Download Laser intensity induced transparency in atom

Chin. Sci. Bull.
DOI 10.1007/s11434-014-0448-6
csb.scichina.com
www.springer.com/scp
Article
Atomic & Molecular Physics
Laser intensity induced transparency in atom-molecular
transition process
Jie Ma • Yuqing Li • Jizhou Wu • Liantuan Xiao
Suotang Jia
•
Received: 8 January 2014 / Accepted: 17 April 2014
Ó Science China Press and Springer-Verlag Berlin Heidelberg 2014
Abstract We propose a new transparency mechanism,
which is based on photoassociation (PA) laser intensity
induced transitional frequency shift for ultracold cesium
molecules formed in PA scheme. The PA laser intensity is
supposed to change before the atom-molecule resonance.
Thus, a remarkable transparent effect for PA laser is
expected to appear in the vicinity of original resonant
transitional line, where the variation of PA laser intensity
induces the shift of the excited molecular levels. The
mechanism is different from electromagnetically induced
transparency effect and interesting for further research on
the scattering length for cesium atomic condensate.
Keywords Atom-molecular transition Ultracold
Cesium molecules Laser induced frequency shift Laser intensity induced transparency
1 Introduction
The atom-molecule system involved in the photoassociation
(PA) process provides a spectacular platform that enables
the physicists implementing various applications on high
sensitive and high resolution measurements [1–3], which
are essential for investigating the long-range molecular
dipole-dipole interaction [4–6], atom-molecule collision
[7, 8] and quantum information processing [9, 10], storage
[11] and quantum simulation [12, 13]. Especially,
J. Ma (&) Y. Li J. Wu L. Xiao S. Jia
State Key Laboratory of Quantum Optics and Quantum Optics
Devices, Institute of Laser Spectroscopy, College of Physics and
Electronics Engineering, Shanxi University,
Taiyuan 030006, China
e-mail: [email protected]
molecular dimmers populated in the ground state can be
obtained by spontaneous decay from the optical excited
molecule formed during single-color PA experiment [14].
Furthermore, the deeply bound ground state molecules can
be produced by two-color PA through optical coupling with
stimulated Raman transition [15, 16]. In the experimental
and theoretical study of two-color PA spectroscopy, there
was an interesting effect, i.e. the Autler–Townes splitting of
the excited molecular level induced by the Raman laser,
which was observed firstly from the signal of atom-loss in
the PA progress in optically trapped 6Li MOT [17].
Importantly, the trapped cold atoms did not lose at the
resonant position of the transitional line. The Electromagnetically Induced Transparency (EIT) [18] has been well
known as a superposition of the long-lived system eigenstates decoupled from the light field [11]. The atom-molecule dark state was also observed in a Rb Bose–Einstein
condensate by two-color PA [19]. So far, EIT has been
demonstrated to extend to Doppler broadened molecular
gas by using two photon transition related to a V-type
molecular system in a vapor cell for sodium molecules [20].
The frequency shift of resonant transitional positions
from atomic scattering states to molecular excited state is a
significant finding. The frequency shifts in 7Li quantum
degenerate gas [21] and Na Bose–Einstein condensate [22]
were analyzed by semi-analytical channel scattering theory
[23]. A more precise measurement for the shifts of the
rovibrational level was developed in ultracold metastable
4
He atoms [24], in which the s-wave scattering length was
determined. Recently, the high sensitive determination of
PA laser-induced frequency shifts for ultralcold cesium
molecules had been reported by employing a frequency
shifter technique [25].
In the photoassociation process, a pair of cold alkali
atoms, mainly at large inter-atomic distance, resonantly
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Chin. Sci. Bull.
absorbs a photon whose frequency red-detuned from the
s?p atomic transition. Thus, a molecule with short lifetime
is obtained mainly populated in a high-lying rovibrational
level in the electronic excited state. In this paper, we theoretically present that a transparency would occur in the
vicinity of the absolute resonance line by changing the PA
laser intensity, as the PA laser frequency detuned to the
atom-molecule resonant transitional line. We show that the
variation of PA laser intensity induces a shift for the
excited molecular levels, and consequently, the PA laser
beam is not absorbed by the atoms with the resonant
transitional frequency, but absorbs at a special red or blue
detuning from the original resonant transitional frequency.
We define this effect as an ‘‘artificial transparency’’, which
occurs due to the manipulation of the PA laser intensity.
2 The semi-analytic line-shape formula
In order to intuitively describe the interaction between the
scattering atoms and laser field, a line-shape formula is
deduced. The line-shape formulas had been suggested
previously for single- [26] and two-color [27] PA spectra
using atomic scattering theory. A general formula shows
that the trap loss probability clearly separates laser intensity and detuning from the overlap integrals of molecular
wave functions [23]. Correspondingly, laser-induced
energy shift and line broadening are contained in this
simplified line-shape formula (1), which is derived from
the scattering matrix element of K rate coefficient,
jsj2 ¼
cC
½E ðD þ E1 Þ2 þ
cþC 2
2
;
ð1Þ
where c and C means spontaneous radiation rate and
stimulated rate, respectively; E is excited molecular
energy, D is the detuning from the resonant transitional
line, and E1 is laser induced energy shift for the excited
molecular level.
In the experiment, laser induced frequency shift of the
atom-molecule resonant transitional line stems from the
laser induced coupling between the atomic scattering state
and the bound molecular state. The energy shifts show a
linear dependence on laser intensity [25]. For the Cesium
molecular case, the slopes for different vibrational levels
and rotational progressions are listed in Table 1. Thus a
simple function of energy shift versus PA laser intensity
can be written as:
E1 ¼ aI þ b;
ð2Þ
where a is the slope for the linear variation of energy shift
versus PA laser intensity, b is the intercept, I is the PA laser
intensity.
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Table 1 The rate of laser induced frequency shift and molecular
energy without perturbation
v
J
Bound energy (cm-1)
Slope (a)
4
4
11,661.954
-0.08396
11
4
11,672.943
-0.13676
17
4
11,681.337
-0.1531
17
3
11,681.326
-0.1207
17
2
11,681.317
-0.21958
3 Cesium atom-molecule system case
In order to demonstrate the laser intensity induced transparency, a specific frequency was chosen, at which the PA
laser intensity was set to 300 W/cm2, such that the resonant
frequency is not influenced by the variation of PA laser
intensity. The binding energy of excited molecule for different vibrational and rovibrational levels was listed in Ref.
[28]. As PA laser intensity changed before the frequency
detuned to the atom-molecule resonant transitional line, the
transparency of PA laser thus occur in the PA process. In
the experiment, a square wave pulse signal can be used to
modulate the acoustic-optical modulator (AOM) through
thus the PA laser intensity can be varied from I1 =
345 W/cm2 to I2 = 255 W/cm2. The start point of changing
PA laser intensity is set corresponding to the original atommolecule resonant line, for example, *300 W/cm2. The
binding energy level (v = 17, J = 2) of excited cesium
molecular (6S1/2 ? 6P3/2) 0g state is chosen for the analysis. The new resonant lines will red and blue shifted for
–10 and ?10 MHz from the original transitional frequency
corresponding to a PA laser intensity of *300 W/cm2.
This is calculated by Eq. (2) of PA laser-induced frequency
shift.
The atomic loss signal emerges as the frequency of PA
laser detuned to the atom-molecule resonant transitional
line where no modulation is applied. The PA laser intensity
is kept to *300 W/cm2, and simultaneously, a direct
current signal with a constant voltage is imported into the
‘‘Mod in’’ port of the AOM. The PA photon will be resonantly absorbed to bind two colliding atoms and form an
excited molecule. As the PA laser red detuned from the
original resonant transitional line, the PA laser intensity is
changed to I1 = 345 W/cm2. And the laser intensity is
averted to I2 = 255 W/cm2 immediately as the PA laser
blue detuned from the transitional line. As a result, the
excited molecular level will red shift for 10 MHz comparing with the original resonant line and blue shifted for
10 MHz, respectively just as Fig. 1 shown. The jdi state is
the scattering state for two colliding ground atoms, and jbi
is the excited molecular level. The jbi state would shift to
jai or jci by changing the PA laser intensity between I1 =
Chin. Sci. Bull.
a
AOM
PA
laser
d
Fig. 1 (Color online) PA laser intensity induced excited molecular
energy shift schemes: The output power of PA laser will be varied
between two different values by using a square wave signal to
modulate AOM. Thus, the excited molecular energy shifts with
different detunings (the two solid lines) to original resonant frequency
(dash line) were obtained
345 W/cm2 and I2 = 255 W/cm2, corresponding to the red
or blue detuning of the original resonant level jbi. As the
PA laser frequency is scanned over a very large range, the
number of the trapped atoms decreases obviously at the
frequency detuned for ; 10 MHz from the original resonant transitional line, thus the fluorescence spectra of the
atoms presents a transparency at the original resonant
transitional position in the single color PA process, i.e.
atoms do not lose by absorbing the photons from the PA
laser.
mainly determined by both c and C for a certain excited
molecular state. According to the result of Ref. [29], the
trap-loss probability reaches maximum amplitude and
keeps invariable as increasing the PA laser intensity since
the saturation intensity. This means that the value of C
keeps invariable as the PA laser intensity reaches the saturation intensity. In order to avoid the influence from the
variation of C, we define the resonant transitional frequency where PA laser intensity is *300 W/cm2 as the
original atom-molecule resonant transitional line. This PA
laser intensity is high enough to achieve the saturation
effect in the PA process, and therefore the value of C is
regarded as a constant and equals to c [29].
The trap-loss probability in PA process is demonstrated
in Fig. 2 for different PA laser intensity. The new resonant
position is obtained by changing the laser intensity and
locates at the red and blue detuning to the original resonant
transitional line with –10 and ?10 MHz respectively. This
results from the variation of PA laser intensity induced
shift of original resonant transitional frequency. Note that
the PA laser intensity is large enough so that the saturation
effect could be observed and thus enabled us simply
employing a parameter for stimulated rate. For cesium
molecule, we can obtain C & c & 10.4 MHz.
Figure 3 shows the transparency occurring on the original resonant transitional line. The PA laser will be
transparent in atom-molecule system when no loss signal
emerges and PA laser is not absorbed by the colliding
Scattering probability (a.u.)
c
b
4 Results and analyses
According to the scattering theory [23], the stimulated rate
of the trapped cold atoms in the PA process, namely C, is a
function of the PA laser intensity I,
4p2
I jh/jf0 ij2 d2 ;
c
ð3Þ
where u and f0 are the wavefunctions for bound excited
molecular state and initial free atomic scattering state in
PA process, respectively. d is the atom-molecule dipole
matrix element and regarded as a constant.
On the other hand, the spontaneous decay rate c is only
determined by the coupling between the bound excited
molecular state u and the ultimate atomic state f1,
c ¼ 2pjh/jf1 ij2 V 2 ;
ð4Þ
where V is the artificial coupling element between the
bound excited molecular state and the ultimate free atomic
state.
C increases with the PA laser intensity I, while c is
almost a constant. When C equals to c, the saturation effect
of PA occurs. The saturation intensity of PA laser Is is
Dispersive index (a.u.)
C¼
0.04
(a)
0.03
0.02
0.01
0.00
(b)
0.0005
0.0000
–0.0005
–100 –80 –60 –40 –20
0
20
40
60
80
100
Detuning (MHz)
Fig. 2 (Color online) a Solid line: the trap-loss probability as a
function of the detuning to the resonant line with I = 390 W/cm2; dash
line: the trap-loss probability corresponds to I = 345 W/cm2; dotted
line: the trap-loss probability corresponds to I = 300 W/cm2. b The
corresponding dispersive curves for curves in a
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Chin. Sci. Bull.
0.02
new different resonant transitional lines are anticipated
locating on both sides of the original resonant transitional
line. The transparency of PA laser would emerge at the
position of the original resonance line when the PA laser
intensity varies before the original resonant transitional
line.
0.01
5 Conclusions
Dispersive index (a.u.)
Scattering probability (a.u.)
0.04
(a)
0.03
(b)
0.0005
0.0000
–0.0005
–100 –80 –60 –40 –20
0
20
40
60
80 100
Detuning (MHz)
Fig. 3 (Color online) PA laser intensity induced transparency.
a Dash line: The trap-loss probability as a function of the detuning
to the resonant line with I = 345 W/cm2; solid line: The trap-loss
probability corresponds to I = 390 W/cm2 before the original
resonance line and then I = 300 W/cm2, and reflects transparency
effect by changing PA laser intensity; b the dispersive curves
corresponds to graph (a)
atoms in PA experiment. In addition, in Fig. 3b, a very
steep dispersive signal indicates that the transparency for
PA laser appears near the original resonant transitional line.
The transparency of PA laser in an atom-molecular
system is proposed by changing the PA laser intensity. The
mechanism resulted in the transparency of PA laser is
different from the EIT effect in the atomic system, which
required a strong coupling laser and a weak probing laser,
and involved in a coherent effect due to the dark quantum
superposition state. We analyze this effect by using the
semi-analytical coupling scattering theory, and the artificial
potential is introduced to derive line-shape formula containing laser intensity induced energy shift. The artificial
channel accounts phenomenologically for trap-loss processes in PA experiment, the energy shift is responsible for
phase shifts due to the interaction between other channels
[23].
According to the experimental result [25], we choose the
excited molecular level (v = 17, J = 2) which has a very
large rate for variation of frequency shift versus PA laser
intensity, and thus obtain more frequency shifts data by
changing PA laser intensity. For comparison, we present
the curve of trap-loss probability in PA process and its
dispersive curve with different laser intensities. The two
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In conclusion, a new transparency mechanism is proposed,
which is based on PA laser intensity induced transitional
frequency shift for cesium molecules. This work is crucial
for investigating the problem of the phase shift between the
colliding scattering atomic pair and the rate of PA. The
theoretical results shown in Fig. 3 are similar as the line
shape of EIT effect or Coupled-Resonator-Induced Transparency (CRIT) effect [30]. The result we presented can be
analyzed by trap-loss probability of PA process. The selfinduced transparency for the PA laser intensity is a different and interesting mechanism comparing with EIT and
CRIT. The current atom-molecular system resorts to only
one laser and does not involve in any coherent effects in the
process. Further more, the location of the transparency can
be controlled by modifying the PA laser intensity and thus
the position of the resonant transitional lines can be easily
relocated.
Acknowledgments This work was supported by the National Basic
Research Program of China (2012CB921603), the National High Technology Research and Development Program of China (2011AA010801),
the Program for Changjiang Scholars and Innovative Research Team in
University (IRT13076), the International Science and Technology
Cooperation Program of China (2011DFA12490), the National Natural
Science Foundation of China (NSFC) (61378014, 61308023 and
10934004), the NSFC Project for Excellent Research Team (61121064),
the Specialized Research Fund for the Doctoral Program of Higher
Education of China (20131401120012) and the Natural Science Foundation (NSF) for Young Scientists of Shanxi Province (2013021005-1).
References
1. Drag C, Tolra BL, Dulieu O et al (2000) Experimental versus
theoretical rates for photoassociation and for formation of ultracold molecules. IEEE J Quantum Electron 36:1378–1388
2. Pichler M, Chen H, Stwalley WC (2004) Photoassociation
spectroscopy of ultracold Cs below the 6P1/2 limit. J Chem Phys
121:1796–1801
3. Pichler M, Chen H, Stwalley WC (2004) Photoassociation
spectroscopy of ultracold Cs below the 6P3/2 limit. J Chem Phys
121:6779–6784
4. Fioretti A, Comparat D, Drag C et al (1999) Long-range forces
between cold atoms. Phys Rev Lett 82:1839–1842
5. Santos L, Shlyapnikov GV, Zoller P et al (2000) Bose–Einstein
condensation in trapped dipolar gases. Phys Rev Lett 85:1791–1794
6. Ospelkaus C, Ospelkaus S, Humbert L et al (2006) Ultracold
heteronuclear molecules in a 3D optical lattice. Phys Rev Lett
97:120402
Chin. Sci. Bull.
7. Staanum P, Kraft SD, Lange J et al (2006) Experimental investigation of ultracold atom-molecule collisions. Phys Rev Lett
96:023201
8. Zahzam N, Vogt T, Mudrich M et al (2006) Atom-molecule
collisions in an optically trapped Gas. Phys Rev Lett 96:023202
9. Carr LD, DeMille D, Krems RV et al (2009) Cold and ultracold
molecules: science, technology and applications. New J Phys
11:055049
10. Yu S, He XD, Xu P et al (2012) Single atoms in the ring lattice
for quantum information processing and quantum simulation.
Chin Sci Bull 57:1931–1945
11. Wang H, Xie CD, Peng KC (2012) Quantum storage of optical
signals and coherent manipulation of quantum states based on
electromagnetically induced transparency. Chin Sci Bull
57:1893–1902
12. Bloch I, Dalibard J, Nascimbène S (2012) Quantum simulations
with ultracold quantum gases. Nat Phys 8:267–276
13. Zhang XF, Chen YH, Liu GC et al (2012) Quantum information
and many body physics with cold atoms. Chin Sci Bull
57:1910–1918
14. Fioretti A, Comparat D, Crubellier A et al (1998) Formation of
cold Cs2 molecules through photoassociation. Phys Rev Lett
80:4402–4405
15. Tsai CC, Freeland RS, Vogels JM et al (1999) Two-color
photoassociation spectroscopy of ground state Rb2. Phys Rev Lett
79:1245–1248
16. Chin C, Vuletic V, Kerman AJ et al (2000) High resolution
Feshbach spectroscopy of cesium. Phys Rev Lett 85:2717–2720
17. Schlöder U, Deuschle T, Silber C et al (2003) Scaling laws for
evaporative cooling in time-dependent optical traps. Phys Rev A
68:051403
18. Harris SE (1997) Electromagnetically induced transparency. Phys
Today 50:24
19. Winkler K, Thalhammer G, Theis M et al (2005) Atom-molecule
dark states in a Bose–Einstein condensate. Phys Rev Lett 95:063202
20. Lazoudis A, Kirova T, Ahmed EH et al (2011) Electromagnetically induced transparency in an open V-type molecular system.
Phys Rev A 83:063419
21. Prodan ID, Pichler M, Junker M et al (2003) Intensity dependence
of photoassociation in a quantum degenerate atomic gas. Phys
Rev Lett 91:080402
22. McKenzie C, Denschlag JH, Häffner H et al (2002) Photoassociation of sodium in a Bose–Einstein condensate. Phys Rev Lett
88:120403
23. Bohn JL, Julienne PS (1999) Semianalytic theory of laser-assisted
resonant cold collisions. Phys Rev A 60:414–425
24. Kim J, Moal S, Portier M et al (2005) Frequency shifts of
photoassociative spectra of ultracold metastable helium atoms: a
new measurement of the s-wave scattering length. Europhys Lett
72:548–554
25. Wu JZ, Ji ZH, Zhang YC et al (2011) High sensitive determination of laser-induced frequency shifts of ultracold cesium
molecules. Opt Lett 36:2038–2040
26. Napolitano R, Weiner J, Williams C et al (1994) Line shapes of
high resolution photoassociation spectra of optically cooled
atoms. Phys Rev Lett 73:1352–1355
27. Bohn JL, Julienne PS (1996) Semianalytic treatment of two-color
photoassociation spectroscopy and control of cold atoms. Phys
Rev A 54:R4637–R4640
28. Ma J, Wu JZ, Zhao YT et al (2010) Determination of the rotational constant of the Cs2 0g- (6s ? 6p3/2) state by trap loss
spectroscopy. Opt Express 18:17089–17095
29. Ma J, Wang LR, Ji WB et al (2007) Saturation of photoassociation in Cs Magneto-optical Trap. Chin Phys Lett 24:1904–1907
30. Di K, Xie CD, Zhang J (2011) Coupled-resonator-induced
transparency with a squeezed vacuum. Phys Rev Lett 106:153602
123