Propagating Quantum Microwaves: Towards Applications in Communication and Sensing

  1. Mateo Casariego,
  2. Emmanuel Zambrini Cruzeiro,
  3. Stefano Gherardini,
  4. Tasio Gonzalez-Raya,
  5. Rui André,
  6. Gonçalo Frazão,
  7. Giacomo Catto,
  8. Mikko Möttönen,
  9. Debopam Datta,
  10. Klaara Viisanen,
  11. Joonas Govenius,
  12. Mika Prunnila,
  13. Kimmo Tuominen,
  14. Maximilian Reichert,
  15. Michael Renger,
  16. Kirill G. Fedorov,
  17. Frank Deppe,
  18. Harriet van der Vliet,
  19. A. J. Matthews,
  20. Yolanda Fernández,
  21. R. Assouly,
  22. R. Dassonneville,
  23. B. Huard,
  24. Mikel Sanz,
  25. and Yasser Omar
The field of propagating quantum microwaves has started to receive considerable attention in the past few years. Motivated at first by the lack of an efficient microwave-to-optical
platform that could solve the issue of secure communication between remote superconducting chips, current efforts are starting to reach other areas, from quantum communications to sensing. Here, we attempt at giving a state-of-the-art view of the two, pointing at some of the technical and theoretical challenges we need to address, and while providing some novel ideas and directions for future research. Hence, the goal of this paper is to provide a bigger picture, and — we hope — to inspire new ideas in quantum communications and sensing: from open-air microwave quantum key distribution to direct detection of dark matter, we expect that the recent efforts and results in quantum microwaves will soon attract a wider audience, not only in the academic community, but also in an industrial environment.

Dissipative stabilization of squeezing beyond \SI{3}{dB} in a microwave mode

  1. R. Dassonneville,
  2. R. Assouly,
  3. T. Peronnin,
  4. A. A. Clerk,
  5. A. Bienfait,
  6. and B. Huard
While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intra-resonator state is limited to 3 dB of squeezing. Here, we implement
a reservoir engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intra-resonator state. The raw measurement provides a lower bound on the squeezing at about 6.7±0.2 dB below the zero-point level. Further, we show how to correct for resonator evolution during the Wigner tomography and obtain a squeezing as high as 8.2±0.8 dB. Moreover, this level of squeezing is achieved with a purity of −0.4±0.4 dB.

Dynamics of a qubit while simultaneously monitoring its relaxation and dephasing

  1. Q. Ficheux,
  2. S. Jezouin,
  3. Z. Leghtas,
  4. and B. Huard
Decoherence originates from the leakage of quantum information into unmonitored degrees of freedom. For a qubit the two main decoherence channels are relaxation and dephasing. Here,
we report an experiment on a superconducting qubit where we retrieve a significant part of the lost information in both of these channels. We demonstrate that raw averaging the corresponding measurement records provides a full quantum tomography of the qubit state where all three components of the effective spin-1/2 are simultaneously measured. From single realizations of the experiment, it is possible to infer the quantum trajectories followed by the qubit state conditioned on relaxation and/or dephasing channels. The incompatibility between these quantum measurements of the qubit leads to observable consequences in the statistics of quantum states. The high level of controllability of superconducting circuits enables us to explore many regimes from Zeno effect to underdamped Rabi oscillations depending on the relative strengths of driving, dephasing and relaxation.

Observing a quantum Maxwell demon at work

  1. N. Cottet,
  2. S. Jezouin,
  3. L. Bretheau,
  4. P. Campagne-Ibarcq,
  5. Q. Ficheux,
  6. J. Anders,
  7. A. Auffèves,
  8. R. Azouit,
  9. P. Rouchon,
  10. and B. Huard
In apparent contradiction to the laws of thermodynamics, Maxwell’s demon is able to cyclically extract work from a system in contact with a thermal bath exploiting the information
about its microstate. The resolution of this paradox required the insight that an intimate relationship exists between information and thermodynamics. Here, we realize a Maxwell demon experiment that tracks the state of each constituent both in the classical and quantum regimes. The demon is a microwave cavity that encodes quantum information about a superconducting qubit and converts information into work by powering up a propagating microwave pulse by stimulated emission. Thanks to the high level of control of superconducting circuits, we directly measure the extracted work and quantify the entropy remaining in the demon’s memory. This experiment provides an enlightening illustration of the interplay of thermodynamics with quantum information.

Quantum simulation of ultrastrongly coupled bosonic modes using superconducting circuits

  1. S. Fedortchenko,
  2. S. Felicetti,
  3. D. Marković,
  4. S. Jezouin,
  5. A. Keller,
  6. T. Coudreau,
  7. B. Huard,
  8. and P. Milman
The ground state of a pair of ultrastrongly coupled bosonic modes is predicted to be a two-mode squeezed vacuum. However, the corresponding quantum correlations are currently unobservable
in condensed matter where such a coupling can be reached, since it cannot be extracted from these systems. Here, we show that superconducting circuits can be used to perform an analog simulation of a system of two bosonic modes in regimes ranging from strong to ultrastrong coupling. More importantly, our quantum simulation set-up enables to detect output excitations that are related to the ground state properties of the bosonic modes. We compute the emission spectra of this physical system and show that the produced state presents single and two-mode squeezing simultaneously.

Using Spontaneous Emission of a Qubit as a Resource for Feedback Control

  1. P. Campagne-Ibarcq,
  2. S. Jezouin,
  3. N. Cottet,
  4. P. Six,
  5. L. Bretheau,
  6. F. Mallet,
  7. A. Sarlette,
  8. P. Rouchon,
  9. and B. Huard
Persistent control of a transmon qubit is performed by a feedback protocol based on continuous weak measurement of its fluorescence. By driving the qubit and cavity with microwave signals
whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we demonstrate the permanent stabilization of the qubit in any direction of the Bloch sphere. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output (MIMO) analog markovian feedback in the quantum regime.

Observing quantum state diffusion by heterodyne detection of fluorescence

  1. P. Campagne-Ibarcq,
  2. P. Six,
  3. L. Bretheau,
  4. A. Sarlette,
  5. M. Mirrahimi,
  6. P. Rouchon,
  7. and B. Huard
A qubit can relax by fluorescence, which prompts the release of a photon into its electromagnetic environment. By counting the emitted photons, discrete quantum jumps of the qubit state
can be observed. The succession of states occupied by the qubit in a single experiment, its quantum trajectory, depends in fact on the kind of detector. How are the quantum trajectories modified if one measures continuously the amplitude of the fluorescence field instead? Using a superconducting parametric amplifier, we have performed heterodyne detection of the fluorescence of a superconducting qubit. For each realization of the measurement record, we can reconstruct a different quantum trajectory for the qubit. The observed evolution obeys quantum state diffusion, which is characteristic of quantum measurements subject to zero point fluctuations. Independent projective measurements of the qubit at various times provide a quantitative validation of the reconstructed trajectories. By exploring the statistics of quantum trajectories, we demonstrate that the qubit states span a deterministic surface in the Bloch sphere at each time in the evolution. Additionally, we show that when monitoring fluorescence, coherent superpositions are generated during the decay from excited to ground state. Counterintuitively, measuring light emitted during relaxation can give rise to trajectories with increased excitation probability.

Optimal design for the Josephson mixer

  1. J.-D. Pillet,
  2. E. Flurin,
  3. F. Mallet,
  4. and B. Huard
We present an optimal design in terms of gain, bandwidth and dynamical range for the Josephson mixer, the superconducting circuit performing three-wave mixing at microwave frequencies.
In a compact all lumped-element based circuit with galvanically coupled ports, we demonstrate non degenerate amplification for microwave signals over a bandwidth up to 50 MHz for a power gain of 20 dB. The quantum efficiency of the mixer is shown to be about 70% and its dynamical range reaches 5 quanta per inverse dynamical bandwidth.