coupled-cluster equations T0 represents single/double/triple... excitations from the reference state. The unperturbed coupled-cluster equations : T 1 0 T 2 0 T 1 0 = T 2 0 = ap t ap a p a a ap,bq t ab pq ap 0 a q a b a a 0

11 Acting by exp(-t0) and projecting by singly and doubly excited determinantal states, With H EDM as perturbation, H = H a + h EDM And T = T 0 + T 1 Perturbed Coupled-cluster equations, H N is the normal ordered Hamiltonian, H N = exp(-t0) H N (T0).

12 Restricting T1 = T T 2 1, set of equations, linear in T1 and non-linear in T0 are obtained. The working equations are Datom = 2 Ref D T 1 Ref D = exp(-t0) D exp (T0).

13 CPHF result (Martensson et.al, 1985) in e cm. Results for 199Hg EDM Hg EDM experiment (Romalis et.al, 2001) in e cm. Present best limit for C T CC theory for EDMs CPHF effects + more Our preliminary results show that the LCCEDM contribution reduces the HF contribution by 1.0 % with an unoptimised basis set. Polarizability of Hg and other atoms Unperturbed CC amplitudes

14 Diamagnetic atoms EDM experiment on 199 Hg is in progress in University of Washington, Seattle. The best limit (present) is D ( 199 Hg ) > e-cm A non-zero value of C T would imply new physics beyond the Standard Model. To set limits on specific models of CP violation, the experimental results must be related to EDMs of fundamental particles.

15 Interpretation of EDM experimental result : Atomic level Nuclear level D Hg = fm 2 S Hg (Dzuba et al ) S Hg = e fm 3 g NN ( Nuclear shell model calculation ) ( Flambaum et. Al ) Quark level g NN = 20 fm -1 ( d d d u ) ( Posepelov ) g NN = CP-odd pion exchange constant, d d and d u are quark chromo EDMs.

16 Conclusions Presence of EDMs is a direct evidence of T violation. The knowledge of the T PT coupling constants and the Schiff moment, Q gives deep insights into the CP violating interactions responsible for their existence at the fundamental level. The observable EDMs can be used to constrain the chromo EDMs of quarks predicted by the non-standard Models.

17 Calculation of Electric quadrupole moment of Sr + Chiranjib Sur K. V. P. Latha Bijaya Kumar Sahoo B. P. Das Rajat Chaudhuri

18 Electric Quadrupole moments in the context of Atomic Clocks : The best clock must be Accurate Stable Reproducible Clocks based on microscopic oscillators - Atomic Clocks The resonant transitions between two non-degenerate energy levels of an atoms are extremely stable and can be most accurate. Two identical atoms have the same unperturbed transition and two clocks based on such transitions generate the same time Property of reproducibility.

19 The basic atomic clock recipe Identify a transition between two non-degenerate atomic states Create an ensemble of such atoms Illuminate the ensemble with radiation from a tunable source an oscillator operating near the transition frequency f 0. At maximum absorption count the number of cycles of the oscillator. A certain number of cycles generate a standard interval of time. The stability, accuracy and the reproducibility of the clock is determined by the matching of the osillator frequency with the resonance frequency of the atom, which is limited by :

20 Environmental perturbations External fields Collisions Doppler shifts 4d Quantum projection noise, etc. 2 D 5/2 Sr : Z = 38 ; 674 nm ( clock transition) 5s 2 S 1/2 The interaction of atomic electric quadrupole moment with external electric field gradient produces the electric quadrupole shift, proportional to the electric quadrupole moment ( to this shift comes only from 4d 2 D 5/2 state. ) in that state. For Sr + the contribution

21 The electric quadrupole moment in a state is (J, M, ) zz (J, M, ) Where ZZ = - e/2 j ( 3 Z j 2 r j 2 ) The closed shell state is exp ( T ) Open shell state is obtained by an electron attachment to a closed-shell reference state. N+1 k = a k 0 0 Exact state : N+1 k = exp ( T ) {1+S} N+1 k And S = cluster operator for valence to valence and valence to virtual excitations.

22 Results Present work in e - a 0 2 MCDF method Itano. et. Al Experiment Barwood et.al 4d 2 D 5/ ( Accepted for publication in Physical Review Letters )

23

24 Sources of an atomic EDM Particle level model Quark level Nucleon level Nuclear level Atomic level E e q q e e N N d para d e Higgs SUSY LR } { d q d c q GGG qq-qq } Dominant { NN-NN d N Q (Schiff moment) d dia Dn T violation is less understood than parity violation and atoms are rich sources of T or CP violation arising from various sectors.