[Paper Review] Squeezed Quantum State of Disoriented Chiral Condensate

Ian I. Kogan|arXiv (Cornell University)|Oct 7, 1993

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper investigates the quantum state of a Disoriented Chiral Condensate (DCC) produced in high-energy collisions, modeling its formation via quantum-mechanical evolution from the vacuum using the squeezed state formalism. It demonstrates that the DCC emerges as a non-classical, squeezed quantum state with suppressed fluctuations in certain field components, offering a quantum description of a phenomenon previously treated semi-classically.

ABSTRACT

We consider the quantum state describing the Disoriented Chiral Condensate (DCC) which may be produced in high energy collisions. Using the approach suggested by Rajagopal and Wilczek to describe the amplification of the long wavelength classical pion modes, we consider the quantum-mechanical evolution of the initial vacuum state into the final squeezed state describing the DCC. The obtained wave function has some interesting properties which are discussed.

Motivation & Objective

• To provide a quantum mechanical description of the Disoriented Chiral Condensate (DCC) formed in high-energy collisions.
• To address the limitations of semi-classical treatments by modeling the DCC as a quantum state evolving from the vacuum.
• To explore the implications of the DCC being a squeezed quantum state, particularly regarding field fluctuations and coherence.
• To apply the formalism of quantum field theory to describe the amplification of long-wavelength pion modes during DCC formation.

Proposed method

• Adopt the approach of Rajagopal and Wilczek to describe the amplification of long-wavelength pion modes in the DCC.
• Model the initial vacuum state as a ground state of the interacting pion field Hamiltonian.
• Use the time-evolution operator in the Heisenberg picture to derive the final quantum state of the system.
• Apply the squeezed state formalism from quantum optics to the pion field, identifying the DCC as a coherent superposition of squeezed states.
• Derive the wave functional of the final state, showing it exhibits non-classical properties such as reduced quantum fluctuations in specific field quadratures.
• Analyze the wave function to identify its symmetry properties and implications for the observability of DCC in high-energy experiments.

Experimental results

Research questions

• RQ1 How does the quantum state of the Disoriented Chiral Condensate evolve from the initial vacuum state during high-energy collisions?
• RQ2 What are the quantum properties of the DCC when described as a squeezed state of pion fields?
• RQ3 Can the semi-classical picture of DCC formation be consistently embedded in a full quantum field theory framework?
• RQ4 What are the implications of field squeezing for the fluctuations and coherence of the pion condensate?
• RQ5 How does the wave functional of the DCC differ from a coherent state, and what observable signatures does this imply?

Key findings

• The final state of the Disoriented Chiral Condensate is identified as a squeezed quantum state, indicating non-classical behavior in the pion field.
• The wave functional of the DCC exhibits reduced quantum fluctuations in specific field quadratures, a hallmark of squeezing.
• The initial vacuum state evolves into a squeezed state through the amplification of long-wavelength pion modes, consistent with the dynamics of spontaneous symmetry breaking.
• The DCC state is not a simple coherent state but a superposition involving squeezing, implying enhanced quantum correlations.
• The formalism provides a quantum foundation for the DCC, reconciling its macroscopic appearance with quantum field theory.
• The results suggest that DCC formation may lead to observable signatures through suppressed fluctuations in certain field components, potentially detectable in high-energy experiments.