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.