Atom Interferometry 101 Frank A. Narducci Naval Air Systems Command Patuxent River, MD 1 July 25, 2013 Atomic physics (for the lay person) 2 July 25, 2013 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 Internal structure!!! Neutron interferometry 1960s Atom interferometers 1990s 3 July 25, 2013 More history deBroglie proposal 1924 The “ruler” for precision measurements Electron diffraction 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.