## Theoretical Quantum Physics Laboratory @unime

The group is part of the macrogroup Micro and Nanosystems (MNS) of the Department MIFT of the University of Messina

Chief Scientist: Prof. Salvatore Savasta

## Main Research Fields

We perform research in theoretical quantum condensed matter physics, including quantum optics, quantum plasmonics, quantum optomechanics, and superconductiong quantum circuits. Our research work explores the interface between atomic physics, quantum optics, nano-science. Particular emphasis is being placed on cavity QED, superconducting Josephson-junction qubits, quantum circuitry and improved designs for their quantum control. We are particularly interested in the ultrastrong coupling between light and matter.

## Main Collaborations:

## Research Highlights:

In quantum electrodynamics, the choice of gauge influences the form of light–matter interactions. However, gauge invariance implies that all physical results should be independent of this formal choice. The Rabi model, a widespread description for the dipolar coupling between a two-level atom and a quantized electromagnetic field, seemingly violates this principle in the presence of ultrastrong light–matter coupling, a regime that is now experimentally accessible in many physical systems. This failure is attributed to the finite-level truncation of the matter system, an approximation that enters the derivation of the Rabi model. Here, we identify the source of gauge violation and provide a general method for the derivation of light–matter Hamiltonians in truncated Hilbert spaces that produces gauge-invariant physical results, even for extreme light–matter interaction regimes. This is achieved by compensating the non-localities introduced in the construction of the effective Hamiltonians. The resulting quantum Rabi Hamiltonian in the Coulomb gauge differs significantly in form from the standard one, but provides the same physical results obtained by using the dipole gauge. These results shed light on gauge invariance in the non-perturbative and extreme-interaction regimes, and solve long-lasting controversies arising from gauge ambiguities in the quantum Rabi and Dicke models.

Ultrastrong coupling between light and matter has, in the past decade, transitioned from a theoretical idea to an experimental reality. It is a new regime of quantum light–matter interaction, which goes beyond weak and strong coupling to make the coupling strength comparable to the transition frequencies in the system. The achievement of weak and strong coupling has led to increased control of quantum systems and to applications such as lasers, quantum sensing, and quantum information processing. Here we review the theory of quantum systems with ultrastrong coupling, discussing entangled ground states with virtual excitations, new avenues for nonlinear optics, and connections to several important physical models. We also overview the multitude of experimental setups, including superconducting circuits, organic molecules, semiconductor polaritons, and optomechanical systems, that have now achieved ultrastrong coupling. We conclude by discussing the many potential applications that these achievements enable in physics and chemistry.

We study the dynamical Casimir effect using a fully quantum-mechanical description of both the cavity field and the oscillating mirror. We do not linearize the dynamics, nor do we adopt any parametric or perturbative approximation. We find that vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited atoms. By considering a coherent drive of the mirror, using a master-equation approach to take losses into account, we are able to study the dynamical Casimir effect for optomechanical coupling strengths ranging from weak to ultrastrong. We find that a resonant production of photons out of the vacuum can be observed even for mechanical frequencies lower than the cavity-mode frequency. Since high mechanical frequencies, which are hard to achieve experimentally, were thought to be imperative for realizing the dynamical Casimir effect, this result removes one of the major obstacles for the observation of this long-sought effect. We also find that the dynamical Casimir effect can create entanglement between the oscillating mirror and the radiation produced by its motion in the vacuum field, and that vacuum Casimir-Rabi oscillations can occur. Finally, we also show that all these findings apply not only to optomechanical systems, but also to parametric amplifiers operating in the fully quantum regime.

We consider two separate atoms interacting with a single-mode optical or microwave resonator. When the frequency of the resonator field is twice the atomic transition frequency, we show that there exists a resonant coupling between *one* photon and *two* atoms, via intermediate virtual states connected by counterrotating processes. If the resonator is prepared in its one-photon state, the photon can be jointly absorbed by the two atoms in their ground state which will both reach their excited state with a probability close to one. Like ordinary quantum Rabi oscillations, this process is coherent and reversible, so that two atoms in their excited state will undergo a downward transition jointly emitting a single cavity photon. This joint absorption and emission process can also occur with three atoms. The parameters used to investigate this process correspond to experimentally demonstrated values in circuit quantum electrodynamics systems.

APS Focus:

Two Atoms Can Jointly Absorb One Photon## Selected Publications:

- Resolution of gauge ambiguities in ultrastrong-coupling cavity quantum electrodynamics
- O. Di Stefano, A. Settineri, V. Macrì, L. Garziano, R. Stassi, S. Savasta, and F. Nori
- Nat. Phys. DOI 10.1038/s41567-019-0534-4 (2019)

- Interaction of mechanical oscillators mediated by the exchange of virtual photon pairs
- O. Di Stefano, A. Settineri, V. Macrì, A. Ridolfo, R. Stassi, A. F. Kockum, S. Savasta, and F. Nori
- Phys. Rev. Lett.
**122**, 030402 (2019)

- Ultrastrong coupling between light and matter
- A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, F. Nori
- Nature Reviews Physics
**1**, 19 (2019)

- Non-perturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings
- V. Macrì, A. Ridolfo, O. Di Stefano, A. Frisk Kockum, F. Nori, S. Savasta
- Physical Review X
**8**, 011031 (2018)

- Quantum nonlinear optics without photons
- R. Stassi, V. Macrì, A. Frisk Kockum, O. Di Stefano, A. Miranowicz, S. Savasta, F. Nori
- Physical Review A
**96**, 023818 (2017).

- Feynman-diagrams approach to the quantum Rabi model for ultrastrong cavity QED: stimulated emission and reabsorption of virtual particles dressing a physical excitation
- O. Di Stefano, R. Stassi, L. Garziano, A. Frisk Kockum, S. Savasta, F. Nori
- New Journal of Physics
**19**, 053010, (2017).

- One Photon Can Simultaneously Excite Two or More Atoms
- L. Garziano, V. Macrì, R. Stassi, O. Di Stefano, F. Nori, S. Savasta
- Physical Review Letters 117, 043601 (2016).
- doi: 10.1103/PhysRevLett.117.043601
**Featured in Physics - Editors' Suggestion**

- Ultrastrong Coupling of Plasmons and Excitons in a Nanoshell
- A. Cacciola, O. Di Stefano, R. Stassi, R. Saija, S. Savasta
- ACS NANO
**8**,11,11483-11492, (2014).

- Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong-Coupling Regime
- R. Stassi,, A. Ridolfo, O. Di Stefano, M. J. Hartmann, S. Savasta
- Physical Review Letters
**110,**6, 243601 (2013).

- All Optical Switch of Vacuum Rabi Oscillations: The Ultrafast Quantum Eraser
- A. Ridolfo, R. Vilardi, O. Di Stefano, S. Portolan, S. Savasta
- Physical Review Letters
**106**, 013601 (2011) - doi: 10.1103/PhysRevLett.106.013601

- Quantum plasmonics with quantum dot-metal nanoparticle molecules: Influence of the Fano effect on photon statistics
- A. Ridolfo, O. Di Stefano. N. Fina, R. Saija, S. Savasta
- Physical Review Letters
**105**(26), 263601 (2010).

- Nanopolaritons: Vacuum Rabi Splitting with a Single Quantum Dot in the Center of a Dimer Nanoantenna
- S. Savasta, R. Saija, A. Ridolfo, O. Di Stefano, P. Denti F. Borghese
- ACS Nano 4(11) pp 6369–6376 (2010)

- Quantum complementarity of microcavity polaritons
- S. Savasta, O. Di Stefano, V, Savona, W. Langbein
- Physical Review Letters
**94**, 246401 (2005).

- Many-body and correlation effects on parametric polariton amplification in semiconductor microcavities
- S. Savasta, O. Di Stefano, R. Girlanda
- Physical Review Letters
**90,**096403 (2003)