We demonstrate the generation of coherent phonons in a quartz bulk acoustic wave (BAW) resonator through the photoelastic properties of the crystal, via coupling to a microwave cavity enhanced by a photonic lambda scheme. This is achieved by imbedding a single crystal BAW resonator between the post and the adjacent wall of a microwave re-entrant cavity resonator. This 3D photonic lumped LC resonator at the same time acts as the electrode of a BAW phonon resonator and allows the direct readout of coherent phonons via the linear piezoelectric response of the quartz. A microwave pump, ωp, is tuned to the cavity resonance ω0, while a probe frequency, ωprobe, is detuned and varied around the red and blue detuned values with respect to the BAW phonon frequency, Ωm. The pump and probe power dependence of the generated phonons unequivocally determines the process to be electrostrictive, with the phonons produced at the difference frequency between the pump and the probe, with no back action effects involved. Thus, the phonons are created without threshold and can be considered analogous to a passive coherent population trapped maser scheme.

1.
M.
Goryachev
,
D. L.
Creedon
,
E. N.
Ivanov
,
S.
Galliou
,
R.
Bourquin
, and
M. E.
Tobar
,
Appl. Phys. Lett.
100
,
243504
(
2012
).
2.
M.
Goryachev
,
D. L.
Creedon
,
S.
Galliou
, and
M. E.
Tobar
,
Phys. Rev. Lett.
111
,
085502
(
2013
).
3.
S.
Galliou
,
M.
Goryachev
,
R.
Bourquin
,
P.
Abbé
,
J. P.
Aubry
, and
M. E.
Tobar
,
Sci. Rep.
3
,
2132
(
2013
).
4.
W. H.
Renninger
,
P.
Kharel
,
R. O.
Behunin
, and
P. T.
Rakich
,
Nat. Phys.
14
,
601
(
2018
).
5.
P.
Kharel
,
G. I.
Harris
,
E. A.
Kittlaus
,
W. H.
Renninger
,
N. T.
Otterstrom
,
J. G. E.
Harris
, and
P. T.
Rakich
,
Sci. Adv.
5
,
eaav0582
(
2019
).
6.
M.
Goryachev
,
Z.
Kuang
,
E. N.
Ivanov
,
P.
Haslinger
,
H.
Müller
, and
M. E.
Tobar
,
IEEE Trans. Ultrason., Ferroelectr., Frequency Control
65
,
991
(
2018
).
7.
A.
Lo
,
P.
Haslinger
,
E.
Mizrachi
,
L.
Anderegg
,
H.
Müller
,
M.
Hohensee
,
M.
Goryachev
, and
M. E.
Tobar
,
Phys. Rev. X
6
,
011018
(
2016
).
8.
P. A.
Bushev
,
J.
Bourhill
,
M.
Goryachev
,
N.
Kukharchyk
,
E.
Ivanov
,
S.
Galliou
,
M. E.
Tobar
, and
S.
Danilishin
,
Phys. Rev. D
100
,
066020
(
2019
).
9.
M.
Goryachev
and
M. E.
Tobar
,
Phys. Rev. D
90
,
102005
(
2014
).
10.
A.
Arvanitaki
,
S.
Dimopoulos
, and
K. V.
Tilburg
,
Phys. Rev. Lett.
116
,
031102
(
2016
).
11.
K.
Vahala
,
M.
Herrmann
,
S.
Knünz
,
V.
Batteiger
,
G.
Saathoff
,
T. W.
Hänsch
, and
T.
Udem
,
Nat. Phys.
5
,
682
(
2009
).
12.
I. S.
Grudinin
,
H.
Lee
,
O.
Painter
, and
K. J.
Vahala
,
Phys. Rev. Lett.
104
,
083901
(
2010
).
13.
I.
Mahboob
,
K.
Nishiguchi
,
A.
Fujiwara
, and
H.
Yamaguchi
,
Phys. Rev. Lett.
110
,
127202
(
2013
).
14.
D.
Navarro-Urrios
,
N. E.
Capuj
,
J.
Gomis-Bresco
,
F.
Alzina
,
A.
Pitanti
,
A.
Griol
,
A.
Martínez
, and
C. M.
Sotomayor Torres
,
Sci. Rep.
5
,
15733
(
2015
).
15.
A.
Godone
,
F.
Levi
,
S.
Micalizio
, and
J.
Vanier
,
Phys. Rev. A
62
,
053402
(
2000
).
16.
17.
A.
Godone
,
F.
Levi
,
S.
Micalizio
, and
C.
Calosso
,
Phys. Rev. A
70
,
012508
(
2004
).
18.
N. D.
Lanzillotti-Kimura
,
A.
Fainstein
,
B.
Perrin
,
B.
Jusserand
,
L.
Largeau
,
O.
Mauguin
, and
A.
Lemaitre
,
Phys. Rev. B
83
,
201103
(
2011
).
19.
N. D.
Lanzillotti-Kimura
,
A.
Fainstein
,
A.
Huynh
,
B.
Perrin
,
B.
Jusserand
,
A.
Miard
, and
A.
Lemaître
,
Phys. Rev. Lett.
99
,
217405
(
2007
).
20.
E.
EerNisse
, in
29th Annual Symposium on Frequency Control
(
Electronic Industries Association
,
1975
), pp.
1
4
.
21.
R.
Besson
, in
31st Annual Symposium on Frequency Control
(
Electronic Industries Association
,
1977
), pp.
147
152
.
22.
D.
Stevens
and
H.
Tiersten
,
J. Acoust. Soc. Am.
79
,
1811
(
1986
).
23.
J.-M. L.
Floch
,
Y.
Fan
,
M.
Aubourg
,
D.
Cros
,
N. C.
Carvalho
,
Q.
Shan
,
J.
Bourhill
,
E. N.
Ivanov
,
G.
Humbert
,
V.
Madrangeas
, and
M. E.
Tobar
,
Rev. Sci. Instrum.
84
,
125114
(
2013
).
24.
H.
Ramp
,
T. J.
Clark
,
B. D.
Hauer
,
C.
Doolin
,
K. C.
Balram
,
K.
Srinivasan
, and
J. P.
Davis
,
Appl. Phys. Lett.
116
,
174005
(
2020
).
25.
N. C.
Carvalho
,
J.
Bourhill
,
M.
Goryachev
,
S.
Galliou
, and
M. E.
Tobar
,
Appl. Phys. Lett.
115
,
211102
(
2019
).

Supplementary Material

You do not currently have access to this content.