Observation of two-mode squeezing in a traveling wave parametric amplifier

  1. Martina Esposito,
  2. Arpit Ranadive,
  3. Luca Planat,
  4. Sebastian Leger,
  5. Dorian Fraudet,
  6. Vincent Jouanny,
  7. Olivier Buisson,
  8. Wiebke Guichard,
  9. Cécile Naud,
  10. José Aumentado,
  11. Florent Lecocq,
  12. and Nicolas Roch
Traveling wave parametric amplifiers (TWPAs) have recently emerged as essential tools for broadband near quantum-limited amplification. However, their use to generate microwave quantum
states still misses an experimental demonstration. In this letter, we report operation of a TWPA as a source of two-mode squeezed microwave radiation. We demonstrate broadband entanglement generation between two modes separated by up to 400 MHz by measuring logarithmic negativity between 0.27 and 0.51 and collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. This work opens interesting perspectives for the exploration of novel microwave photonics experiments with possible applications in quantum sensing and continuous variable quantum computing.

A reversed Kerr traveling wave parametric amplifier

  1. Arpit Ranadive,
  2. Martina Esposito,
  3. Luca Planat,
  4. Edgar Bonet,
  5. Cécile Naud,
  6. Olivier Buisson,
  7. Wiebke Guichard,
  8. and Nicolas Roch
Traveling wave parametric amplification in a nonlinear medium provides broadband quantum-noise limited gain and is a remarkable resource for the detection of electromagnetic radiation.
This nonlinearity is at the same time the key to the amplification phenomenon but also the cause of a fundamental limitation: poor phase matching between the signal and the pump. Here we solve this issue with a new phase matching mechanism based on the sign reversal of the Kerr nonlinearity. We present a novel traveling wave parametric amplifier composed of a chain of superconducting nonlinear asymmetric inductive elements (SNAILs) which allows this sign reversal when biased with the proper magnetic flux. Compared to previous state of the art phase matching approaches, this reversed Kerr phase matching mechanism avoids the presence of gaps in transmission, reduces gain ripples, and allows in situ tunability of the amplification band over an unprecedented wide range. Besides such notable advancements in the amplification performance, with direct applications to superconducting quantum computing, the in-situ tunability of the nonlinearity in traveling wave structures, with no counterpart in optics to the best of our knowledge, opens exciting experimental possibilities in the general framework of microwave quantum optics and single-photon detection.

Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits

  1. Sebastien Leger,
  2. Javier Puertas Martinez,
  3. Karthik Bharadwaj,
  4. Remy Dassonneville,
  5. Jovian Delaforce,
  6. Farshad Foroughi,
  7. Vladimir Milchakov,
  8. Luca Planat,
  9. Olivier Buisson,
  10. Cecile Naud,
  11. Wiebke Hasch-Guichard,
  12. Serge Florens,
  13. Izak Snyman,
  14. and Nicolas Roch
Electromagnetic fields possess zero point fluctuations (ZPF) which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain,
these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by ZPF in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modelling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about 30 environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

Fabrication and characterization of aluminum SQUID transmission lines

  1. Luca Planat,
  2. Ekaterina Al-Tavil,
  3. Javier Puertas Martinez,
  4. Remy Dassonneville,
  5. Farshad Foroughi,
  6. Sebastien Leger,
  7. Karthik Bharadwaj,
  8. Jovian Delaforce,
  9. Vladimir Milchakov,
  10. Cecile Naud,
  11. Olivier Buisson,
  12. Wiebke Hasch-Guichard,
  13. and Nicolas Roch
We report on the fabrication and characterization of 50 Ohms, flux-tunable, low-loss, SQUID-based transmission lines. The fabrication process relies on the deposition of a thin dielectric
layer (few tens of nanometers) via Atomic Layer Deposition (ALD) on top of a SQUID array, the whole structure is then covered by a non-superconducting metallic top ground plane. We present experimental results from five different samples. We systematically characterize their microscopic parameters by measuring the propagating phase in these structures. We also investigate losses and discriminate conductor from dielectric losses. This fabrication method offers several advantages. First, the SQUID array fabrication does not rely on a Niobium tri-layer process but on a simpler double angle evaporation technique. Second, ALD provides high quality dielectric leading to low-loss devices. Further, the SQUID array fabrication is based on a standard, all-aluminum process, allowing direct integration with superconducting qubits. Moreover, our devices are in-situ flux tunable, allowing mitigation of incertitude inherent to any fabrication process. Finally, the unit cell being a single SQUID (no extra ground capacitance is needed), it is straightforward to modulate the size of the unit cell periodically, allowing band-engineering. This fabrication process can be directly applied to traveling wave parametric amplifiers.

A photonic crystal Josephson traveling wave parametric amplifier

  1. Luca Planat,
  2. Arpit Ranadive,
  3. Remy Dassonneville,
  4. Javier Puertas Martinez,
  5. Sebastien Leger,
  6. Cecile Naud,
  7. Olivier Buisson,
  8. Wiebke Hasch-Guichard,
  9. Denis M. Basko,
  10. and Nicolas Roch
An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies
such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier.

Understanding the saturation power of Josephson Parametric Amplifiers made from SQUIDs arrays

  1. Luca Planat,
  2. Remy Dassonneville,
  3. Javier Puertas Martinez,
  4. Farshad Foroughi,
  5. Olivier Buisson,
  6. Wiebke Hasch-Guichard,
  7. Cecile Naud,
  8. R. Vijay,
  9. Kater Murch,
  10. and Nicolas Roch
We report on the implementation and detailed modelling of a Josephson Parametric Amplifier (JPA) made from an array of eighty Superconducting QUantum Interference Devices (SQUIDs),
forming a non-linear quarter-wave resonator. This device was fabricated using a very simple single step fabrication process. It shows a large bandwidth (45 MHz), an operating frequency tunable between 5.9 GHz and 6.8 GHz and a large input saturation power (-117 dBm) when biased to obtain 20 dB of gain. Despite the length of the SQUID array being comparable to the wavelength, we present a model based on an effective non-linear LC series resonator that quantitatively describes these figures of merit without fitting parameters. Our work illustrates the advantage of using array-based JPA since a single-SQUID device showing the same bandwidth and resonant frequency would display a saturation power 15 dB lower.

Probing a transmon qubit via the ultra-strong coupling to a Josephson waveguide

  1. Javier Puertas Martinez,
  2. Sebastien Leger,
  3. Nicolas Gheereart,
  4. Remy Dassonneville,
  5. Luca Planat,
  6. Farshad Foroughi,
  7. Yuriy Krupko,
  8. Olivier Buisson,
  9. Cecile Naud,
  10. Wiebke Guichard,
  11. Serge Florens,
  12. Izak Snyman,
  13. and Nicolas Roch
Exploring the quantum world often starts by drawing a sharp boundary between a microscopic subsystem and the bath to which it is invariably coupled. In most cases, knowledge of the
physical processes occuring in the bath is not required in great detail. However, recent developments in circuit quantum electrodynamics are presenting regimes where the actual dynamics of engineered baths, such as microwave photon resonators, becomes relevant. Here we take a major technological step forward, by tailoring a centimeter-scale on-chip bath from a very long metamaterial made of 4700 tunable Josephson junctions. By monitoring how each measurable bosonic resonance of the circuit acquires a phase-shift due to its interaction with a transmon qubit, one can indirectly measure qubit properties, such as transition frequency, linewidth and non-linearity. This new platform also demonstrates the ultra-strong coupling regime for the first time in the context of Josephson waveguides. Our device combines a large number of modes (up to 10 in the present setup) that are simultaneously hybridised with the two-level system, and a broadening dominated by the artificial environment that is a sizeable fraction of the qubit transition frequency. Finally, we provide a quantitative and parameter-free model of this large quantum system, and show that the finite environment seen by the qubit is equivalent to a truly macroscopic bath.

A tunable Josephson platform to explore many-body quantum optics in circuit-QED

  1. Javier Puertas Martinez,
  2. Sebastien Leger,
  3. Nicolas Gheeraert,
  4. Remy Dassonneville,
  5. Luca Planat,
  6. Farshad Foroughi,
  7. Yuriy Krupko,
  8. Olivier Buisson,
  9. Cecile Naud,
  10. Wiebke Guichard,
  11. Serge Florens,
  12. Izak Snyman,
  13. and Nicolas Roch
The quest to understand interaction between light and matter stretches back to the ray optics of Euclid and Ptolemy. In recent decades, studies at the quantum scale were performed by
coupling an isolated emitter to a single mode of the electromagnetic field, standard quantum optics providing a complete toolbox for describing such a setup. Current efforts aim to explore the coherent dynamics of systems containing an emitter coupled to several electromagnetic degrees of freedom. Combining superconducting metamaterials and qubits could allow for the observation of genuinely macroscopic quantum effects such as a giant Lamb shift or non-classical states of multimode optical fields. In this work, we couple a transmon qubit to a high impedance, centimeter-scale, metamaterial waveguide, made of 4700 in-situ tunable Josephson junctions. Our device combines three essential properties required to go beyond the standard quantum optics paradigm and reach the multi-mode, many-body regime, namely: a tunable waveguide with a high density of electromagnetic modes, a qubit non-linearity comparable to the other relevant energy scales, and ultrastrong coupling between the qubit and the waveguide modes. Besides providing experimental evidence for these non-trivial requirements, we also develop a quantitative theoretical description that does not contain any phenomenological parameters and that accurately takes into account vacuum fluctuations of our large scale quantum circuit in the regime of ultrastrong coupling and intermediate non-linearity. Furthermore, we show that the influence on the transmon of our fully controllable on-chip environment well approximates that of the macroscopic bath envisioned in the celebrated work of Caldeira and Leggett. Our work demonstrates that Josephson waveguides offer a promising platform to explore many-body quantum optics.

Unexpectedly allowed transition in two inductively coupled transmons

  1. Étienne Dumur,
  2. Bruno Küng,
  3. Alexey Feofanov,
  4. Thomas Weißl,
  5. Yuriy Krupko,
  6. Nicolas Roch,
  7. Cécile Naud,
  8. Wiebke Guichard,
  9. and Olivier Buisson
We present experimental results in which the unexpected zero-two transition of a circuit composed of two inductively coupled transmons is observed. This transition shows an unusual
magnetic flux dependence with a clear disappearance at zero magnetic flux. In a transmon qubit the symmetry of the wave functions prevents this transition to occur due to selection rule. In our circuit the Josephson effect introduces strong couplings between the two normal modes of the artificial atom. This leads to a coherent superposition of states from the two modes enabling such transitions to occur.