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Novel approaches to optomechanical transduction

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In recent years, mechanical oscillators received attention as a promising tool for frequency conversion between microwaves and light. A general, bi-directional transducer with high efficiency is still far from reach of current technology; finding new strategies for optomechanical transduction allows us to relax the requirements and bring these systems closer to an experimental realization. An interesting example is generation of entanglement between two superconducting qubits using measurement and postselection. Here, the mechanical oscillators interacts directly with the superconducting transmon qubit in such a way that it feels a qubit-state dependent force. This force can then be read out using a cavity field; reading out two such systems sequentially realizes an effective total spin measurement. Starting from a suitable initial state and employing postselection, entanglement can be generated. Another interesting approach is to use an array of optomechanical transducers in which the output fields of one transducer are fed into the input of the next. The periodicity of the array results in a joint dispersion relation for the propagating microwave and optical fields. The resulting structure can be used to control the conversion bandwidth and forward and backward scattering.

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Novel approaches to optomechanical transduction

  1. 1. Novel approaches to optomechanical transduction Ondřej Černotík and Klemens Hammerer Institute for Theoretical Physics, Leibniz University Hannover, Germany APS March Meeting New Orleans, 16 March 2017
  2. 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. 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)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(!)
  4. 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) 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
  5. 5. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 5 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
  6. 6. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 6 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)
  7. 7. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ g1 g2 7 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]
  8. 8. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 8 Transducer bandwidth can be increased by increasing the array size.
  9. 9. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 9 Reflection from a large number of cavities introduces a phase shift.
  10. 10. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 10 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
  11. 11. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 11 We must also limit backscattering. RL ⌘ = L R ⌧ 1Needs
  12. 12. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 12 Transducer array is an interesting platform for frequency conversion. + Large bandwidth + Multimode operation - Needs an array - Phase shift
  13. 13. Ondrej Cernotík (Hannover): Novel approaches to optomechanical transductionˇˇ 13 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

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