Quantum memories

158 Pages·2015·8.97 MB·English

by  Adrien Nicolas

THÈSE DE DOCTORAT
DE L’UNIVERSITÉ PIERRE ET MARIE CURIE
Spécialité : Physique
école doctorale : « La physique, de la particule à la matière condensée »
réalisée
au Laboratoire Kastler Brossel
présentée par
Adrien NICOLAS
pour obtenir le grade de :
DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE
Sujet de la thèse :
Optical quantum memories with cold atomic ensembles :
a free space implementation for multimode storage,
or a nanofiber-based one for high collection efficiency
soutenue le 30 septembre 2014
devant le jury composé de :
Mme Laurence Pruvost Rapporteur
M. Barak Dayan Rapporteur
Mme Eleni Diamanti Examinateur
M. Fabio Sciarrino Examinateur
M. Jérôme Tignon Examinateur
M. Julien Laurat Directeur de thèse

ii
iii
Contents
Acknowledgements vii
Introduction ix
Notions and notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
1 Quantum information and quantum memories 1
1.1 Quantum information science . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Quantum communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Historical development and main features. . . . . . . . . . . . . . . . 4
1.2.2 Current limitation of practical long distance QKD. . . . . . . . . . . 5
1.2.3 Quantum repeaters: the need for quantum memories for light. . . . . 5
1.3 Quantum memories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Definition and requirements . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Physical substrates and protocols: many candidates . . . . . . . . . 9
1.3.3 The archenemy of quantum memories: decoherence . . . . . . . . . . 11
1.3.4 A closely related cousin: the DLCZ protocol . . . . . . . . . . . . . . 11
1.3.5 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 EIT, slow and stopped light for quantum memories 17
2.1 Electromagnetically Induced Transparency and slow light . . . . . . . . . . 18
2.1.1 Linear susceptibility in EIT systems . . . . . . . . . . . . . . . . . . 18
2.1.2 Slow light in an EIT medium . . . . . . . . . . . . . . . . . . . . . . 20
2.2 EIT quantum memory in an ensemble of atoms . . . . . . . . . . . . . . . . 21
2.2.1 Stopping light in an EIT medium . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Dark state polariton description . . . . . . . . . . . . . . . . . . . . . 23
2.2.3 The role of the ensemble: collective enhancement . . . . . . . . . . . 24
2.2.4 A glance beyond the simple model . . . . . . . . . . . . . . . . . . . 25
2.2.5 Inhomogeneous broadening and decoherence: the dark side of using
an ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Implementation in a cold atomic ensemble . . . . . . . . . . . . . . . . . . . 31
2.3.1 Preparation of the memory medium in a magneto-optical trap . . . . 31
2.3.2 Measure and control of decoherence sources . . . . . . . . . . . . . . 34
2.3.a Magnetic field fluctuations . . . . . . . . . . . . . . . . . . 34
2.3.b MOT temperature . . . . . . . . . . . . . . . . . . . . . . . 38
2.3.3 Signal generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.4 Filtering the single-photon signal pulses . . . . . . . . . . . . . . . . 40
2.4 EIT and stopped light measurements . . . . . . . . . . . . . . . . . . . . . . 42
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2.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Storage of a Qubit encoded in orbital angular momentum 47
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1 Transverse Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.1 Laguerre-Gaussian modes and light orbital angular momentum . . . 48
3.1.a Laguerre-Gaussian modes . . . . . . . . . . . . . . . . . . . 48
3.1.b Interference with a gaussian beam . . . . . . . . . . . . . . 50
3.1.c Hermite-Gaussian modes . . . . . . . . . . . . . . . . . . . 50
3.1.2 Quantum information using OAM . . . . . . . . . . . . . . . . . . . 51
3.2 Experimental generation of an OAM Qubit . . . . . . . . . . . . . . . . . . 54
3.2.1 Generating transverse modes with a spatial light modulator . . . . . 54
3.2.2 Quality of the experimentally generated modes . . . . . . . . . . . . 55
3.3 Quantum state tomography of OAM qubits . . . . . . . . . . . . . . . . . . 61
3.3.1 Qubit tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.2 How to detect the OAM state of a single-photon ? . . . . . . . . . . 62
3.3.3 Interferometric setup for quantum state tomography of OAM qubits 63
3.3.a Interferometer and mode projectors . . . . . . . . . . . . . 63
3.3.b Variation and measurement of the interferometer phase . . 65
3.3.c Calibration procedure and benchmarking . . . . . . . . . . 70
3.3.4 Example of OAM tomography in the single-photon regime . . . . . . 75
3.4 A quantum memory for OAM encoded Qubits . . . . . . . . . . . . . . . . . 78
3.4.1 EIT optical memory and OAM preservation . . . . . . . . . . . . . . 78
3.4.2 memory decay time for stored LG modes . . . . . . . . . . . . . . . . 78
3.4.3 Full characterization of the quantum storage . . . . . . . . . . . . . . 78
3.4.a Full Qubit tomography and quantum storage . . . . . . . . 78
3.4.b Weak-coherent-state qubits and quantum storage . . . . . . 79
3.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 Towards a nanofiber-based light-matter interface 91
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1 Nanofibers as a light-matter interface . . . . . . . . . . . . . . . . . . . . . . 92
4.1.1 Light propagation in a nanofiber-based waveguide . . . . . . . . . . . 93
4.1.2 A two-color dipole trap in the evanescent field of the nanofiber . . . 94
4.2 Setting up the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2.1 Nanofiber fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2.2 Preparing the free-space MOT . . . . . . . . . . . . . . . . . . . . . 97
4.2.3 MOT-nanofiber interfacing. . . . . . . . . . . . . . . . . . . . . . . . 99
4.3 Spectral filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3.1 Position of the problem and possible solutions . . . . . . . . . . . . . 102
4.3.2 Alignment and characterization of the filtering setup . . . . . . . . . 103
4.3.3 Leakage due to the background emission of the Red magic diode . . 105
4.3.4 Spectral filtering setup: a short summary . . . . . . . . . . . . . . . 106
4.4 Recent progress and towards optical quantum memories . . . . . . . . . . . 107
4.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Conclusion 109
CONTENTS v
A Appendix 111
A.1 Derivation of the EIT linear susceptibility . . . . . . . . . . . . . . . . . . . 111
A.1.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.1.2 Derivation of the expression of the linear susceptibility . . . . . . . . 113
A.1.3 Comparison with notation systems from other works . . . . . . . . . 115
A.2 EIT linear susceptibility: from EIT to ATS . . . . . . . . . . . . . . . . . . 116
A.3 Cesium D2 line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
A.4 HG modes discrimination with a slit-wheel . . . . . . . . . . . . . . . . . . . 118
A.5 Possibility of higher-dimensional OAM tomography . . . . . . . . . . . . . . 119
A.6 Example of data table for complete qubit tomography . . . . . . . . . . . . 121
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vii
Acknowledgements
I would like to thank those who gave me the taste for science and constantly stimulated
my curiosity and pushed me forward, which of course include my parents, my grandma
and my godfather in a first place. I would not have gone here without them, and not
only for biological reasons! Later in high school and especially in classes prépa, I had
some wonderful science teachers who definitely had a great influence on me, in particular
Emanuel Goldztejn, who gave me my liking for mathematics, Stéphane Mansuy, Jean-
Claude Sifre and Jean-Pierre Lecardonnel.
I’m also thankful to the team who welcomed me in the lab: Julien and Elisabeth for
their trust as they recruited me as a PhD student, Michaël, who guided my first steps in
experimental optics. I appreciated very much the work with Dominik and I’m thankful
to him for introducing me to Python and for sharing some late and friendly evenings in
the lab. I also enjoyed every occasion he gave me to practice my german. Thanks to
Baptiste with whom discussions were always pleasant and insightful. Thanks also to the
rest of the team, past and present, whether I worked with them directly or indirectly, or
merely enjoyed some chat during the pauses: Lambert, Lucile, Oxana, Sasha, Valentina,
Christophe, Olivier, Anna, Kun, Josselin... Special thanks also to all the non-scientific or
parascientific people in the lab: Monique, Thierry, Laëtitia, Michel and Delphine, Annick
and Bintou, Corinne and Serge, Pascal, Jean-Michel, Gaël and Arnaud, Brigitte and Jean-
Pierre, Florence... You make the lab a more humane place!
Thanks also to all my friends from out-of-the-lab, especially to Jean-Raphaël for the
stimulatingintellectualchallengesinhighschool,whichkindofincludethenumerousgames
we created and played in our younger days.
Most of all of course, I thank my beloved wife for patiently enduring “to have a student
at home for three long years”, and whose organizational skills were my most precious help
during the writing of this manuscript.
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