The Ramsey Method Ramsey interferometry

ramsey fringes

ramsey improved upon rabi s method splitting 1 interaction zone 2 short interaction zones, each applying





π
2




{\displaystyle {\frac {\pi }{2}}}

pulse. 2 interaction zones separated longer non-interaction zone. making 2 interaction zones short, atoms spend shorter time in presence of external electromagnetic fields in rabi model. advantageous because longer atoms in interaction zone, more inhomogeneities (such inhomogeneous field) lead reduced precision in determining



Δ


{\displaystyle \delta }

. non-interaction zone in ramsey s model can made longer 1 interaction zone in rabi s method because there no perpendicular field





b


⊥




{\displaystyle \mathbf {b} _{\perp }}

being applied in non-interaction zone (although there still





b


∥




{\displaystyle \mathbf {b} _{\|}}

).

the hamiltonian in rotating frame 2 interaction zones same of rabi method, , in non-interaction zone hamiltonian







σ

z


^





{\displaystyle {\hat {\sigma _{z}}}}

term. first



π

/

2


{\displaystyle \pi /2}

pulse applied atoms in ground state, whereupon atoms reach non-interaction zone , spins precess z-axis time



t


{\displaystyle t}

.



π

/

2


{\displaystyle \pi /2}

pulse applied , probability measured—practically experiment must done many times, because 1 measurement not enough determine probability of measuring value. (see bloch sphere description below). applying evolution atoms of 1 velocity, probability find atom in excited state function of detuning , time of flight



t


{\displaystyle t}

in non-interaction zone (taking




|

Δ

|

≪

Ω

⊥




{\displaystyle |\delta |\ll \omega _{\perp }}

here):

this probability function describes well-known ramsey fringes.

if there distribution of velocities , hard pulse




(

|

Δ

|

≪

Ω

⊥


)



{\displaystyle \left(|\delta |\ll \omega _{\perp }\right)}

applied in interaction zones of spins of atoms rotated





π
2




{\displaystyle {\frac {\pi }{2}}}

on bloch sphere regardless of whether or not excited same resonance frequency, ramsey fringes similar discussed above. if hard pulse not applied, variation in interaction times must taken account. results ramsey fringes in envelope in shape of rabi method probability atoms of 1 velocity. line width



δ


{\displaystyle \delta }

of fringes in case determines precision



Δ


{\displaystyle \delta }

can determined , is:

by increasing time of flight in non-interaction zone,



t


{\displaystyle t}

, or equivalently increasing length



l


{\displaystyle l}

of non-interaction zone, line width can improved as 0.6 times of other methods.

because ramsey s model allows longer observation time, 1 can more precisely differentiate between



ω


{\displaystyle \omega }

,




ω

0




{\displaystyle \omega _{0}}

. statement of time-energy uncertainty principle: larger uncertainty in time domain, smaller uncertainty in energy domain, or equivalently frequency domain. thought of way, if 2 waves of same frequency superimposed upon each other, impossible distinguish them if resolution of our eyes larger difference between 2 waves. after long period of time difference between 2 waves become large enough differentiate two.

early ramsey interferometers used 2 interaction zones separated in space, possible use 2 pulses separated in time, long pulses coherent. in case of time-separated pulses, longer time between pulses, more precise measurement.