Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at arbitrary fast speed, and in the meanwhile reduce the work fluctuation. In both systems, we use a time-dependent harmonic oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improved the converging rate of the Jarzynski equality between the work function and the free energy. As an application, we show that the fast-forward process not only maximizes the output power but also improve the efficiency of a quantum engine.
Adiabatic processes are important for studying the dynamics of a time-dependent system. Conventionally, the adiabatic processes can only be achieved by varying the system slowly. We speed up both classical and quantum adiabatic processes by adding control protocols. In classical systems, we work out the control protocols by analyzing the classical adiabatic approximation. In quantum systems, we follow the idea of transitionless driving by Berry [J. Phys. A: Math. Theor. Vol.42 365303 (2009)]. Such fast-forward adiabatic processes can be performed at arbitrary fast speed, and in the meanwhile reduce the work fluctuation. In both systems, we use a time-dependent harmonic oscillator model to work out explicitly the work function and the work fluctuation in three types of processes: fast-forward adiabatic processes, adiabatic processes, and non-adiabatic processes. We show the significant reduction on work fluctuation in fast-forward adiabatic process. We further illustrate how the fast-forward process improved the converging rate of the Jarzynski equality between the work function and the free energy. As an application, we show that the fast-forward process not only maximizes the output power but also improve the efficiency of a quantum engine.
Adiabatic invariants -- quantities that are preserved under the slow driving of a system's external parameters -- are important in classical mechanics, quantum mechanics and thermodynamics. Adiabatic processes allow a system to be guided to evolve to a desired final state. However, the slow driving of a quantum system makes it vulnerable to environmental decoherence, and for both quantum and classical systems, it is often desirable and time-efficient to speed up a process. {\it Shortcuts to adiabaticity} are strategies for preserving adiabatic invariants under rapid driving, typically by means of an auxiliary field that suppresses excitations, otherwise generated during rapid driving. Several theoretical approaches have been developed to construct such shortcuts. In this dissertation we focus on two different approaches, namely {\it counterdiabatic} driving and {\it fast-forward} driving, which were originally developed for quantum systems. The counterdiabatic approach introduced independently by Dermirplak and Rice [{\it J. Phys. Chem. A}, 107:9937, 2003], and Berry [{\it J. Phys. A: Math. Theor.}, 42:365303, 2009] formally provides an exact expression for the auxiliary Hamiltonian, which however is abstract and difficult to translate into an experimentally implementable form. By contrast, the fast-forward approach developed by Masuda and Nakamura [{\it Proc. R. Soc. A}, 466(2116):1135, 2010] provides an auxiliary potential that may be experimentally implementable but generally applies only to ground states. The central theme of this dissertation is that classical shortcuts to adiabaticity can provide useful physical insights and lead to experimentally implementable shortcuts for analogous quantum systems. We start by studying a model system of a tilted piston to provide a proof of principle that quantum shortcuts can successfully be constructed from their classical counterparts. In the remainder of the dissertation, we develop a general approach based on {\it flow-fields} which produces simple expressions for auxiliary terms required for both counterdiabatic and fast-forward driving. We demonstrate the applicability of this approach for classical, quantum as well as stochastic systems. We establish strong connections between counterdiabatic and fast-forward approaches, and also between shortcut protocols required for classical, quantum and stochastic systems. In particular, we show how the fast-forward approach can be extended to highly excited states of quantum systems.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
Given the increasing use of shortcuts to adiabaticity (STA) to optimize the power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero-temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation.
To optimize the performance of a heat engine in a finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a C/τ^{2} scaling for long control time τ. There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work cannot be neglected in some quantum systems with simple energy-level structure, e.g., the two-level system or the quantum harmonic oscillator. In this paper, we build the finite-time quantum Otto engine on these simple systems, and find that the oscillating extra work leads to a jagged edge in the constraint relation between the output power and the efficiency. By optimizing the control time of the adiabatic processes, the oscillation in the extra work is utilized to enhance the maximum power and the efficiency. We further design special control schemes with the zero extra work at the specific control time. Compared to the linear control scheme, these special control schemes of the finite-time adiabatic process improve the maximum power and the efficiency of the finite-time Otto engine.
In this work we study the effect of quantum and thermal fluctuations on the statistics of quantum heat engine performance parameters, like efficiency and power. We begin by deriving an explicit solution for the characteristic function of the heat distribution of a thermal quantum harmonic oscillator. We then derive a general framework based on the standard two-point-measurement scheme to compute the efficiency distribution of a quantum Otto cycle. We analyze the generic properties of this distribution for scale-invariant driving Hamiltonians which describe a large class of single-particle, many-body, and nonlinear systems. We find that the efficiency is deterministic and that its mean is equal to the macroscopic efficiency for adiabatic driving. We continue our research by studying the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follow the ’universal’ theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We can relate this unusual property to the perfect anticorrelation between work output and heat input that suppresses thermal as well as quantum fluctuations. We then probe our findings in an experimental NMR setup using spin-1/2 systems and find them to agree rather well with our theoretical predictions. Afterward, we move on to the finite-time quantum Carnot cycle and investigate its power fluctuations. In particular, we consider how level degeneracy and level number, two commonly found properties in quantum systems, influence the relative work fluctuations. We find that their optimal performance may surpass those of nondegenerate two-level engines or harmonic oscillator motors. Our results highlight that these parameters can be employed to realize high-performance, high-stability cyclic quantum heat engines.
Finite-time quantum heat engines (QHEs) typically extract less work than their quasistatic counterparts because fast driving generates coherences and non-adiabatic transitions during the work strokes, a phenomenon commonly referred to as quantum friction. Quantum lubrication denotes a broad class of strategies that use auxiliary systems or controls to mitigate this loss. In this work, we introduce a lubrication protocol based on the quantum Zeno dynamics (QZD). By coupling the working medium to an auxiliary lubricant system and frequently monitoring the lubricant, we confine the joint evolution to a Zeno subspace and obtain an effective shortcut to adiabaticity during the work strokes of a QHE running an Otto cycle. In the ideal Zeno limit, the protocol reproduces the transitionless dynamics required to preserve populations in the instantaneous energy basis and recover the Otto efficiency at finite stroke duration. We also analyze several implementation-dependent thermodynamic costs, including switching, driving, monitoring, and imperfect thermalization, in order to assess how these costs constrain the practical gains in efficiency and power. Our results identify QZD as a conceptually distinct route to quantum lubrication and highlight quantum heat engines as a useful setting in which to study the interplay between strong coupling, measurement, and quantum thermodynamic control.