Easy Access to Energy Fluctuations in Nonequilibrium Quantum Many-Body Systems

Abstract

We combine theoretical and experimental efforts to propose a method for studying energy fluctuations, in particular, to obtain the related bi-stochastic matrix of transition probabilities by means of simple measurements at the end of a protocol that drives a many-body quantum system out-ofequilibrium. This scheme is integrated with numerical optimizations in order to ensure a proper analysis of the experimental data, leading to physical probabilities. The method is experimentally evaluated employing a two interacting spin-1/2 system in a nuclear magnetic resonance setup. We show how to recover the transition probabilities using only local measures which enables an experimental verification of the detailed fluctuation theorem in a many-body system driven out-ofequilibrium.

Work Statistics and Entanglement Across the Fermionic Superfluid‐Insulator Transition

“…Experimentally, the quantum work is accessible by means of spectroscopic methods, [62][63][64] and the work distribution has been reconstructed in a liquid-state nuclear magnetic resonance platform using small molecules as working fluid. [64,65] In a sudden quench, the transitions are instantaneous and the system does not have time to adapt. If the system is prepared in a superposition of the eigenstates |n 0 ⟩ of Ĥ(⃗ g 0 ) with weights p n , the work probability distribution P(W) is calculated as follows [66]…”

“…In this process, all possible transitions between the eigenestates of the initial $$\hat{H}(\vec{g}_0)$$ and final $$\hat{H}(\vec{g}_f)$$ Hamiltonians may be involved, determining the change in energy, as well as its fluctuations. Experimentally, the quantum work is accessible by means of spectroscopic methods, [ 62–64 ] and the work distribution has been reconstructed in a liquid‐state nuclear magnetic resonance platform using small molecules as working fluid. [ 64,65 ]…”

“…Experimentally, the quantum work is accessible by means of spectroscopic methods, [ 62–64 ] and the work distribution has been reconstructed in a liquid‐state nuclear magnetic resonance platform using small molecules as working fluid. [ 64,65 ]…”

Quantum quench thermodynamics at high temperatures

“…There are several proposals on how this can be done, as well as successful experimental implementations [50,51,[62][63][64][65]. In [66] the authors present a general method for obtaining the transition probabilities p i | j in a many-body system and use it to verify the Jarzynski relation for two qubits.…”