[Paper Review] Squeezed vacua in loop quantum gravity

Eugenio Bianchi, Jonathan Guglielmon+2 more|arXiv (Cornell University)|May 17, 2016

Noncommutative and Quantum Gravity Theories46 references13 citations

TL;DR

This paper introduces squeezed vacua in loop quantum gravity—a new overcomplete basis of quantum states that encode prescribed correlations between geometric operators. By analyzing long-range correlations, the authors demonstrate how these states can facilitate the semiclassical spacetime reconstruction program, offering a promising pathway toward emergent classical geometry from quantum gravity.

ABSTRACT

We introduce squeezed vacua in loop quantum gravity, a new overcomplete basis of states that contain prescribable correlations between geometric operators. We study the behavior of long-range correlations and discuss the relevance of these states for the reconstruction of a semiclassical spacetime from loop quantum gravity.

Motivation & Objective

• To develop a new class of quantum states in loop quantum gravity that encode controllable correlations between geometric observables.
• To explore how long-range quantum correlations in these states may support the emergence of classical spacetime geometry.
• To provide a framework for testing semiclassical limits in loop quantum gravity using a non-Fock, overcomplete basis.

Proposed method

• Constructing squeezed vacua as coherent superpositions of spin network states with engineered entanglement between spatial regions.
• Defining the states via a unitary squeezing transformation acting on a reference vacuum state in the kinematical Hilbert space.
• Using the holonomy-flux algebra to characterize geometric operators and their correlations in the squeezed vacuum framework.
• Analyzing the two-point correlation functions of area and volume operators to quantify long-range entanglement.
• Employing the kinematical framework of loop quantum gravity to ensure consistency with quantum geometric constraints.
• Applying techniques from quantum optics and condensed matter to adapt the concept of squeezing to quantum gravity.

Experimental results

Research questions

• RQ1 How can quantum states in loop quantum gravity be engineered to contain specific, controllable correlations between geometric operators?
• RQ2 What is the behavior of long-range correlations in these squeezed vacua, and how do they scale with spatial separation?
• RQ3 Can these states serve as a viable basis for the semiclassical limit of loop quantum gravity?
• RQ4 To what extent do squeezed vacua exhibit properties resembling classical spacetime geometry?
• RQ5 How do the correlations in these states compare to those in standard Fock-like vacua or other quantum gravity states?

Key findings

• Squeezed vacua provide a new overcomplete basis in loop quantum gravity that allows for the explicit prescription of correlations between geometric operators.
• The states exhibit long-range correlations that decay slowly with spatial separation, indicating non-local quantum entanglement across geometric regions.
• These correlations are tunable via the squeezing parameters, enabling systematic study of their role in semiclassical emergence.
• The framework supports a consistent semiclassical limit where geometric operators display classical-like behavior in expectation values.
• The construction preserves the fundamental quantum geometric structure of loop quantum gravity, including holonomy and flux operators.
• The results suggest that squeezed vacua are a promising candidate for constructing effective spacetime geometries from quantum states.