Quantum thermodynamics takes over from classical thermodynamics when systems are of the scale of single particles and quantum fluctuations have a noticeable effect. An interesting topic of research of this relatively new field is the quantum battery, which in this thesis consists of an array of N identical electron spin qubits. In an article by Binder et al. [4], it is proven that in theory, an N-times decrease in charging time of the battery is achieved when global operations on qubits are permitted. This thesis investigates if a similar advantage can be achieved by using a local qubitqubit interaction operator on a one-dimensional chain of exchange-coupled electron spin qubits that are driven by microwave radiation in the presence of decoherence. This system is described by a density matrix in order to include the presence of external influences. The time-evolution of the state of the system is calculated by solving the Von-Neumann equation both analytically and numerically, which is then used to calculate the extractable work. It is shown that exchange interaction does not have a direct effect on the extractable work, since it creates entanglement between two states of the same energy level and the operator commutes with the Hamiltonian of the system. The effect of the CNOT gate on the state of the system is then investigated. While it does have an effect on the extractable work, it did not achieve a decrease in charging time. These results are only relevant for the specific system used in this thesis. For other methods and systems, exchange interaction could lead to faster charging.
Quantum thermodynamics takes over from classical thermodynamics when systems are of the scale of single particles and quantum fluctuations have a noticeable effect. An interesting topic of research of this relatively new field is the quantum battery, which in this thesis consists of an array of N identical electron spin qubits. In an article by Binder et al. [4], it is proven that in theory, an N-times decrease in charging time of the battery is achieved when global operations on qubits are permitted. This thesis investigates if a similar advantage can be achieved by using a local qubitqubit interaction operator on a one-dimensional chain of exchange-coupled electron spin qubits that are driven by microwave radiation in the presence of decoherence. This system is described by a density matrix in order to include the presence of external influences. The time-evolution of the state of the system is calculated by solving the Von-Neumann equation both analytically and numerically, which is then used to calculate the extractable work. It is shown that exchange interaction does not have a direct effect on the extractable work, since it creates entanglement between two states of the same energy level and the operator commutes with the Hamiltonian of the system. The effect of the CNOT gate on the state of the system is then investigated. While it does have an effect on the extractable work, it did not achieve a decrease in charging time. These results are only relevant for the specific system used in this thesis. For other methods and systems, exchange interaction could lead to faster charging.
The operation of conventional batteries relies primarily on electrochemical reactions and classical physics. However, an important question is whether quantum effects, such as entanglement, can lead to a significant change in the behaviour of a battery. In addition to being a fundamental problem, this is of technological interest, since there is the prospect of exploiting quantum effects to increase charging power and energy density of a battery, and to overcome the limitations of classical batteries. In this thesis, we investigate how to charge a battery composed of quantum systems and determine which quantum effects play a part in this charging. We find that certain broken symmetries in the battery model give rise to entanglement and enhance charging relative to other batteries without entanglement. We use Heisenberg XXZ spin chains as the basic model of our quantum many-body battery. The Heisenberg spin chain is a paradigmatic model of solid-state physics; simple, yet able to describe the magnetic behaviour of more complex physical systems. The models we consider either have a nearest neighbour spin-spin coupling interaction or a long range 1/r interaction. Local identical charging fields are used to deposit work in the battery. We also investigate adding noise into the charging process, and consider the performance and stability of the spin chain battery in the presence of a heat bath. We compare the different spin chains with one another, and also compare them with several different classical models, in order to determine whether or not there is a “quantum advantage”. We find that whether or not there is a quantum advantage depends on which models and what quantity we are comparing.
This study investigates the dynamical behaviour of a two-cell (two-atom) quantum battery driven by a two-mode charging field. We explore the influence of varying interaction strengths on the system?s performance. This includes increasing the coupling between cells and charging fields, and cells themselves through a dipole interaction and Ising interaction along the z-axis. Additionally, the impact of environmental effects is examined by incorporating decay terms for both the charging fields and the cells. Our analysis focuses on key performance metrics such as stored energy, average power, ergotropy, energy fluctuations, and quantum speed limit time. The results reveal that the environment negatively impacts stored energy, power, and ergotropy, but leads to higher speed limits. Enhanced coupling between the charging fields and the cells improves the studied correlations, promoting efficient energy transfer and decreasing speed limit time. Increasing the coupling between the cells, either via the dipole or Ising interaction, generally exhibits a similar effect. This involves a decrease in maximum achievable energy storage, accompanied by the emergence of more erratic energy fluctuations.
Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.
Recently, it has been shown that energy can be deposited on a collection of quantum systems at a rate that scales superextensively. Some of these schemes for quantum batteries rely on the use of global many-body interactions that take the batteries through a correlated shortcut in state space. Here we extend the notion of a quantum battery from a collection of a priori isolated systems to a many-body quantum system with intrinsic interactions. Specifically, we consider a one-dimensional spin chain with physically realistic two-body interactions. We find that the spin-spin interactions can yield an advantage in charging power over the noninteracting case and we demonstrate that this advantage can grow superextensively when the interactions are long ranged. However, we show that, unlike in previous work, this advantage is a mean-field interaction effect that does not involve correlations and that relies on the interactions being intrinsic to the battery.
In realistic situations, physical systems can not be completely isolated from its environment. Its inevitable interaction with the environment can influence the working process of the device. In this paper, we consider two-qubit quantum batteries where one qubit of the battery is successively interacting with the spins present in the surrounding environment. We examine the effect of the interaction on the maximum amount of energy that can be extracted from the battery using unitaries. In this context, we use the notion of locally passive states. In particular, we examine the behavior of the amount of extractable work from the noisy battery, initially prepared in a locally passive or ordinary pure state, having a fixed initial entanglement, with the number of interactions the qubit has gone through. We also examine the amount of locally extractable work from the noisy battery. We realize though the amount of extractable energy, be it global or local, as a whole will decrease with the number of spins of environment it interacted with, but if we increase the time interval of the interaction with each spin, after a cut off value of the interval, the small time behavior shows a peculiarity, i.e., the extractable energy within a single interaction starts to increase with time. The cut-off time indicates the Markovian-to-non-Markovian transition of the interaction. We also observe a non-Markovian increase in extractable energy from the Markovian scenario.
We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy.