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Condensed matter physics of cold atoms. Rosen-Zener Tunneling and Rosen-Zener Ramsey Interferometer. Li-Bin Fu ( 傅立斌 ) Institute of applied physics and computational mathematics, Beijing. Beijing, Sep 22 2009. Collaborators. Beijing institute of applied physics and computational - PowerPoint PPT Presentation
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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)