Slides for a presentation I gave at the Spring meeting of the German Physical Society in Mainz on March 10, 2017. In the presentation, I discuss new approaches to frequency conversion of electromagnetic fields using optomechanical interaction. The main figure of merit we are trying to optimize is the transduction bandwidth. I show that the bandwidth can be enhanced by using spatially adiabatic state transfer in an array of conventional optomechanical transducers.

1. Novel approaches to
optomechanical transduction
Ondřej Černotík and Klemens Hammerer
Institut für Theoretische Physik, Leibniz Universität Hannover
DPG Frühjahrstagung Mainz, 10 March 2017

2. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ
Superconducting systems are among the
best candidates for
quantum computers.
2
R. Schoelkopf
Light is ideal for quantum communication
owing to low losses and noise.
A. Zeilinger

3. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ
Mechanical oscillators can mediate
coupling between microwaves and light.
3
R. Andrews et al., Nature Phys. 10, 321 (2014)

4. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ
Mechanical oscillators can mediate
coupling between microwaves and light.
4
R. Andrews et al., Nature Phys. 10, 321 (2014)a1,out
a2,outa2,in
a1,in
a1
a2
g2
g1
b
H = g1(a†
1b + b†
a1) + g2(a†
2b + b†
a2)
˙a(t) = Aa(t) + Bain(t)
aout(t) = Ca(t) + Dain(t)
aout(!) = S(!)ain(!) = [D C(A + i!1)B]ain(!)

5. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ
Mechanical oscillators can mediate
coupling between microwaves and light.
5
R. Andrews et al., Nature Phys. 10, 321 (2014)a1,out
a2,outa2,in
a1,in
a1
a2
g2
g1
b
H = g1(a†
1b + b†
a1) + g2(a†
2b + b†
a2)
g2
1
1
+
g2
2
2
⌧ i
L. Tian, PRL 108, 153604 (2012)
Y.-D. Wang and A.A. Clerk, PRL
108, 153603 (2012)
g2
1
1
=
g2
2
2
Impedance matching
i ⌧ !mResolved-sideband regime
Strong cooperativity Ci =
4g2
i
i ¯n
1

6. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 6
Better performance can be achieved by
optimizing for a specific task.
-
O. Cernotík and K. Hammerer, PRA 94, 012340 (2016)ˇ
| 0i = (|0i + |1i)(|0i + |1i)
!
8
<
:
|00i
|11i
|01i + |10i
/ h 1
z + 2
zi

7. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 7
We can also use new designs to improve
efficiency and bandwidth.
z
H = g1(z)(a†
1b + b†
a1) + g2(z)(a†
2b + b†
a2)

8. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ
g1
g2
8
Highly efficient transduction is possible
using adiabatic state transfer.
L. Tian, PRL 108, 153604 (2012)
Y.-D. Wang and A.A. Clerk, PRL 108,
153603 (2012)
z
H =
q
g2
1(z) + g2
2(z)(d†
1b + b†
d1)
d1 =
1
p
g2
1(z) + g2
2(z)
[g1(z)a1 + g2(z)a2]
d2 =
1
p
g2
1(z) + g2
2(z)
[g2(z)a1 g1(z)a2]

9. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 9
Transducer bandwidth can be increased
by increasing the array size.

10. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 10
Reflection from a large number of cavities
introduces a phase shift.

11. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 11
High conversion efficiency is possible in
presence of losses and noise.
¯n ⌧ gi
4g2
i
i ¯n
1
4g2
i
i ¯n
1
i ⌧ !m i ⌧ !m i, ! ⌧ !m
i ⌧ gi int ⌧ i
(
int ⌧ i
prop ⌧
g2
i
i
Temporal
adiabatic
Single
transducer
Transducer
array
Mechanical
noise
Counterrotating
terms
Optical losses

12. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 12
We must also limit backscattering.
RL
⌘ =
L
R
⌧ 1Needs

13. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 13
Transducer array is an interesting platform
for frequency conversion.
+ Large bandwidth
+ Multimode operation
- Needs an array
- Phase shift

14. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 14
Generalizations of the system are
possible.
• Continuum implementation
P. Rakich and F. Marquadt, arXiv:1610.03012
H. Zoubi and K. Hammerer, PRA 94, 053827 (2016)
• Spatially adiabatic dynamics