[Paper Review] Dynamical engineering of squeezed thermal states

Léonce Dupays, Aurélia Chenu|arXiv (Cornell University)|Aug 7, 2020

Quantum Information and Cryptography2 references4 citations

TL;DR

This paper presents a dynamical engineering approach using shortcuts to adiabaticity to rapidly prepare squeezed thermal states in harmonic oscillators under both unitary and open quantum dynamics. By deriving counter-diabatic Hamiltonians and tailored dissipators, the method enables arbitrary-time creation of such states at controlled temperature and entropy, with explicit solutions for laser amplitude, phase, and dephasing in trapped-ion systems via stochastically driven Raman transitions.

ABSTRACT

Control protocols known as shortcuts to adiabaticity allow to drive a quantum system from an initial to a final state arbitrarily fast. These techniques have recently been proposed for open quantum systems, thus extending their application to allow for fast thermalization. Here, we engineer dynamical schemes for the fast preparation of squeezed thermal states at controlled temperature. We derive the equations of motion of squeezed thermal states in harmonic oscillators under unitary and open dynamics, allowing for temperature and entropy variations between the initial and final states. The counter-diabatic Hamiltonians and associated dissipators are provided, and whenever possible, given in a form relevant to experimental application.The technique is detailed in the setting of trapped-ion experiments with two-photon Raman interaction, where the desired open dynamics is obtained from stochastically shaking the trapping potential, or driving the system with a laser of stochastic amplitude. In this context, we find solutions for the control parameters---namely laser amplitude, phase, and dephasing strength---that allow creating a squeezed thermal state at controlled temperature in arbitrary time.

Motivation & Objective

• To develop fast, non-adiabatic protocols for preparing squeezed thermal states in open quantum systems.
• To extend shortcuts to adiabaticity to open systems, enabling rapid thermalization and entropy control.
• To provide experimentally relevant control parameters—laser amplitude, phase, and dephasing—for realizing the desired dynamics in trapped-ion platforms.
• To derive equations of motion for squeezed thermal states under both unitary and open dynamics, allowing for arbitrary initial and final temperatures and entropies.
• To demonstrate feasibility in realistic trapped-ion experiments using two-photon Raman transitions with stochastic driving.

Proposed method

• Derive the equations of motion for squeezed thermal states in harmonic oscillators under unitary and open dynamics, incorporating temperature and entropy variations.
• Construct counter-diabatic Hamiltonians to suppress diabatic excitations during fast state engineering.
• Design dissipators compatible with the target dynamics to enable fast thermalization at controlled temperature.
• Map the control protocols to experimentally accessible parameters: laser amplitude, phase, and dephasing strength in trapped-ion systems.
• Utilize stochastically shaken trapping potentials or stochastically driven lasers to realize the desired open dynamics via two-photon Raman transitions.
• Provide analytical solutions for control parameters that achieve the target squeezed thermal state in arbitrary time.

Experimental results

Research questions

• RQ1 Can shortcuts to adiabaticity be extended to open quantum systems to enable fast preparation of squeezed thermal states?
• RQ2 What control protocols—specifically Hamiltonians and dissipators—are required to engineer arbitrary-time evolution to a squeezed thermal state with controlled temperature and entropy?
• RQ3 How can the dynamics be realized in experimentally feasible setups, such as trapped ions with stochastically driven Raman transitions?
• RQ4 What are the explicit time-dependent control parameters (laser amplitude, phase, dephasing) that achieve the target state in arbitrary time?
• RQ5 How do temperature and entropy evolve during the fast dynamical process, and can they be independently controlled?

Key findings

• The paper derives exact equations of motion for squeezed thermal states under both unitary and open dynamics, enabling arbitrary initial and final temperatures and entropies.
• Counter-diabatic Hamiltonians are constructed to suppress non-adiabatic transitions during fast state engineering, ensuring high-fidelity state preparation.
• Tailored dissipators are derived to enable fast thermalization at a desired temperature, extending shortcuts to adiabaticity to open systems.
• Explicit solutions for laser amplitude, phase, and dephasing strength are provided, allowing the preparation of a squeezed thermal state in arbitrary time in trapped-ion systems.
• The method is realizable in trapped-ion experiments using two-photon Raman transitions with stochastically driven lasers or stochastically shaken potentials.
• The approach enables full control over the final state's temperature and squeezing, with no constraints on the evolution time.