T ECHNISCHE U NIVERSITÄT KAISERSLAUTERN K. Bergmann Lecture 6 Lecture course - Riga, fall 2013 Coherent light-matter interaction: Optically driven adiabatic transfer processes

summary of 5 th lecture reconsidered Rabi oscillations from the perspective of adiabatic states: interference of the amplitudes of adiabatic states (accumulation of a phase difference due to AT-splitting)  time 0 

 = ½  o Coherent Population Return (CPR) |1> |a - > initially: population of and/or only |1> |a - > at the end: population of and/or only |2> |a + > DURING radiative interaction: X % admixture of population of but NO coupling to |a + > |a - > X decreases with increasing  summary of 5 th lecture: CPR - facts key conclusion: detection during radiative interaction  power broadening observed detection after radiative interaction  NO power broadening observed |a + > |1> |2> |1> |2>  oo

 = ½  o |1>, |2> |a + > |a - > |o>|o> all population in |1> or |a - > no population in |2> or |a + > |1>, |2> |a - > |o>|o> all population in |a - > when AF less population in |1> some population in |2> summary of 5 th lecture: CPR – with Gaussian pulse shape |1> |2>  oo adiabatic state vector |a - > rotates smoothly into new position (new direction) state vector |  o > follows adiabatically the larger , the smaller the angle of rotation for given  o the larger  o, the larger the max. angle of rotation for given 

 = ½  o |1>, |2> |a + > |a - > |o>|o> all population in |1> or |a - > no population in |2> or |a + > summary of 5 th lecture: CPR – sudden switch on |1> |2>  oo adiabatic state vector |a - > rotates suddenly into new position (new direction) state vector |  o > cannot follow states |a - > and |a + > populated |1>, |2> |a - > |o>|o> sudden change of direction of |a - > |a + > sudden rotation back |a + > and |a - > projected on |1> and |2> result depends on relative phase |1> and |2> populated

the goals for this lecture understanding the complex structure of spectra in a level system radiatively coupled 3-level system in the rate equation limit understanding the phenomenon of electromagnetically induced transparency (EIT) – a qualitative approach approaching the RWA Hamiltonian for the radiatively coupled 3-level system 7 th lecture: the properties of the 3-level RWA Hamiltonian and the basics of the STIRAP process outlook

Understanding the (complex) spectral properties in coherently driven level systems or probing Autler-Townes structure AT induced between a pair of levels WITH population experiments by Aigars Ekers spectral properties of coherently driven level systems

strong weak Ref spectral properties of coherently driven level systems Na 2 fluorescence from level f as a function of S-laser frequency for varies settings of P-laser frequency what do we want to explained ? ? detunings  s and  s are small, not exceeding the Rabi frequency by much.

2 1 3 SS PP bare states 1 3 SS adiab. states  P = SS adiab. states  P > 0 2´ 3´ 1´ SS PP bare states 3´ SS adiab. states  P = 0 SS adiab. states  P > 0 3´ Lamba system, initially: level 1 populated, levels 2 and 3 empty Ladder system, initially: level 1´ populated, levels 2´ and 3´ empty spectral properties of coherently driven level systems coupling / excitation / population flow possible when adiabatic states are in resonance this radiation obesrved

strong weak excitation to state f is possible at two locations (or two times) look at population flow to level f followed by spont. emission Ref spectral properties of coherently driven level systems Na 2  P = 0  S > E f - E e

PP SS |f> weak  S, some excitation to level f, followed by spontaneous emission e f g SS PP bare states |a + > =  + |g> +  + |e> |a - > =  - |g> +  - |e> spectral properties of coherently driven level systems m/s : 1 µs coupling f f e

PP SS |a + > =  + |g> +  + |e> |a - > =  - |g> +  - |e> |f> strong  S, strong excitation to level f, followed by spontaneous emission e f g SS PP bare states spectral properties of coherently driven level systems

PP SS |f> very strong  S, all the population driven through level f, followed by spontaneous emission e f g SS PP bare states |a + > =  + |g> +  + |e> |a - > =  - |g> +  - |e> spectral properties of coherently driven level systems

PP SS |a + > =  |g> +  |e> |a - > =  |g> -  |e> |f>  interference structure, reminiscent of Rabi oscillation (but of entirely different origin) population may reach level f via two different paths e f g SS PP bare states spectral properties of coherently driven level systems

PP SS |a + > =  |g> +  |e> |a - > =  |g> -  |e> increase detuning no excitation, except …….. e f g SS PP bare states spectral properties of coherently driven level systems coupling strength at crossing changes, because  changes

increase detuning no excitation, except …….. when  P is increased PP SS |a + > =  |g> +  |e> |a - > =  |g> -  |e> 2´ 3´ 1´ SS PP bare states |f> |a + > =  + |g> +  + |e> |a - > =  - |g> +  - |e> spectral properties of coherently driven level systems

increase detuning no excitation, except ……when  P is increased ….. or  P is increased SS PP |a + > =  + |g> +  + |e> |a - > =  - |g> +  - |e> e f g SS PP bare states spectral properties of coherently driven level systems

e f g SS PP bare states laser induced fluorescence from level 3´, as a function of the S-laser frequency for various P-laser detunings  S and  P kept constant spectral properties depend sensitivily on all parameters:  P,  S,  P,  S Ref spectral properties of coherently driven level systems

Ref. 71 contribution of individual m-states, J = 7 sum over all m-states sum over all m-states and averaged over Doppler width exp. data theory spectral properties of coherently driven level systems features are difficult to pre- dict in the bare state picture but relatively easily under- stood in the adiabatic state approach

3Coherent excitation in a 3-level system 3.1 Rate equations, optical pumping, preview of STIRAP features 3.2 Electromagnetically induced transparency 3.3 The 3-level Hamiltonian

3.1 Rate equation (incoherent radiation) and optical pumping, coincident pulses delayed pulses 50% 33% maximum transfer: 33% reached without loss through spontaneous emission maximum transfer: 25 % reached without loss through spontaneous emission P S 4 loss to other levels 50% 33%

3.1 two sequential  - pulses in a three level system COMPLETE transfer from level 1 to level 3 via coupling through the (possibly rapidly decaying) state 2 File: Pi21 one problem: all population reaches level 2 and much of it is lost by spontaneous emission to other states.

1 2 3 S P COMPLETE population transfer from |1> → |3> via resonant coupling through the (possibly rapidly decaying) state |2> 3.1 preview of STIRAP features Stimulated Raman Adiabatic Passage The interaction with the S–laser, coupling the two unpopulated levels, starts FIRST. Does this make sense ??? The interaction with the P–laser, coupling level 2 to the populated level 1 begins LATER – but a suitable overlap between S and P is needed.

The STIRAP puzzles S P Turn on the Stokes laser first ! - ?? The initial population resides in state 1 !! The population in state 3 not depleted (by S-laser optical pumping) ! - ?? No radiative loss from state 2 ! - ?? The S- and P-Laser are tuned to resonance, afterall !! COMPLETE population transfer from |1> → |3> via resonant coupling through the (possibly rapidly decaying) state |2> 3.1 preview of STIRAP features Stimulated Raman Adiabatic Passage

3.1 STIRAP The “building blocks” of STIRAP are: The Autler-Townes (AT) effect (splitting) The adiabatic passage (AP) process The phenomenon of electro-magnetically induced transparency (EIT) AT – EIT – AP properly combined  STIRAP discussed to be discussed

Lorentzian profile Intensity ≠ 0 ? P – laser frequency two transition dipole moments: 180 o out of phase adiabatic fluorescence bare PP 1 3 SS 2 AT 3.2 Electromagnetically induced transparency amplitude of transition dipole moment:   File: Lorentz0 …50_2xSUM needed

3.2 electromagnetically induced transparency (EIT) spectral profile probed on |1> -- |2> transition as coupling  of |2> -- |3> increases probe laser frequency (|1> -- |2>) intensity  = decay rate of level |2> start EIT/AT File: EIT_Final-1

3.2 electromagnetically induced transparency (EIT)  much smaller than  : (  = natural line width ) interference structure ( narrow ) observed, which is called: EIT  larger than  : two separate features (of width ≈  ) observed, called AT-splitting also zero (EIT) between AT-components

Experiment exactly zero P S Ne* PP SS adiabat. states Ref Electromagnetically induced transparency 1 3 PP SS bare states 2

3.2 Electromagnetically induced transparency P S = 55 mW P S = 35 mW P S = 11 mW P S = 1,4 mW P P = 6,2 mW P P = 3,4 mW P P = 4,0 mW P P = 6,9 mW  S = 7.4 rad/ns  S = 5,9 rad/ns  S = 3,3 rad/ns  S = 1,2 rad/ns  P = 0.02 rad/ns Ref. 24

337.1 nm nm Sr cell detector transmission less than Electromagnetically induced transparency Ref. 76 WITHOUT 570 nm radiation WITH 570 nm radiation

Questions related to the topics discussed in lecture 6 (6.2) What physical mechanism causes electromagnetically induced transparency (EIT) and what is the connection, if any, between EIT and the Autler-Townes splitting ? (6.1) Draw the adiabatic state energies for a three-level system g, e, f with  e,g =  P, P-field detuning =  P and  e,f =  S, S-field detuning =  S for the following conditions: (a)  P = 0,  S = 0, (b)  P = 0,  S > 0, (c)  P > 0,  S < 0. Also assume that the S-field intensity is constant while the P-pulse is on and  P is much larger  S than.

end of 6 th lecture Coherent light-matter interaction: Optically driven adiabatic transfer processes