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TitleQuantum metrology with high-density atomic vapors and squeezed states of light
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Table of Contents
	Context and motivation
	Thesis Outline
Theoretical background
	Phase estimation
		Polarimetry detection
		Phase estimation with coherent states
	Squeezed states of light
		Quadrature squeezing
		Polarization squeezing
		Phase estimation with squeezed states
	Linear magneto-optical effects
		Introduction and background
		Faraday effect
		Macaluso-Corbino effect
		Spin noise spectroscopy
	Nonlinear magneto-optical rotation (NMOR)
	Fundamental limits of optical magnetometers
		Atomic projection noise
		Photon shot noise
Experimental setup for squeezed-light atomic spectroscopy
	Atomic system and temperature control
		The vapor cell
		Heating circuit and temperature stabilization
	Magnetic shielding and magnetic coils
		Magnetic Shielding
		Uniform fields and gradient Coils
	Generation and detection of polarization squeezing
		The squeezer
		Detection and quantum noise lock
		Optimization of the source and detection losses
	Laser frequency stabilization
Squeezed-light spin noise spectroscopy
	Mode of operation
		Detector signal
		Photon shot-noise
		Atomic noise
	Experimental Setup
	Data analysis and results
Quantum limits of noise spectroscopies
	Theory of noise in fitting power spectra
		Theoretical covariance of fit parameters
	Optical noise spectroscopy
		Specifics of atomic response
	Analytical results
	Experimental results
	Improvement by squeezing
Shot-noise-limited optical magnetometer with sub-picotesla sensitivity at room temperature
	Amplitude modulated optical rotation (AMOR) magnetometry
	Experimental setup
	AMOR signal and magnetic sensitivity
	Optimization of the magnetometer sensitivity
	Quantum noise analysis
	Shot-noise limited performance and conclusions
	Summary and outlook
List of Publications
Document Text Contents
Page 1

Quantum metrology with high-density

atomic vapors and squeezed states of light


submitted for the degree of
Doctor of Philosophy

Vito Giovanni Lucivero

ICFO - Institut de Ci�encies Fot�oniques
BIST - Barcelona Institute of Science and Technology

UPC - Universitat Politecnica de Catalunya

Thesis Advisor: Prof. Dr. Morgan W.Mitchell

Barcelona, May 2016

Page 2


Page 97

84 Chapter 4. Squeezed-light spin noise spectroscopy

4.3 Theory

In what follows we remind expressions for the shot-noise background, Sph, and the

height of the Lorentzian spin noise, S
at , appearing in the function used to fit the

power spectral density (PSD) of the polarimeter output as described in Section

4.5. These have been already derived in section (2.3.4). Using these expressions

we obtain the signal-to-noise ratio (SNR) ηi = S
at /Sph which is used to estimate

η for 85Rb as a function of probe light power and density. In generating these

estimates we use the parameters quoted in Table 4.1.

4.3.1 Detector signal

In our experiment we analyze S(ν), the power spectral density (PSD) of VDPD, the

output voltage of the polarimeter detector described in Chapter (3), expressed in

V2/Hz. Because the scalar signal is acquired by combining polarization rotation

information over A, the area of the beam, we write the signal as

VDPD(t) = 2G<[PΘFR(t) + PSN(t)], (4.2)

where G = 106 V/A is the transimpedance gain, P =

A dxdy I(x, y) is the total

power of the beam reaching the detector with intensity I(x, y), and ΘFR � 1 is

the Faraday rotation (FR) angle as defined in Eq. (2.35) below. < = Qq/Eph is

the detector responsivity, where Q denotes the quantum-efficiency of the detector,

Eph = h̄ω = 2.4910
−19J is the photon energy at 795 nm, and q = 1.610−19C. PSN

is a white-noise component due to shot noise, that we compute in the next section.

Page 98

4.3. Theory 85

4.3.2 Photon shot-noise

The contribution from photon shot-noise to S(ν) is given by

Sph = 2G
2q(<P )ξ2, (4.3)

where ξ2 represents the light-squeezing parameter.

Figure 4.1 shows Sph, as estimated by fitting the measured spin noise spec-

trum, at different atomic densities for a coherent probe (hollow symbols) and

squeezed probe (filled symbols). The dashed lines and solid lines in Fig. 4.1 cor-

respond to a fit of the data using Eq. (4.3), with Q and ξ2 as the free parameter

in the fit for coherent-probe and squeezed-probe data, respectively. From the

coherent-probe data, for which ξ2 = 1, we obtain Q = 0.87. The different slopes

observed for the squeezing-probe data can be explained by the degradation of

squeezing due to light absorption, given by [39]

ξ2 = 1− (1− ξ20) exp[−OD], (4.4)

where OD is the optical depth experienced by the light beam. For our experimen-

tal conditions ξ20 = 0.55, obtained by fitting the measured ξ
2 to Eq. (4.4) and can

be considered as the squeezing parameter of the transmitted light when the cell

is at room temperature.

Page 193

Much gratitude to my best spanish friend, which is not catalan, but he is

from Valencia, Mister Paco Castera for having shared one amazing year in the

atico together with several concerts and travels. I also thank Carlos and Almu

for their friendship and constant presence on my birthday, typically with a buen

jamon. Thanks to Maria Surrymury Subbrillo for her constant friendship and

energy during these years, thanks also to Irene, Estela, Cristina, Bea, Lucia and,

I mean, again, 5 years and half are really a lot. I would like to thank all my

other flatmates in Barcelona: Asier Larretxea, Amélie Araguas, Thomas Koffel,

Tabarca e Giovanna, Monsieur cabrón Simo Tadili, las filosofas catalanas Alba

y Raquel y sobre todo Nicolò, Emanuele and Michele for having shared three

amazing and unforgettable years in the fantastic Pisazo. Thank you very much

for these great living experiences.

Special thanks to my parents, to which this thesis is dedicated, to my fa-

ther Giacomo Lucivero, for his continuous and wise suggestions, for the constant

support, for having taught me the importance and fairness in work, for being an

exceptional father and also the most lovely and wise professor I ever met; and to

my mother Rosa Petruzzella for her constant love and support, for being always

close apart from the distance, for having taught me that “il toro va preso per le

corna”, even before coming to Spain. And well, she is also the most lovely and

wise professoressa I ever met. I feel very lucky to have parents like them and this

achievement would not have been possible without their guidance and support. I

also thank my sister Marilena Lucivero and my brother in law Michele Guarino for

having supported me in choosing Barcelona, without any doubt, for their support

and for giving me the opportunity to become uncle twice, indeed I also thank my

lovely nephews Matteo and Stefano for all the games and dances that we have

Page 194

done during these years, when I was back home. I want also to thank all my en-

tire family, especially my grandparents Giovanni and Titina fot their love, support

and inspiration. Special thanks to my friends Aldo, Leandro, Bruno, Mario e la

“storica e mitica comitiva del viale” for being as they are and for being always a

safe harbour where to come back. Thanks to my old good friends Fedele, Chiara,

Giorgia and thanks to Manuela for hosting me in New York in a delicate moment

for my next future.

Last but not least, I am deeply grateful to Stefania Franklin, michuicanovia,

for her love and support, patience and impatience during the last two years. I

have been lucky to meet you in Barcelona and I am sure (I don’t just hope) that

together we can find the key for making of our future a wonderful adventure.

The show must go on! (Queen)

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