Non-abelian Thouless pumping in a photonic lattice

Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-abelian gauge fields in photonic and optical lattices.

Non-abelian gauge fields lie at the very heart of many modern physical theories. We need new experimental routes and observables to disclose the importance of the Wilczek and Zee holonomy. We have shown that properly
designed photonic lattices enable the control of the beam evolution by non-commutative fields. These lattices may lead to the direct observation of the quantization of the displacement due to a non-abelian Chern number. This work can be extended in several directions, including nonlinear effects or considering the propagation of non-classical light in non-abelian lattices. Both these possibilities are unexplored so far and open several new questions concerning – for example – the effect of the non-abelian holonomy on entanglement or the impact of nonlinearity in breaking the hidden symmetries. Non-abelian topological photonics may stimulate further developments and applications for classical and quantum information and tests of fundamental physics.

Brosco, Pilozzi, Fazio, and Conti, in https://arxiv.org/abs/2010.15159

Simulating general relativity and non-commutative geometry by nonparaxial quantum fluids

We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schroedinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub Planckian phenomenology.

https://iopscience.iop.org/article/10.1088/1367-2630/ab5da8

Planckian signatures in optical harmonic generation and supercontinuum

Many theories of quantum gravity, as string theory, loop quantum gravity, and doubly special relativity, predict the existence of a minimal length scale and outline the need to generalize the uncertainty principle. This generalized uncertainty principle relies on modified commutation relations that – if applied to the second quantization – imply an excess energy of the electromagnetic quanta with respect to ω. Here we show that this “dark energy of the photon” is amplified during nonlinear optical process. Therefore, if one accepts the minimal length scenario, one must expect to observe specific optical frequencies in optical harmonic generation by intense laser fields. Other processes as four-wave mixing and supercontinuum generation may also contain similar spectral features of quantum-gravity. Nonlinear optics may hence be helpful to falsify some of the most investigated approaches to the unification of quantum mechanics and general relativity.

C. Conti in arXiv:1805.11716

Solitons and Black Holes in the Sine-Gordon Equation

The intriguing connection between black holes’evaporation and physics of solitons is opening novel roads to finding observable phenomena. It is known from the inverse scattering transform that velocity is a fundamental parameter in solitons theory. Taking this into account, the study of Hawking radiation by a moving soliton gets a growing relevance. However, a theoretical context for the description of this phenomenon is still lacking. Here, we adopt a soliton geometrization technique to study the quantum emission of a moving soliton in a one-dimensional model. Representing a black hole by the one soliton solution of the Sine-Gordon equation, we consider Hawking emission spectra of a quantized massless scalarfield on the soliton-induced metric. We study the relation between the soliton velocity and the black hole temperature. Our results address a new scenario in the detection of new physics in the quantum gravity panorama.

L. Villari, G. Marcucci, M.C. Braidotti and C. Conti, J. Phys. Comm. 2 (2018) 005016

Quantum-gravity-slingshot: orbital precession due to the modified uncertainty principle, from analogs to tests of Planckian physics with quantum fluids

Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and direct tests of the modified uncertainty principle expected to be valid at the Planck scale. We consider a quantum clock realized by a long-lasting quantum fluid wave-packet orbiting in a trapping potential. We investigate the hydrodynamics of the Schr\”odinger equation encompassing kinetic terms due to Planck-scale effects. We study the resulting generalized mechanics and validate the predictions by quantum simulations. Wave-packet orbiting generates a continuous amplification of the quantum gravity effects. The non-commutative variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is strongly resembling the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results can be employed to emulate quantum gravity in the laboratory, or to realize human-scale experiments to determine bounds for the most studied quantum-gravity models and probe Planckian physics.

Giulia Marcucci and Claudio Conti, arXiv:1805.03600