Summer Project Report 2011

8/6/2019 Summer Project Report 2011

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“Study and Characterization of Rubidium Diode

Laser and its application in Doppler free

Spectroscopy”

SUMMER PROJECT REPORT

(MAY – JULY 2011)

Anat Siddharth

Second Year Undergraduate

Engineering Physics, IIT Guwahati

Under the guidance of Prof. Vasant Natarajan

Atomic and Optical Physics Lab, Physics Department Indian Institute of Science - Bangalore 560 012, India



1

Preface

The content of this report includes my understanding and summary of

concepts that I learnt during the experiments that I did in the span of 2 months(May-July 2011) in the atomic and optical physics lab of physics department at

Indian Institute of Science, Bangalore under the supervision of Prof. Vasant

Natarajan. Initially I assembled an extended cavity diode laser (ECDL) of

wavelength 795 nm. Then I made a saturation absorption spectroscopy

arrangement to observe spectrum of D1 line of rubidium atoms. The Doppler

free spectroscopy arrangement also enabled me to do frequency locking of the

laser using Pound-Drever-Hall (PDH) technique. Then I used the laser to

measure the hyperfine splitting of the rubidium atoms using an acousto-optic

modulator and the saturation absorption spectroscopy arrangement.

I have divided the report into three parts. In the first part I have tried to

explain the concept behind Doppler free spectroscopy by saturation

absorption and the experiment that I performed. The second part elucidates

about the various part to set up a laser and also about the PDH technique used

for doing frequency locking of laser. The last part includes the working

principle of acousto-optic modulator (AOM) for frequency shifting of laser

which is used for measuring the hyperfine interval of 85

Rb. Also includes a brief

explanation on hyperfine structures.



2

Acknowledgement

I express my gratitude towards my mentor and guide, Prof. Vasant Natarajan,

for giving me an opportunity to work in his lab. He regularly took updatesabout the progress of my work and experimental findings, pointed out

fallacies, explained the intricacies behind practical work and appreciated

genuine results. It was a novel experience to work in the lab which encouraged

me to work hard and to experiment with an open perspective. I am deeply

indebted to senior PhD student Alok Kumar Singh for encouraging and helping

me and for explaining things about the equipments and the physics behind it. I

am also thankful for the thought provoking discussions with my co-intern,

Karan Kapoor who helped me with the project.

Finally, I would like to thank other members of the lab especially Ketan Sir (PhD

student) for clarifying all kinds of doubt that I had regarding the experiment.

Anat Siddharth



3

1 Introduction

1.1 Setting up and characterization of diode laser

1.1.1 Grating stabilized diode laser

The set-up of a grating stabilized diode laser is shown in Figure 2.1. The light

from the laser diode is emitted from a small rectangular surface, has a large

divergence and it is collimated with a lens. The diode is a 6 mW (DL100) laser

at 795 nm. Around 30% of the output power is feed back by means of a

reflection gold-coated diffraction grating that is held on a piezo electric

transducer, which can be adjusted. The grating is placed to feed back the first-

order diffracted light to the diode, this set-up is known as the Littrow

configuration.

Fig 2.1: Grating stabilized diode laser.

The laser head DL 100 provides three means to change its output frequency:

1. DC driving temperature

2. DC driving current

3. Piezo voltage, controlling the grating angle in the ECDL.

The temperature of the laser diode is maintained by a Peltier element placed

between the diode-mounting block and the base plate of the entire set up and

it is measured with DTC 110 temperature sensor. The temperature is



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controlled to 23.4oC by the temperature controller. The complete arrangement

is enclosed in casing to prevent the laser from instabilities due to air currents

and moisture etc. A grating stabilized infrared diode laser is used at a

wavelength of 795nm to enhance the locking electronics and to do

spectroscopy experiments.

1.1.2 Laser diode

The diode lasers have a continuous wave output with high electrical to optical

efficiency (around 35%). In this section the construction, working principle and

characteristics of the laser diode is described in more detail. The construction

of a typical laser diode is shown in Figure 2.2.

Fig 2.2: Construction of laser diode.

The laser light is generated by sending current (injection current) through the

active region of the diode between the n- and p-type cladding layers (Figure

2.2). When the positive terminal of a DC source is connected to the p-region

and the negative terminal to the n-region, the diode is said to be forward-

biased. The electrons in the n-region and the holes in the p-region movetowards the active region where they recombine. The negative terminal of the

source injects new electrons into the n region, which can continue the

conduction process.

At the same time the positive terminal extracts electrons from the p-region,

thus creating new holes that are free to migrate toward the active region.

When an electron recombines with a hole (in the active layer) the electron

goes from the conduction band towards the valence band in that layer.Because of the energy difference (band gap) between these two states a



5

photon will be emitted (spontaneous emission). Another process is that a

photon that is generated by spontaneous emission forces an electron and hole

to recombine, sending out another photon that has the same wavelength as

the incoming photon (stimulated emission). At high injection currents this

process dominates and coherent light is emitted and the diode “lases”.

The light is emitted from a small rectangular surface and thus has a large

divergence. The wavelength of the laser diode is, as mentioned earlier,

primarily determined by the band gap of the semiconductor material, but also

depends on the temperature of the diode and the current density. Due to this,

the laser is tuneable over a range of 15-20 nm.

Changing the injection current will change the refraction index of the activearea, which will change the laser frequency because the optical path length in

the cavity has changed. Since the laser diode works like a cavity, constructive

interference can only occur at certain wavelengths; thus the wavelength of the

laser is tuned by changing the injection current.

If the laser diode is tuned by adjusting current at constant temperature or vice

versa, mode hops occur, i.e. a hop over a relatively large wavelength will occur

followed by a short continual dependence of the basic wavelength on current.These mode points can be shifted by adjusting the temperature.

Fig 2.3: ECDL diode laser.



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1.1.3 Diffraction grating

The wavelength of the laser can be selected by using a diffraction grating by

changing the angle of the grating. A diffraction grating is placed in the output

beam of a laser diode, which feeds back a part of the laser light into the diode.The main advantage is, as mentioned, that it is possible to tune the wavelength

of the laser by rotating the grating.

Another advantage is that the output power can be increased because the

laser light travels through the active region of the diode again, which enhances

the stimulated emission process.

Fig 2.3: Diffraction of light on a grating surface.

1.1.3.1 Littrow Configuration

The light emitted from the front facet of the laser diode is collimated by a

multi-element lens with a very short focal length and then strikes a reflection

grating. The grating is adjusted in a “Littrow” set up, i.e. the first diffraction

order of the grating is reflected back towards the laser diode, passing through

the collimator again and focused back into the laser diode resonator. The

common Littrow configuration (see Figure 2.4) contains a collimating lens and

a diffraction grating as the end mirror. The first-order diffracted beam provides

optical feedback to the laser diode chip, which has an anti-reflection coating

on the right-hand side. The emission wavelength can be tuned by rotating the

diffraction grating. A disadvantage is that this also changes the direction of the

output beam, which is inconvenient for many applications.



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Fig 2.3: Littrow configuration.

The littrow angle α is determined by the equation:

Sin α = kλ /2d (6)

where angle α is given with reference to the grating normal; k is the diffraction

order (in our case k=1 for the output beam).

1.1.3.2 Aligning the grating

Injecting light back into the laser from the grating gives rise to a buildup of light

at a frequency determined by the external cavity, leading to preferential lasing

on this mode and simultaneously a reduction in the laser threshold. It is

important to make sure the grating is crudely aligned, which can usually doneby physically checking that the first order reflected light is heading back into

the collimation lens. Note when the alignment is close you can commonly see

two spots in the zeroth order reflected beam. One of these is the laser output

and the other is a reflection of the first order light from some point on the

laser diode junction. If you reach this stage then further course alignment is

simple - you simply adjust the grating mount until the two spots overlap. Note

also that the vertical alignment is the most critical, as generally the laser will

inject over a range of wavelengths (equivalently grating angles or horizontal

know position) whereas in the vertical direction there is only one correct

alignment.

1.1.3.3 Vertical flash test

Having crudely aligned the grating, operate the laser at a current close to

threshold. This current may be just above or just below, and should be

adjusted as the alignment progresses. View the laser output on the IR cardwhilst adjusting the vertical alignment of the grating. When the laser is injected



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the threshold is reduced, the output power therefore increases suddenly and a

flash is observed on the IR card (the biggest flash is observed when the laser is

initially below threshold, so experiment with different laser currents). The laser

current can then be reduced and the process repeated iteratively to converge

on the best alignment and lowest threshold. It is instructive to also observe the

behavior as the horizontal grating alignment is changed.

1.1.4 Laser locking

Locking a laser actually means keep it at fixed optical frequency. If the laser is

locked, the line-width can be reduced and the drift over long time is

suppressed. In a standard application the tunable laser output will be passed

through a spectroscopy unit where the frequency of this light is spectrallyanalyzed. Most commonly people use single pass absorption or saturated

absorption, or more sophisticated, polarization spectroscopy to generate a

suitable error signal that is then fed back into the laser tuning control input.

Another very common technique to lock a diode laser is the RF sideband

modulation technique described first by Pound and then realized in the optical

domain by Drever and Hall (Pound-Drever-Hall method). The laser is locked

employing locking electronics to one of the fringes of higher frequency

stability. The error signal measures the deviation in frequency to this

reference. The error signal is filtered (with the locking electronics) and feed

back to the laser. This feedback signal “pushes” the laser frequency towards

the reference point.

The phase of the feedback signal is an important parameter. The phase must

be in a certain range to “push” the laser frequency towards the direction of the

reference. When the phase is changed by 180° the frequency will shift in the

wrong direction and the laser will be pushed away from the reference.



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1.2 Doppler-free saturation absorption spectroscopy of

rubidium atoms

1.2.1 Introduction

Our rubidium sample can be theoretically treated as a hydrogen-like atom

because of its single valence electron. It thus has predictable fine and

hyperfine corrections to the Hamiltonian, resulting in a splitting of its energy

levels. Rubidium can absorb radiation when the frequency corresponds to a

difference in energy levels, exciting the valence electron to a higher energy.

This decreases the intensity of radiation that passes through the sample, an

effect that is measured with an oscilloscope. By determining the frequencies atwhich the sample absorbs radiation, an absorption spectrum can be obtained.

This technique is known as spectroscopy, and it allows the different energy

levels to be measured.

The absorption spectra in traditional linear spectroscopy are characterized by

broad signals around each absorbed frequency, despite the fact that the atom

can only absorb at specific frequencies. This is a result of the Doppler Effect;

the frequency of the radiation in the frame of the atom is different from thefrequency in the laboratory frame. By sending a pump beam through the

sample in the opposite direction as the probe beams, the resonant frequency

can be precisely determined. This is known as saturated absorption

spectroscopy because tuning the laser above or below the resonant frequency

will cause saturation of atoms moving at a certain speed, in either the positive

or negative direction. When the laser is tuned to the resonant frequency, the

difference between the probe beam that passes through the pump beam

(which is unable to be absorbed by the already-excited atoms at rest) and the

probe beam that is less affected by the pump beam gives the Doppler-free

emission spectrum.

Using only the Coulomb interaction to derive the energy levels for the

electrons of the hydrogen atom gives the Bohr energies of order α2mc

2, where

α is the fine structure constant. Taking into account relativistic corrections and

spin-orbit coupling the degeneracy of the Bohr levels is broken into the fine

structure of order α4mc2. Finally considering the dipole moments of the



10

electrons and the proton breaks the fine structure into the hyperfine structure

of order (m/mp) α4mc

2.

Unfortunately normal spectroscopy cannot usually resolve the hyperfine

structure of atoms due to the broadening of the spectral peaks from theDoppler effect. In the case of rubidium the hyperfine structure is on the order

of 100MHz while the Doppler broadened peaks are on the order of 500 MHz,

completely obscuring the hyperfine structure while using normal spectroscopy.

However, using Doppler-free spectroscopy, these Doppler broadened lines can

be resolved to the hyperfine structure.

1.2.2 Absorption Spectroscopy

When light (for example a laser beam) travels through a medium (in our case

rubidium vapor cell), the atoms or molecules of this medium can absorb the

light. A lower energetic state of the molecule can absorb a photon and the

molecule gets excited to higher energy states. In this process the transmitted

laser beam loses its intensity. This absorption process is only possible when the

wavelength of the incoming light corresponds to the energy difference

between the two states of the molecule. The intensity (IT) transmitted through

an absorbing path x is given by

IT(ω)=Ioe-α(ω)x (1)

In this equation, α(ω) is the absorption coefficient and it depends on the

frequency ω of the light. I0 is the intensity of the incoming light. We observe a

broad absorption spectrum due to Doppler effect which the spectral

resolution.

1.2.3 Doppler Broadening

The energy associated with transitions for a valence electron of an atom is

given by difference between the excited state energy and the ground state

energy, which used with Planck’s law, gives the frequency ν0 of transitions

between these two states:

∆E = ћ ν0 (2)



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When an electron in an excited state decays down to the ground state of the

atom, it emits a photon of frequency ν0.

An atom can undergo three basic transition processes: stimulated absorption,

stimulated emission, and spontaneous emission. Stimulated emission andabsorption are related to interactions with a laser or other forms of

electromagnetic fields. Spontaneous emission is a transition that occurs

regardless of any sort of laser field and the frequency, direction, and

polarization of emitted photons does not correspond to the external field.

Random thermal motion of atoms or molecules creates a Doppler shift in the

emitted or absorbed radiation. The spectral lines of such atoms or molecules

are said to be Doppler broadened since the frequency of the radiation emittedor absorbed depends on the atomic velocities. Individual spectral lines may not

be resolved due to Doppler broadening, and, hence, subtle details in the

atomic or molecular structure are not revealed.

We first consider the Doppler Effect qualitatively. If an atom is moving towards

or away from a laser light source, then it "sees" radiation that is blue or red

shifted, respectively. If an atom is at rest, relative to the laser, it absorbs

radiation of frequency ν0 but when the atom is approaching the laser, it willsee blue-shifted radiation, hence for absorption to occur the frequency of the

laser must be less than ν0 in order for it to be blue-shifted to the resonance

value of ν0. Similarly, if the atom is receding from the laser, the laser frequency

must be greater than ν0 for absorption to occur.

We now offer a more quantitative argument of the Doppler Effect and atomic

resonance, where, as before, ν0, is the atomic resonance frequency when the

atom is at rest in the frame of the laser. If the atom is moving along the z axis,say, relative to the laser with νz<<c, then the frequency of the absorbed

radiation in the rest frame of the laser will be νL, where

νL = ν0 (3)

If νz is negative (motion toward the laser) then νz< ν0, that is, the atom moving

toward the laser observes radiation that is blue-shifted from νL up to ν0. If νz is

positive (motion away from the laser) then νL >ν0, that is, the atom observes



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radiation that is red-shifted from νL down to ν0. Therefore, an ensemble of

atoms having a distribution of speeds will absorb light over a range of

frequencies.

Fig 1.1: Principle of saturation absorption spectroscopy.

The probability that an atom has a velocity between νz and νz+dνz is given bythe Maxwell distribution

P(νz)dνz = exp dνz (4)

where M is the mass of the atom, k is the Boltzmann constant, and T is the

absolute temperature.

The half width, which is the full-width at half maximum amplitude (FWHM), of

the Doppler broadened line, is given by

∆ν1/2 = 2 (5)

The profile of a Doppler-broadened spectral line is shown in Figure 1.2



13

Fig 1.2: Doppler-broadened spectral line, where ∆ν1/2 is the FWHM and ν0 is the absorbed

frequency when the atom is at rest in the frame of the laser.

So from Eq. (5) the FWHM of a Doppler broadened line is a function of ν0, M,and T.

1.2.4 Saturated Absorption Spectroscopy

The method for saturated absorption spectroscopy of rubidium allows for very

precise measurements of the hyperfine structure of these atoms. From basic

laser spectroscopy, one is able to observe Doppler broadened absorption. As

adjustments are made, it becomes possible to resolve the saturated absorption

lines that correspond to specific atomic transitions and crossover resonances.

In order to counteract the Doppler broadening and obtain higher resolution, a

counter propagating “pump” beam is passed through the cell. The Doppler

shifted resonance frequency for atoms moving with velocity vz is opposite to

that of the probe beam. That is, the pump beam interacts with the group of

atoms with velocities -vz, exactly opposite the group the probe beam interacts

with. The large absorption dips are only seen when the laser frequency is on

resonance and both beams interact with the same group of atoms, which

effectively picks out atoms with zero velocity and eliminates Doppler

broadening. A strong enough pump beam at a resonant frequency causes rapid

transitions that evenly distribute the population of atoms between the ground

and excited state. When this occurs, the laser is said to saturate the transition,

hence the name saturated absorption. The largest saturated absorption dip is

seen when the pump is on resonance. This process is called “hole burning.”



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1.3 Measurement of hyperfine interval in the 5P1/2 state of 85Rb by acousto-optic modulation.

1.3.1 Atomic structure of rubidium

The ground electron configuration of rubidium (Rb) is: ls2; 2s

2, 2p

6; 3s

2, 3p

6,

3d10

; 4s2, 4p

6; 5s

1, and with its single 5s

1electron outside of closed shells it has

an energy-level structure that resembles hydrogen. For Rb in its first excited

state the single electron becomes a 5p1

electron. Also natural rubidium has

two isotopes, the 28% abundant87

Rb, where the nuclear spin quantum

number I = 3/2, and the 72%85

Rb, where I = 5/2.

1.3.2 Term States

A term state is a state specified by the angular momentum quantum numbers

s, l, and j (or S, L, and J), and the notation for such a state is2s+1

l j (or2s+1

L j). The

spectroscopic notation for l values is l = 0(S), 1(P), 2(D), 3(F), 4(G), 5(H), and so

on. The total angular momentum J is defined by,

J = L + S (8)

where their magnitudes are

J=ћ ; L=ћ ; S=ћ ; (9)

and the possible values of the total angular momentum quantum number j

are | l -s|, | l -s|+1,…, l +s-1, l +s, where for a single electron s=1/2. The 5s1

electron gives rise to a 52S1/2 ground term state. The first excited term state

corresponds to the single electron becoming a 5p’ electron, and there are two

term states, the 52P1/2 and the 5

2P3/2.

1.3.3 Hamiltonian

Assuming an infinitely massive nucleus, the non relativistic Hamiltonian for an

atom having a single electron is given by:

–

(10)



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The five terms in the equation is termed as K, V, HSO, H1,hyp, H2,hyp respectively. K

is the kinetic energy of the single electron where , classically is the

mechanical momentum of the electron of mass m. V is the Coulomb

interaction of the single electron with the nucleus and the core electrons (this

assumes the nucleus and core electrons form a spherical symmetric potential

with charge where is an effective atomic number).

HSO is the spin orbit interaction, where L and S are the orbital and spin angular

momenta of the single electron. H1,hyp is the magnetic hyperfine interaction,

where J and I are the total electron and nuclear angular momenta,

respectively. This interaction is where, is the nuclear magnetic

dipole moment, is proportional to I, and , the magnetic field produced at the

nucleus by the single electron, is proportional to J. Hence the interaction is

expressed as where is called the magnetic hyperfine structure constant,

and it has units of energy, that is, the angular momenta I and J are

dimensionless.

H2,hyp is the electric quadrupole hyperfine interaction, where β is the electric

quadrupole interaction constant, and non-bold I and J are angular momenta

quantum numbers. The major electric pole of the rubidium nucleus is the

spherically symmetric electric monopole, which gives rise to the Coulomb

interaction; however, it also has an electric quadrupole moment (but not an

electric dipole moment). The electrostatic interaction of the single electron

with the nuclear electric quadrupole moment is , that is, it is the product

of the electron's charge and the electrostatic quadrupole potential. Although it

is not at all obvious, this interaction can be expressed in terms of I and J. In

both hyperfine interactions I and J are dimensionless, that is, the constants α

and β have units of joules.

1.3.4 K+V

The K + V interactions separate the 5s ground configuration and the 5p excited

configuration. Qualitatively, if the potential energy is not a strictly Coulomb

potential energy then for a given value of n, electrons with higher l have a

higher orbital angular momentum (a more positive kinetic energy) and on the

average are farther from the nucleus (a less negative Coulomb potential

energy), hence higher l value means a higher (more positive) energy. This



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scenario does not occur in hydrogen because the potential energy is

coulombic.

1.3.5 Fine splitting, HSO

Fine structure, the splitting of spectral lines into several distinct components, is

found in all atoms. The interactions that give rise to fine structure do depend

on the particular atom. Ignoring relativistic terms in H, it is HSO that produces

the fine structure splitting of rubidium.

Using equations (8) and (9) and forming the dot product of , we solve for

and obtain

Hence, (11)

The separation of the 52S1/2 and the 5

2P3/2 states, in units of wavelength, is

780.023 nm, and the separation of the 52S1/2 and the 5

2P1/2 states is 794.764

nm. It is the transition between the 52S1/2 and the 5

2P1/2 states that will be

studied using the 795-nm laser.

1.3.6 Hyperfine splitting, Hhyp

For either hyperfine interaction, the interaction couples the electron angular

momentum J and the nuclear angular momentum I to form the total angular

momentum, which we label as F, where

(12)

and the possible quantum numbers F are |J - I|, |J - I| + 1,…, J + I - 1, J + I. The

energy levels are split by the hyperfine interaction into the levels. These levels

are known as hyperfine levels, where the total angular momentum quantum

numbers are labeled as F’ and F. The selection rules for electric dipole

transitions are given by

(13)



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In addition to the normal resonance lines, there are "crossover" resonances

peculiar to saturated absorption spectroscopy, which occur at frequencies

for each pair of normal transitions at frequency and

To determine the energy of hyperfine levels, we use equation (12) and byforming the dot product of we solve for and obtain

(14)

Rubidium 85 and 87 D1 transitions, with frequency splitting between the

hyperfine energy levels are shown on the next page.



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Fig 3.1: 85Rb and 87Rb D1 transition hyperfine structure.



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1.3.7 Acousto optic modulator

An acousto optic modulator (AOM), also called bragg cell uses the acousto

optic effect to diffract and shift the frequency of light using sound waves

(usually at radio frequency). A piezoelectric transducer is attached to materialsuch as glass. An oscillating electric signal drives the transducer to vibrate,

which creates sound waves in the glass. These can be thought of as moving

periodic planes of compression and expansion that change the index of

refraction. Incoming light scatters off the resulting periodic index modulation.

A diffracted beam emerges at an angle θ which depends on the wavelength of

light λ relative to the wavelength of sound Λ

(15)

where m=…., -2, -1, 0, 1, 2,…. is the order of diffraction. Diffraction from a

sinusoidal modulation in a thin crystal solely results in m = -1, 0, 1 diffraction

orders. Cascaded diffraction in medium thickness crystal leads to higher orders

of diffraction.

The amount of light diffracted by the sound wave depends on the intensity of

the sound. Hence the intensity of the sound can be used to modulate theintensity of light in the diffracted beam. Light is scattered due to moving plane,

hence frequency f of the diffracted beam of order m will be Doppler shofted by

amount equal to frequency of sound wave F .

Fig 3.2: Acousto-optic Modulator.



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2 Objectives

I. To set up an extended cavity diode laser (ECDL) of 795 nm having narrow

linewidth for carrying out spectroscopic applications using rubidiumatoms. Hence perform its frequency locking using saturation absorption

spectroscopy and Pound-Drever-Hall (PDH) technique.

II. To study Doppler-free saturation absorption spectroscopy of rubidium

atoms using counter propagating pump and probe beams passing

through a rubidium vapor cell and observe the hyperfine energy splitting

in the 52P3/2 states of

85Rb and

87Rb.

III. To measure hyperfine interval in 5P1/2 state of 85

Rb using acousto-optic

modulator. (AOM causes frequency shift to a part of a laser beam. As a

result, each isotope generates two peaks in the spectrum separated by

the acousto-optic shift, which permits the frequency to be calibrated).



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3 Experimentation

3.1 Apparatus and Instrumentation

i. 795-nm diode laser system

ii. Current Control, Temperature Control, Scan Control (TOPTICA

Instruments)

iii. Rubidium vapor cell

iv. Differential photodiode

v. 3/8"-thick transparent plastic or glass (beam splitter)

vi. 4 flat mirrors, 4 mirror mounts, 9 or more posts (for mounting vapor cell,

photodiode detectors, mirrors, and beam splitter)

vii. Digital Oscilloscope

viii. IR detection card and CCD surveillance camera

ix. Acousto-optic modulator

x. Frequency synthesizer



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3.2 Experiments

I. There are many different ways to lock a laser. But one thing they have in

common; to lock a laser to a certain frequency an error signal must be

created. This error signal tells if the laser frequency is too high or toolow compared to the frequency that the laser has to be locked to

(locking point). The error signal is feed back to a locking circuit, which

creates the right gain and phase to ”push” the laser towards this locking

point and actually lock it. In general the error signal often crosses zero

exactly at the locking point and is positive at one side (for example when

the frequency is to low) and negative at the other side (when the

frequency is to high).

The simplest set-up can be achieved with the PID 100 and an external

frequency reference. The PID 100 (TOPTICA module) is a proportional

(P), integrative (I) and derivative (D) action controller that processes the

error signal of the laser frequency and then amplifies it to the power

level of the frequency determining element. These elements are the

grating angle via piezoelectric actuator and the laser diode current via

feed forward, via BIAS-T or via FET CURRENT CONTROL.

The Pound-Drever Detector PDD 110 (TOPTICA module) serves to lock a

diode laser to the frequency of maximum absorption or transmission of

a reference medium, e.g. an atomic transition or an optical resonator.

The PDD 110 features an internal HF modulation source with variable

output amplitude. The diode laser is modulated and the modulated

signal after the reference medium is detected by an external photodiode. In the phase detector section of the PDD 110, the photo diode

signal is mixed with the internal HF signal. The Pound-Drever error signal

is derived from the phase delay of the modulated light. The PDD 100

determines the phase delay (dispersion) of modulated laser light while

passing through a reference medium by comparing the phase of carrier

and side bands and generates the Pound-Drever signal. With the help of

the PID 100 controller one can use the Pound-Drever signal output to

lock the laser to the frequency of maximum absorption in the reference



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medium. The PDD 100 also performs a phase sensitive measurement,

but due to the modulation frequency of 20 MHz provided by an internal

local oscillator, but this set-up usually is described in the frequency

regime (carrier frequency and sidebands). The PDD 100 needs the BIAS-T

option and the PID 100 controller. The bias-t is mainly suited for

sideband generation to the carrier. The radio frequency modulation (20

MHz) is introduced onto the driving current.

Fig 2.5: Connections required for generating error signal and locking the laser using TOPTICA

modules.



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II. The apparatus for the Doppler-free saturated absorption spectroscopy

of rubidium is shown in Figure 1.3. The output beam from the laser is

split into two beams, one less intense probe beams and a more intense

pump beam, at the thick beam splitter. The probe beam passes through

the rubidium cell from top to bottom, and is detected by a photodiode.

After being reflected twice by the mirrors, the more intense pump beam

passes through the rubidium cell from bottom to top. Inside the

rubidium cell there is a region of space where the pump and a probe

beam overlap and, hence, interact with the same atoms.

Fig 1.3: Apparatus for Saturation Absorption Spectroscopy.

III. The experiment for measuring hyperfine interval using AOM was

arranged as shown in the figure 3.2. The laser light was supplied by a

diode laser. Part of the laser beam was passed through an acousto-optic

modulator. The AOM had a diffraction efficiency of 30% for shifting light

at 795 nm by 310-410 MHz. The modulation frequency was supplied by

a frequency synthesizer. This signal was then amplified to a power

of 1 W. The frequency-shifted laser beams were spatially deflected afew mill radians, and the trajectory of the unshifted beam at frequency

was unaffected. The first order diffracted beam was combined with the

zero order using a beam splitter and then the combined beam was

passed through the saturation absorption spectroscopy arrangement.



25

Fig 3.2: Hyperfine interval measurement using acousto optic modulation.

4. Results and Discussion

i. The laser frequency can be modulated by modulating the injection

current to create an error signal that is suitable for locking the laser to

an absorption line. The laser frequency ωL is modulated by a modulationfrequency that tunes ωL periodically from ωL to ωL+∆ωL. Therefore the

laser frequency is given by

ωL(t)= ωo + Asin(2 ) (7)

In this equation ωo is the centre frequency of an absorption line and A

the amplitude which corresponds with ∆ωL. When the modulation

sweep ∆ωL is small enough it results in the first derivative of the

absorption spectrum. This is shown in the figure 2.4. The created signal

goes exactly through zero at ωo, which makes it suitable as an error

signal to lock the laser to this centre frequency



26

Fig 2.4: Error signal using frequency modulation.

ii. The signal from the probe beam will be a non linear, absorption

spectroscopy signal, where the spectral lines will be Doppler-broadened.

The signal is shown in Figure 1.4, and it was photographed from the

screen of an oscilloscope. The larger amplitude Doppler-broadened

signal is that of the 72% abundant85

Rb and the smaller amplitude signal

is that of the 28% abundant87

Rb (not in figure). The87

Rb transition is the

F= 2 to F' = 1,2 and 3 transition, and the85

Rb transition is F=3 to F'= 2, 3,

and 4. In the figure you can see there is a nonlinear, saturated

absorption spectroscopy signal "riding on" the Doppler-broadened line.

The peaks are the hyperfine structure of 85

Rb riding on the Doppler-

broadened line.



27

Fig 1.4: Doppler free non linear saturation spectroscopy probe signals.

Each absorption peak shown below corresponds to a specific

resonance or crossover resonance for rubidium. Looking at the figure,

from right to left are the resonances and crossover resonances of 85

Rb.

In Figure 1.4, the probe beams give the Doppler-free signal, which

showed three peaks at -21.0 ms, -2.5 ms and 14.5 ms on the

oscilloscope. The linewidth (FWHM) calculated for the peaks are shown

in the table below.

Linewidth (FWHM) [MHz]

85Rb 17.4 + 1087

Rb 30.2 + 10

iii. Each transition was excited by the frequency-shifted and unshifted laser

beams, producing two fluorescent peaks. The scan time between

these two peaks corresponds to the acousto-optic frequency if the

two laser beams are perfectly superimposed. Figure below shows a

frequency shifted peak at a frequency of 300 MHz.



28

5. Conclusion

This project at the atomic and optical physics lab at physics department in

Indian Institute of Science, Bangalore gave me an opportunity to developproper insight of diode lasers and its application in Doppler free spectroscopy.

This experience also consolidated by understanding of the atomic structures,

hyperfine structures etc. It was a novel experience to work in a well equipped

lab and observe results that I had read in theories so far.

The use of laser locking in AMO physics to stabilize lasers in the laboratory

makes results more reliable and reproducible. Locking the laser frequency to a

particular absorption resonance requires creating a feedback loop, in whichthe lock-in amplifier provides an error signal proportional to the laser detuning

from the desired frequency, and produces the required adjustment when fed

back to the laser controller. The Doppler-free saturated absorption

spectroscopy experiment utilizes this technique and allows for a much more

precise laser lock. The transition of the outer electron of 87

Rb between the

52S1/2 and the 5

2P1/2 states corresponds to a separation of roughly 795 nm, the

wavelength of the diode laser used for this experiment.

For the Doppler-free saturated absorption spectroscopy part of the

experiment, the diode laser was broken into three beams, a more intense

pump beam and two less intense probe beams. Two probe beams were sent

through the Rb cell and into photodiode detectors connected to an

oscilloscope. When their frequencies were modulated, a Doppler broadened

signal was seen on the oscilloscope because the random thermal motion of the

atoms caused a distribution of atoms to see the laser at a resonance

frequency. Then a pump beam was crossed with one of the probe beams, and

through hyperfine pumping and saturation it decreased the population of

atoms in the ground state. Only when the laser was tuned to a resonance

frequency would the pump beam and the probe beam be interacting with the

same atoms, resulting in a dip in the probe beam signal. Subtraction the two

probe beams resulted in a Doppler-free signal, which was identified as the

hyperfine splitting of the ground state.



29

We then use an acousto-optic modulator (AOM) for frequency calibration to

make precise hyperfine-interval measurements in the first excited P3/2 state of 85,87

Rb. The main advantage of using an AOM is that the frequency-scan axis

(with respect to the probe beam) is both linear and calibrated by the RF

frequency of the driver powering the AOM, thus allowing the hyperfine

interval to be measured accurately. The experiment could not be completed

due to insufficient time.

For precise error signal and frequency locking Doppler free spectroscopy with

Zeeman modulation can be done. Diode lasers with Doppler free spectroscopy

can be further applied in precise measurement of hyperfine interval using

electro-optic modulator also. It can also be used in non linear magnetic optic

rotation (NMOR). If given an opportunity I would like to pursue my interest and

perform further related experiments



References

1. Sara L. Campbell and Javier M. G. Duarte (2008), “Doppler-free saturation

absorption spectroscopy of Rubidium atoms”, MIT Department of Physics. 2. Philip J. Ilten (2007), “Doppler-free Spectroscopy of Rubidium”, MIT

Department of Physics.

3. A. Banerjee, D. Das and V. Natarajan, “Absolute frequency measurements of

the D1 lines in 39K,85

Rb, and87

Rb with ∼ 0.1 ppb uncertainty”, Europhys.

Lett., 65 (2), pp. 172 –178 (2004).

4. A. Krishna, K. Pandey, A. Wasan and V. Natarajan, “High-resolution hyperfine

spectroscopy of excited states using electromagnetically induced

transparency”, Europhys. Lett., 72 (2), pp. 221 –227 (2005).

5. W. A. van Wijngaarden and J. Li, “Measurement of isotope shifts and

hyperfine splitting of ytterbium by means of acousto-optic modulation”,

Vol. 11, No. 11/November 1994/J. Opt. Soc. Am. B.

6. C.J. Foot, “Atomic Physics”, Oxford (2005).

7. D.J. Griffith, “Introduction to Quantum Mechanics”, Prentice Hall (1995).

8. W. Demtroder, “Laser Spectroscopy Basic Concepts and Instrumentation”,

Springer (2003).9. http://www.toptica.com/products/itemlayer/59/Appl_1012_laser_locking_0

80917.pdf

10. Saturated Absorption Spectroscopy. Experiment SAS. University of Florida

Dept. of Physics.

http://www.phys.ufl.edu/courses/phy4803L/group_III/sat_absorbtion/SatA

bs.pdf.

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Summer Project Report 2011

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