W. L. Yang

We demonstrate for the first time a linear-zigzag phase transition induced solely by temperature of the $^{40}$Ca$^{+}$ ion crystals in a surface-electrode trap. In contrast to the previously observed counterparts based on change of the mechanical equilibrium conditions of the ions, our presented structural phase transition occurs due to controllable influence of thermal fluctuation. The ions' temperature is well controlled by tuning the cooling laser and the experimental observation could be fully understood by classical Langevin equation in addition to the effects from thermal fluctuation. Our experimental investigation indicates the fantastic role of thermal fluctuation played in the thermodynamic process at atomic level, which might bridge the thermodynamics from the macroscopic domain to the quantum regime.

Most non-equilibrium processes in thermodynamics are quantified only by inequalities, however the Jarzynski relation presents a remarkably simple and general equality relating non-equilibrium quantities with the equilibrium free energy, and this equality holds in both classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in 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 non-equilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.

One of the outstanding challenges to information processing is the eloquent suppression of energy consumption in execution of logic operations. Landauer principle sets an energy constraint in deletion of a classical bit of information. Although some attempts have been paid to experimentally approach the fundamental limit restricted by this principle, exploring Landauer principle in a purely quantum mechanical fashion is still an open question. Employing a trapped ultracold ion, we experimentally demonstrate a quantum version of Landauer principle, i.e., an equality associated with energy cost of information erasure in conjunction with entropy change of the associated quantized environment. Our experimental investigation substantiates an intimate link between information thermodynamics and quantum candidate systems for information processing.

Here we respond to a comment [arXiv:1802.01382] submitted recently on 'Experimental Verification of a Jarzynski-Related Information-Theoretic Equality by a Single Trapped Ion' PRL 120 010601 (2018). We consider that the argument is the thermalization in a quantum system, which is different from the counterpart in conventional thermodynamics.

The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited recently due to new proposed forms of measurement uncertainty relations. The present work is associated with a new error trade-off relation for compatible observables approximating two incompatible observables, in keeping with the spirit of Heisenberg's original ideas of 1927. We report the first \textsl{direct} test and confirmation of the tight bounds prescribed by such an error trade-off relation, based on an experimental realisation of optimal joint measurements of complementary observables using a single ultracold $^{40}Ca^{+}$ ion trapped in a harmonic potential. Our work provides a prototypical determination of ultimate joint measurement error bounds with potential applications in quantum information science for high-precision measurement and information security.

We show how to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By adiabatically sweeping down/up the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination. Based on current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.

We propose how to explore the Franck-Condon (FC) physics via a single ion confined in a spin-dependent potential, formed by the combination of a Paul trap and a magnetic field gradient. The correlation between electronic and vibrational degrees of freedom, called as electron-vibron coupling, is induced by a nonzero gradient. For a sufficiently strong electron-vibron coupling, the FC blockade of low-lying vibronic transitions takes place. We analyze the feasibility of observing the FC physics in a single trapped ion, and demonstrate various potential applications of the ionic FC physics in quantum state engineering and quantum information processing.

The main idea in the original Grover search (Phys. Rev. Lett. 79, 325 (1997)) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black box giving us information about the target state. We design quantum circuits to accomplish a complete Grover search involving both the Oracle's job and the amplification of the target state, which are employed to solve Satisfiability (SAT) problems. We explore how to carry out the quantum circuits by currently available ion-trap quantum computing technology.