We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.

1.
M.
Poot
and
H. S.
van der Zant
,
Phys. Rep.
511
,
273
(
2012
).
2.
K. L.
Ekinci
,
Y. T.
Yang
, and
M. L.
Roukes
,
J. Appl. Phys.
95
,
2682
(
2004
).
3.
R.
Lifshitz
and
M. C.
Cross
, in
Reviews of Nonlinear Dynamics and Complexity
, edited by
H. G.
Schuster
(
Wiley
,
2008
), Vol.
1
.
4.
R. B.
Karabalin
,
M. C.
Cross
, and
M. L.
Roukes
,
Phys. Rev. B
79
,
165309
(
2009
).
5.
I.
Kozinsky
,
H. W. C.
Postma
,
O.
Kogan
,
A.
Husain
, and
M. L.
Roukes
,
Phys. Rev. Lett.
99
,
207201
(
2007
).
6.
M. D.
LaHaye
,
J.
Suh
,
P. M.
Echternach
,
K. C.
Schwab
, and
M. L.
Roukes
,
Nature
459
,
960
(
2009
).
7.
J. D.
Teufel
,
T.
Donner
,
D.
Li
,
J. W.
Harlow
,
M. S.
Allman
,
K.
Cicak
,
A. J.
Sirois
,
J. D.
Whittaker
,
K. W.
Lehnert
, and
R. W.
Simmonds
,
Nature
475
,
359
(
2011
).
8.
S.
Gröblacher
,
S.
Gigan
,
H. R.
Böhm
,
A.
Zeilinger
, and
M.
Aspelmeyer
,
Europhys. Lett.
81
,
54003
(
2008
).
9.
J. D.
Teufel
,
D.
Li
,
M. S.
Allman
,
K.
Cicak
,
A. J.
Sirois
,
J. D.
Whittaker
, and
R. W.
Simmonds
,
Nature
471
,
204
(
2011
).
10.
S.
Agarwal
and
J. H.
Eberly
,
Phys. Rev. A
86
,
022341
(
2012
).
11.
E.
Buks
,
S.
Zaitsev
,
E.
Segev
,
B.
Abdo
, and
M. P.
Blencowe
,
Phys. Rev. E
76
,
026217
(
2007
).
12.
K. L.
Ekinci
and
M. L.
Roukes
,
Rev. Sci. Instrum.
76
,
061101
(
2005
).
13.
S.
Etaki
,
M.
Poot
,
K.
Onomitsu
,
H.
Yamaguchi
, and
H. S.
van der Zant
,
C. R. Phys.
12
,
817
(
2011
).
14.
S.
Etaki
,
M.
Poot
,
I.
Mahboob
,
K.
Onomitsu
,
H.
Yamaguchi
, and
H. S. J.
van der Zant
,
Nat. Phys.
4
,
785
(
2008
).
15.
K.
Schwab
,
Appl. Phys. Lett.
80
,
1276
(
2002
).
16.
M.
Dykman
,
Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits
(
Oxford University Press
,
Oxford
,
2012
).
17.
M.
Defoort
,
V.
Puller
,
O.
Bourgeois
,
F.
Pistolesi
, and
E.
Collin
, e-print arXiv:1409.6971[cond-mat] (
2014
).
18.
L. G.
Villanueva
,
E.
Kenig
,
R. B.
Karabalin
,
M. H.
Matheny
,
R.
Lifshitz
,
M. C.
Cross
, and
M. L.
Roukes
,
Phys. Rev. Lett.
110
,
177208
(
2013
).
19.
E.
Kenig
,
M. C.
Cross
,
L. G.
Villanueva
,
R. B.
Karabalin
,
M. H.
Matheny
,
R.
Lifshitz
, and
M. L.
Roukes
,
Phys. Rev. E
86
,
056207
(
2012
).
20.
B.
Yurke
and
D.
Stoler
,
Phys. Rev. Lett.
57
,
13
(
1986
).
21.
I.
Katz
,
A.
Retzker
,
R.
Straub
, and
R.
Lifshitz
,
Phys. Rev. Lett.
99
,
040404
(
2007
).
22.
I.
Katz
,
R.
Lifshitz
,
A.
Retzker
, and
R.
Straub
,
New J. Phys.
10
,
125023
(
2008
).
23.
M.
Ludwig
,
B.
Kubala
, and
F.
Marquardt
,
New J. Phys.
10
,
095013
(
2008
).
24.
J.
Qian
,
A. A.
Clerk
,
K.
Hammerer
, and
F.
Marquardt
,
Phys. Rev. Lett.
109
,
253601
(
2012
).
25.
F.
Xue
,
Y.-x.
Liu
,
C.
Sun
, and
F.
Nori
,
Phys. Rev. B
76
,
064305
(
2007
).
26.
M.
Poot
,
S.
Etaki
,
I.
Mahboob
,
K.
Onomitsu
,
H.
Yamaguchi
,
Y. M.
Blanter
, and
H. S. J.
van der Zant
,
Phys. Rev. Lett.
105
,
207203
(
2010
).
27.
B. H.
Schneider
,
S.
Etaki
,
H. S. J.
van der Zant
, and
G. A.
Steele
,
Sci. Rep.
2
,
599
(
2012
).
28.
S.
Etaki
,
F.
Konschelle
,
Y. M.
Blanter
,
H.
Yamaguchi
, and
H. S. J.
van der Zant
,
Nat. Commun.
4
,
1803
(
2013
).
29.
S.
Zaitsev
,
A. K.
Pandey
,
O.
Shtempluck
, and
E.
Buks
,
Phys. Rev. E
84
,
046605
(
2011
).
30.
S. H.
Strogatz
,
Nonlinear Dynamics and Chaos: With Applications To Physics, Biology, Chemistry, and Engineering
, 1st ed. (
Westview Press
,
2001
).
31.
D.
Yuvaraj
,
G.
Bachar
,
O.
Suchoi
,
O.
Shtempluck
, and
E.
Buks
, e-print arXiv:1107.0635 (
2011
).
32.
E.
Buks
and
M. P.
Blencowe
,
Phys. Rev. B
74
,
174504
(
2006
).
33.
M. P.
Blencowe
and
E.
Buks
,
Phys. Rev. B
76
,
014511
(
2007
).
34.
P. D.
Nation
,
M. P.
Blencowe
, and
E.
Buks
,
Phys. Rev. B
78
,
104516
(
2008
).
35.
R.
Kubo
,
K.
Matsuo
, and
K.
Kitahara
,
J. Stat. Phys.
9
,
51
(
1973
).
36.
P.
Colet
,
M.
San Miguel
,
J.
Casademunt
, and
J. M.
Sancho
,
Phys. Rev. A
39
,
149
(
1989
).
37.
M. O.
Caceres
,
C. E.
Budde
, and
G. J.
Sibona
,
J. Phys. A
28
,
3877
(
1995
).
38.
D. J.
Van Harlingen
,
T. L.
Robertson
,
B. L. T.
Plourde
,
P. A.
Reichardt
,
T. A.
Crane
, and
J.
Clarke
,
Phys. Rev. B
70
,
064517
(
2004
).
39.
R. H.
Koch
,
D. P.
DiVincenzo
, and
J.
Clarke
,
Phys. Rev. Lett.
98
,
267003
(
2007
).
40.
S. M.
Anton
,
C. D.
Nugroho
,
J. S.
Birenbaum
,
S. R.
O'Kelley
,
V.
Orlyanchik
,
A. F.
Dove
,
G. A.
Olson
,
Z. R.
Yoscovits
,
J. N.
Eckstein
,
D. J.
Van Harlingen
 et al,
Appl. Phys. Lett.
101
,
092601
(
2012
).
41.
S. M.
Anton
,
J. S.
Birenbaum
,
S. R.
O'Kelley
,
V.
Bolkhovsky
,
D. A.
Braje
,
G.
Fitch
,
M.
Neeley
,
G. C.
Hilton
,
H.-M.
Cho
,
K. D.
Irwin
 et al,
Phys. Rev. Lett.
110
,
147002
(
2013
).
42.
M.
Khapaev
,
A.
Kidiyarova-Shevchenko
,
P.
Magnelind
, and
M.
Kupriyanov
,
IEEE Trans. Appl. Supercond.
11
,
1090
(
2001
).
43.
A.
De Waele
and
R.
De Bruyn Ouboter
,
Physica
42
,
626
(
1969
).
44.
L. D.
Landau
and
E. M.
Lifshitz
,
Mechanics
, 3rd ed. (
Butterworth-Heinemann
,
1976
), Vol.
1
.
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