We investigate the Shortcuts To Adiabaticity (STA) of a quantum harmonic oscillator under time-dependent frictional force, using invariant based inverse engineering method with a class of invariants characterized by a time-dependent frictional coefficient. We discuss the implementation of shortcut protocol in a generalized framework for any arbitrary time-dependent frictional interaction and study a class of such interaction from which the STA for the quantum harmonic oscillator can be obtained. We also discuss the application of the above protocol for the harmonic oscillator with time-varying mass. For an illustration, we consider the coupled photonic lattice as a harmonic oscillator with time-varying mass and frequency and discuss implementing the above protocol.
A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. With the help of phenomenological response functions a simple expression for the excess work is found -- quantifying the nonequilibrium excitations. For two specific examples, the quantum parametric oscillator and the spin-1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. Finally, we propose a de…
We consider a finite-time quantum Otto cycle with single and two-spin-$1/2$ systems as its working medium. In order to mimic adiabatic dynamics at a finite-time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and non-adiabatic performances of the same cycle. Our findings clearly indicate that the use of shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and non-adiabatic counterparts for differe…
In this paper, we study the role and relevance of the cost for an invariant-based shortcut to adiabaticity enabled qubit heat engine operates in a quantum Otto cycle. We consider a qubit heat engine with Landau-Zener Hamiltonian and improve its performance using the Lewis-Riesenfeld invariant-based shortcut to adiabaticity method. Addressing the importance of cost for better performance, the paper explores its relationship with the work and efficiency of the heat engine. We analyze the cost variation with the time duration of non-adiabatic unitary processes involved in the heat engine cycle. T…
We study the environment assisted local transitionless dynamics in closed spin systems driven through quantum critical points. In general shortcut to adaiabaticity (STA) in quantum critical systems requires highly non-local control Hamiltonians. In this work we develop an approach to achieve local shortcuts to adiabaticity (LSTA) in spin chains, using local control fields which scale polynomially with the system size, following universal critical exponents. We relate the control fields to reduced fidelity susceptibility and use transverse Ising model in one dimension to exemplify our generic r…
Quantum heat engines are modeled by thermodynamic cycles with quantum-mechanical working media. Since high engine efficiencies require adiabaticity, a major challenge is to yield a nonvanishing power output at finite cycle times. Shortcuts to adiabaticity using counter-diabatic (CD) driving may serve as a means to speed up such, otherwise infinitely long, cycles. We introduce local approximate CD protocols for many-body spin quantum heat engines and show that this method improves the efficiency and power for finite cycle times considerably. The protocol does not require a priori knowledge of t…
A $\textit{shortcut to adiabaticity}$ is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a $\textit{counterdiabatic}$ Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a $\textit{fast-forward}$ potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from $\textit{flow fields}$ that describe the desired adiab…
We study transitionless quantum driving in an infinite-range many-body system described by the Lipkin-Meshkov-Glick model. Despite the correlation length being always infinite the closing of the gap at the critical point makes the driving Hamiltonian of increasing complexity also in this case. To this aim we develop a hybrid strategy combining shortcut to adiabaticity and optimal control that allows us to achieve remarkably good performance in suppressing the defect production across the phase transition.
We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-dr…
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol fo…
We apply the method of shortcuts to adiabaticity to nonequilibrium systems. For unitary dynamics, the system Hamiltonian is separated into two parts. One of them defines the adiabatic states for the state to follow and the nonadiabatic transitions are prevented by the other part. This property is implemented to the nonequilibrium entropy production and we find that the entropy is separated into two parts. The separation represents the Pythagorean theorem for the Kullback-Leibler divergence and an information-geometric interpretation is obtained. We also study a lower bound of the entropy, whic…
We consider a paradigmatic quantum harmonic Otto engine operating in finite time. We investigate its performance when shortcut-to-adiabaticity techniques are used to speed up its cycle. We compute efficiency and power by taking the energetic cost of the shortcut driving explicitly into account. We analyze in detail three different shortcut methods, counterdiabatic driving, local counterdiabatic driving and inverse engineering. We demonstrate that all three lead to a simultaneous increase of efficiency and power for fast cycles, thus outperforming traditional heat engines.
Adiabatic quantum state evolution can be accelerated through a variety of shortcuts to adiabaticity. In one approach, a counterdiabatic quantum Hamiltonian $\hat H_{CD}$ is constructed to suppress nonadiabatic excitations. In the analogous classical problem, a counterdiabatic classical Hamiltonian $H_{CD}$ ensures that the classical action remains constant even under rapid driving. Both the quantum and classical versions of this problem have been solved for the special case of scale-invariant driving, characterized by linear expansions, contractions or translations of the system. Here we inves…
Shortcuts to Adiabaticity (STA) constitute driving schemes that provide an alternative to adiabatic protocols to control and guide the dynamics of classical and quantum systems without the requirement of slow driving. Research on STA advances swiftly with theoretical progress being accompanied by experiments on a wide variety of platforms. We summarize recent developments emphasizing advances reported in this focus issue while providing an outlook with open problems and prospects for future research.
Counterdiabatic driving (CD) exploits auxiliary control fields to tailor the nonequilibrium dynamics of a quantum system, making possible the suppression of dissipated work in finite-time thermodynamics and the engineering of optimal thermal machines with no friction. We show that while the mean work done by the auxiliary controls vanishes, CD leads to a broadening of the work distribution. We derive a fundamental inequality that relates nonequilibrium work fluctuations to the operation time and quantifies the thermodynamic cost of CD in both critical and noncritical systems.
Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We then study the distribution function of the work done on a small system initially prepared at thermal equilibrium. It is found that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case probabilities of having very large or almost zero work values are suppressed. In the quantum case negative work may be totally removed from the otherwise non-positive-definite work values. We also apply our findings to a micro Otto-cy…
We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical expression of the efficiency at maximum power for this kind of engines. This expression satisfies the universal law of efficiency at maximum power up to the second order of the Carnot efficiency. We also analyze the issue of power at any given efficiency for general low-dissipation e…
Geometric quantum speed limits quantify the trade-off between the rate with which quantum states can change and the resources that are expended during the evolution. Counterdiabatic driving is a unique tool from shortcuts to adiabaticity to speed up quantum dynamics while completely suppressing nonequilibrium excitations. We show that the quantum speed limit for counterdiabatically driven systems undergoing quantum phase transitions fully encodes the Kibble-Zurek mechanism by correctly predicting the transition from adiabatic to impulse regimes. Our findings are demonstrated for three scenario…
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counter-diabatic Hamiltonian to stifle non-adiabatic transitions. Here this strategy is cast in terms of a generator of adiabatic transport, leading to a classical analogue: dissipationless classical driving. For the single-particle piston, this approach yields simple and exact expressions for both the classical and quantal counter-diabatic terms. These results are further generalized to even-power-law potentials in one degree of freedom.
We propose a quantum Otto cycle in a two spin-$1/2$ anisotropic XY model in a transverse external magnetic field. We first characterize the parameter regime that the working medium operates as an engine in the adiabatic regime. Then, we consider finite-time behavior of the engine with and without utilizing a shortcut to adiabaticity (STA) technique. STA schemes guarantee that the dynamics of a system follows the adiabatic path, at the expense of introducing an external control. We compare the performance of the non-adiabatic and STA engines for a fixed adiabatic efficiency but different parame…
The strategy of shortcuts to adiabaticity enables us to realize adiabatic dynamics in finite time. In the counter-diabatic driving approach, an auxiliary Hamiltonian which is called the counter-diabatic Hamiltonian is appended to an original Hamiltonian to cancel out diabatic transitions. The counter-diabatic Hamiltonian is constructed by using the eigenstates of the original Hamiltonian. Therefore, it is in general difficult to construct the counter-diabatic Hamiltonian for quantum many-body systems. Even if the counter-diabatic Hamiltonian for quantum many-body systems is obtained, it is gen…
We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show th…
When a Brownian particle in contact with a heat bath at a constant temperature is controlled by a time-dependent harmonic potential, its distribution function can be rigorously derived from the Kramers equation with the consideration of the inertial effect of the Brownian particle. Based on this rigorous solution and the concept of shortcuts to adiabaticity, we construct a stochastic heat engine by employing the time-dependent harmonic potential to manipulate the Brownian particle to complete a thermodynamic cycle. We find that the efficiency at maximum power of this stochastic heat engine is …
Driving a homogeneous system across a quantum phase transition in a quench-time $τ_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hatξ\proptoτ_Q^{ν/(1+zν)}$ within the KZ time window $\hat t\proptoτ_Q^{zν/(1+zν)}$, where $z$ and $ν$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity of the inhomogenous front is below the characteristic KZ velocity $\hat v \propto \h…
