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Effect of Magnetic Fields on Coherent
Spectroscopy of Alkali Atoms
Leah MargalitUnder the supervision of
Prof. Arlene Wilson-Gordon
Department of Chemistry
Bar-Ilan University
Introduction
Energy levels of 87Rb267 MHz
157 MHz
794.7nm 780nm
6835 MHz
812 MHz72 MHz
(a) (b)
1gF 6835 MHz
1gF
2gF 2gF
1eF
eF =2 1eF
eF =3
eF =0
2eF
21/25 S
21/25 P
21/25 S
23/25 P
The fine and hyperfine energy levels of (a) D1 line and (b) D2 line of 87Rb.
Introduction
Zeeman Effect
Fg=1
Fg=2
Fe=1
Fe=2
5S1/2
5P1/2
794.7nm
6835MHz
812MHz
-1
-1
-1
-11
0 1
1
10
0
02
2
2
2
In the presence of a magnetic field
The magnetic field lifts the )2F+1(
degeneracy in eachhyperfine level by:
B F FE g BM
Introduction
Selection rules and light polarization
B
z
x
y
1() M
1() M
1() M
0() M 0
1
-10
Introduction
Coherence effects: Coherent Population Trapping (CPT)
g1g2
e
Two-photon or Raman resonance when
Fields are equally intense
Population trapped in lower levels and maximal coherence created
Zero absorption at line center )/=0(
1 2
1 2
Pump – probe configuration
The Hanle configuration
Introduction
B
t
Zero crossing
-0.1 -0.05 0 0.05 0.10.2
0.4
0.6
0.8
1
1.2
Bz (G)
Abs
orpt
ion
(cm
-1)
B
Abs
orpt
ion
CPT applications
Introduction
Atomic clock Magnetometry Slow light
Motivation
-1
-1 1
10
0-2 2
-1 10-2 2 -1 -0.5 0 0.5 1
x 108
10
15
20
25
30
35
40
[Hz]
Pro
be a
bs
Introduction
Motivation
-1
-1 1
10
0-2 2
-1 10-2 2
B
Introduction
We examined the effect of different magneticfields on the absorption spectrum of alkali atoms.
Static magnetic field )dc( Oscillating magnetic field )ac(
Longitudinal to the light propagation direction )LMF(
transverse to the light propagation direction )TMF(
B B
BB
kk
I. Degenerate Two Level System )DTLS(. II. Three level Lambda System.
Content
Hanle configuration Pump- probe configuration
I. Degenerate two-level system in presence of TMF
TMF in DTLS
Simplest CPT transition: Fg=1 Fe=0
The quantization axis is chosen to be along the axis of light propagation.
The TMF leads to the transfer of population to adjacent Zeeman sublevels.
The quantization axis is chosen to be along the total magnetic field .
The linear polarization now becomes + polarization.
There are two theoretical approaches to dealing with the presence of a transverse magnetic field (TMF) in addition to a LMF.
Hanle configuration
TMF in DTLS L. Margalit, M. Rosenbluh and A. D. Wilson-Gordon PRA 87, 033808 (2013)
-0.1 -0.05 0 0.05 0.10.2
0.4
0.6
0.8
1
1.2
Bz (G)
Abs
orpt
ion
(cm
-1)
-0.1 -0.05 0 0.05 0.10.2
0.4
0.6
0.8
1
1.2
Bz (G)
Abs
orpt
ion
(cm
-1)
Bx=0
Bx=0.01G
Peak at Bz=0 and dips at Bz =± Bx/2.
numerical results for Fg=1 Fe=0 transition in presence of TMF
Hanle configuration numerical results for Fg=1 Fe=0 transition in presence of TMF
TMF in DTLS L. Margalit, M. Rosenbluh and A. D. Wilson-Gordon PRA 87, 033808 (2013)
-0.1 -0.05 0 0.05 0.10.2
0.4
0.6
0.8
1
1.2
Bz (G)
Abs
orpt
ion
(cm
-1)
0 0.25 0.50
5
10
15
Bx (G)
Spl
ittin
g (M
Hz)
Bx=0
Bx=0.01G
TMF in DTLS
Simplified Bloch equations (resonant pump)
1 1 1 1 3 1
3 1 3 1 1 2 1
2 1 2 1 2 1 1 3 1
1 ) '( ) (,
) 2 '( 2 2 ,
) '( )1 3 (.
eg eg g g g g
g g g g eg g g
g g g g g e g g g g
i iV
i iV iA
i iV iA
1 1 1 1
1
21
1 1
2 )1 3 (,
) '( ) '(g g g g
eg
iV iA VD
i d
2 2 2
1
2 41 ,) '() 2 '(
V d A VDi i d
2) '() 2 '( 2d i i A
Solution
11 1where / , , A / 2B z F eg B x FB g B g
Absorption has maximum at =0 )Bz=0(,
and minima at = A )Bz = Bx/2(.
TMF in DTLS
Ground-state populations
-0.1 -0.05 0 0.05 0.10.1
0.2
0.3
0.4
0.5
Bz (G)
Pop
ulat
ion
of F
g=1, m
F=1
-0.1 -0.05 0 0.05 0.10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Bz (G)
popu
latio
n of
Fg=1
, mF=0
(b)(a)The redistribution of the population by the combined effects of the TMF and the collisions cause to population trapping in the Zeeman sublevels.
1, 1g gF m
without magnetic field
with TMF
Degree of coherence: Sij=|ij|2/iijj
TMF in DTLS
E B
||E B
TMF leads to formation of two new systems!!!
TMF in DTLS
The quantization axis is chosen to be along the
total magnetic field .
-0.1 -0.05 0 0.05 0.10.2
0.4
0.6
0.8
1
1.2
Bz (G)
Abs
orpt
ion
(cm
-1)
Bx=0
Bx=0.01G
TMF in DTLS
-0.1 -0.05 0 0.05 0.1
0.35
0.4
0.45
0.5
0.55
Bz [G]
Abs
orpt
ion
[cm
-1]
0
1
2
3
4
5
(a)
Adding ByThis method can be generalized to any transverse magnetic field in the xy plane by changing the direction of the polarization .
Varying angle between linear polarization and TMF:deepest dips when they are parallel
-4 -2 0 2 40.015
0.02
0.025
0.03
0.035
0.04
[Degree]
Spl
ittin
g [G
]
(b)
Pump-probe configurationnumerical results for Fg=1 Fe=0 transition in presence of LMF and TMF
-0.5 0 0.5 1 1.5
0.1
0.15
0.2
0.25
0.3
0.35
2 (MHz)
Pro
be a
bsor
ptio
n (c
m-1
)
b
c d
a
TMF in DTLS
a. No magnetic field.
b. only LMF
c. only TMF
d. LMF and TMF
LMF shifts spectrum, TMF splits spectrum
II. Coherence-population-trapping transients induced by an acmagnetic field
LMF modulation
The Atomic system
D1 line of 87Rb
LMF modulation
0 0 0 0sin ) ( , 4 , 0.3ms2
B B t t B G t L. Margalit, M. Rosenbluh and A. D. Wilson-Gordon, PRA 85, 063809 (2012)
Transient sequence
LMF modulation
Transient components
LMF modulation
Resonant pump, detuned probe
Sequence of transients
DHCT – deviation from half-cycle time ;no change in presence of buffer gas
Applications: Magnetometry
200Hz200Hz & Bdc=0.2G
III. Coherent-population-trapping transients induced by amodulated transverse magnetic field
TMF modulation
Steady-state absorption in presence of different magnetic fields
In total (4I+1) dips .
: Two photon detuning: Zeeman splitting between adjacent sublevels
a. No MF
b. only LMF )=0, 2(
c. LMF and TMF )=0, , 2, 3(
d. only TMF )=, 3(
L. Margalit, M. Rosenbluh and A. D. Wilson-Gordon, PRA 88, 023827 (2013)
See K. Cox et al. PRA 83, 015801 (2011)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
a
1
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
a
b
1
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
a
b
c
2
3
1
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
a
b
cd
2
3
1
TMF modulation
0 1 2 3 4 5 6 7
0
2
4
6
8
10
12
t (ms)P
robe
Abs
orpt
ion
(cm
-1)
Bx=0 Bx=0
total probe
2
3
0 1 2 3 4 5 6 7
-0.1
0
0.1TMF
TMF
(G)
Effect of modulating TMF on probe absorption at point 1: zero Raman detuning =0 c b
All the Λ subsystems with δ=0 energy difference between the lower sublevels, in the presence of TMF.
2,4 5 6
00.1z xB B G
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
b
c
1
TMF modulation
TMF Modulation in the absence of Bz
The time evolution in this case is similar to that obtained in the presence of a modulated LMF
∆=0, point 1 ∆= -30, point 3
There are two sets of transients: the transients that occur just after the TMF reaches its maximal absolute value and the transients that occur immediately after the TMF passes through zero
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.52
4
6
8
10
12
14
16
(MHz)
Pro
be A
bsor
ptio
n (c
m-1
)
a
b
cd
2
3
1
TMF modulation
TMF modulation as a function of detuning in the absence of LMF
0xB
Summery
Conclusions The absorption spectra in DTLS are split in the presence of a TMF and
that the splitting is proportional to the magnitude of the TMF.
The TMF leads to the creation of new two-photon detuned subsystems formed by the Zeeman sublevels.
The effects of LMF and TMF are distinguished from each other.
LMF modulation- variation in the contributions to the absorption that derive from the original subsystems due to their entry and exit from CPT.
TMF modulation - creation and destruction of new subsystems.
Acknowledgments
AcknowledgmentsProf Arlene Wilson-GordonThe Chemistry department, Bar Ilan University
Prof Michael Rosenblue, head of the Physics department, Bar Ilan University
Prof Ferruccio Renzoni. The Physics and Astronomy department, of the University College London.
Prof Dimitry Budker, the Physics department, Berkeley University
Coupling of surfaceplasmon resonances
motivationTo understand the coupling nature of metal nano-holes surface plasmons and investigate its polarization influence in terms of hybridization model.
200nm
Surface plasmons Surface plasmon resonances – the collective coherence oscillation
of conduction electrons in metallic nanostructure .
CTC=350nm CTC=400nm CTC=450nm
Surface plasmon in 2D hole arrays
Plasmon wavelength increases with the periodicity.
3
The Hybridization model
Changing the polarization results in scanning the various modes exist in the system.
Nano fabrication
CTC= 400 nm
CTC= 500 nm
CTC= 600 nm
CTC= 700 nm
CTC= 300 nm
CTC=250 nm
1
3
3
nm4001 2
[nm]300 400 500 600 700 800 900
180
190
200
210
220
230
240
CTC= 400 nm
CTC= 500 nm
CTC= 600 nm
CTC= 700 nm
CTC= 300 nm
200 300 400 500 600 700 800 900 10000
0.01
0.02
0.03
0.04
0.05
0.06
0.07
[nm]
CTC=700nmCTC=600nmCTC=500nmCTC=400nmCTC=300nm
The dimers mode and its amplitude is change as a function of the dimers distance.
Spectral measurements
Kelvin Probe Force Microscopy (KPFM) measurement
Plasmoelectric surface potential as large as 100mV. Energy application: Conversion of optical power to an electric potential!
AFM: height topography Surface potential
Height mergepotential
A change in the surface potential in the vicinity of the structures
Height Potential Merge
Thank you for the listening!
LMF modulation
47
Why is Λ1 is more oscillatory than Λ3?
Lower level coherence of Λ1 and Λ3
Two processes occur simultaneously in the system: energy change of the sublevels and transfer of population.
A single Λ system: only the amplitudes of the oscillations change when the initial population of the system is changed.
LMF modulation
48
When during the time evolution of a system some parameter is suddenly changed in a significant way, the system undergoes for a while a complicated dynamic evolution that it is a transient and then a stationary state is reached.
What is a transient?
1 .Until the system achieves CPT 2 .CPT is first established and then a change is been made.
Jyotsna and Agarwal, PRA 52, 3147 )1995(. Valente et al. PRA 65, 023814 )2002(.
49LMF modulation
1. Initially, pop =1/8 in each mg’ Zeeman sublevel.
2. Constant magnetic field traps pop in sublevel Fg’=2, mg’=2 (trap state).
3. At same time, clock transition 2 which is always in two-photon resonance enters dark state.
4. As B0, 1,3 and TLS become resonant and pumping from them is more efficient.
5. At B=0, 1,3 exhibit CPT and then population flows into these subsystems from the trap state.
6. As |B| increases again, pop flows back into trap state.
Population evolution
The transfer of population occurs via decay to a reservoir (γ ) and collisional decay rate which are the same for 1 and 3.
Pop transfer from trap state goes mainly to the nearby 3 rather than 1, which leads to damping of the oscillations in lower-level coherence.
Increasing the Rabi frequency in a single system leads to the same effect.