[Paper Review] Tuneable interacting bosons for relativistic and quantum information processing

Chester Moore, David Edward Bruschi|arXiv (Cornell University)|Jan 8, 2016

Quantum Information and Cryptography3 references3 citations

TL;DR

This paper derives analytical solutions for the time evolution of two-mode interacting bosons under a time-dependent two-mode squeezing Hamiltonian with smooth switching. It reveals exact expressions for particle number, entanglement, and energy changes, enabling precise control for quantum information and relativistic quantum systems.

ABSTRACT

We study the full time evolution of a system of two modes of a bosonic quantum field that interact through quadratic hamiltonians. We specialise to a time dependent two-mode squeezing Hamiltonian where the coupling is switched on and off smoothly. We find the analytical solutions to the time evolution after the interaction is turned off, which apply to arbitrary coupling functions. We investigate the final state of the system and compute all physically relevant quantities, such as average particle number, entanglement and change in energy. Our techniques can be applied to a wide range of scenarios, which include implementations of time dependent two-mode squeezing, coupled harmonic oscillators, harmonic oscillators coupled to light. Furthermore, these techniques can be extended to more complicated time-dependent quadratic Hamiltonians. We briefly discuss possible applications within the area of relativistic and quantum information.

Motivation & Objective

• To model the full time evolution of two-mode bosonic systems under time-dependent quadratic Hamiltonians.
• To derive exact analytical solutions after interaction is switched off, applicable to arbitrary coupling functions.
• To compute key physical quantities such as average particle number, entanglement, and energy change.
• To demonstrate the method's broad applicability to systems like coupled harmonic oscillators and light-matter interactions.
• To explore potential applications in relativistic and quantum information processing.

Proposed method

• Uses a time-dependent two-mode squeezing Hamiltonian with smooth on/off switching of coupling.
• Solves the time evolution equations analytically for arbitrary coupling functions.
• Applies techniques from quantum optics and time-dependent quadratic Hamiltonians to derive exact final state expressions.
• Computes expectation values of physical observables using the derived time-evolved states.
• Extends the framework to more complex time-dependent quadratic Hamiltonians beyond two-mode squeezing.
• Employs standard quantum field theory and bosonic operator formalism to model the system dynamics.

Experimental results

Research questions

• RQ1 How does the system evolve under a time-dependent two-mode squeezing Hamiltonian with arbitrary coupling functions?
• RQ2 What are the exact expressions for particle number, entanglement, and energy change after interaction is switched off?
• RQ3 How can the analytical solutions be generalized to other systems like coupled harmonic oscillators or light-matter coupling?
• RQ4 What are the physical implications of smooth switching in the coupling strength?
• RQ5 What are the potential applications in relativistic and quantum information processing?

Key findings

• Exact analytical solutions for the time evolution are derived after the interaction is turned off, valid for arbitrary coupling functions.
• The final state of the system is fully characterized, including average particle number, entanglement, and energy change.
• Entanglement and particle number depend explicitly on the shape and duration of the coupling function.
• The method applies broadly to systems such as coupled harmonic oscillators and light-matter interactions.
• The framework can be extended to more complex time-dependent quadratic Hamiltonians.
• The results provide a foundation for precise control in quantum information and relativistic quantum systems.