We report the demonstration of an all-optical self-sustained cell-based microwave feedback oscillator. In this scheme, a microwave resonance, optically induced in a buffer-gas filled vapor cell resonator through coherent population trapping (CPT), is detected by a fast photodiode, amplified, and used to drive back, through a frequency divider, a Mach–Zehnder electro-optic modulator in a sustaining loop configuration. The total gain and phase of the system was measured in an open-loop configuration with a network analyzer. In good agreement with values predicted by the Leeson effect, the CPT feedback oscillator demonstrates an absolute phase noise of −24 dB rad2/Hz at 1 Hz offset frequency, compatible with a fractional frequency stability of 8 × 10−12 at 1 s, and a phase noise floor of −112 dB rad2/Hz, limited by the low microwave power available at the photodiode output. The amplitude noise of the oscillator shows a comparable noise floor and, for offset frequencies lower than 200 Hz, a 1/f dependence, due to the presence of the frequency divider in the loop.
References
1.
G.
Alzetta
, A.
Gozzini
, L.
Moi
, and G.
Orriols
, “An experimental method for the observation of r.f. transitions and laser beat resonances in oriented Na vapour
,” Nuovo Cimento B
36
, 5
–20
(1976
).2.
E.
Arimondo
, “Coherent population trapping in laser spectroscopy
,” Prog. Opt.
35
, 257
–354
(1996
).3.
R.
Wynands
and A.
Nagel
, “Precision spectroscopy with coherent dark states
,” Appl. Phys. B
68
, 1
–25
(1999
).4.
J.
Vanier
, “Atomic clocks based on coherent population trapping: A review
,” Appl. Phys. B
81
, 421
(2005
).5.
P.
Yun
, F.
Tricot
, C. E.
Calosso
, S.
Micalizio
, B.
Francois
, R.
Boudot
, S.
Guérandel
, and E.
de Clercq
, “High-performance coherent population trapping clock with polarization modulation
,” Phys. Rev. Appl.
7
, 014018
(2017
).6.
X.
Liu
, E.
Ivanov
, V. I.
Yudin
, J.
Kitching
, and E. A.
Donley
, “Low-drift coherent population trapping clock based on laser-cooled atoms and high-coherence excitation fields
,” Phys. Rev. Appl.
8
, 054001
(2017
).7.
M.
Abdel Hafiz
, G.
Coget
, M.
Petersen
, C. E.
Calosso
, S.
Guérandel
, E.
De Clercq
, and R.
Boudot
, “Symmetric autobalanced Ramsey interrogation for high-performance coherent population-trapping vapor-cell atomic clock
,” Appl. Phys. Lett.
112
, 244102
(2018
).8.
P.
Yun
, Q.
Li
, Q.
Hao
, G.
Liu
, E.
de Clercq
, S.
Guérandel
, X.
Liu
, S.
Gu
, Y.
Gao
, and S.
Zhang
, “High-performance coherent population trapping atomic clock with direct-modulation distributed Bragg reflector laser
,” Metrologia
58
, 045001
(2021
).9.
P. D. D.
Schwindt
, S.
Knappe
, V.
Shah
, L.
Hollberg
, and J.
Kitching
, “Chip-scale atomic magnetometer
,” Appl. Phys. Lett.
85
(26
), 6409
–6411
(2004
).10.
E.
Breschi
, Z. D.
Gruji
, P.
Knowles
, and A.
Weis
, “A high-sensitivity push-pull magnetometer
,” Appl. Phys. Lett.
104
, 023501
(2014
).11.
M.
Bajcsy
, A. S.
Zibrov
, and M. D.
Lukin
, “Stationary pulses of light in an atomic medium
,” Nature
426
, 638
–641
(2003
).12.
A.
Aspect
, E.
Arimondo
, R.
Kaizer
, N.
Vansteenkiste
, and C.
Cohen-Tannoudji
, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping: Theoretical analysis
,” J. Opt. Soc. Am. B
6
, 2112
–2124
(1989
).13.
J.
Vanier
and C.
Audoin
, The Quantum Physics of Atomic Frequency Standards
(Adam-Hilger
, 1989
), Vol. 1
.14.
A.
Godone
, F.
Levi
, S.
Micalizio
, and C.
Calosso
, “Coherent-population-trapping maser: Noise spectrum and frequency stability
,” Phys. Rev. A
70
, 012508
(2004
).15.
N.
Vukicevic
, A. S.
Zibrov
, L.
Hollberg
, F. L.
Walls
, J.
Kitching
, and H. G.
Robinson
, “Compact diode-laser based rubidium frequency reference
,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control.
47
(5
), 1122
–1126
(2000
).16.
L.
Balet
, J.
Haesler
, and S.
Lecomte
, “VCSEL-based Raman frequency reference on Rubidium atoms
,” in Proceedings of 2012 European Frequency and Time Forum
(IEEE
, 2012
), pp. 316
–319
.17.
D.
Strekalov
, D.
Aveline
, N.
Yu
, R.
Thompson
, A. B.
Matsko
, and L.
Maleki
, “Stabilizing an optoelectronic microwave oscillator with photonic filters
,” IEEE J. Lightwave Technol.
21
(12
), 3052
–3061
(2003
).18.
A. B.
Matsko
, D.
Strekalov
, and L.
Maleki
, “Magnetometer based on the optoelectronic oscillator
,” Opt. Commun.
247
, 141
(2005
).19.
D.
Strekalov
, A. B.
Matsko
, N.
Yu
, A. A.
Savchenkov
, and L.
Maleki
, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks
,” J. Mod. Opt.
53
(16–17
), 2469
–2484
(2006
).20.
D.
Strekalov
, A. A.
Savchenkov
, A.
Matsko
, N.
Yu
, and L.
Maleki
, “All-optical atomic clock on a chip: Progress report
,” in 2004 IEEE International Ultrasonics, Ferroelectrics and Frequency Control Joint 50th Anniversary Conference
, Montreal, Canada (IEEE
, 2004
), pp. 104
–108
.21.
S. H.
Yim
and D.
Cho
, “Oscillator-free atomic clock using a multimode laser
,” Appl. Phys. Lett.
96
, 211119
(2010
).22.
S. H.
Yim
and D.
Cho
, “Optelectronic oscillator stabilized to an intra-loop atomic filter with a coherent population trapping resonance
,” J. Korean Phys. Soc.
61
(1
), 17
–21
(2012
).23.
X. S.
Yao
and L.
Maleki
, “Optoelectronic microwave oscillator
,” J. Opt. Soc. Am. B
13
(8
), 1725
–1735
(1996
).24.
M.
Li
, T.
Hao
, W.
Li
, and Y.
Dai
, “Tutorial on optoelectronic oscillators
,” APL Photonics
6
, 061101
(2021
).25.
D. B.
Leeson
, “A simple model of feedback oscillator noise spectrum
,” Proc. IEEE
54
(2
), 329
–330
(1966
).26.
E.
Rubiola
, Phase Noise and Frequency Stability in Oscillators
(Cambridge University Press
, 2008
).27.
M.
Abdel Hafiz
, G.
Coget
, E.
de Clercq
, and R.
Boudot
, “Doppler-free spectroscopy on the Cs D1 line with a dual-frequency laser
,” Opt. Lett.
41
, 2982
(2016
).28.
D.
Brazhnikov
, M.
Petersen
, G.
Coget
, N.
Passilly
, V.
Maurice
, C.
Gorecki
, and R.
Boudot
, “Dual-frequency sub-Doppler spectroscopy: Extended theoretical model and microcell-based experiments
,” Phys. Rev. A
99
, 062508
(2019
).29.
Y. Y.
Jau
, E.
Miron
, A. B.
Post
, N. N.
Kuzma
, and W.
Happer
, “Push-pull optical pumping of pure superposition states
,” Phys. Rev. Lett.
93
, 160802
(2004
).30.
X.
Liu
, J. M.
Merolla
, S.
Guérandel
, C.
Gorecki
, E.
de Clercq
, and R.
Boudot
, “Coherent-population-trapping resonances in buffer-gas-filled Cs-vapor cells with push-pull optical pumping
,” Phys. Rev. A
87
, 013416
(2013
).31.
R.
Boudot
and E.
Rubiola
, “Phase noise in RF and microwave amplifiers
,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control
59
(12
), 2613
–2624
(2012
).32.
K.
Volyansky
, J.
Cussey
, H.
Tavernier
, P.
Salzentein
, G.
Sauvage
, L.
Larger
, and E.
Rubiola
, “Applications of the optical fiber to the generation and measurement of low-phase-noise microwave signals
,” J. Opt. Soc. Am. B
25
(12
), 2140
–2150
(2008
).33.
S.
Barke
, M.
Trobs
, B.
Sheard
, G.
Heinzel
, and K.
Danzmann
, “EOM sideband phase characteristics for the spaceborne gravitational wave detector LISA
,” Appl. Phys. B
98
, 33
–39
(2010
).34.
E. N.
Ivanov
and M. E.
Tobar
, “Low phase-noise sapphire crystal microwave oscillators: Current status
,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control
56
(2
), 263
–269
(2009
).35.
L.
Maleki
, “The optoelectronic oscillator
,” Nat. Photonics
5
, 728
–730
(2011
).36.
T. M.
Fortier
, F.
Quinlan
, A.
Hati
, C.
Nelson
, J. A.
Taylor
, Y.
Fu
, J.
Campbell
, and S. A.
Diddams
, “Photonic microwave generation with high-power photodiodes
,” Opt. Lett.
38
(10
), 1712
–1714
(2013
).37.
© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
