November 6-8, 2019

This meeting intends to develop synergies and continue with existing collaborations between the QUINFOG group at the Institute of Fundamental Physics in Madrid (IFF-CSIC) and the groups of Institute of Quantum Optics and Quantum Information (IQOQI) leaded by Prof. Romero-Isart and Prof. Kirchmair, respectively.

This is the first edition of this Meeting and it happens at the premises of CSIC (Spanish Research Council) in Madrid.

- A. González-Tudela (IFF-CSIC)
- C. González-Ballestero (IQOQI)

### Program (preliminary)

Wednesday 6th | Thursday 7th | Friday 8th | |
---|---|---|---|

9:15-10.00 | Pino | Sabin | |

10.00-10.45 | Rodá | Hümmer | |

10:45-11.15 | Coffee break | Coffee break | |

11.15-12.00 | Torrontegui | Weiss | |

12.00-12.45 | Kustura+Ballestero | Porras | |

12:45-15.00 | Arrival+Lunch | Lunch | Lunch |

15:00-15.45 | Arrival+Lunch | Sharafiev | Discussions+departure |

15:45-16.30 | Ramos | Rubio-Lopez | |

16.30-17.15 | Casulleras | Discussions | |

17:15-… | Discussions | Discussions | |

Free-time | Free-time | ||

20:00 | Dinner | Dinner |

### Logistics

The workshop will take place at the Residencia de Estudiantes, located in Calle del Pinar, 21-23, Madrid. Follow these instructions to locate our premises and find connections to and from the airport.

### Participants

- A. González Tudela (IFF)
- D. Porras (IFF)
- J. J. García-Ripoll (IFF)
- E. Torrontegui (IFF)
- T. Ramos (IFF)
- M. Pino (IFF)
- Ming Li (IFF)
- E. Petrovish-Navarro (IFF-Universidad Nacional de Colombia)
- Luciano Pereira (IFF)
- C. Sabin (IFF)
- A. Agustí (IFF)
- O. Romero-Isart (IQOQI)
- C. González-Ballestero (IQOQI)
- Adrian Ezequiel Rubio López (IQOQI)
- Talitha Weiss (IQOQI)
- Katja Kustura (IQOQI)
- Silvia Casulleras Guárdia (IQOQI)
- Marc Rodá Llordés (IQOQI)
- David Spiegl (IQOQI)
- Patrick Maurer (IQOQI)
- Daniel Hümmer (IQOQI)
- G. Kirchmair (IQOQI)
- M. Juan (IQOQI)
- A. Sharafiev (IQOQI)

### Contributions

#### Talks

**T. Ramos** (IFF)*Scattering tomography of nanophotonic devices*

We present a method for experimentally obtaining the multi-photon scattering matrix and photon correlations from the output of nanophotonic devices. The tomography requires the preparation of coherent state pulses and the measurement of high order homodyne correlations. We explain the basic steps for the reconstruction of single- and two- photon processes and exemplify it with a single two-level system as scatterer. We analyze the effect of

dephasing noise in the reconstruction and test the method with experimental data from a quantum dot coupled to a photonic waveguide. We also discuss prospects for using the method to characterize the effect of interactions that do not conserve the number of photons such as in the case of an emitter with ultrastrong coupling to a photonic waveguide. We show the full generality of the multi-photon method which can be applied to learn about multi-

photon processes in more complex quantum many-body systems.

If time allows, we will also present the main ideas for an implementation of a synchronized multi-photon source using a cavity or circuit QED setup.

**D. Porras** (IFF)*Topological amplification in driven-dissipative lattices*

A proper characterization of non-trivial topological phases

in dissipative systems is highly non-trivial. Quantum simulators offer

us exciting possibilities to implement quantum many-body phases which

should show the emergence of topological non-trivial phenomena. One

example is actually trapped ion systems, where synthetic gauge fields

acting on vibronic exitations have recently been demonstrated [1].

Other experimental systems include of course usual suspects such as

superconducting circuits and ultracold atom steups.

In this work [2] we present a definition of topological invariants for

driven dissipative lattices that relies on a formal mapping between a

non-Hermitian coupling matrix and an effective band Hamiltonian. In a

nutshell, our work allows to extend the formalism of topological band

theory to dissipative bosonic lattices. This formalism shows a link

between directional amplification and non-trivial topological

phenomena, leading to the concept of “topological amplifier”. We

present a proposal to implement our ideas with superconducting circuits.

[1] Philip Kiefer et al, Phys. Rev. Lett. (to appear 2019)

[2] D. Porras and S. Fernández-Lorenzo, Phys. Rev. Lett. 122, 143901 (2019)

**M. Pino **(IFF)*Mediator assisted cooling in quantum annealing*

We show a significant reduction of errors for an architecture of quantum annealers where bosonic modes mediate the interaction between qubits. These systems have a large redundancy in the subspace of solutions, supported by arbitrarily large bosonic occupations. We explain how this redundancy leads to a mitigation of errors when the bosonic modes operate in the ultrastrong coupling regime. Numerical simulations also predict a large increase of qubit coherence for a specific annealing problem with mediated interactions. We provide evidences that noise reduction occurs in more general types of quantum computers with similar architectures.

**C. Sabin** (IFF)*Pairs and triplets of entangled microwave photons*

We will discuss the generation of multimode entangled states of propagating microwaves, by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. Moreover, by exploiting an asymmetric SQUID we can also demonstrate direct three-photon spontaneous parametric downconversion, with photon triplets generated in a single cavity mode or split between multiple modes. Interestingly, a different notion of multimode entanglement emerges in this genuine non-gaussian case.

References

Generating multimode entangled microwaves with a superconducting parametric cavity CW Sandbo Chang, M Simoen, José Aumentado, Carlos Sabín, P Forn-Díaz, AM Vadiraj, Fernando Quijandría, G Johansson, I Fuentes, CM Wilson, Phys. Rev. Appl. 10, 044019 (2018).

Observation of Three-Photon Spontaneous Parametric Downconversion in a Superconducting Parametric Cavity CW Chang, Carlos Sabín, P Forn-Díaz, Fernando Quijandría, AM Vadiraj, I Nsanzineza, G Johansson, CM Wilson, arXiv: 1907.08692.

**E. Torrontegui** (IFF)*To be announced*

** Talitha Weiss **(IQOQI)*Quantum Motional State Tomography with Non-quadratic Potentials and Neural Networks*

Cooling levitated nanoparticles into their motional ground state and then preparing a non-classical state is a central goal of the field of levitated optomechanics. The exceptionally high isolation of levitated systems is a key advantage for this purpose but turns into a challenge when trying to measure and verify the prepared state. We investigate the motion of a particle in a quartic potential, where the non-linearity allows to gather information about higher order moments of the quantum state, even if only the position-trajectory is measured. Thus, a quantum state tomography protocol could consist of the state preparation within a usual harmonic potential, followed by an evolution in a quartic potential. We successfully train neural networks to deduce the initially prepared quantum state from simulated trajectories of position and position variance and return the associated density matrix. In particular, we show and investigate this neural-network based quantum state reconstruction for states of different dimensionality. We discuss how the achieved fidelity depends on the provided trajectory length and study the impact of decoherence. Moreover, we discuss the feasibility of our approach ranging from a

trapped ion to a levitated nanoparticle and find that it depends on the interplay of decoherence and non-linearity strength. Notably, the proposed scheme for quantum state tomography does not explicitly depend on the quarticity of the potential: Any other non-linearity could in principle be used as well to reconstruct a quantum state in the described way.

**Marc Rodà Llordés **(IQOQI)*Magnetization of a metallic nanoparticle under ultrafast rotation*Recent experiments have demonstrated nanoparticles rotating at GHz frequencies. We study the exotic properties of metallic nanoparticles in such regime. In particular we find that the magnetic moment acquired due to the rotation shows step-like increments as the rotational frequency is increased.

**Silvia Casulleras Guàrdia **(IQOQI)*Self-focusing of pulses in a waveguide with a quadratic dispersion relation*

We theoretically demonstrate the existence of self-focusing pulses that propagate in vacuum inside a waveguide

with a quadratic dispersion relation. We are studying how to use such pulses to selectively address single qubits

within a sub-wavelength array inside the waveguide.

**D. Hümmer **(IQOQI)*Heating in nanophotonics trap for cold atoms*

In recent years, it has become feasible to trap and control ensembles of individual atoms in the optical near-field of nanoscale photonic structures, such as optical nanofibers. However, observed heating rates of the atomic motion are around three orders of magnitude larger than in comparable free-space traps [1]. This strong heating hampers progress in the field of nanophotonic atom traps and may render trapping impossible for many trap designs.

Here, we identify a set of thermally excited mechanical modes of the waveguide as the source of the strong heating in nanofiber-based traps [2]. We present a general theoretical description of the effective interaction between the center of mass of the atom and vibrations of the waveguide. The latter adiabatically change the optical fields surrounding the fiber, both by displacement of the fiber surface (radiation pressure), and by strain-induced inhomogeneity and anisotropy of the electric permittivity (photoelastic effect). In consequence, the optical potential fluctuates, leading to an effective atom-phonon coupling.

Applying this framework to nanofiber-based traps, we predict atom heating rates in excellent quantitative agreement with experimental observations. This understanding enables us to propose ways to minimize the heating. Beyond answering a decade-old question and providing the means to overcome a main

limitation of current nanophotonic cold-atom systems, our results are highly relevant for optomechanics experiments such as optically trapped dielectric nanoparticles close to photonic crystals or surfaces.

[1] Y. Meng, A. Dareau, P. Schneeweiss, and A. Rauschenbeutel, Phys. Rev. X 8, 031054.

[2] D. Hümmer, P. Schneeweiss, A. Rauschenbeutel, O. Romero-Isart, arXiv:1902.02200.

**Double feature: Carlos González Ballestero+Katja Kustura **(IQOQI)*Quantum acoustomechanics with a micromagnet +Open quantum dynamics in a driven encironment*

We show how to efficiently couple the internal acoustic phonons of a levitated micromagnet to its external motion, using its magnetic degree of freedom, i. e. a magnon. Such a possibility is enabled by a magnon-phonon coupling that is calculated to be 9 orders of magnitude stronger than in larger, less isolated nanoparticles. The resulting acousto-mechanical interaction allows us to implement acoustic ground-state cooling of the nanoparticle motion, removing the need for narrow cavities or external feedback. Moreover, this allows to probe the so-far elusive acoustic phonons of levitated nanoparticles through the nanoparticle motion, by using state-of-the-art experimental techniques.

+

Low-temperature decoherence in many quantum systems, such as magnons or NV centers, can be attributed to the interaction with the atomic impurities in the sample. To model such low-temperature behaviour, we propose a model describing effective dynamics of a harmonic oscillator in the presence of two-level atomic impurities based on master equation formalism. In this unconventional scenario, probing the system with the external driving field affects not only the system, but also the two-level atom environment, thereby modifying the effective dynamics of the system.

**A. E. Rubio-López** (IQOQI)*Nonequilibrium internal phenomena of nanoparticles & radiation reaction*

In this talk I will comment on Refs. [1,2]. In the first part of the talk [1], I will comment on the microscopic physics of nanoparticles that lead to understand that typical macroscopic approaches based on the quasiequilibrium approximation are unsuitable for describing the thermalization process in full picture. According to these remarks, we design a minimal model for capturing these aspects of nanoparticles, which finally leads to discrepancies with other approaches in the thermalization dynamics. In the second part [2], I will comment on the fundamental problem of radiation reaction (standing for acausality and divergent time evolution). Studying the case of a jiggling dipole (a dipole with a fluctuating center of mass), we show that the derived theory is free of issues. Furthermore, as an additional and intriguing feature, we show that quantum (zero-point fluctuations of the electromagnetic field are necessary to fulfil the second law of thermodynamics.

[1] A. E. Rubio López, C. Gonzalez-Ballestero, and O. Romero-Isart. “Internal quantum dynamics of a

nanoparticle in a thermal electromagnetic field: A minimal model”, Phys. Rev. B 98, 155405 (2018).

[2] A. E. Rubio López, and O. Romero-Isart. “Radiation reaction of a jiggling dipole in a quantum

electromagnetic field”, ArXiv:1905.06068 (submitted to Phys. Rev. Left., 2019).

**A. Sharafiev** (IQOQI) *Taking advantage of 3rd dimension in superconducting quantum circuits experiments*

During first part of the talk I will introduce 3D circuit Quantum Electrodynamics (QED) platform we are currently using in the laboratory, its advantages and drawbacks in comparison with more conventional on-chip technology. While outlining all our experimental activities in this area, I will make an emphasis on a 3D waveguide QED as it allows for simulating quantum systems in regimes which are difficult to access with other platforms. The difference between “theoretical” and “real-life” wavequide QED will be discussed. After the introduction, I will concentrate on particular experiments on direct “single photon wavefunction” measurements and collective effects in rectangular waveguide.