Rosen-Zener Tunneling and Rosen-Zener Ramsey Interferometer

Li-Bin Fu ( 傅立斌 ) Institute of applied physics and computational mathematics, Beijing

Condensed matter physics of cold atoms KITPC

Beijing, Sep 22 2009

Collaborators

Beijing institute of applied physics and computationalMathematics Prof. Jie Liu DiFa Ye Sheng-Chang Li

East China Normal UniversityProf. Weiping Zhang

Australian National UniversityDr. Chaohong Lee

Outline

Nonlinear Rosen-Zener tunneling Rosen-Zener interference with Double-Well BE

Cs Ramsey Interferometer via nonlinear RZ proce

ss

S-GS-G

Rosen-Zener Tunneling

Detector

B=B(z) is a spatial dependent transversl field

The Model of Rosen-Zener tunneling

For γ=0 , the problem is solvable. The transition probability is defined as the population of (0,1)

Nonlinear Rosen-Zener Model

Two components BECs

Transition Probability of adiabatic case (T>>1) for γ=0

For the linear case, we can obtain the transition probability (see fig .a)

For weak nonlinear case, we find the interesting case that the transition probablity is rectangular oscillation. (seeing fig. b and c)

For strong nonliear case, transition probability is zero in adiabatic regime.

Eigen Levels

Nonliearity leads toextra egien levels. Theconfigurations of new levels play important role in adiabatic process.

The bifurcation of fixed points gives rise to rectangular oscillation

|b|2

θ=θa-θb

The period of rectangular oscillation

The small oscillation around fixed piont

The phase at the bifurcation point determine the evoluton direction

Then we obtain the period as

Analytic results for sudden limits

With the transformation

One gets

RZT for nondegenerated case γ≠0

Nonlinear Rosen-Zener Rosen-Zener interference with Double-Well BE

Cs Ramsey Interferometer via nonlinear RZ proce

ss

Rosen-Zener interference with Double-Well BECs

Coherent Transition of atoms in Double Well

Simple model

Simple model

Results of the Simple model

Phase locking effectplays the key role ofthe coherent tran-sition.

Interference Pattern

Phase sensitive aroundthe first excited state.

Nonlinear Rosen-Zener Rosen-Zener interference with Double-Well BE

Cs Ramsey Interferometer via nonlinear RZ proce

ss

Ramsey Interferometer via nonlinear RZ process

Various Interference Pattern

Theoretical Prediction of frequencies of Fringes

The fringers frequencies determinedby the accumulated phase during thesecond stage, which is

where s is the population differenceof the first RZ process, then the frequencies are

Theoretical prediction of frequencies of Fringes

The transition probability of the first stage

Then the frequencies of Ramsey fringes

For sudden limit

For adiabatic limit

The population difference ofthe first stage

The frequncies of Ramsey fringes

Theoretical prediction of frequencies of Fringes

The transition probability of the first stage

Then the frequencies of Ramsey fringes

For sudden limit

For adiabatic limit

The population difference ofthe first stage

The frequncies of Ramsey fringes

Frequencies of Fringes

Sudden limit

Adiabatic limit

General case

The oscillation near c=0 is due to breakdown of adiabatic evolution

The oscillation near c=0

Adiabatic condition

Summary

Nonlinear Rosen-Zener Tunneling The nonlinearity could dramatically affect the transition

dynamics leading to many interesting phenomena Realization RZ interferences in Double-Well BECs Ramsy interference with Rosen-Zener Process The frequency of Ramsey pattern is dependent both on

nonliearity and energy bias.

1. DiFa Ye, Li-Bin Fu, and Jie Liu, Phys. Rev. A 77 013402 (2008)2. Li-Bin Fu, Di-Fa Ye, Chaohong Lee, Weiping Zhang, Jie Liu, Phys. Rev. A 80 13619 (2009)

3. Sheng-Chang Li, Li-Bin Fu, Wen-Shan Duan, Jie Liu , Phys. Rev. A 78 063621 (2008)