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# Quantum control of an oscillator using a stimulated Josephson nonlinearity

## Abstract

Superconducting circuits extensively rely on the Josephson junction as a nonlinear electronic element for manipulating quantum information and mediating photon interactions. Despite continuing efforts in pushing the coherence of Josephson circuits, the best photon lifetimes have been demonstrated in microwave cavities. Nevertheless, architectures based on quantum memories require a qubit element for logical operations at the cost of introducing additional loss channels and limiting process fidelities. Here, we directly operate the oscillator as an isolated two-level system by tailoring its Hilbert space. Implementing a flux-tunable inductive coupling between two resonators, we can selectively Rabi drive the lowest eigenstates by dynamically activating a three-wave interaction through parametric flux modulation. Measuring the Wigner function confirms that we can prepare arbitrary states confined in the single-photon manifold, with measured coherence times limited by the oscillator intrinsic quality factor. This architectural shift in engineering oscillators with stimulated nonlinearity can be exploited for designing long-lived quantum modules and offers flexibility in studying non-equilibrium physics with photons in a field-programmable simulator.

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## Data availability

The data represented in Fig. 3b are available as source data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

## References

1. 1.

Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

2. 2.

Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718/719, 1–102 (2017).

3. 3.

Wendin, G. Quantum information processing with superconducting circuits: a review. Rep. Prog. Phys. 80, 106001 (2017).

4. 4.

Clarke, J., Cleland, A. N., Devoret, M. H., Esteve, D. & Martinis, J. M. Quantum mechanics of a macroscopic variable: the phase difference of a Josephson junction. Science 239, 992–997 (1988).

5. 5.

Reagor, M. et al. Quantum memory with millisecond coherence in circuit QED. Phys. Rev. B 94, 014506 (2016).

6. 6.

Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

7. 7.

Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014).

8. 8.

Naik, R. K. et al. Random access quantum information processors using multimode circuit quantum electrodynamics. Nat. Commun. 8, 1904 (2017).

9. 9.

Leghtas, Z. et al. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347, 853–857 (2015).

10. 10.

Touzard, S. et al. Coherent oscillations inside a quantum manifold stabilized by dissipation. Phys. Rev. X 8, 021005 (2018).

11. 11.

Bretheau, L., Campagne-Ibarcq, P., Flurin, E., Mallet, F. & Huard, B. Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 348, 776–779 (2015).

12. 12.

Bertet, P., Harmans, C. J. P. M. & Mooij, J. E. Parametric coupling for superconducting qubits. Phys. Rev. B 73, 064512 (2006).

13. 13.

Niskanen, A. O. Quantum coherent tunable coupling of superconducting qubits. Science 316, 723–726 (2007).

14. 14.

McKay, D. C. et al. Universal gate for fixed-frequency qubits via a tunable bus. Phys. Rev. Appl. 6, 064007 (2016).

15. 15.

Reagor, M. et al. Demonstration of universal parametric entangling gates on a multi-qubit lattice. Sci. Adv. 4, eaao3603 (2018).

16. 16.

Zakka-Bajjani, E. et al. Quantum superposition of a single microwave photon in two different ‘colour’ states. Nat. Phys. 7, 599–603 (2011).

17. 17.

Lu, Y. et al. Universal stabilization of a parametrically coupled qubit. Phys. Rev. Lett. 119, 150502 (2017).

18. 18.

Bergeal, N. et al. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature 465, 64–68 (2010).

19. 19.

Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nat. Phys. 4, 929–931 (2008).

20. 20.

Yamamoto, T. et al. Flux-driven Josephson parametric amplifier. Appl. Phys. Lett. 93, 042510 (2008).

21. 21.

Lecocq, F. et al. Nonreciprocal microwave signal processing with a field-programmable Josephson amplifier. Phys. Rev. Appl. 7, 024028 (2017).

22. 22.

Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146–151 (2017).

23. 23.

Bishop, L. S. et al. Nonlinear response of the vacuum Rabi resonance. Nat. Phys. 5, 105–109 (2009).

24. 24.

Greentree, A. D., Tahan, C., Cole, J. H. & Hollenberg, L. C. L. Quantum phase transitions of light. Nat. Phys. 2, 856–861 (2006).

25. 25.

Hartmann, M. J., Brandão, F. G. S. L. & Plenio, M. B. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849–855 (2006).

26. 26.

Angelakis, D. G., Santos, M. F. & Sougato, B. Photon-blockade induced Mott transitions and XY spin models in coupled cavity arrays. Phys. Rev. A 76, 031805 (2007).

27. 27.

Carusotto, I. et al. Fermionized photons in an array of driven dissipative nonlinear cavities. Phys. Rev. Lett. 103, 033601 (2009).

28. 28.

Hartmann, M. J. Polariton crystallization in driven arrays of lossy nonlinear resonators. Phys. Rev. Lett. 104, 113601 (2010).

29. 29.

Houck, A. A., Tureci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).

30. 30.

Schmidt, S. & Koch, J. Circuit QED lattices: towards quantum simulation with superconducting circuits. Ann. Phys. (Berl.) 525, 395–412 (2013).

31. 31.

Raftery, J., Sadri, D., Schmidt, S., Türeci, H. E. & Houck, A. A. Observation of a dissipation-induced classical to quantum transition. Phys. Rev. X 4, 031043 (2014).

32. 32.

Fitzpatrick, M., Sundaresan, N. M., Li, A. C. Y., Koch, J. & Houck, A. A. Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Phys. Rev. X 7, 011016 (2017).

33. 33.

Jin, J., Rossini, D., Fazio, R., Leib, M. & Hartmann, M. J. Photon solid phases in driven arrays of nonlinearly coupled cavities. Phys. Rev. Lett. 110, 163605 (2013).

34. 34.

Peropadre, B. et al. Tunable coupling engineering between superconducting resonators: from sidebands to effective gauge fields. Phys. Rev. B 87, 134504 (2013).

35. 35.

Kounalakis, M., Dickel, C., Bruno, A., Langford, N. K. & Steele, G. A. Tuneable hopping and nonlinear cross-Kerr interactions in a high-coherence superconducting circuit. npj Quantum Inf. 4, 38 (2018).

36. 36.

Collodo, M. C. et al. Observation of the crossover from photon ordering to delocalization in tunably coupled resonators. Phys. Rev. Lett. 122, 183601 (2019).

37. 37.

Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

38. 38.

Frattini, N. E. et al. 3-wave mixing Josephson dipole element. Appl. Rev. Lett. 110, 222603 (2017).

39. 39.

Vool, U. et al. Driving forbidden transitions in the fluxonium artificial atom. Phys. Rev. Appl. 9, 054046 (2018).

40. 40.

Markovic, D. et al. Demonstration of an effective ultrastrong coupling between two oscillators. Phys. Rev. Lett. 121, 040505 (2018).

41. 41.

Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

42. 42.

Holland, E. T. et al. Single-photon-resolved cross-Kerr interaction for autonomous stabilization of photon-number states. Phys. Rev. Lett. 115, 180501 (2015).

43. 43.

Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

44. 44.

Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).

45. 45.

Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013).

46. 46.

Shalibo, Y. et al. Direct Wigner tomography of a superconducting anharmonic oscillator. Phys. Rev. Lett. 110, 100404 (2013).

47. 47.

Wenner, J. et al. Surface loss simulations of superconducting coplanar waveguide resonators. Appl. Rev. Lett. 99, 113513 (2011).

48. 48.

Wang, C. et al. Surface participation and dielectric loss in superconducting qubits. Appl. Rev. Lett. 107, 162601 (2015).

49. 49.

Reagor, M. et al. Reaching 10 ms single photon lifetimes for superconducting aluminum cavities. Appl. Rev. Lett. 102, 192604 (2013).

50. 50.

Romanenko, A. et al. Three-dimensional superconducting resonators at T < 20 mK with the photon lifetime up to τ = 2 seconds. Preprint at https://arxiv.org/abs/1810.03703 (2018).

## Acknowledgements

We thank M. Mirrahimi and J. A. Aumentado for valuable discussions, G. Zhang and P. Mundada for technical contributions and MIT Lincoln Labs for providing a travelling-wave parametric amplifier for this experiment. This work was supported by the Army Research Office through grant no. W911NF-15-1-0421.

## Author information

Authors

### Contributions

A.V. designed the device, performed the experiments and analysed the data. Z.H., P.G. and J.K. provided theoretical support. A.A.H. supervised the whole experiment. All authors contributed to the preparation of this manuscript.

### Corresponding authors

Correspondence to Andrei Vrajitoarea or Andrew A. Houck.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Gerhard Kirchmair, Anton Kockum and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Information.

## Source data

### Source Data Fig. 3

Source data for Fig. 3b (experimental)

### Source Data Fig. 3

Source data for Fig. 3b (theory)

## Rights and permissions

Reprints and Permissions

Vrajitoarea, A., Huang, Z., Groszkowski, P. et al. Quantum control of an oscillator using a stimulated Josephson nonlinearity. Nat. Phys. 16, 211–217 (2020). https://doi.org/10.1038/s41567-019-0703-5

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