of 7
ARTICLE
Mechanical on-chip microwave circulator
S. Barzanjeh
1
, M. Wulf
1
, M. Peruzzo
1
, M. Kalaee
2,3
, P.B. Dieterle
2,3
, O. Painter
2,3
& J.M. Fink
1
Nonreciprocal circuit elements form an integral part of modern measurement and commu-
nication systems. Mathematically they require breaking of time-reversal symmetry, typically
achieved using magnetic materials and more recently using the quantum Hall effect, para-
metric permittivity modulation or Josephson nonlinearities. Here we demonstrate an on-chip
magnetic-free circulator based on reservoir-engineered electromechanic interactions.
Directional circulation is achieved with controlled phase-sensitive interference of six distinct
electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-
on-insulator platform is compatible with both superconducting qubits and silicon photonics,
and its noise performance is close to the quantum limit. With a high dynamic range, a tunable
bandwidth of up to 30 MHz and an in situ recon
fi
gurability as beam splitter or wavelength
converter, it could pave the way for superconducting qubit processors with multiplexed on-
chip signal processing and readout.
DOI: 10.1038/s41467-017-01304-x
OPEN
1
Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria.
2
Kavli Nanoscience Institute and Thomas J. Watson, Sr., Laboratory of Applied
Physics, California Institute of Technology, Pasadena, CA 91125, USA.
3
Institute for Quantum Information and Matter, California Institute of Technology,
Pasadena, CA 91125, USA. Correspondence and requests for materials should be addressed to S.B. (email:
shabir.barzanjeh@ist.ac.at
)
or to J.M.F. (email:
j
fi
nk@ist.ac.at
)
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DOI: 10.1038/s41467-017-01304-x
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1
N
onreciprocal devices are quintessential tools to suppress
spurious modes, interferences and unwanted signal
paths
1
. More generally, circulators can be used to realize
chiral networks
2
in systems where directional matter-light
coupling is not easily accessible. In circuit quantum electro-
dynamics
3
circulators are used for single-port coupling or as
isolators to protect the vulnerable cavity and qubit states from
electromagnetic noise and strong parametric ampli
fi
er drive
tones. State-of-the-art passive microwave circulators are based on
magneto-optic effects that require sizable magnetic
fi
elds
4
,
5
,
incompatible with ultra-low loss superconducting circuits. Due to
the design principle their size is at least on the order of the
wavelength and during manufacturing they need to be tuned and
optimized one by one. Commercial circulators can therefore not
be integrated on-chip causing additional losses and forming a
major roadblock towards a fully integrated quantum processor
based on superconducting qubits.
Many recent theoretical and experimental efforts have been
devoted to overcome these limitations both in the optical
6
8
and
microwave regimes
9
18
. In parallel, the rapidly growing
fi
eld
of optomechanical and electromechanical systems has shown
promising potential for applications in quantum information
processing and communication, in particular for microwave
to optical conversion
19
,
20
and ampli
fi
cation
21
. Very recently,
several theoretical proposals
22
24
have pointed out that reservoir-
engineered optomechanical systems
25
can lead to nonreciprocity
and
fi
rst isolators have just been demonstrated in the optical
domain
26
28
.
Here we present an on-chip microwave circulator using a
frequency tuneable silicon-on-insulator electromechanical sys-
tem
29
that is compatible with superconducting qubits
30
. The
device can be recon
fi
gured in situ as a
fi
lter, splitter, mixer, iso-
lator or circulator. For the
fi
rst mechanically mediated microwave
circulator, we achieve an isolation of up to 24
38 dB, compared to
total losses of 4.7
8.5 dB and at most 4
7 added noise quanta
over an instantaneous bandwidth of 630 Hz.
Results
Device characterization and tunability
. The main elements of
the microchip circulator device are shown in Fig.
1
a, b. The
circuit comprises three high-impedance spiral inductors (
L
i
)
capacitively coupled to the in-plane vibrational modes of a
dielectric nanostring mechanical resonator. The nanostring
Resonator 1
Port 1
Port 2
C
s,1
C
m
,1
C
m
,3
C
m
,2
C
m
L
1
C
s,3
L
3
C
s,2
L
2
a
1,in
a
3,out
Port 1
a
3,in
a
3,out
Port 2
a
2,in
a
2,out
V
dc
Mode 2
Mode 1
V
dc
Resonator 1
Resonator 2
Resonator 3
–4
–2
0
2
4
11.38
11.37
9.58
9.59
9.60
9.77
9.78
9.79
9.80
Frequency (GHz)
a
d
c
b
0
–2
–4
–6
0
–10
–20
0
–20
–40
(dB)
Nanostring
V
dc
(V)
Resonator 3
Resonator 2
Fig. 1
Microchip circulator and tunability.
a
Scanning electron micrograph of the electromechanical device including three microwave resonators, two
physical ports labelled 1 and 2, one voltage bias input (
V
dc
) on the top left. The inset shows the spiral inductor cross-overs in the green dashed boxed area.
The total device area is 0.3 mm by 0.45 mm. Scale bar (yellow) corresponds to 100
μ
m.
b
Enlarged view of the silicon nanostring mechanical oscillator with
four vacuum-gap capacitors coupled to the three coil inductors and one voltage bias input. Insets show details of the nanobeam as indicated by the dash
ed
and dotted rectangles. Scale bar (yellow) corresponds to 10
μ
m.
c
Electrode design and electrical circuit diagram of the device. The input modes
a
i
,in
couple
inductively to the microwave resonators with inductances
L
i
, coil capacitances
C
i
, additional stray capacitances
C
s
,
i
and the motional capacitances
C
m
,
i
. The
re
fl
ected tones
a
i
,out
pass through a separate chain of ampli
fi
ers each, and are measured at room temperature using a phase-locked spectrum analyzer (not
shown). The simulated displacement of the lowest frequency in-plane
fl
exural modes of the nanostring are shown in the two insets. Colour indicates
relative displacement.
d
Resonator re
fl
ection measurement of the three microwave resonators of an identical device, as a function of the applied bias
voltage and a
fi
t (dashed lines) to
Δ
ω
=
α
1
V
2
+
α
2
V
4
with the tunabilties
α
1
/2
π
=
0.53 MHz/V
2
and
α
2
/2
π
=
0.05 MHz/V
4
with a total tunable bandwidth
of 30 MHz for resonator 2 at 9.8 GHz
ARTICLE
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oscillator consists of two thin silicon beams that are connected by
two symmetric tethers and fabricated from a high resistivity
silicon-on-insulator device layer
29
. Four aluminium electrodes are
aligned and evaporated on top of the two nanostrings, forming
one half of the vacuum gap capacitors that are coupled to three
microwave resonators and one DC voltage bias line as shown
schematically in Fig.
1
c (see Supplementary Tables
1
and
2
for
details). The device is mounted on the mixing chamber plate of a
cryogen-free dilution refrigerator at a temperature of
T
f
=
10 mK
and all incoming lines are strongly
fi
ltered and attenuated to
suppress Johnson and phase noises.
The voltage bias line can be used to generate an attractive force
that pulls the nanobeam and tunes the operating point
frequencies of the device
31
. Figure
1
d shows the measured
resonance frequency change as a function of the applied bias
voltage
V
dc
. As expected, resonators 1 and 3 are tuned to higher
frequency due to an increased vacuum gap, whereas resonator 2 is
tuned to lower frequency. At a large tunable bandwidth of up to
30 MHz, as obtained for resonator 2, the ability to excite the
motion directly and to modulate the electromechanical coupling
in situ represents an important step towards new optomechanical
experiments and more practicable on-chip reciprocal and
nonreciprocal devices.
As a
fi
rst step, we carefully calibrate and characterize the
individual electromechanical couplings and noise properties,
similar to ref.
32
. The measured thermalization temperature of
the two mechanical modes are 18 and 25 mK and the
fi
nal
occupancy for the reported device reached as low as 0.6 and 2
quanta for standard motional sideband cooling. We then measure
the bidirectional frequency conversion between two microwave
resonator modes as mediated by one mechanical mode
33
. The
incoming signal photons can also be distributed to two ports with
varying probability as a function of the parametric drive strength
and in direct analogy to a tunable beam splitter. We present the
relevant sample parameters in Supplementary Tables
1
and
2
, the
theoretical analysis in Supplementary Note
2
and experimental
results of this bidirectional frequency conversion process in
Supplementary Fig.
1
.
Theoretical model
. Directionality is achieved by engaging the
second mechanical mode, a method that was developed in parallel
to this work
34
,
35
for demonstrating nonreciprocity in single-port
electromechanical systems. In fact, creating a parametric coupling
between the two electromagnetic and the two mechanical modes
by four microwave pumps with frequencies slightly detuned from
the lower motional sidebands of the resonances, creates two paths
for exchanging photons, as shown in Fig.
2
a. Nonreciprocity
appears when these paths interfere destructively, leading to
breaking the symmetry between the two directions. For a detailed
description, we begin with the theoretical model describing two
microwave cavities with resonance frequencies
ω
i
and total line-
widths
κ
i
with
i
=
1, 2 parametrically coupled to two distinct
modes of a mechanical resonator with resonance frequencies
ω
m
,
j
and damping rates
γ
m
,
j
with
j
=
1, 2. To establish the parametric
coupling, we apply four microwave tones, with frequencies
detuned by
δ
j
from the lower motional sidebands of the reso-
nances, as shown in Fig.
2
a. In a reference frame rotating at the
frequencies
ω
i
and
ω
m
,
j
+
δ
j
, the linearized Hamiltonian in the
resolved sideband regime (
ω
m
,
j

κ
1
,
κ
2
) is given by (
ħ
=
1)
H
¼
P
j
¼
1
;
2
δ
j
b
j
b
j
þ
P
i
;
j
¼
1
;
2
G
ij
e
i
φ
ij
a
i
b
j
þ
e

i
φ
ij
a
i
b
j

þ
H
off
;
ð
1
Þ

= –102.6°

= +102.6°
C
1
C
2
C
1
M
2
M
1
C
2
a
b
c
G
11
G
12
a
1,in
a
1,out
a
2,in
a
2,out
G
21
G
22
PSD
Transmission (dB)
Probe detuning (Hz)
Pump phase (°)
–40
–700
–180
–90
0
90
180
–180
–90
0
90
180
–350
350
700
0
–700
–350
350
700
0
–30
–20
–10
0
Probe detuning (Hz)
–500
500
0
–500
500
0
0
–20
–40
(dB)

2
+

m
,2

1
+

m
,1

2
+

m
,2

1
+

m
,1

d
,12

d
,11

d
,22

d
,21

S
12
S
21
C
2
C
1
|
S
12
|
2
Data
|
S
21
|
2
Data
|
S
12
|
2
Theory
|
S
21
|
2
Theory
Fig. 2
Electromechanical isolator.
a
Mode coupling diagram for
electromechanically induced nonreciprocity. Two microwave cavities (
C
1
and
C
2
) are coupled to two mechanical modes (
M
1
and
M
2
)withthe
electromechanical coupling rates
G
ij
(where
i
,
j
=
1, 2), inducing two distinct
signal conversion paths. Power spectral density (PSD) of the two microwave
cavities and arrows indicating the frequency of the four microwave pump
tones slightly detuned by
δ
i
from the lower motional sidebands of the
resonances. All four pumps are phase-locked while the signal tone is applied.
Only one of the microwave source phases is varied to
fi
nd the optimal
interference condition for directional transmission between ports 1 and 2.
b
Measured power transmission (dots) in forward
|
S
21
|
2
(cavity 1
cavity 2)
and backward directions
|
S
12
|
2
(cavity 2
cavity 1) as a function of probe
detuning for two different phases
φ
102.6
º
. The solid lines show the
results of the coupled-mode theory model discussed in the text. Grey shaded
areas denote cavity loss and green shaded areas insertion loss.
c
Experimental
data and theoretical model of measured transmission coef
fi
cients
|
S
12
|
2
and
|
S
21
|
2
as a function of signal detuning and pump phase
φ
.Dashedlinesindicate
the line plots for the two phases
φ
102.6
º
as shown in
b
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3
where
a
i
(
b
j
) is the annihilation operator for the cavity
i
(mechanics
j
),
G
ij
¼
g
0
;
ij
ffiffiffiffiffi
n
ij
p
and
g
0ij
are the effective and vacuum
electromechanical coupling rates between the mechanical mode
j
and cavity
i
, respectively, while
n
ij
is the total number of photons
inside the cavity
i
due to the drive with detuning
Δ
ij
, and
φ
ij
is
the relative phase set by drives. Here,
Δ
11
=
Δ
21
=
ω
m
,1
+
δ
1
and
Δ
22
=
Δ
12
=
ω
m
,2
+
δ
2
are the detunings of the drive tones with
respect to the cavities and
H
off
describes the time-dependent
coupling of the mechanical modes to the cavity
fi
elds due to the
off-resonant drive tones. These additional coupling terms create
cross-damping
36
and renormalize the mechanical modes, and can
only be neglected in the weak coupling regime for
G
ij
;
κ
j

ω
m
;
j
;
ω
m
;
2

ω
m
;
1




.
To see how the nonreciprocity arises, we use the quantum
Langevin equations of motion along with the input
output
theorem to express the scattering matrix
S
ij
of the system
described by the Hamiltonian (1), and relating the input photons
a
in,
i
(
ω
i
) at port
i
to the output photons
a
out,
j
(
ω
j
) at port
j
via
a
out
;
i
¼
P
j
¼
1
;
2
S
ij
a
in
;
i
with
i
=
1, 2. The dynamics of the four-
mode system described by Hamiltonian (1) is fully captured by a
set of linear equations of motion as veri
fi
ed in Supplementary
Notes
3
6
. Solving these equations in the frequency domain,
using the input
output relations, and setting
φ
22
=
φ
,
φ
11
=
φ
21
=
φ
12
=
0, the ratio of backward to forward transmission reads
λ
:
¼
S
12
ð
ω
Þ
S
21
ð
ω
Þ
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
C
11
C
21
p
Σ
m
;
2
ð
ω
Þþ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
C
12
C
22
p
Σ
m
;
1
ð
ω
Þ
e
i
φ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
C
11
C
21
p
Σ
m
;
2
ð
ω
Þþ
ffiffiffiffiffiffiffiffiffiffiffiffiffi
C
12
C
22
p
Σ
m
;
1
ð
ω
Þ
e

i
φ
:
ð
2
Þ
Here,
Σ
m
,
j
=
1+2
i
[(
1)
j
δ
ω
]/
γ
m
,
j
is the inverse of the mechan-
ical susceptibility divided by the mechanical linewidth
γ
m
,
j
and
C
ij
¼
4
G
2
ij
=
ð
κ
i
γ
m
;
j
Þ
is the electromechanical cooperativity. Note
that, in Eq. (
2
) we assume the device satis
fi
es the impedance-
matching condition on resonance, i.e.,
S
ii
(
ω
=
0)
=
0, which can
be achieved in the high-cooperativity limit (
C
ij

1).
Inspection of Eq. (
2
) reveals the crucial role of the relative
phase between the drive tones
φ
and the detuning
δ
to obtain
nonreciprocal transmission. When the cooperativities for all four
electromechanical couplings are equal (
C
ij
¼C
) then perfect
isolation, i.e.
λ
=
0, occurs for
tan
½
φ
ð
ω
Þ¼
δγ
m
;
1
þ
γ
m
;
2

þ
ωγ
m
;
2

γ
m
;
1

γ
m
;
1
γ
m
;
2
=
2

2
δ
2

ω
2
ðÞ
:
ð
3
Þ
Equation (
3
) shows that on resonance (
ω
=
0) tan[
φ
]
/
δ
,
highlighting the importance of the detuning
δ
to obtain
nonreciprocity. Tuning all four drives to the exact red sideband
frequencies (
δ
=
0) results in bidirectional behaviour (
λ
=
1). At
the optimum phase
φ
given by Eq. (
3
),
ω
=
0, and for two
mechanical modes with identical decay rates (
γ
m
,1
=
γ
m
,2
=
γ
) the
transmission in forward direction is given by
S
21
¼
ffiffiffiffiffiffiffiffiffi
η
1
η
2
p
4
i
δ
1

2
i
δ
=
γ
ðÞ
C
γ
1
þ
1
þ
4
δ
2
=
γ
2
2
C

2
2
6
4
3
7
5
ð
4
Þ
where
η
1(2)
=
κ
ext,1(2)
/
κ
1(2)
is the resonator coupling ratio and
κ
i
=
κ
int,
i
+
κ
ext,
i
is the total damping rate. Here
κ
int,
i
denotes the
internal loss rate and
κ
ext,
i
the loss rate due to the cavity to
waveguide coupling. Equation (
4
) shows that the maximum of the
transmission in forward direction,
S
21
jj
2
¼
η
1
η
2
1
2

1

,
occurs when 2
1
þ
4
δ
2
=
γ
2
and for large cooperativities
C
1. These conditions, as implemented in our experiment,
enable the observation of asymmetric frequency conversion with
strong isolation in the backward direction and small insertion loss
in forward direction.
Bidirectional wavelength conversion
. For bidirectional
wavelength conversion, higher cooperativity enhances the band-
width, as shown in Supplementary Note
2
. In contrast, the-
bandwidth of the nonreciprocal conversion is independent of
cooperativity and set only by the intrinsic mechanical linewidths
γ
m
,
i
, which can be seen in Eq. (
2
). This highlights the fact that
the isolation appears when the entire signal energy is dissipated
in the mechanical environment, a lossy bath that can be
engineered effectively
25
. In the present case it is the off-resonant
coupling between the resonators and the mechanical oscillator
that modi
fi
es this bath. The applied drives create an
effective interaction between the mechanical modes, where one
mode acts as a reservoir for the other and vice versa. This changes
both the damping rates and the eigenfrequencies of the
mechanical modes.
It, therefore, increases the instantaneous bandwidth of the
conversion and automatically introduces the needed detuning,
which is fully taken into account in the theory.
Two-port microwave isolator
. Using the on-chip electro-
mechanical microwave circuit shown in Fig.
1
a, we experimen-
tally realize directional wavelength conversion between two
superconducting coil resonators at (
ω
1
,
ω
2
)/2
π
=
(9.55, 9.82) GHz
coupled to two different physical waveguide ports and measure-
ment lines with (
η
1
,
η
2
)
=
(0.74, 0.86). Here we use the two
lowest-frequency vibrational in-plane modes of the mechanical
resonator at (
ω
m
,1
,
ω
m
,2
)/2
π
=
(4.34, 5.64) MHz with intrinsic
damping rates (
γ
m
,1
,
γ
m
,2
)/2
π
=
(4, 8) Hz. The vacuum electro-
mechanical coupling strengths for these mode combinations are
(
g
0,11
,
g
0,12
,
g
0,21
,
g
0,22
)/2
π
=
(33, 34, 13, 31) Hz. The microwave
resonators are driven with four coherent microwave sources with
powers (
P
11
,
P
12
,
P
21
,
P
22
)
=
(
73.3,
68.7,
66.9,
67.4) dBm at
the device inputs that correspond to the single cavity
single
mechanical cooperativities (
C
11
,
C
12
,
C
21
,
C
22
)
=
(47, 43.8, 41.9,
56.9). Transmission parameters are measured by using a weak
probe signal with a signal power of only
117 dBm at the device
inputs.
Figure
2
b shows the measured transmission of the wavelength
conversion in the forward
|
S
21
|
2
and backward directions
|
S
12
|
2
as
a function of probe detuning for two different phases as set by
one out of the four phase-locked microwave drives. At
φ
=
102.6
º
and over a bandwidth of 518 Hz, we measure high
transmission from cavity 1 to 2 with an insertion loss of 2.4 dB
due to
fi
nite input matching and a resonator loss of 1.9 dB due to
fi
nite intrinsic resonator linewidths. In the backward direction,
the transmission is suppressed by up to 40.4 dB. Likewise, at the
positive phase of
φ
=
102.6
º
the transmission from cavity 1 to 2 is
suppressed while the transmission from cavity 2 to 1 is high. In
both cases, we observe excellent agreement with theory (solid
lines). Figure
2
c shows the
S
parameters for the whole range of
phases
φ
, which are symmetric and bidirectional around
φ
=
0.
We
fi
nd excellent agreement with theory over the full range of
measured phases with
<
10% deviation to independently cali-
brated drive photon numbers and without any other free
parameters.
Extension to a microwave circulator
. The described two-port
isolator can be extended to an effective three-port device by
parametrically coupling the third microwave resonator capaci-
tively to the dielectric nanostring, as shown in Fig.
1
a. The third
resonator at a resonance frequency of
ω
3
/2
π
=
11.30 GHz is
coupled to the waveguide with
η
3
=
0.52 and to the two in-plane
mechanical modes with (
g
0,31
,
g
0,32
)/2
π
=
(22, 45) Hz. Similar to
the isolator, we establish a parametric coupling between cavity
and mechanical modes using six microwave pumps with
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frequencies slightly detuned from the lower motional sidebands
of the resonances, which for certain pump phase combinations
can operate as a three-port circulator for microwave photons, see
Fig.
3
a. The pump powers at the device inputs are (
P
11
,
P
12
,
P
21
,
P
22
,
P
31
,
P
32
)
=
(
72.5,
69,
67.5,
68,
69,
70) corresponding
to the single resonator cooperativities (
C
11
,
C
12
,
C
21
,
C
22
,
C
31
,
C
32
)
=
(56.5, 40.9, 35, 49.6, 99.2, 49, 6). Using an additional
microwave source as a weak probe signal with a signal power of
only
117 dBm at the device inputs, we measure the power
transmission between all ports and directions as shown in Fig.
3
b
3
3
a
b
c
Transmission (dB)
–40
–30
–20
–10
0
Pump phase (°)
–180
–90
0
90
180
–180
–90
0
90
180
Probe detuning (Hz)
–700
–350
350
700
0
–700
–350
350
700
0
–700
–350
350
700
0
Data
S
12
2
Data
S
23
2
Data
S
31
2
Theory
S
12
2
Theory
S
23
2
Theory
S
31
2
C
1
G
11
G
31
G
21
G
22
G
32
G
12
a
3,in
a
3,out
a
2,in
a
2,out
a
1,in
a
1,out
C
2
C
1
C
1
C
3
C
3
C
2
C
2
C
1
C
3
C
2
C
2
Probe detuning (Hz)
–600
600
0
–600
600
0
–600
600
0
0
–20
–40
(dB)
M
1
M
2
Fig. 3
Electromechanical circulator.
a
Mode coupling diagram describing the coupling between three microwave cavities (
C
1
,
C
2
and
C
3
) and two
mechanical modes (
M
1
and
M
2
) with electromechanical coupling rates
G
ij
(where
i
=
1, 2, 3 and
j
=
1, 2), creating a circulatory frequency conversion
between the three cavity modes, as indicated by the grey arrow.
b
Measured power transmission in forward
|
S
21
|
2
,
|
S
32
|
2
and
|
S
13
|
2
(red dots) and backward
directions
|
S
12
|
2
,
|
S
23
|
2
and
|
S
31
|
2
(blue dots) as a function of probe detuning for a pump phase
φ
=
54
º
. The solid lines show the prediction of the coupled-
mode theory model discussed in the text. The inset shows the signal propagation between the three resonator modes and the black arrow indicates the
circulator direction. Grey shaded areas denote cavity loss and green shaded areas insertion loss.
c
Measured
S
parameters and theoretical model as a
function of detuning and pump phase. Dashed lines indicate the line plot positions shown in
b
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for a single
fi
xed phase of
φ
=
54
º
, optimized experimentally for
forward circulation.
At this phase, we see high transmission in the forward
direction
S
21,32,13
with an insertion loss of (3.8, 3.8, 4.4) dB, due to
imperfect input matching, and an isolation in the backward
direction
S
12,23,31
of up to (18.5, 23, 23) dB over a bandwidth of
628.5 Hz. The full dependence of the circulator scattering
parameters on the drive phase is shown in Fig.
3
c, where we
see excellent agreement with theory. The added noise photon
number of the device is found to be (
n
add,21
,
n
add,32
,
n
add,13
)
=
(4, 6.5, 3.6) in the forward direction and (
n
add,12
,
n
add,23
,
n
add,31
)
=
(4, 4, 5.5) in the backward direction, limited by the
thermal occupation of the mechanical modes and discussed in
more detail in Supplementary Fig.
3
.
Discussion
In conclusion, we demonstrated a frequency tunable and in situ
recon
fi
gurable signal processing device that can act as a
fi
lter,
wavelength converter, beam splitter, isolator or circulator for
microwave photons. The circulator is highly directional and
operates with relatively low loss and added noise. Improvements
of the circuit design and fabrication will help to increase the
instantaneous bandwidth and decrease the insertion losses.
Compared to the so far signi
fi
cantly higher bandwidth Josephson
devices, a mechanical approach is insensitive to magnetic
fi
eld
noise and offsets, mechanical devices have higher dynamical
range due to the smaller nonlinearity, and well-con
fi
ned
mechanical modes are typically less prone to parasitic coupling
when integrated in larger systems. In addition, mechanical sys-
tems have the potential for hybrid microwave and optical signal
processing, in particular for non-reciprocity between microwave
and optical propagating
fi
elds. The presented external voltage bias
offers new ways to achieve directional ampli
fi
cation and
squeezing of microwave
fi
elds in the near future.
Data availability
. The data that support the
fi
ndings of this study
are available from the corresponding author upon reasonable
request.
Received: 16 June 2017 Accepted: 8 September 2017
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Acknowledgements
We thank Nikolaj Kuntner for the development of the Python virtual instrument
panel and Georg Arnold for supplementary device simulations. This work was
supported by IST Austria and the European Union
s Horizon 2020 research and
innovation program under grant agreement No 732894 (FET Proactive HOT). S.B.
acknowledges support from the European Union
s Horizon 2020 research and innova-
tion program under the Marie Sklodowska Curie grant agreement No 707438 (MSC-IF
SUPEREOM). OJP acknowledges support from the AFOSR-MURI Quantum Photonic
Matter, the Institute for Quantum Information and Matter, an NSF Physics Frontiers
Center (grant PHY-1125565) with support of the Gordon and Betty Moore Foundation,
and the Kavli Nanoscience Institute at Caltech.
Author contributions
S.B. and J.M.F. conceived the ideas for the experiment. S.B. developed the theoretical
model, performed and analysed the measurements. S.B., M.W., M.P. and J.M.F. designed
the microwave circuit and built the experimental setup. M.K., P.B.D., J.M.F. and O.P.
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designed the mechanical nanobeam oscillator. J.M.F. and M.K. fabricated the sample.
P.B.D. and O.P. contributed to sample fabrication. S.B. and J.M.F. wrote the manuscript.
J.M.F. supervised the research.
Additional information
Supplementary Information
accompanies this paper at doi:
10.1038/s41467-017-01304-x
.
Competing interests:
The authors declare no competing
fi
nancial interests.
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