Optically polarized atoms

Censorship Optically polarized atoms Dr. A. O. Sushkov, May 2007 A 12-T superconducting NMR magnet at the EMSL(PNNL) laboratory, Richland, WA Marcis Auzinsh, University of Latvia Dmitry Budker, UC Berkeley and LBNL Simon M. Rochester, UC Berkeley

Linear Polarization Medium  Circular Components Magnetic Field Chapter 4: Atoms in external fields • 1845, Michael Faraday: magneto-optical rotation

Zeeman effect: a brief history • Faraday looked for effect of magnetic field on spectra, but failed to find it • 1896, Pieter Zeeman: sodium lines broaden under B • 1897, Zeeman observed splitting of Cd lines into three components (“Normal” Zeeman effect) • 1897, Hendrik Lorentz: classical explanation of ZE • 1898, discovery of Resonant Faraday Effect by Macaluso and Corbino

Resonant Faraday Rotation rotation of the plane of linear light polarization by a medium in a magnetic field applied in the direction of light propagation in the vicinity of resonance absorption lines D.Macaluso e O.M.Corbino, Nuovo Cimento 8, 257 (1898) Diffraction Grating Monochromator Electromagnet Polarizer Flames of Na and Li Analyzer Photographic Plate

“Normal” Zeeman effect • Energy in external field: • Consider an atom with S=0  J=L • In this case, • For magnetic field along z: • This is true for other states in the atom • If we have an E1 transition, , • A transition generally splits into 3 lines • This agrees with Lorentz’ classical prediction (normal modes), not the case for S0

“Normal” Zeeman effectE1 selection rule: DM=0,1 M= -2 -1 0 1 2 Three lines !

“Normal” Zeeman effectClassical Model: electron on a spring Eigenmodes: B Three eigenfrequencies !

Zeeman effect when S0 • The magnetic moment of a state with given J is composed of

Zeeman effect for hyperfine levels • Neglect interaction of nuclear magnetic moment with external magnetic field (it is ~2000 x smaller) • However, average μnow points along F, not J • Avector-model calculations a la the one we just did yields:

The actual calculation… • Definition of gF : • The magnetic moment is dominated by the electron, for which we have: • To find μ, we need to find the average projection of J on F, so that • Now, find • Finally,

Zeeman effect for hyperfine levels (cont’d) • Consider 2S1/2atomic states (H, the alkalis, group 1B--Cu, Ag, and Au ground states) • L=0; J=S=1/2 F=I1/2 • This can be understood from the fact thatμ comes fromJ

Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling • Hyperfine energies are diagonal in the coupled basis: • However, Zeeman shifts are diagonal in the uncoupled basis: because • The bases are related, e.g., for S=I=1/2 (H) F,MF MS, MI

Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling

Zeeman effect for hyperfine levels in stronger fields: magnetic decoupling • Breit-Rabi diagrams • Nonlinear Zeeman Effect (NLZ) • But No NLZ for • F=I+1/2, |M|=F states • Looking more closely at the upper two levels for H : • These levels eventually cross! (@ 16.7 T)

Atoms in electric field: the Stark effectorLoSurdo phenomenon Johannes Stark (1874-1957) Nazi Fascist

Electric: Atoms in electric field: the Stark effectorLoSurdo phenomenon Magnetic: However, things are as different as they can be… Permanent dipole: OK NOT OK (P and T violation) First-order effect Second-order effect

Atoms in electric field: the Stark effectPolarizability of a conducting sphere • Outside the sphere, the electric field is a sum of the applied uniform field and a dipole field • Field lines at the surface are normal, for example, at equator: 

Atoms in electric field: the Stark effectClassical insights • Natural scale for atomic polarizability is the cube of Bohr radius • (a0)3is also the atomic unit of polarizability • In practical units:

Atoms in electric field: the Stark effectHydrogen ground state n l m Neglect spin! • Polarizability can be found from

Atoms in electric field: the Stark effectHydrogen ground state (cont’d) • The calculation simplifies by approximating =1

Atoms in electric field: the Stark effectHydrogen ground state (cont’d) • Alas, this is Hydrogen, so use explicit wavefunction: • Finally, our estimate is • Exact calculation:

Atoms in electric field: the Stark effectPolarizabilities of Rydberg states • The sum is dominated by terms with ni  nk • Better overlap of wavefunctions • Smaller energy denominators • dik  n2 . Indeed, • (Ek-Ei)-1scale as n3

Atoms in electric field: the linearStark effect • Stark shifts increase, while energy intervals decrease for largen • When shifts are comparable to energy intervals – the nondegenerate perturbation theory no longer works even for lab fields <100 kV/cm  use degenerate perturbation theory • Also in molecules, where opposite-parity levels are separated by rotational energy ~10-3 Ry • Also in some special cases in non-Rydberg atoms: H, Dy, Ba… • In some Ba states, polarizability is >106 a.u. C.H. Li, S.M. Rochester, M.G. Kozlov, and D. Budker, Unusually large polarizabilities and "new" atomic states in Ba, Phys. Rev. A69, 042507 (2004)

The bizarreStarkeffect in Ba Chih-Hao Li Misha Kozlov

The bizarreStarkeffect in Ba (cont’d)

The bizarreStarkeffect in Ba (cont’d) C.H. Li, S.M. Rochester, M.G. Kozlov, and D. Budker, Unusually large polarizabilities and "new" atomic states in Ba, Phys. Rev. A69, 042507 (2004)

Atoms in electric field: the linearStarkeffectHydrogen 2s-2p states • Opposite-parity levels are separated only by the Lamb shift •  • Secular equation with a 2x2 Hamiltonian: • Eigenenergies: Not EDM ! Quadratic Linear

Atoms in electric field: the linearStarkeffectHydrogen 2s-2p states (cont’d) Neglect spin! • Linear shift occurs for • Lamb Shift: ωsp/21058 GHz • 

Atoms in electric field: polarizability formalism • Back to quadratic Stark, neglect hfs • Quantization axis along E  MJis a good quantum # • Shift is quadratic inE  same for MJand -MJ • A slightly involved symmetry argument based on tensors leads to the most general form of shift Scalar polarizability Tensor polarizability

Optically polarized atoms