Quantum probe of an on-chip broadband interferometer for quantum microwave photonics

  1. P. Eder,
  2. T. Ramos,
  3. J. Goetz,
  4. M. Fischer,
  5. S. Pogorzalek,
  6. J. Puertas Martínez,
  7. E. P. Menzel,
  8. F. Loacker,
  9. E. Xie,
  10. J.J. Garcia-Ripoll,
  11. K. G. Fedorov,
  12. A. Marx,
  13. F. Deppe,
  14. and R. Gross
Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics. To this end, the strong nonlinearities
of superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain. In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task. In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters. By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment. At high frequencies, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit. At low frequencies, we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators. Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.

Finite-time quantum correlations of propagating squeezed microwaves

  1. Kirill G. Fedorov,
  2. S. Pogorzalek,
  3. U. Las Heras,
  4. M. Sanz,
  5. P. Yard,
  6. P. Eder,
  7. M. Fischer,
  8. J. Goetz,
  9. E. Xie,
  10. K. Inomata,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. E. Solano,
  14. A. Marx,
  15. F. Deppe,
  16. and R. Gross
Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of incompatible observables between two subsystems. At the same time, these subsystems
themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication, quantum computation, and quantum illumination. Propagating microwave TMS states can be produced by a beam splitter distributing single mode squeezing emitted from Josephson parametric amplifiers (JPA) into two output paths. In this work, we experimentally quantify the dephasing process of quantum correlations in propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain an insight into quantum entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation.

Second-order decoherence mechanisms of a transmon qubit probed with thermal microwave states

  1. J. Goetz,
  2. F. Deppe,
  3. P. Eder,
  4. M. Fischer,
  5. M. Müting,
  6. J. P. Martínez,
  7. S. Pogorzalek,
  8. F. Wulschner,
  9. E. Xie,
  10. K. G. Fedorov,
  11. A. Marx,
  12. and R. Gross
Thermal microwave states are omnipresent noise sources in superconducting quantum circuits covering all relevant frequency regimes. We use them as a probe to identify three second-order
decoherence mechanisms of a superconducting transmon. First, we quantify the efficiency of a resonator filter in the dispersive Jaynes-Cummings regime and find evidence for parasitic loss channels. Second, we probe second-order noise in the low-frequency regime and demonstrate the expected T3 temperature dependence of the qubit dephasing rate. Finally, we show that qubit parameter fluctuations due to two-level states are enhanced under the influence of thermal microwave states. In particular, we experimentally confirm the T2-dependence of the fluctuation spectrum expected for noninteracting two-level states.

Photon Statistics of Propagating Thermal Microwaves

  1. J. Goetz,
  2. S. Pogorzalek,
  3. F. Deppe,
  4. K. G. Fedorov,
  5. P. Eder,
  6. M. Fischer,
  7. F. Wulschner,
  8. E. Xie,
  9. A. Marx,
  10. and R. Gross
In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n2+n photon number
variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers 0.05≲n≲1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.

Displacement of propagating squeezed microwave states

  1. Kirill G. Fedorov,
  2. L. Zhong,
  3. S. Pogorzalek,
  4. P. Eder,
  5. M. Fischer,
  6. J. Goetz,
  7. E. Xie,
  8. F. Wulschner,
  9. K. Inomata,
  10. T. Yamamoto,
  11. Y. Nakamura,
  12. R. Di Candia,
  13. U. Las Heras,
  14. M. Sanz,
  15. E. Solano,
  16. E. P. Menzel,
  17. F. Deppe,
  18. A. Marx,
  19. and R. Gross
Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an
important role in quantum teleportation protocols with continuous variables. In our experiments we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states stays constant over a wide range of the displacement power.

Tunable coupling of transmission-line microwave resonators mediated by an rf SQUID

  1. F. Wulschner,
  2. J. Goetz,
  3. F. R. Koessel,
  4. E. Hoffmann,
  5. A. Baust,
  6. P. Eder,
  7. M. Fischer,
  8. M. Haeberlein,
  9. M. J. Schwarz,
  10. M. Pernpeintner,
  11. E. Xie,
  12. L. Zhong,
  13. C. W. Zollitsch,
  14. B. Peropadre,
  15. J.J. García-Ripoll,
  16. E. Solano,
  17. K. Fedorov,
  18. E. P. Menzel,
  19. F. Deppe,
  20. A. Marx,
  21. and R. Gross
We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance
between the resonators. From the mode distance observed in spectroscopy experiments, we derive a coupling strength ranging between -320MHz and 37 MHz. In the case where the coupling strength is about zero, the microwave power cross transmission between the two resonators can be reduced by almost four orders of magnitude compared to the case where the coupling is switched on. In addition, we observe parametric amplification by applying a suitable additional drive tone.

Ultrastrong coupling in two-resonator circuit QED

  1. A. Baust,
  2. E. Hoffmann,
  3. M. Haeberlein,
  4. M. J. Schwarz,
  5. P. Eder,
  6. J. Goetz,
  7. F. Wulschner,
  8. E. Xie,
  9. L. Zhong,
  10. F. Quijandria,
  11. D. Zueco,
  12. J.J. García-Ripoll,
  13. L. Garcia-Alvarez,
  14. G. Romero,
  15. E. Solano,
  16. K. G. Fedorov,
  17. E. P. Menzel,
  18. F. Deppe,
  19. A. Marx,
  20. and R. Gross
We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically
to the qubit. With a coupling strength as high as 17% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings model. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.

Tunable and Switchable Coupling Between Two Superconducting Resonators

  1. A. Baust,
  2. E. Hoffmann,
  3. M. Haeberlein,
  4. M. J. Schwarz,
  5. P. Eder,
  6. E. P. Menzel,
  7. K. Fedorov,
  8. J. Goetz,
  9. F. Wulschner,
  10. E. Xie,
  11. L. Zhong,
  12. F. Quijandria,
  13. B. Peropadre,
  14. D. Zueco,
  15. J.J. García-Ripoll,
  16. E. Solano,
  17. F. Deppe,
  18. A. Marx,
  19. and R. Gross
We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current
flux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit drive power and the dynamic range of the resonator input power