Theoretical study of reflection spectroscopy for superconducting quantum parametrons

  1. S. Masuda,
  2. A. Yamaguchi,
  3. T. Yamaji,
  4. T. Yamamoto,
  5. T. Ishikawa,
  6. Y. Matsuzaki,
  7. and S. Kawabata
Superconducting parametrons in the single-photon Kerr regime, also called KPOs, have been attracting increasing attention in terms of their applications to quantum annealing and universal
quantum computation. It is of practical importance to obtain information of superconducting parametrons operating under an oscillating pump field. Spectroscopy can provide information of a superconducting parametron under examination, such as energy level structure and occupation of energy levels, and also useful information for calibration of the pump field. We theoretically study the reflection spectroscopy of superconducting parametrons, and develop a method to obtain the reflection coefficient. We present formulae of the reflection coefficient, the nominal external and the internal decay rates, and examine the obtained spectra.

Spectroscopic observation of crossover from classical Duffing oscillator to Kerr parametric oscillator

  1. T. Yamaji,
  2. S. Kagami,
  3. A. Yamaguchi,
  4. T. Satoh,
  5. K. Koshino,
  6. H. Goto,
  7. Z. R. Lin,
  8. Y. Nakamura,
  9. and T. Yamamoto
We study microwave response of a Josephson parametric oscillator consisting of a superconducting transmission-line resonator with an embedded dc-SQUID. The dc-SQUID allows to control
the magnitude of a Kerr nonlinearity over the ranges where it is smaller or larger than the photon loss rate. Spectroscopy measurements reveal the change of the microwave response from a classical Duffing oscillator to a Kerr parametric oscillator in a single device. In the single-photon Kerr regime, we observe parametric oscillations with a well-defined phase of either 0 or π, whose probability can be controlled by an externally injected signal.

Tunable quantum gate between a superconducting atom and a propagating microwave photon

  1. K. Koshino,
  2. K. Inomata,
  3. Z. R. Lin,
  4. Y. Tokunaga,
  5. T. Yamamoto,
  6. and Y. Nakamura
We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit
is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, SWAP‾‾‾‾‾‾‾√, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.

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.

Correlated emission lasing in harmonic oscillators coupled via a single three-level artificial atom

  1. Z.H. Peng,
  2. Yu-xi Liu,
  3. J.T. Peltonen,
  4. T. Yamamoto,
  5. J. S. Tsai,
  6. and O. Astafiev
A single superconducting artificial atom provides a unique basis for coupling electromagnetic fields and photons hardly achieved with a natural atom. Bringing a pair of harmonic oscillators
into resonance with transitions of the three-level atom converts atomic spontaneous processes into correlated emission dynamics. We demonstrate two-mode correlated emission lasing on harmonic oscillators coupled via the fully controllable three-level artificial atom. Correlation of two different color emissions reveals itself as equally narrowed linewiths and quench of their mutual phase-diffusion. The mutual linewidth is more than four orders of magnitude narrower than the Schawlow-Townes limit. The interference between the different color lasing fields demonstrates the two-mode fields are strongly correlated.

Josephson parametric phase-locked oscillator and its application to dispersive readout of superconducting qubits

  1. Z. R. Lin,
  2. K. Inomata,
  3. K. Koshino,
  4. W. D. Oliver,
  5. Y. Nakamura,
  6. J. S. Tsai,
  7. and T. Yamamoto
The parametric phase-locked oscillator (PPLO), also known as a parametron, is a resonant circuit in which one of the reactances is periodically modulated. It can detect, amplify, and
store binary digital signals in the form of two distinct phases of self-oscillation. Indeed, digital computers using PPLOs based on a magnetic ferrite ring or a varactor diode as its fundamental logic element were successfully operated in 1950s and 1960s. More recently, basic bit operations have been demonstrated in an electromechanical resonator, and an Ising machine based on optical PPLOs has been proposed. Here, using a PPLO realized with Josephson-junction circuitry, we demonstrate the demodulation of a microwave signal digitally modulated by binary phase-shift keying. Moreover, we apply this demodulation capability to the dispersive readout of a superconducting qubit. This readout scheme enables a fast and latching-type readout, yet requires only a small number of readout photons in the resonator to which the qubit is coupled, thus featuring the combined advantages of several disparate schemes. We have achieved high-fidelity, single-shot, and non-destructive qubit readout with Rabi-oscillation contrast exceeding 90%, limited primarily by the qubit’s energy relaxation.

Microwave Down-Conversion with an Impedance-Matched Λ System in Driven Circuit QED

  1. K. Inomata,
  2. K. Koshino,
  3. Z. R. Lin,
  4. W. D. Oliver,
  5. J. S. Tsai,
  6. Y. Nakamura,
  7. and T. Yamamoto
By driving a dispersively coupled qubit-resonator system, we realize an „impedance-matched“ Λ system that has two identical radiative decay rates from the top level and
interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect (99.7%) extinction of the reflection and highly efficient (74%) frequency down-conversion. These proof-of-principle results lead to deterministic quantum gates between material qubits and microwave photons and open the possibility for scalable quantum networks interconnected with waveguide photons.

Single-shot readout of a superconducting flux qubit with a flux-driven Josephson parametric amplifier

  1. Z. R. Lin,
  2. K. Inomata,
  3. W. D. Oliver,
  4. K. Koshino,
  5. Y. Nakamura,
  6. J. S. Tsai,
  7. and T. Yamamoto
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing
of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.

Squeezing with a flux-driven Josephson parametric amplifier

  1. L. Zhong,
  2. E. P. Menzel,
  3. R. Di Candia,
  4. P. Eder,
  5. M. Ihmig,
  6. A. Baust,
  7. M. Haeberlein,
  8. E. Hoffmann,
  9. K. Inomata,
  10. T. Yamamoto,
  11. Y. Nakamura,
  12. E. Solano,
  13. F. Deppe,
  14. A. Marx,
  15. and R. Gross
Josephson parametric amplifiers (JPA) are promising devices for applications in circuit quantum electrodynamics (QED) and for studies on propagating quantum microwaves because of their
good noise performance. In this work, we present a systematic characterization of a flux-driven JPA at millikelvin temperatures. In particular, we study in detail its squeezing properties by two different detection techniques. With the homodyne setup, we observe squeezing of vacuum fluctuations by superposing signal and idler bands. For a quantitative analysis we apply dual-path cross-correlation techniques to reconstruct the Wigner functions of various squeezed vacuum and thermal states. At 10 dB signal gain, we find 4.9+-0.2 dB squeezing below vacuum. In addition, we discuss the physics behind squeezed coherent microwave fields. Finally, we analyze the JPA noise temperature in the degenerate mode and find a value smaller than the standard quantum limit for phase-insensitive amplifiers.

Observation of three-state dressed states in circuit quantum electrodynamics

  1. K. Koshino,
  2. H. Terai,
  3. K. Inomata,
  4. T. Yamamoto,
  5. W. Qiu,
  6. Z. Wang,
  7. and Y. Nakamura
We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field
may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.