Novel approaches to optomechanical transduction

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

Novel approaches to optomechanical transduction

Ondrej Cernotik

Novel approaches to optomechanical transduction