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