Atom Interferometry 101. Frank A. Narducci Naval Air Systems Command Patuxent River, MD

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1 Atom Interferometry 101 Frank A. Narducci Naval Air Systems Command Patuxent River, MD 1

2 Atomic physics (for the lay person) 2

$Electron diffraction 1930 The Nobel Prize in Physics 1937 was awarded jointly to Clinton Joseph Davisson and George$

3 History debroglie proposal 1924 The Nobel Prize in Physics 1929 was awarded to Louis de Broglie "for his discovery of the wave nature of electrons". Electron diffraction 1930 The Nobel Prize in Physics 1937 was awarded jointly to Clinton Joseph Davisson and George Paget Thomson "for their experimental discovery of the diffraction of electrons by crystals" Electron interferometry 1950s Neutron interferometry 1960s Internal structure!!! Atom interferometers 1990s 3

$More history debroglie proposal 1924 The ruler for precision measurements Electron diffraction 1930$

4 More history debroglie proposal 1924 The ruler for precision measurements Electron diffraction 1930 Electron interferometry 1950s Neutron interferometry 1960s Atom interferometers 1990s X 1000 X 100 4

5 Why?? 5

6 Outline Interaction of two level atom with single mode field Schrodinger Eq. Density Matrix Rabi flopping Ramsey interference Spin echo Two time correlation functions 6

7 Hamiltonian 2> 1> Fully quantum mechanical Semi-classical 7

8 Rabi frequency As we ll see, this is the rate the atom oscillates between ground and excited states 8

9 The Schrodinger Equation 9

10 Some more algebra In principle, numerically integrable 10

11 Change to rotating frame 11

12 Final set of equations Laser detuning from atomic resonance where 12

13 Solving the equations Solving this system by eigenvalue method Generalized Rabi frequency 13

14 General solution 14

15 Most general form 15

16 Compact notation Amplitudes as if the atom was initially in the ground or excited state Amplitude of ground state as if atom started in the ground state 16

17 Compact notation Amplitudes as if the atom was initially in the ground or excited state Amplitude of excited state as if atom started in the ground state 17

18 Compact notation Amplitudes as if the atom was initially in the ground or excited state Similarly 18

19 Finally. Basically, we now have the probability amplitudes to find the atom in the excited or ground states as a function of time Now..on to some physics 19

20 What does this look like? 20

21 Simple solution For atom initially in the ground state Therefore 21

22 Steady state As constructed, there is no steady state System continues to oscillate forever We have ignored spontaneous emission! 22

23 Inclusion of spontaneous emission Put in by hand But here we ll skip to the end 23

24 Dynamics No nice analytic solution exists Analytic solutions exist if Spontaneous emission is ignored (as shown before) Detuning is taken to be zero Strongly driven Weakly driven 24

25 Steady State Re-arranging Powerbroadened Linewidth Natural Linewidth 25

26 Justification for ignoring spontaneous emission 26

27 Three level system 27

28 System of equations 28

29 Adiabatically eliminate the 3 rd level 29

30 One more transformation 30

31 One more transformation 31

32 One more transformation 32

33 One more transformation 33

34 Going back 34

35 Definition of pulse 35

36 Definition of pulse 36

37 Single pulse experiments Consider an atom initially in the ground state Apply a pulse that is nominally a /2 pulse Denote that time by (for perfect /2 pulses) 37

38 38

39 Double pulse sequence- Ramsey As before, begin with the atom in the ground state Again, apply a single pulse of length Now, allow atom to evolve freely for a time (taking to be the state of zero energy) 39

40 Double pulse sequence- Ramsey Now apply second pulse (assumed identical to the first one) 40

41 Simplification By physics Same function as before 41

42 Simplification By physics Interference!!! 42

43 43

44 Recall 44

45 Overview of AI Sensors z e> e> g> g> /2 /2 T t 45

46 and just for fun Make T1 as long as possible 46

47 Even more fun. 47

48 48

49 Questions? 49

Frequency Tunable Atomic Magnetometer based on an Atom Interferometer

Frequency Tunable Atomic Magnetometer based on an Atom Interferometer D.A. Braje 1, J.P. Davis 2, C.L. Adler 2,3, and F.A. Narducci 2 Blaubeuren Quantum Optics Summer School 29 July 2013 1 MIT Lincoln