We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: A chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output (average value and standard deviation) and efficiency of the engine are derived. We prove the efficiency is controlled by the ``local entanglement gap,'' the energy difference between the many-body ground state and the lowest-energy eigenstate of the local Hamiltonian. In all the examples analyzed in this work, for a large number of coupled subsystems, the average work output scales linearly or faster and dominates over fluctuations, while the efficiency limits to a constant. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output.
We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: A chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output (average value and standard deviation) and efficiency of the engine are derived. We prove the efficiency is controlled by the ``local entanglement gap,'' the energy difference between the many-body ground state and the lowest-energy eigenstate of the local Hamiltonian. In all the examples analyzed in this work, for a large number of coupled subsystems, the average work output scales linearly or faster and dominates over fluctuations, while the efficiency limits to a constant. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output.
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.
Quantum fluctuations, which result from the Heisenberg uncertainty principle, explain a number of physical observations, from the finite mass of elementary particles to the Lamb shift in hydrogen and the Casimir effect. The local violation of the conservation of energy raises the question of whether the energy of quantum fluctuations can sustain the cycle of a quantum engine. So far, a proposal has hinted that this is possible, but contains important caveats. In this Letter, we predict that quantum fluctuations can power an autonomous spintronic quantum information engine by converting entanglement energy into useful electrical work. Our two-stroke engine operates on two entangled spin quantum dots (QDs) that are connected in series with two fully spin-polarized baths. The ultrafast measurement stroke breaks the entanglement, thereby energizing the system on average. This energy is released into the leads as electrical current when the thermalizing stroke equilibrates the QDs with the electrode baths. Using a master equation approach, we analytically demonstrate the efficiency of the quantum fluctuation-driven engine, and we study the cycle numerically to gain insight into the relevant parameters to maximize power. Our results suggest that quantum fluctuations and the measurement back-action alone cannot explain prior experimental results. Measuring the spin dynamics of the engine's ferromagnetic electrodes should help determine its efficiency. This electronically driven feedback on quantum entanglement should also boost quantum chemistry, biology and cognition.
We show that ferromagnetic interactions can enhance the adiabatic performance of a quantum spin chain engine at low temperatures. The enhancement in work output is particular pronounced, increasing exponentially with interaction strength. The performance enhancement occurs in the paramagnetic phase and is qualitatively explained by considering just the ground and first excited state, in which case the system exhibits bipartite entanglement. As the temperature is increased, thermal occupation of higher energy states diminishes performance. We find that these thermal fluctuations are smallest for long-range interactions, resulting in the highest efficiency. Diabatic work extraction degrades performance due to quantum friction. We identify an approximate, experimentally realisable counterdiabatic drive that can mitigate friction for weak interactions.
In a classic thought experiment, Szilard suggested a heat engine where a single particle, for example an atom or a molecule, is confined in a container coupled to a single heat bath. The container can be separated into two parts by a moveable wall acting as a piston. In a single cycle of the engine, work can be extracted from the information on which side of the piston the particle resides. The work output is consistent with Landauers principle that the erasure of one bit of information costs the entropy kB ln 2, exemplifying the fundamental relation between work, heat and information. Here we apply the concept of the Szilard engine to a fully interacting quantum many-body system. We find that a working medium of a number of bosons (larger or equal two) with attractive interactions is clearly superior to other previously discussed setups. In sharp contrast to the classical case, we find that the average work output increases with the particle number. The highest overshoot occurs for a small but finite temperature, showing an intricate interplay between thermal and quantum effects. We anticipate that our finding will shed new light on the role of information in controlling thermodynamic fluctuations in the deep quantum regime, which are strongly influenced by quantum correlations in interacting systems.
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes --- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced ``control-marginal state" --- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.
Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation.Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with ``little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for ``little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated.Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance.It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood.Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods.Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).