Category: Quantum Gravity

3D+1 Quantum Nonlocal Solitons with Gravitational Interaction

https://arxiv.org/abs/2202.10741

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves (nonlocal solitons), are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay of the quantum diffusion of the soliton parameters and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensiona

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 ℏω. 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