Optimal limits of continuously monitored thermometers and their Hamiltonian structure
arXiv:2408.01313 · doi:10.1103/PhysRevA.111.L020401
Abstract
We investigate the fundamental and practical precision limits of thermometry in bosonic and fermionic environments by coupling an -level probe to them and continuously monitoring it. Our findings show that the ultimate precision limit, quantified by the Fisher information, scales linearly with , offering an exponential improvement over equilibrium thermometry, where the scaling is only . For a fixed Hamiltonian structure, we develop a maximum likelihood estimation strategy that maps the observed continuously monitored trajectories of the probe into temperature estimates with minimal error. By optimizing over all possible Hamiltonian structures, we discover that the optimal configuration is an effective two-level system, with both levels exhibiting degeneracy that increases with -a stark contrast to equilibrium thermometry, where the ground state remains non-degenerate. Our results have practical implications. First, continuous monitoring is experimentally feasible on several platforms and accounts for the preparation time of the probe, which is often overlooked in other approaches such as prepare-and-reset. Second, the linear scaling is robust against deviations from the effective two-level structure of the optimal Hamiltonian. Additionally, this robustness extends to cases of initial ignorance about the temperature. Thus, in global estimation problems, the linear scaling remains intact even without adaptive strategies.
A robustness analysis is added in this version
References in corpus (53)
- Topological Insulators
- Non-Abelian Anyons and Topological Quantum Computation
- Quantum feedback control of a superconducting qubit: Persistent Rabi oscillations
- Local emergence of thermal correlations in an isolated quantum many-body system
- Ultracold atoms out of equilibrium
- Individual quantum probes for optimal thermometry
- Quantum feedback: theory, experiments, and applications
- Quantum thermodynamic devices: from theoretical proposals to experimental reality
- Thermometry in the quantum regime: Recent theoretical progress
- The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
- Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
- Quantum metrology in Lipkin-Meshkov-Glick critical systems
- All-optical nanoscale thermometry with silicon-vacancy centers in diamond
- Quantum Limits of Thermometry
- In situ thermometry of a cold Fermi gas via dephasing impurities
- Using polarons for sub-nK quantum non-demolition thermometry in a Bose-Einstein condensate
- Collisional quantum thermometry
- Qubit thermometry for micromechanical resonators
- Measurement-induced nonlocal entanglement in a hot, strongly-interacting atomic system
- Probing the temperature of cold many-body quantum systems
- Optomechanical Raman-Ratio Thermometry
- Fundamental limits on low-temperature quantum thermometry with finite resolution
- Noisy quantum metrology enhanced by continuous nondemolition measurement
- Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry
- Thermometry Precision in Strongly Correlated Ultracold Lattice Gases
- Optimal Probes for Global Quantum Thermometry
- Hyper-acceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment
- Fundamental limits in Bayesian thermometry and attainability via adaptive strategies
- Tight bound on finite-resolution quantum thermometry at low temperatures
- Bath-Induced Correlations Enhance Thermometry Precision at Low Temperatures
- Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes
- Spectroscopy and critical quantum thermometry in the ultrastrong coupling regime
- Optimal cold atom thermometry using adaptive Bayesian strategies
- 500 microkelvin nanoelectronics
- Sub-nK thermometry of an interacting -dimensional homogeneous Bose gas
- Improved thermometry of low-temperature quantum systems by a ring-structure probe
- Few-fermion thermometry
- Optimal nonequilibrium thermometry in Markovian environments
- Universal locality of quantum thermal susceptibility
- Uninformed Bayesian Quantum Thermometry
- A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback
- Cooling low-dimensional electron systems into the microkelvin regime
- Quantum metrology including state preparation and readout times
- Quantum scale estimation
- Quantum-limited thermometry of a Fermi gas with a charged spin particle
- Optimal Thermometers with Spin Networks
- Machine classification for probe based quantum thermometry
- Strongly coupled fermionic probe for nonequilibrium thermometry
- Thermometry by correlated dephasing of impurities in a 1D Fermi gas
- The Emergency of Pico-Kelvin Physics
- Probe thermometry with continuous measurements
- Energy measurements remain thermometrically optimal beyond weak coupling
- Stochastic metrology and the empirical distribution