Experimental Verification of a Jarzynski-Related Information-Theoretic Equality by a Single Trapped Ion

Abstract

Most nonequilibrium processes in thermodynamics are quantified only by inequalities; however, the Jarzynski relation presents a remarkably simple and general equality relating nonequilibrium quantities with the equilibrium free energy, and this equality holds in both the classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in the quantum regime using a single ultracold ^{40}Ca^{+} ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements. By considering both initially pure and mixed states, respectively, we verify, in an exact and fundamental fashion, the nonequilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.

Quantum corrections of work statistics in closed quantum systems

“…Eq. (19) originates from the quantum corrections to the classical distribution [27]. We immediately find that Eq.…”

“…The reader is reminded that the operator Λ ′ in this equation is defined with respect to z ′ = (x ′ , p ′ ). A very analogous expression for K (2) (z, t) can also be obtained, and it obviously depends on the initial condition (19) in addition to functions K (0) and K (1) . Based on these above observations, we arrive at the series expansion of the CF (3) in powers ofh as follows:…”

One-Shot Information-Theoretical Approaches to Fluctuation Theorems

“…This facilitates, for instance, the experimental testing of recent advances in modern thermodynamics that involve Rényi divergences between a state and its thermal equilibrium state [18,[66][67][68][69]. Through the use of single-qubit probes [70][71][72][73] (a type of Ramsey interferometry -see [74]), one can characterize the work-distribution, and then use the above equalities to determine the Rényi divergences between the initial and final thermal states [75]. We conclude by noting that recent developments in field of quantum fluctuation relations extend their remit beyond the regime of assumptions made by Tasaki (e.g.…”

Duality in quantum work

“…Traditionally, quantum work is defined as the difference of the energies obtained by two-point measurement scheme (TPM): performing two projective energy measurements at the beginning and the end of external protocol. Based on TPM, the extension of classical fluctuation theorems [5][6][7][8][9][10][11][12] to the quantum regime is obtained [4,[12][13][14][15][16][17][18][19][20][21][22][23], see reviews [22,23] for detail discussion, and these fluctuation theorems have been experimentally verified in various systems [24][25][26][27][28][29][30]. However, if the system is initially in the superposition of some energy levels, quantum coherence will be completely destroyed by the first measurement, and the work fluctuation relation is not "quantum" to some extent.…”