Resolving the energy levels of a nanomechanical oscillator

Nature

Volumn 571, Issue 7766, 2019, Pages 537-540

  Arrangoiz Arriola, Patricio ^a,b   Wollack, E Alex ^a,b   Wang, Zhaoyou ^a,b   Pechal, Marek ^a,b   Jiang, Wentao ^a,b   McKenna, Timothy P ^a,b   Witmer, Jeremy D ^a,b   Van Laer, Raphaël ^a,b   Safavi Naeini, Amir H ^a,b  

^a STANFORD UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOENGINEERING; CONTROLLED STUDY; DYNAMICS; ELECTRODYNAMICS; INFORMATION PROCESSING; LETTER; LIMIT OF QUANTITATION; MEASUREMENT ACCURACY; MEASUREMENT PRECISION; MICROWAVE RADIATION; OSCILLATION; PIEZOELECTRICITY; PRIORITY JOURNAL; SUPERCONDUCTIVITY;

EID: 85069677529     PISSN: 00280836     EISSN: 14764687     Source Type: Journal    
DOI: 10.1038/s41586-019-1386-x     Document Type: Article

References (40)

1. Brune, M. et al. From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase sensitive detection. Phys. Rev. Lett. 72, 3339–3342 (1994).
2. Bertet, P. et al. Direct measurement of the Wigner function of a one-photon Fock state in a cavity. Phys. Rev. Lett. 89, 200402 (2002).
3. Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).
4. Braginsky, V. B. & Khalili, F. Y. Quantum nondemolition measurements: the route from toys to tools. Rev. Mod. Phys. 68, 1–11 (1996).
5. Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).
6. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).
7. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).
8. Gustafsson, M. V. et al. Propagating phonons coupled to an artificial atom. Science 346, 207–211 (2014).
9. Cohen, J. D. et al. Phonon counting and intensity interferometry of a nanomechanical resonator. Nature 520, 522–525 (2015).
10. Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016).
11. Chu, Y. et al. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666–670 (2018).
12. Satzinger, K. J. et al. Quantum control of surface acoustic-wave phonons. Nature 563, 661–665 (2018).
13. Viennot, J. J., Ma, X. & Lehnert, K. W. Phonon-number-sensitive electromechanics. Phys. Rev. Lett. 121, 183601 (2018).
14. Mabuchi, H. Cavity quantum electrodynamics: coherence in context. Science 298, 1372–1377 (2002).
15. Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).
16. Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).
17. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008).
18. Miao, H., Danilishin, S., Corbitt, T. & Chen, Y. Standard quantum limit for probing mechanical energy quantization. Phys. Rev. Lett. 103, 100402 (2009).
19. Ludwig, M., Safavi-Naeini, A. H., Painter, O. & Marquardt, F. Enhanced quantum nonlinearities in a two-mode optomechanical system. Phys. Rev. Lett. 109, 063601 (2012).
20. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
21. Brune, M., Haroche, S., Lefevre, V., Raimond, J. M. & Zagury, N. Quantum nondemolition measurement of small photon numbers by Rydberg-atom phase-sensitive detection. Phys. Rev. Lett. 65, 976–979 (1990).
22. Lachance-Quirion, D. et al. Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet. Sci. Adv. 3, e1603150 (2017).
23. Ioffe, L. B., Geshkenbein, V. B., Helm, C. & Blatter, G. Decoherence in superconducting quantum bits by phonon radiation. Phys. Rev. Lett. 93, 057001 (2004).
24. Barends, R. et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013).
25. Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).
26. Schuster, D. I. et al. ac Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2005).
27. Safavi-Naeini, A. H. & Painter, O. Proposal for an optomechanical traveling wave phonon–photon translator. New J. Phys. 13, 013017 (2011).
28. Bochmann, J., Vainsencher, A., Awschalom, D. D. & Cleland, A. N. Nanomechanical coupling between microwave and optical photons. Nat. Phys. 9, 712–716 (2013).
29. MacCabe, G. S. et al. Phononic bandgap nano-acoustic cavity with ultralong phonon lifetime. Preprint at http://arxiv.org/abs/1901.04129 (2019).
30. Pechal, M., Arrangoiz-Arriola, P. & Safavi-Naeini, A. H. Superconducting circuit quantum computing with nanomechanical resonators as storage. Quantum Sci. Technol. 4, 015006 (2018).
31. Vlastakis, B. et al. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 342, 607–610 (2013).
32. Sletten, L. D. et al. Resolving phonon Fock states in a multimode cavity with a double-slit qubit. Phys. Rev. X 9, 021056 (2019).
33. Wang, C. et al. Integrated high quality factor lithium niobate microdisk resonators. Opt. Express 22, 30924–30933 (2014).
34. Dolan, G. J. Offset masks for liftoff photoprocessing. Appl. Phys. Lett. 31, 337–339 (1977).
35. Kelly, J. Fault-Tolerant Superconducting Qubits. PhD thesis, Univ. of California, Santa Barbara (2015); https://web.physics.ucsb.edu/~martinisgroup/theses/Kelly2015.pdf.
36. Dunsworth, A. et al. Characterization and reduction of capacitive loss induced by sub-micron Josephson junction fabrication in superconducting qubits. Appl. Phys. Lett. 111, 022601 (2017).
37. Vidal-Álvarez, G., Kochhar, A. & Piazza, G. Delay lines based on a suspended thin film of X-cut lithium niobate. In 2017 IEEE Int. Ultrasonics Symp. (IEEE, 2017).
38. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).
39. COMSOL Multiphysics version 4.4 (2013); http://www.comsol.com.
40. Arrangoiz-Arriola, P. & Safavi-Naeini, A. H. Engineering interactions between superconducting qubits and phononic nanostructures. Phys. Rev. A 94, 063864 (2016).