Taking the temperature of a pure quantum state

Abstract

Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research. The observation of thermalisation in completely isolated quantum systems, such as cold-atom quantum simulators, implies that a temperature can be assigned even to individual, pure quantum states. Here, we propose a scheme to measure the temperature of such pure states through quantum interference. Our proposal involves interferometry of an auxiliary qubit probe, which is prepared in a superposition state and subsequently decoheres due to weak coupling with a closed, thermalised many-body system. Using only a few basic assumptions about chaotic quantum systems -- namely, the eigenstate thermalisation hypothesis and the emergence of hydrodynamics at long times -- we show that the qubit undergoes pure exponential decoherence at a rate that depends on the temperature of its surroundings. We verify our predictions by numerical experiments on a quantum spin chain that thermalises after absorbing energy from a periodic drive. Our work provides a general method to measure the temperature of isolated, strongly interacting systems under minimal assumptions.

5+6 pages, 4+3 figures. Comments welcome. v2: Improved text and figures for clarity. v3: Final author version

References in corpus (9)

• Thermalization and its mechanism for generic isolated quantum systems
• The Kernel Polynomial Method
• Equilibrium states of generic quantum systems subject to periodic driving
• Individual quantum probes for optimal thermometry
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Single-qubit thermometry
• Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
• Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations
• Non-destructive selective probing of phononic excitations in a cold Bose gas using impurities

Cited by in corpus (16)

• Operational definition of the temperature of a quantum state
• Multi-spin probes for thermometry in the strong-coupling regime
• Sub-nK thermometry of an interacting $d$-dimensional homogeneous Bose gas
• Optimal nonequilibrium thermometry in Markovian environments
• Thermodynamics of decoherence
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
• Invasiveness of non-equilibrium quantum thermometry
• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Thermometry by correlated dephasing of impurities in a 1D Fermi gas
• Entropy and Temperature in finite isolated quantum systems
• Quantum master equation from the eigenstate thermalization hypothesis
• Spectral Bounds on Entropy and Ergotropy via Statistical Effective Temperature in Classical Polarization and Quantum Thermal States
• Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
• Resolving the Debate Between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures
• Taking the temperature of quantum many-body scars
• Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas