Atom Interferometry 101

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

1 July 25, 2013 Atomic (for the lay person)

2 July 25, 2013 History

deBroglie proposal 1924

The in Physics 1929 was awarded to "for his discovery of the wave nature of ".

1930 The 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 Internal structure!!! Neutron interferometry 1960s

Atom interferometers 1990s

3 July 25, 2013 More history

deBroglie proposal 1924 The “ruler” for precision measurements

1930

Electron interferometry 1950s X 1000

Neutron interferometry 1960s

X 100

Atom interferometers 1990s

4 July 25, 2013 Why??

5 July 25, 2013 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 July 25, 2013 Hamiltonian

|2>

|1>

Fully quantum mechanical

Semi-classical

7 July 25, 2013 Rabi frequency

• As we’ll see, this is the rate the atom oscillates between ground and excited states

8 July 25, 2013 The Schrodinger Equation

9 July 25, 2013 Some more algebra

In principle, numerically integrable

10 July 25, 2013 Change to rotating frame

11 July 25, 2013 Final set of equations

Laser detuning from atomic resonance

where

12 July 25, 2013 Solving the equations

Solving this system by eigenvalue method

Generalized Rabi frequency

13 July 25, 2013 General solution

14 July 25, 2013 Most general form

15 July 25, 2013 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 July 25, 2013 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 July 25, 2013 Compact notation • Amplitudes as if the atom was initially in the ground or excited state

• Similarly

18 July 25, 2013 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 July 25, 2013 What does this look like?

20 July 25, 2013 Simple solution • For atom initially in the ground state

• Therefore

21 July 25, 2013 Steady state… • As constructed, there is no “steady state” – System continues to oscillate forever

We have ignored spontaneous emission!

22 July 25, 2013 Inclusion of spontaneous emission • Put in “by hand” – –

•

But here we’ll skip to the end…

23 July 25, 2013 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 July 25, 2013 Steady State

Re-arranging

Powerbroadened Linewidth

Natural Linewidth

25 July 25, 2013 Justification for ignoring spontaneous emission

26 July 25, 2013 Three level system

27 July 25, 2013 System of equations

28 July 25, 2013 Adiabatically eliminate the 3rd level

29 July 25, 2013 One more transformation

30 July 25, 2013 One more transformation

31 July 25, 2013 One more transformation

32 July 25, 2013 One more transformation

33 July 25, 2013 Going back…

34 July 25, 2013 Definition of pulse 

35 July 25, 2013 Definition of pulse



36 July 25, 2013 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 July 25, 2013 38 July 25, 2013 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 July 25, 2013 Double pulse sequence-“Ramsey” • Now apply second pulse (assumed identical to the first one)

40 July 25, 2013 Simplification

• By physics

Same function as before

41 July 25, 2013 Simplification

• By physics

Interference!!!

42 July 25, 2013 43 July 25, 2013 Recall

44 July 25, 2013 Overview of AI Sensors

z

|e> |e> |g>

|g>

/2  /2

T t

45 July 25, 2013 …and just for fun

Make T1 as long as possible

46 July 25, 2013 Even more fun….

47 July 25, 2013 48 July 25, 2013 Questions?

49 July 25, 2013