Three-level Photon Echo for Quasi-degenerated Levels
Ahmadi T, Pulkin S.A, Sheftsov V
Department of general physics, St. Petersburg state university, St. Petersburg, Russia Email: tara.ahmadi.smart@gmail.com
Abstract—Quantum optical data storage is a key element in quantum information processing. However, most modified photon echoes protocols are still limited by lack of resonance signal to explain time scales of different systems. In this paper, we studied three-pulse photon-echo system by using density matrix in Λ-scheme. . It will be shown that the time position of three-pulse echo signals is proportional to ratio of detuning frequencies from the resonance frequencies of transitions in a non-uniform distribution. In the last part of paper, you can see the importance effect of frequency distance between two degenerate levels (d) on the delay time of signal.
Keywords—three-level photon echo, polarization, proportion of frequencies, delay time, decay coefficient.
I. INTRODUCTION
Photon echo spectroscopy is the most important way which can deeply extract microscopic information about the time scales of molecular and collective dynamics of condensed phase. Photon echo spectroscopy can cover any inhomogeneous broadening of medium.
II. THEORETICAL FRAMEWORK
In this work, we find out that proportion
is valid where .
The density matrix equations were solved numerically. We found, that the position of three-level photon echo signal is:
Polarization of signal usually depends on frequencies between levels and detuning frequencies. This relationship gets an exponentially resonance for signal polarization between ground level and a degenerated level.
(
) Where is half-width of inhomogeneous contour.
III. NUMERICAL FRAMEWORK
We got some numerical simulations by using RWA (rotating wave approximation) for the medium population. The relevant system properties are: duration of the signal pulses of 100 fs, the transition probabilities are denoted by γ21 and γ23 ~ 1010c-1, Homogeneous broadening Г ~ 1012 c-1, γ13=0, Г13=0, Δ12=50 γ. On Fig.1, one can see one of the results
Fig.1: (Top) intensity of echo signal as a function of delay time with different “d”, Blue =0.05, Red=0.10,(Bottom) Red=0,Blue=∞
The period of exponential decay is proportional to the detuning time. We can get a-decay coefficient from this figure as
which has a good agreement with theory.
( )
IV. CONCLUSION
We carried out numerical simulation of an atomic medium for two driving pulses and one signal pulse for neighbor quasi- degenerated level transition in Λ-scheme. . Basic on the calculations the ratio of pulse signal to interval between 1 and 2 is
. In other words by using the effect of frequency distance on the time of echo signal occurrence, it’s possible to increase memory time of this dot to 500μs.
Increasing memory time of quantum dots is one of the most important tasks of quantum electronics.
References
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[2] S. A. Pul’kin,Computer simulation of femtosecond 3-pulses 2-colors phton echo,Opt. Spectrosc. 93,2, 2002
[3] X.H.Yang, Ultrafast coherent population transfer by 2-laser pulses, Eur.Phy.D 57,253258, 2010