H. T. Quan

Decay of Loschmidt echo enhanced by quantum criticality

We study the transition of a quantum system from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system E coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of E modeled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of E strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing S vanish sharply.

Quantum thermodynamic cycles and quantum heat engines

In order to describe quantum heat engines, here we systematically study isothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. Relations and mappings between these two quantum heat engines are also investigated by considering their respective quantum thermodynamic processes. In addition, we discuss the role of Maxwells demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.

Experimental test of the quantum Jarzynski equality with a trapped-ion system

The Jarzynski equality, relating non-equilibrium processes to free-energy differences between equilibrium states, has been verified in a number of classical systems. An ion-trap experiment now succeeds in demonstrating its quantum counterpart.

Maxwell's demon assisted thermodynamic cycle in superconducting quantum circuits

We propose a quantum analog of the internal combustion engine used in most cars. Specifically, we study how to implement the Otto-type quantum heat engine (QHE) with the assistance of a Maxwells demon. Three steps are required: thermalization, quantum measurement, and quantum feedback controlled by the Maxwell demon. We derive the positive-work condition of this composite QHE. Our QHE can be constructed using superconducting quantum circuits. We explicitly demonstrate the essential role of the demon in this macroscopic QHE.

Quantum heat engine with multilevel quantum systems

By reformulating the first law of thermodynamics in the fashion of quantum-mechanical operators on the parameter manifold, we propose a universal class of quantum heat engines (QHE) using the multilevel quantum system as the working substance. We obtain a general expression of work for the thermodynamic cycle with two thermodynamic adiabatic processes, which are implied in quantum adiabatic processes. We also classify the conditions for a 3-level QHE to extract positive work, which is proved to be looser than that for a 2-level system under certain conditions. As a realistic illustration, a 3-level atom system with dark state configuration manipulated by a classical radiation field is used to demonstrate our central idea.

Mixed-state fidelity and quantum criticality at finite temperature

We extend to finite temperature the fidelity approach to quantum phase transitions (QPTs). This is done by resorting to the notion of mixed-state fidelity that allows one to compare two density matrices corresponding to two different thermal states. By exploiting the same concept we also propose a finite-temperature generalization of the Loschmidt echo. Explicit analytical expressions of these quantities are given for a class of quasifree fermionic Hamiltonians. A numerical analysis is performed as well showing that the associated QPTs show their signatures in a finite range of temperatures.

Quantum-classical transition of photon-Carnot engine induced by quantum decoherence

We study the physical implementation of the photon-Carnot engine (PCE) based on the cavity quantum electrodynamics system [M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther, Science 299, 862 (2003)]. Here we analyze two decoherence mechanisms for the more practical systems of PCE, the dissipation of photon field, and the pure dephasing of the input atoms. As a result we find that (i) the PCE can work well to some extent even in the existence of the cavity loss (photon dissipation) and (ii) the short-time atomic dephasing, which can destroy the PCE, is a fatal problem to be overcome.

Space-Time Crystals of Trapped Ions

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.

Redundant imprinting of information in nonideal environments: Objective reality via a noisy channel

Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, E , is in a non-ideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, S, and an environment fragment, F , is given solely by F ’s entropy increase. This demonstrates that the environment’s capacity for recording the state of S is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with S, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that when decoherence is not complete the deviation of the mutual information from F ’s entropy change is quantified by the quantum discord, i.e., the excess mutual information between S and F is information regarding the initial coherence between pointer states of S. In addition to illustrating these results with a single qubit system interacting with a multi-qubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of S. Our results demonstrate that Quantum Darwinism is robust with respect to non-ideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.

Quantum-Classical Correspondence Principle for Work Distributions

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with one degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions, and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.