## Tesi etd-09232014-174458 |

Thesis type

Tesi di laurea magistrale

Author

FARAONI, GIULIA

URN

etd-09232014-174458

Title

Nonlinear light propagation through a strongly interacting Rydberg gas

Struttura

FISICA

Corso di studi

FISICA

Commissione

**relatore**Prof. Arimondo, Ennio

**relatore**Prof. WeidemÃ¼ller, Matthias

Parole chiave

- Nonlinear optics
- Electromagnetically-induced transparency
- Rydberg atoms

Data inizio appello

20/10/2014;

ConsultabilitÃ

completa

Riassunto analitico

Interfacing light with matter is one of the fundamental tasks in physics. To

understand and control atom-light interactions at the level of individual quanta is at

the heart of modern quantum optics (see, for instance, Nobel prize in physics 2012).

Of great interest in current experiments is the regime of strong coupling between

light and matter, in which the coherent and reversible light-matter coupling dominates

over dissipative processes. This almost ideal light-matter interface can be practically

realized using electromagnetically-induced transparency (EIT) [1]. The key element

of EIT is the creation of a dark state [2] as a consequence of a quantum interference

effect arising in a three-level system coherently coupled by a weak probe field and a

strong coupling field, with two stable or metastable states and one rapidly decaying

level. The destructive interference of the two different excitation pathways driven

by the laser fields leads to cancellation of absorption on resonance and renders the

medium transparent for the probe light.

Even more interesting is to investigate what happens when light is coupled to

a strongly interacting atomic many-body system. Rydberg atoms are the optimal

candidates for studying the effects of strong dipole-dipole interactions on light propagation.

Rydberg atoms are atoms excited in high-lying energy states (principal

quantum number n > 20), with a relatively long lifetime (100 mus) and a large orbital

radius (1 mum) [3]. The large radius of Rydberg atoms is responsible for their

enormous dipole moments, resulting in an exaggerated response to electric fields and

in very strong long-range dipole-dipole interactions between atoms excited in Rydberg

states.

When atoms are excited to Rydberg states with coherent light fields, the interactions

give rise to strong atomic correlations and lead to many-body phenomena,

of which the most outstanding is the dipole blockade [4], for which the presence of a

previously excited Rydberg atom prevents the excitation of another atom to a Rydberg

state within a certain blockade volume. This enables deterministic creation of

a single excitation for atoms confined within the blockade volume, making Rydberg

atoms ideally suited for applications in quantum information processing, such as the

implementation of quantum gates. Moreover, since each blockade volume collectively

shares a single excitation, also the interaction with the light field is modied and

all the atoms within this volume act as an effective two-level atom with enhanced

coupling to the light field.

Lately, several experiments combining the extraordinary properties of Rydberg atoms with the strong atom-light coupling achievable under EIT conditions have

been performed, revealing the striking effect of dipole blockade on EIT. A single Rydberg

excitation can switch the optical response of the surrounding atoms within a

blockade volume from the transparent EIT condition to the resonant scattering limit,

thus restoring the absorption of the probe light on resonance. This controlled switching

between different optical responses due to Rydberg-Rydberg interactions leads to

a huge nonlinear optical response of the atomic system to the probe light field, which

depends on the atomic density, as well as on the probe intensity.

EIT in Rydberg gases has been extensively studied, both theoretically and experimentally,

in recent years. One motivation is the possibility of exploiting the

nonlinear optical response of the gas to achieve effective photon-photon interactions

in the atomic medium. However, already the simulation of classical light propagating

through a strongly interacting gas is a theoretical challenge due to the high

complexity of the underlying many-body physics. Various approaches using different

approximations have been pursued to tackle light propagation through Rydberg-EIT

media.

In this thesis a theoretical as well as an experimental study of the nonlinear optical

response of a strongly interacting Rydberg gas under EIT configuration is presented.

The theoretical investigation of the many-body state of the system is performed applying

a simplified model based on a rate equation (RE) approach, where interactions

among Rydberg atoms are only included as energy shifts of the Rydberg states. The

combination of the RE model with a semianalytical model recently developed to

treat the collective effects emerging at high atomic densities (> 10^12 cm^(-3)), allows to

demonstrate that the nonlinear optical susceptibility of an interacting Rydberg-EIT

medium can be calculated very efficiently in terms of single atom properties alone.

Numerical simulations are performed assuming realistic values for the parameters of

the system such as atomic density, laser intensities, interaction strengths. The results

are then compared to experimental data. The experimental study is carried out on

an ultracold cloud of 87Rb atoms confined in an optical dipole trap. The setup used

to prepare the cold atomic sample and to excite the atoms to Rydberg states under

EIT configuration is outlined in the thesis. Measurements of probe light absorption

are obtained by analysing absorption images of the atomic cloud taken at different

atomic densities. The comparison of the theoretical model with the data reveals that

the model well reproduces the experimental results in a wide range of densities and

for different sets of parameters. Moreover, compared with previous similar works, the

model developed in this thesis allows to achieve a better quantitative understanding

of the nonlinear optical response of the Rydberg-EIT medium to a resonant probe

light.

Another feature of EIT in interacting Rydberg gas which is covered in this thesis

concerns the possibility of exploiting the strong interactions between atoms in

different Rydberg states combined with the optical nonlinearity of the atomic gas to develop a powerful non-destructive and spatially resolved imaging technique, potentially

able to detect a single Rydberg "impurity" embedded in a background of

"probe" atoms subject to EIT conditions. Such an imaging technique has been recently

experimentally realized within the research group where I performed my thesis

work, following a prevoius theoretical proposal [5]. The model described in this thesis

is extended to treat the effects of one impurity at the center of the atomic cloud on

the absorption of the probe light. Performing simulations of the imaging process,

including experimentally relevant noise sources, it is shown that it should be possible

to achieve the single particle sensitivity. It is furthermore demonstrated that interactions

between background atoms heavily decrease the sensitivity of the imaging

scheme, consequently, minimizing these interactions is crucial to achieve the desired

high sensitivity.

The experimental implementation of the imaging technique is presented, together

with measurements of nonlinear absorption in presence of different number of impurities,

at different atomic densities. The experimental results show that a minimum

number of around 30 impurities excited at the center of the atomic cloud is necessary

to clearly distinguish the absorption of the probe light due to the impurities, from

that due to interactions among background atoms. This demonstrates that with the

current experimental setup it is not possible to detect a single impurity. As a consequence,

the theoretical model for the absorption in presence of only one impurity at

the center of the cloud can not be tested. The motivations which prevent achieving

the single atom sensitivity with the present imaging technique are discussed, together

with possible improvements of the experimetal setup.

References:

[1] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced

transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).

[2] E. Arimondo, G. Orriolis, Nonabsorbing atomic coherences by coherent

two-photon transitions in a three-level optical pumping, Nuovo Cimento Lett., 17,

133 (1976).

[3] T. Gallagher, Rydberg Atoms, Cambridge Monographs on Atomic, Molecular and

Chemical Physics, Cambridge University Press (2005).

[4] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, P.

Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic

Ensembles, Phys. Rev. Lett. 87, 037901 (2001).

[5] G. Gunter, M. Robert-de-Saint-Vincent, H. Schempp, C. S. Hofmann, S.

Whitlock, and M. Weidemuller, Interaction-Enhanced Imaging of Individual Rydberg

Atoms in Dense Gases, Phys. Rev. Lett. 108, 013002 (2012).

understand and control atom-light interactions at the level of individual quanta is at

the heart of modern quantum optics (see, for instance, Nobel prize in physics 2012).

Of great interest in current experiments is the regime of strong coupling between

light and matter, in which the coherent and reversible light-matter coupling dominates

over dissipative processes. This almost ideal light-matter interface can be practically

realized using electromagnetically-induced transparency (EIT) [1]. The key element

of EIT is the creation of a dark state [2] as a consequence of a quantum interference

effect arising in a three-level system coherently coupled by a weak probe field and a

strong coupling field, with two stable or metastable states and one rapidly decaying

level. The destructive interference of the two different excitation pathways driven

by the laser fields leads to cancellation of absorption on resonance and renders the

medium transparent for the probe light.

Even more interesting is to investigate what happens when light is coupled to

a strongly interacting atomic many-body system. Rydberg atoms are the optimal

candidates for studying the effects of strong dipole-dipole interactions on light propagation.

Rydberg atoms are atoms excited in high-lying energy states (principal

quantum number n > 20), with a relatively long lifetime (100 mus) and a large orbital

radius (1 mum) [3]. The large radius of Rydberg atoms is responsible for their

enormous dipole moments, resulting in an exaggerated response to electric fields and

in very strong long-range dipole-dipole interactions between atoms excited in Rydberg

states.

When atoms are excited to Rydberg states with coherent light fields, the interactions

give rise to strong atomic correlations and lead to many-body phenomena,

of which the most outstanding is the dipole blockade [4], for which the presence of a

previously excited Rydberg atom prevents the excitation of another atom to a Rydberg

state within a certain blockade volume. This enables deterministic creation of

a single excitation for atoms confined within the blockade volume, making Rydberg

atoms ideally suited for applications in quantum information processing, such as the

implementation of quantum gates. Moreover, since each blockade volume collectively

shares a single excitation, also the interaction with the light field is modied and

all the atoms within this volume act as an effective two-level atom with enhanced

coupling to the light field.

Lately, several experiments combining the extraordinary properties of Rydberg atoms with the strong atom-light coupling achievable under EIT conditions have

been performed, revealing the striking effect of dipole blockade on EIT. A single Rydberg

excitation can switch the optical response of the surrounding atoms within a

blockade volume from the transparent EIT condition to the resonant scattering limit,

thus restoring the absorption of the probe light on resonance. This controlled switching

between different optical responses due to Rydberg-Rydberg interactions leads to

a huge nonlinear optical response of the atomic system to the probe light field, which

depends on the atomic density, as well as on the probe intensity.

EIT in Rydberg gases has been extensively studied, both theoretically and experimentally,

in recent years. One motivation is the possibility of exploiting the

nonlinear optical response of the gas to achieve effective photon-photon interactions

in the atomic medium. However, already the simulation of classical light propagating

through a strongly interacting gas is a theoretical challenge due to the high

complexity of the underlying many-body physics. Various approaches using different

approximations have been pursued to tackle light propagation through Rydberg-EIT

media.

In this thesis a theoretical as well as an experimental study of the nonlinear optical

response of a strongly interacting Rydberg gas under EIT configuration is presented.

The theoretical investigation of the many-body state of the system is performed applying

a simplified model based on a rate equation (RE) approach, where interactions

among Rydberg atoms are only included as energy shifts of the Rydberg states. The

combination of the RE model with a semianalytical model recently developed to

treat the collective effects emerging at high atomic densities (> 10^12 cm^(-3)), allows to

demonstrate that the nonlinear optical susceptibility of an interacting Rydberg-EIT

medium can be calculated very efficiently in terms of single atom properties alone.

Numerical simulations are performed assuming realistic values for the parameters of

the system such as atomic density, laser intensities, interaction strengths. The results

are then compared to experimental data. The experimental study is carried out on

an ultracold cloud of 87Rb atoms confined in an optical dipole trap. The setup used

to prepare the cold atomic sample and to excite the atoms to Rydberg states under

EIT configuration is outlined in the thesis. Measurements of probe light absorption

are obtained by analysing absorption images of the atomic cloud taken at different

atomic densities. The comparison of the theoretical model with the data reveals that

the model well reproduces the experimental results in a wide range of densities and

for different sets of parameters. Moreover, compared with previous similar works, the

model developed in this thesis allows to achieve a better quantitative understanding

of the nonlinear optical response of the Rydberg-EIT medium to a resonant probe

light.

Another feature of EIT in interacting Rydberg gas which is covered in this thesis

concerns the possibility of exploiting the strong interactions between atoms in

different Rydberg states combined with the optical nonlinearity of the atomic gas to develop a powerful non-destructive and spatially resolved imaging technique, potentially

able to detect a single Rydberg "impurity" embedded in a background of

"probe" atoms subject to EIT conditions. Such an imaging technique has been recently

experimentally realized within the research group where I performed my thesis

work, following a prevoius theoretical proposal [5]. The model described in this thesis

is extended to treat the effects of one impurity at the center of the atomic cloud on

the absorption of the probe light. Performing simulations of the imaging process,

including experimentally relevant noise sources, it is shown that it should be possible

to achieve the single particle sensitivity. It is furthermore demonstrated that interactions

between background atoms heavily decrease the sensitivity of the imaging

scheme, consequently, minimizing these interactions is crucial to achieve the desired

high sensitivity.

The experimental implementation of the imaging technique is presented, together

with measurements of nonlinear absorption in presence of different number of impurities,

at different atomic densities. The experimental results show that a minimum

number of around 30 impurities excited at the center of the atomic cloud is necessary

to clearly distinguish the absorption of the probe light due to the impurities, from

that due to interactions among background atoms. This demonstrates that with the

current experimental setup it is not possible to detect a single impurity. As a consequence,

the theoretical model for the absorption in presence of only one impurity at

the center of the cloud can not be tested. The motivations which prevent achieving

the single atom sensitivity with the present imaging technique are discussed, together

with possible improvements of the experimetal setup.

References:

[1] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced

transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).

[2] E. Arimondo, G. Orriolis, Nonabsorbing atomic coherences by coherent

two-photon transitions in a three-level optical pumping, Nuovo Cimento Lett., 17,

133 (1976).

[3] T. Gallagher, Rydberg Atoms, Cambridge Monographs on Atomic, Molecular and

Chemical Physics, Cambridge University Press (2005).

[4] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, P.

Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic

Ensembles, Phys. Rev. Lett. 87, 037901 (2001).

[5] G. Gunter, M. Robert-de-Saint-Vincent, H. Schempp, C. S. Hofmann, S.

Whitlock, and M. Weidemuller, Interaction-Enhanced Imaging of Individual Rydberg

Atoms in Dense Gases, Phys. Rev. Lett. 108, 013002 (2012).

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