Novel approaches to optomechanical transduction

Ondřej Černotík and Klemens HammererInstitut für Theoretische Physik, Leibniz Universität Hannover

DPG Frühjahrstagung Mainz, 10 March 2017

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

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)

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

a2g2

g1b

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

(!)

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

a2g2

g1b

H = g1(a†1b+ b†a1) + g2(a

†2b+ b†a2)

g211

+g222

⌧ i

L. Tian, PRL 108, 153604 (2012)

Y.-D. Wang and A.A. Clerk, PRL 108, 153603 (2012)

g211

=g222

Impedance matching

i ⌧ !mResolved-sideband regime

Strong cooperativity Ci =4g2ii�n

� 1

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�1z + �2

zi

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)

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

g21(z) + g22(z)(d†1b+ b†d1)

d1 =1p

g21(z) + g22(z)[g1(z)a1 + g2(z)a2]

d2 =1p

g21(z) + g22(z)[g2(z)a1 � g1(z)a2]

Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 9

Transducer bandwidth can be increased by increasing the array size.

Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 10

Reflection from a large number of cavities introduces a phase shift.

Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 11

High conversion efficiency is possible in presence of losses and noise.

�n ⌧ gi4g2ii�n

� 14g2ii�n

� 1

i ⌧ !m i ⌧ !m i,! ⌧ !m

i ⌧ gi int ⌧ i

(int

⌧ i

prop

⌧ g2i

i

Temporal adiabatic

Single transducer

Transducer array

Mechanical noise

Counterrotating terms

Optical losses

Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 12

We must also limit backscattering.

RL

⌘ =L

R⌧ 1Needs

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

Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 14

Generalizations of the system are possible.

• Continuum implementationP. Rakich and F. Marquadt, arXiv:1610.03012 H. Zoubi and K. Hammerer, PRA 94, 053827 (2016)

• Spatially adiabatic dynamics