Thermodynamics of Optical Bloch Equations

Abstract

Optical Bloch Equations (OBE) describe the coherent exchange of energy between a quantum bit (qubit) and a quasi-resonant driving field in the presence of a thermal bath. Despite it being an ubiquitous process in quantum technologies, a sound thermodynamic analysis is still missing. We hereby provide such an analysis, by deriving the relevant framework from first principles. Building on a microscopic model of the bath, we first express heat, work and entropy production for the closed qubit-bath system where these definitions are unambiguous. We coarse-grain the obtained expressions, using a methodology similar to the derivation of the dynamical master equation and giving rise to consistent expressions of the First and Second Law. We verify that long coarse graining times yield the Floquet Master Equation and its already known thermodynamic description. Conversely, short coarse-graining times yield the OBE and its consistent thermodynamic framework, whose variables explicitly depend on the quantum coherences in the qubit's energy basis. These quantum signatures in the heat and in the entropy production flows allow us to characterize a genuinely quantum non-equilibrium situation, where the coherences created by the driving field are continuously erased by the bath. Our findings can be readily extended to larger open quantum systems. They carry the seeds for future thermodynamic analyses of quantum gates and the design of quantum engines in the strong coherent driving regime.

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References in corpus (38)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum information with Rydberg atoms
• Coherent control of macroscopic quantum states in a single-Cooper-pair box
• Trapped-Ion Quantum Computing: Progress and Challenges
• Quantum Thermodynamics
• Superconducting Circuits and Quantum Information
• Entropy production as correlation between system and reservoir
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Experimental demonstration of quantum effects in the operation of microscopic heat engines
• Markovian master equations for quantum thermal machines: local vs global approach
• Reconciliation of quantum local master equations with thermodynamics
• Cavity-assisted quantum bath engineering
• The role of quantum measurement in stochastic thermodynamics
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• The role of quantum coherence in non-equilibrium entropy production
• A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Markovian Master Equation and Thermodynamics of Two-level System in Strong Laser Field
• Collective operation of quantum heat machines via coherence recycling, and coherence induced reversibility
• Time Dependent Markovian Quantum Master Equation
• Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines
• Quantum Otto cycle with inner friction: finite-time and disorder effects
• Stochastic thermodynamics of rapidly driven systems
• Energy flow in periodic thermodynamics
• Mimicking Nonequilibrium Steady States with Stochastic Pumps
• Friction due to inhomogeneous driving of coupled spins in a quantum heat engine
• Quantum Error-Correction-Enhanced Magnetometer Overcoming the Limit Imposed by Relaxation
• Supremacy of incoherent sudden cycles
• Detailed Fluctuation Theorems: A Unifying Perspective
• A minimal model of an autonomous thermal motor
• Energetic footprints of irreversibility in the quantum regime
• Enhanced energy transfer to an optomechanical piston from indistinguishable photons
• Quantifying the quantum heat contribution from a driven superconducting circuit
• Coarse-graining in the derivation of Markovian master equations and its significance in quantum thermodynamics
• Thermodynamic analysis of quantum error correcting engines
• Thermodynamics of a Periodically Driven Qubit
• Ability of Markovian Master Equations to Model Quantum Computers and Other Systems Under Broadband Control

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• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
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• Stochastic Thermodynamic Cycles of a Mesoscopic Thermoelectric Engine
• Quantifying the quantum heat contribution from a driven superconducting circuit
• Nonequilibrium heat transport and work with a single artificial atom coupled to a waveguide: emission without external driving
• Response theory for nonequilibrium steady-states of open quantum systems
• Nonequilibrium thermodynamics of quantum coherence beyond linear response
• Contributions from populations and coherences in non-equilibrium entropy production
• Closed-System Solution of the 1D Atom from Collision Model
• Coarse-graining master equation for periodically driven systems
• On the role of initial coherence in the spin phase-space entropy production rate
• Quantum thermodynamics of periodically driven polaritonic systems
• Nonresonant two-level transitions: Lessons from quantum thermodynamics
• First Law of Quantum Thermodynamics in a Driven Open Two-Level System
• Quantum quench thermodynamics at high temperatures
• Quantum-based solution of time-dependent complex Riccati equations
• Chiral thermodynamics in tailored chiral optical environments
• Thermodynamics of autonomous optical Bloch equations
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes
• Probing non-classical light fields with energetic witnesses in Waveguide Quantum Electro-Dynamics
• $\text{Symdyn}$: an automated algebraic solution for high-order quantum systems